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Pomax
@@ -1,3 +1,21 @@
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<!--
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=
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\begin{bmatrix}
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1 & t & t^2
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\end{bmatrix}
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\cdot
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\begin{bmatrix}
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1 & 0 & 0 \\
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-2 & 2 & 0 \\
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1 & -2 & 1
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\end{bmatrix}
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\cdot
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||||
\begin{bmatrix}
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z^2 \cdot P_3 - 2 \cdot z \cdot (z-1) \cdot P_2 + (z-1)^2 \cdot P_1 \\
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z \cdot P_3 - (z-1) \cdot P_2 \\
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P_3
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\end{bmatrix}
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-->
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<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="77.333ex" height="9.333ex" style="vertical-align: -4ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2242.4 33268.5 3984.8" xmlns="http://www.w3.org/2000/svg">
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<defs>
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||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-3D" d="M722 347c0 -11 -9 -20 -20 -20h-626c-11 0 -20 9 -20 20s9 20 20 20h626c11 0 20 -9 20 -20zM722 153c0 -11 -9 -20 -20 -20h-626c-11 0 -20 9 -20 20s9 20 20 20h626c11 0 20 -9 20 -20Z"></path>
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Before Width: | Height: | Size: 12 KiB After Width: | Height: | Size: 12 KiB |
@@ -1,3 +1,19 @@
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<!--
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B(t) = \begin{bmatrix}
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1 & t & t^2 & t^3
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\end{bmatrix}
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\cdot
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\begin{bmatrix}
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1 & 0 & 0 & 0\\
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-3 & 3 & 0 & 0\\
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3 & -6 & 3 & 0\\
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-1 & 3 & -3 & 1
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\end{bmatrix}
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\cdot
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\begin{bmatrix}
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P_1 \\ P_2 \\ P_3 \\ P_4
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\end{bmatrix}
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-->
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<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="53.167ex" height="12.167ex" style="vertical-align: -5.5ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2863.9 22926.4 5227.9" xmlns="http://www.w3.org/2000/svg">
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<defs>
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<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D435" d="M756 545c0 -95 -105 -169 -209 -188c97 -11 155 -69 155 -141c0 -98 -118 -216 -276 -216h-357c-18 0 -27 0 -27 11c0 20 10 20 27 20c79 0 81 8 91 47l134 537c3 12 4 15 4 19c0 13 -9 14 -27 16c-17 2 -38 2 -38 2c-19 0 -28 0 -28 11c0 20 10 20 29 20h336 c120 0 186 -64 186 -138zM665 549c0 44 -21 103 -109 103h-129c-43 0 -45 -3 -54 -38l-62 -248h146c122 0 208 95 208 183zM609 227c0 43 -19 117 -115 117h-189l-69 -279c-5 -18 -5 -20 -5 -23c0 -8 3 -9 13 -10c6 -1 8 -1 22 -1h136c118 0 207 97 207 196Z"></path>
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Before Width: | Height: | Size: 11 KiB After Width: | Height: | Size: 11 KiB |
@@ -1,3 +1,6 @@
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<!--
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b = \frac{cos(φ)-1}{sin(φ)}
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-->
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<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="15.5ex" height="6ex" style="vertical-align: -2.5ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1549.3 6701 2598.7" xmlns="http://www.w3.org/2000/svg">
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<defs>
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<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D44F" d="M415 282c0 -144 -123 -293 -241 -293c-74 0 -127 62 -127 157c0 35 4 51 16 101l82 326c5 21 14 55 14 62c0 10 -2 17 -50 17c-15 0 -24 0 -24 12c0 18 11 19 19 20c26 2 99 10 122 10c13 0 13 -11 13 -11l-74 -301c30 31 71 60 117 60c80 0 133 -69 133 -160zM343 326 c0 64 -27 94 -63 94c-26 0 -71 -15 -120 -80c-9 -11 -9 -13 -15 -35l-22 -92c-16 -63 -16 -82 -16 -101c0 -74 33 -101 67 -101c39 0 85 36 118 103c18 38 51 153 51 212Z"></path>
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Before Width: | Height: | Size: 6.0 KiB After Width: | Height: | Size: 6.0 KiB |
@@ -1,3 +1,10 @@
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<!--
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\begin{array}{l}
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... &= {n \choose k} \left (
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k \cdot t^{k-1} (1-t)^{n-k} + t^k \cdot (1-t)^{n-k-1} \cdot (n-k) \cdot -1
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\right )
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\end{array}
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-->
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<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="63.167ex" height="2.833ex" style="vertical-align: -0.833ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 0ex; margin-top: 1px;" viewBox="0 -874.1 27215.9 1248.3" xmlns="http://www.w3.org/2000/svg">
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<defs>
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<path stroke-width="10" id="E1-LATINMODERNMAIN-2E" d="M192 53c0 -29 -24 -53 -53 -53s-53 24 -53 53s24 53 53 53s53 -24 53 -53Z"></path>
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Before Width: | Height: | Size: 8.7 KiB After Width: | Height: | Size: 8.8 KiB |
@@ -1,3 +1,35 @@
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<!--
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T_1 =
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\left [ \begin{array}
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01 & 0 & -{P_1}_x \\
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0 & 1 & -{P_1}_y \\
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0 & 0 & 1
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\end{array} \right ]
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\cdot
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\left [
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\begin{matrix}
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x \\
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y \\
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1
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\end{matrix}
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\right ]
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=
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\left [
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\begin{matrix}
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1 \cdot x + 0 \cdot y - {P_1}_x \cdot 1 \\
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0 \cdot x + 1 \cdot y - {P_1}_y \cdot 1 \\
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0 \cdot x + 0 \cdot y + 1 \cdot 1
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\end{matrix}
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\right ]
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=
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\left [
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\begin{matrix}
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x - {P_1}_x \\
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y - {P_1}_y \\
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1
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\end{matrix}
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\right ]
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-->
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<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="71.333ex" height="9.333ex" style="vertical-align: -4.167ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2251.2 30694.3 4002.3" xmlns="http://www.w3.org/2000/svg">
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<defs>
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<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D447" d="M704 666c0 -3 -1 -13 -2 -17l-27 -174c-2 -15 -4 -23 -15 -23c-9 0 -12 7 -12 13c0 3 2 15 3 19c4 26 8 65 8 80c0 78 -45 82 -146 82c-21 0 -54 0 -63 -2c-12 -3 -16 -9 -23 -37l-133 -531c-4 -15 -4 -21 -4 -21c0 -16 8 -19 37 -22c26 -2 39 -2 64 -2c26 0 34 0 34 -11 c0 -20 -12 -20 -22 -20c-28 0 -58 2 -87 2l-83 1l-85 -1c-27 0 -55 -2 -82 -2c-6 0 -17 0 -17 12c0 19 6 19 42 19c107 0 110 11 119 48l134 534c1 3 4 15 4 21c0 8 0 12 -28 12h-39c-148 0 -174 -18 -228 -173c-6 -16 -7 -21 -17 -21c-7 0 -12 5 -12 11c0 0 5 16 6 18 l60 176c7 19 8 20 32 20h555c17 0 27 0 27 -11Z"></path>
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|
Before Width: | Height: | Size: 14 KiB After Width: | Height: | Size: 14 KiB |
@@ -1,3 +1,27 @@
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<!--
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||||
=
|
||||
\begin{bmatrix}
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1 & t & t^2
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\end{bmatrix}
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\cdot
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 \\
|
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-2 & 2 & 0 \\
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1 & -2 & 1
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||||
\end{bmatrix}
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\cdot
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\left (
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\begin{bmatrix}
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(z-1)^2 & -2 \cdot z \cdot (z-1) & z^2 \\
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0 & -(z-1) & z \\
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||||
0 & 0 & 1
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||||
\end{bmatrix}
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\cdot
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||||
\begin{bmatrix}
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P_1 \\ P_2 \\ P_3
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||||
\end{bmatrix}
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\right )
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-->
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||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="77.5ex" height="9.333ex" style="vertical-align: -4ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2242.4 33361.1 3984.8" xmlns="http://www.w3.org/2000/svg">
|
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<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-3D" d="M722 347c0 -11 -9 -20 -20 -20h-626c-11 0 -20 9 -20 20s9 20 20 20h626c11 0 20 -9 20 -20zM722 153c0 -11 -9 -20 -20 -20h-626c-11 0 -20 9 -20 20s9 20 20 20h626c11 0 20 -9 20 -20Z"></path>
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|
Before Width: | Height: | Size: 14 KiB After Width: | Height: | Size: 14 KiB |
@@ -1,3 +1,10 @@
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<!--
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\begin{align}
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a &= v_1-2v_2+v_3 = 3(-p_1 + 3p_2 - 3p_3 + p_4) \\
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b &= 2(v_2-v_1) = 6(p_1 - 2p_2 + p_3) \\
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c &= v_1 = 3(p_2-p_1)
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\end{align}
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-->
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<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="46.333ex" height="8.833ex" style="vertical-align: -3.833ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2150.9 19964.5 3801.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D44E" d="M498 143c0 0 -13 -63 -30 -99c-16 -32 -39 -55 -74 -55c-48 0 -83 33 -91 75c-60 -71 -110 -75 -130 -75c-78 0 -133 66 -133 160c0 146 124 293 241 293c45 0 74 -27 92 -64c3 22 18 44 42 44c17 0 29 -10 29 -27c0 -4 0 -6 -7 -34l-36 -140l-22 -90 c-11 -44 -13 -52 -13 -74c0 -20 3 -46 30 -46c41 0 59 59 76 124c3 14 4 18 14 18c3 0 12 0 12 -10zM361 332c0 6 -14 88 -79 88c-40 0 -85 -37 -116 -96c-23 -46 -55 -169 -55 -219c0 -39 14 -94 64 -94c28 0 69 16 113 71c15 17 15 19 20 37l50 196c1 5 3 11 3 17Z"></path>
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|
Before Width: | Height: | Size: 11 KiB After Width: | Height: | Size: 11 KiB |
@@ -1,3 +1,31 @@
|
||||
<!--
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||||
=
|
||||
\begin{bmatrix}
|
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1 & t & t^2 & t^3
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||||
\end{bmatrix}
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\cdot
|
||||
\begin{bmatrix}
|
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1 & 0 & 0 & 0 \\
|
||||
0 & 0 & 1 & 0 \\
|
||||
-3 & 3 & -2 & -1 \\
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2 & -2 & 1 & 1
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||||
\end{bmatrix}
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\cdot
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||||
\left (
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\frac{1}{2}
|
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\cdot
|
||||
\begin{bmatrix}
|
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0 & 2 & 0 & 0 \\
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0 & 0 & 2 & 0 \\
|
||||
-τ & 0 & τ & 0 \\
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||||
0 & -τ & 0 & τ
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||||
\end{bmatrix}
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\right )
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\cdot
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||||
\begin{bmatrix}
|
||||
P_1 \\ P_2 \\ P_3 \\ P_4
|
||||
\end{bmatrix}
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-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="78.833ex" height="12.167ex" style="vertical-align: -5.5ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2863.9 33967 5227.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-3D" d="M722 347c0 -11 -9 -20 -20 -20h-626c-11 0 -20 9 -20 20s9 20 20 20h626c11 0 20 -9 20 -20zM722 153c0 -11 -9 -20 -20 -20h-626c-11 0 -20 9 -20 20s9 20 20 20h626c11 0 20 -9 20 -20Z"></path>
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||||
|
Before Width: | Height: | Size: 14 KiB After Width: | Height: | Size: 15 KiB |
@@ -1,3 +1,25 @@
|
||||
<!--
|
||||
=
|
||||
\begin{bmatrix}
|
||||
1 & t & t^2
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 \\
|
||||
0 & z & 0 \\
|
||||
0 & 0 & z^2
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 \\
|
||||
-2 & 2 & 0 \\
|
||||
1 & -2 & 1
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
P_1 \\ P_2 \\ P_3
|
||||
\end{bmatrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="53.333ex" height="9ex" style="vertical-align: -4ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2184.4 22954.2 3868.8" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-3D" d="M722 347c0 -11 -9 -20 -20 -20h-626c-11 0 -20 9 -20 20s9 20 20 20h626c11 0 20 -9 20 -20zM722 153c0 -11 -9 -20 -20 -20h-626c-11 0 -20 9 -20 20s9 20 20 20h626c11 0 20 -9 20 -20Z"></path>
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|
Before Width: | Height: | Size: 10 KiB After Width: | Height: | Size: 10 KiB |
@@ -1,3 +1,6 @@
|
||||
<!--
|
||||
P_x = cos(\frac{φ}{2}) \ , \ \ P_y = sin(\frac{φ}{2})
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="29.667ex" height="4.5ex" style="vertical-align: -1.667ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1213.3 12793.8 1932.7" xmlns="http://www.w3.org/2000/svg">
|
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<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D443" d="M754 532c0 -112 -139 -216 -281 -216h-170l-62 -250c-1 -6 -3 -11 -3 -17c0 -18 28 -18 65 -18c19 0 28 0 28 -11c0 -20 -13 -20 -20 -20c-21 0 -43 2 -65 2l-64 1l-127 -3c-3 0 -15 0 -15 12c0 19 11 19 28 19c79 0 81 8 91 47l134 537c3 12 4 15 4 19 c0 11 -6 14 -22 16c-12 1 -30 2 -43 2c-20 0 -29 0 -29 12c0 19 11 19 30 19h324c131 0 197 -74 197 -151zM661 556c0 69 -53 96 -136 96h-96c-43 0 -45 -3 -54 -38l-68 -272h141c44 0 104 8 154 53c39 36 59 122 59 161Z"></path>
|
||||
|
Before Width: | Height: | Size: 8.0 KiB After Width: | Height: | Size: 8.1 KiB |
@@ -1,3 +1,9 @@
|
||||
<!--
|
||||
\begin{matrix}
|
||||
f(a) = \cos(a) \\
|
||||
f(b) = \sin(b)
|
||||
\end{matrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="14.5ex" height="5.833ex" style="vertical-align: -2.333ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1521.9 6216.1 2543.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D453" d="M552 636c0 -38 -29 -60 -55 -60c-19 0 -37 12 -37 35c0 15 10 50 54 54c-19 18 -45 18 -49 18c-21 0 -38 -15 -47 -34c-6 -12 -20 -83 -24 -104c-11 -58 -10 -56 -21 -114h83c17 0 27 0 27 -11c0 -20 -10 -20 -30 -20h-86l-60 -317c-1 -7 -24 -128 -56 -191 c-18 -38 -58 -97 -113 -97c-41 0 -85 24 -85 69c0 38 29 60 55 60c19 0 37 -12 37 -35c0 -15 -9 -51 -55 -54c19 -18 44 -18 48 -18c52 0 69 91 87 188l75 395h-66c-19 0 -28 0 -28 12c0 19 11 19 30 19h69c24 126 27 136 33 157c30 99 93 117 127 117c41 0 87 -23 87 -69Z"></path>
|
||||
|
Before Width: | Height: | Size: 6.1 KiB After Width: | Height: | Size: 6.2 KiB |
@@ -1,3 +1,44 @@
|
||||
<!--
|
||||
{
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 & 0 \\
|
||||
-3 & 3 & 0 & 0 \\
|
||||
3 & -6 & 3 & 0 \\
|
||||
-1 & 3 & -3 & 1
|
||||
\end{bmatrix}
|
||||
}^{-1}
|
||||
\cdot
|
||||
\frac{1}{2}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
0 & 2 & 0 & 0 \\
|
||||
-τ & 0 & τ & 0 \\
|
||||
2τ & τ-6 & -2(τ-3) & -τ \\
|
||||
-τ & 4-τ & τ-4 & τ
|
||||
\end{bmatrix}
|
||||
=
|
||||
{
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 & 0 \\
|
||||
-3 & 3 & 0 & 0 \\
|
||||
3 & -6 & 3 & 0 \\
|
||||
-1 & 3 & -3 & 1
|
||||
\end{bmatrix}
|
||||
}^{-1}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 & 0 \\
|
||||
-3 & 3 & 0 & 0 \\
|
||||
3 & -6 & 3 & 0 \\
|
||||
-1 & 3 & -3 & 1
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
A
|
||||
\ =\
|
||||
I \cdot A
|
||||
\ =\
|
||||
A
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="129.333ex" height="12.667ex" style="vertical-align: -5.667ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -3068.9 55658.5 5461.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-5B" d="M256 -230c0 -11 -9 -20 -20 -20h-122v1000h122c11 0 20 -9 20 -20s-9 -20 -20 -20h-82v-920h82c11 0 20 -9 20 -20Z"></path>
|
||||
|
Before Width: | Height: | Size: 17 KiB After Width: | Height: | Size: 18 KiB |
@@ -1,3 +1,9 @@
|
||||
<!--
|
||||
\left\{\begin{array}{l}
|
||||
\vec{v}_x = \{C,A\}_x = \frac{4}{3} \cdot (B_x - C_x) \\
|
||||
\vec{v}_y = \{C,A\}_y = \frac{4}{3} \cdot (B_y - C_y)
|
||||
\end{array}\right.
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="33.333ex" height="7.333ex" style="vertical-align: -3.167ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1846.5 14353.3 3193" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-7B" d="M425 -238c0 -7 -5 -12 -12 -12c-105 0 -196 52 -196 125v250c0 58 -55 113 -130 113c-7 0 -12 5 -12 12s5 12 12 12c75 0 130 55 130 113v250c0 73 91 125 196 125c7 0 12 -5 12 -12s-5 -12 -12 -12c-75 0 -130 -49 -130 -101v-250c0 -58 -48 -104 -115 -125 c67 -21 115 -67 115 -125v-250c0 -52 55 -101 130 -101c7 0 12 -5 12 -12Z"></path>
|
||||
|
Before Width: | Height: | Size: 11 KiB After Width: | Height: | Size: 11 KiB |
@@ -1,3 +1,12 @@
|
||||
<!--
|
||||
Bézier(k,t) = \sum_{i=0}^{k}
|
||||
\underset{binomial\ term}{\underbrace{\binom{k}{i}}}
|
||||
\cdot\
|
||||
\underset{polynomial\ term}{\underbrace{(1-t)^{k-i} \cdot t^{i}}}
|
||||
\ \cdot \
|
||||
\underset{new\ weights}{\underbrace{\left ( \frac{(k-i) \cdot w_i + i \cdot w_{i-1}}{k} \right )}}
|
||||
\ ,\ with\ k = n+1
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="91.167ex" height="9.833ex" style="vertical-align: -5.667ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1771.7 39239.4 4219.2" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D435" d="M756 545c0 -95 -105 -169 -209 -188c97 -11 155 -69 155 -141c0 -98 -118 -216 -276 -216h-357c-18 0 -27 0 -27 11c0 20 10 20 27 20c79 0 81 8 91 47l134 537c3 12 4 15 4 19c0 13 -9 14 -27 16c-17 2 -38 2 -38 2c-19 0 -28 0 -28 11c0 20 10 20 29 20h336 c120 0 186 -64 186 -138zM665 549c0 44 -21 103 -109 103h-129c-43 0 -45 -3 -54 -38l-62 -248h146c122 0 208 95 208 183zM609 227c0 43 -19 117 -115 117h-189l-69 -279c-5 -18 -5 -20 -5 -23c0 -8 3 -9 13 -10c6 -1 8 -1 22 -1h136c118 0 207 97 207 196Z"></path>
|
||||
|
Before Width: | Height: | Size: 26 KiB After Width: | Height: | Size: 26 KiB |
@@ -1,3 +1,6 @@
|
||||
<!--
|
||||
\int_{0}^{z}\sqrt{f_x'(t)^2+f_y'(t)^2} dt
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="23.167ex" height="5.5ex" style="vertical-align: -2.167ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1431.5 9952.8 2374.4" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNSIZE1-222B" d="M943 1268c0 -35 -25 -50 -49 -50c-23 0 -48 16 -48 49c0 25 17 47 50 49c-4 4 -29 23 -60 23c-39 0 -73 -129 -85 -178c-34 -129 -71 -329 -108 -542c-54 -321 -119 -640 -196 -956c-71 -290 -128 -524 -280 -524c-61 0 -111 42 -111 93c0 35 25 50 49 50 c23 0 48 -16 48 -49c0 -25 -17 -47 -49 -49c0 0 25 -23 61 -23c81 0 127 188 145 261c33 139 62 306 88 459c110 654 246 1156 249 1167c55 204 111 313 187 313c55 0 109 -39 109 -93Z"></path>
|
||||
|
Before Width: | Height: | Size: 8.0 KiB After Width: | Height: | Size: 8.0 KiB |
@@ -1,3 +1,29 @@
|
||||
<!--
|
||||
Q = M^{-1} \cdot Z \cdot M =
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 \\
|
||||
1 & \frac{1}{2} & 0 \\
|
||||
1 & 1 & 1
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 \\
|
||||
0 & z & 0 \\
|
||||
0 & 0 & z^2
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 \\
|
||||
-2 & 2 & 0 \\
|
||||
1 & -2 & 1
|
||||
\end{bmatrix}
|
||||
=
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 \\
|
||||
-(z-1) & z & 0 \\
|
||||
(z - 1)^2 & -2 \cdot (z-1) \cdot z & z^2
|
||||
\end{bmatrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="102ex" height="9.667ex" style="vertical-align: -4.333ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2343.6 43911 4187.1" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D444" d="M740 436c0 -193 -147 -371 -302 -430c10 -76 25 -103 71 -103c35 0 93 25 117 96c2 6 4 11 12 11c4 0 11 -3 11 -10c0 -11 -48 -194 -167 -194c-83 0 -83 78 -83 110c0 13 0 15 4 77c-39 -11 -73 -15 -98 -15c-144 0 -256 101 -256 267c0 233 220 460 436 460 c149 0 255 -108 255 -269zM652 468c0 134 -73 212 -173 212c-73 0 -167 -46 -240 -148c-76 -108 -102 -250 -102 -319c0 -90 34 -168 112 -199c0 0 -6 12 -6 32c0 52 49 102 102 102c73 0 83 -73 88 -108c168 94 219 328 219 428zM406 41c0 61 -19 85 -61 85 s-80 -40 -80 -80c0 -43 32 -43 46 -43c28 0 58 7 84 18c10 4 11 5 11 20Z"></path>
|
||||
|
Before Width: | Height: | Size: 14 KiB After Width: | Height: | Size: 15 KiB |
@@ -1,3 +1,6 @@
|
||||
<!--
|
||||
A = B - \frac{C - B}{ratio(t)} = B + \frac{B - C}{ratio(t)}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="34.5ex" height="5.667ex" style="vertical-align: -2.5ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1405.4 14835 2454.8" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D434" d="M721 20c0 -20 -12 -20 -18 -20c-25 0 -88 3 -113 3c-41 0 -84 -3 -125 -3c0 0 -14 0 -14 11c0 20 10 20 24 20c20 0 72 3 72 33c0 10 -14 146 -16 167h-251c-68 -116 -69 -116 -76 -128c-8 -14 -14 -25 -14 -37c0 -25 24 -33 47 -35c7 0 16 -1 16 -12 c0 -19 -13 -19 -19 -19c-32 0 -67 3 -100 3c-28 0 -59 -3 -86 -3c-8 0 -13 5 -13 11c0 19 9 19 21 20c44 3 83 17 123 84l348 584c6 10 10 17 26 17c17 0 17 -4 19 -24l61 -625c3 -29 3 -36 65 -36c13 0 23 0 23 -11zM528 262l-32 330l-197 -330h229Z"></path>
|
||||
|
Before Width: | Height: | Size: 7.6 KiB After Width: | Height: | Size: 7.7 KiB |
@@ -1,3 +1,15 @@
|
||||
<!--
|
||||
=
|
||||
\begin{bmatrix}
|
||||
1 & t & t^2
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\underset{...into\ this...}{\underbrace{ M \cdot M^{-1} \cdot Z \cdot M }}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
P_1 \\ P_2 \\ P_3
|
||||
\end{bmatrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="39.333ex" height="8.833ex" style="vertical-align: -3.833ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2163.9 16961.3 3827.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-3D" d="M722 347c0 -11 -9 -20 -20 -20h-626c-11 0 -20 9 -20 20s9 20 20 20h626c11 0 20 -9 20 -20zM722 153c0 -11 -9 -20 -20 -20h-626c-11 0 -20 9 -20 20s9 20 20 20h626c11 0 20 -9 20 -20Z"></path>
|
||||
|
Before Width: | Height: | Size: 13 KiB After Width: | Height: | Size: 13 KiB |
@@ -1,3 +1,6 @@
|
||||
<!--
|
||||
\left || B'(t) \right || = \int^1_0 \sqrt{ B_x''(t)^2 + B_y''(t)^2}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="33.667ex" height="5.833ex" style="vertical-align: -2.167ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1589.9 14516.7 2532.8" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E2-LATINMODERNMAIN-7C" d="M159 -230c0 -11 -9 -20 -20 -20s-20 9 -20 20v960c0 11 9 20 20 20s20 -9 20 -20v-960Z"></path>
|
||||
|
Before Width: | Height: | Size: 8.3 KiB After Width: | Height: | Size: 8.4 KiB |
@@ -1,3 +1,6 @@
|
||||
<!--
|
||||
B_{n,k}(t) \frac{d}{dt} = {n \choose k} t^k (1-t)^{n-k} \frac{d}{dt}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="32.5ex" height="5.167ex" style="vertical-align: -2ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1394.4 13977.2 2214.4" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D435" d="M756 545c0 -95 -105 -169 -209 -188c97 -11 155 -69 155 -141c0 -98 -118 -216 -276 -216h-357c-18 0 -27 0 -27 11c0 20 10 20 27 20c79 0 81 8 91 47l134 537c3 12 4 15 4 19c0 13 -9 14 -27 16c-17 2 -38 2 -38 2c-19 0 -28 0 -28 11c0 20 10 20 29 20h336 c120 0 186 -64 186 -138zM665 549c0 44 -21 103 -109 103h-129c-43 0 -45 -3 -54 -38l-62 -248h146c122 0 208 95 208 183zM609 227c0 43 -19 117 -115 117h-189l-69 -279c-5 -18 -5 -20 -5 -23c0 -8 3 -9 13 -10c6 -1 8 -1 22 -1h136c118 0 207 97 207 196Z"></path>
|
||||
|
Before Width: | Height: | Size: 7.7 KiB After Width: | Height: | Size: 7.8 KiB |
@@ -1,3 +1,20 @@
|
||||
<!--
|
||||
\begin{bmatrix}
|
||||
(z-1)^2 & -2 \cdot z \cdot (z-1) & z^2 \\
|
||||
0 & -(z-1) & z \\
|
||||
0 & 0 & 1
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
P_1 \\ P_2 \\ P_3
|
||||
\end{bmatrix}
|
||||
=
|
||||
\begin{bmatrix}
|
||||
z^2 \cdot P_3 - 2 \cdot z \cdot (z-1) \cdot P_2 + (z-1)^2 \cdot P_1 \\
|
||||
z \cdot P_3 - (z-1) \cdot P_2 \\
|
||||
P_3
|
||||
\end{bmatrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="89.5ex" height="9.333ex" style="vertical-align: -4ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2242.4 38512.4 3984.8" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-5B" d="M256 -230c0 -11 -9 -20 -20 -20h-122v1000h122c11 0 20 -9 20 -20s-9 -20 -20 -20h-82v-920h82c11 0 20 -9 20 -20Z"></path>
|
||||
|
Before Width: | Height: | Size: 14 KiB After Width: | Height: | Size: 14 KiB |
@@ -1,3 +1,9 @@
|
||||
<!--
|
||||
\left \{ \begin{matrix}
|
||||
tangent_x(t) = B'_x(t) \\
|
||||
tangent_y(t) = B'_y(t)
|
||||
\end{matrix} \right.
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="23ex" height="6.167ex" style="vertical-align: -2.5ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1594.6 9934.1 2689.2" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-7B" d="M425 -238c0 -7 -5 -12 -12 -12c-105 0 -196 52 -196 125v250c0 58 -55 113 -130 113c-7 0 -12 5 -12 12s5 12 12 12c75 0 130 55 130 113v250c0 73 91 125 196 125c7 0 12 -5 12 -12s-5 -12 -12 -12c-75 0 -130 -49 -130 -101v-250c0 -58 -48 -104 -115 -125 c67 -21 115 -67 115 -125v-250c0 -52 55 -101 130 -101c7 0 12 -5 12 -12Z"></path>
|
||||
|
Before Width: | Height: | Size: 9.2 KiB After Width: | Height: | Size: 9.3 KiB |
@@ -1,3 +1,10 @@
|
||||
<!--
|
||||
\begin{align*}
|
||||
linear &= (1-t) + t \\
|
||||
square &= (1-t)^2 + 2 \cdot (1-t) \cdot t + t^2 \\
|
||||
cubic &= (1-t)^3 + 3 \cdot (1-t)^2 \cdot t + 3 \cdot (1-t) \cdot t^2 + t^3
|
||||
\end{align*}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="55.333ex" height="9.333ex" style="vertical-align: -4ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2241.8 23818.9 3983.7" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D459" d="M258 683l-144 -578c-5 -19 -6 -24 -6 -48c0 -14 0 -46 30 -46c40 0 59 59 76 124c3 14 4 18 14 18c3 0 12 0 12 -10c0 0 -12 -60 -30 -98c-17 -36 -42 -56 -75 -56c-47 0 -91 35 -91 92c0 16 2 23 5 34l126 500l3 20c0 8 -1 17 -49 17c-15 0 -25 0 -25 11 c0 19 11 20 19 21c26 2 99 10 122 10c13 0 13 -11 13 -11Z"></path>
|
||||
|
Before Width: | Height: | Size: 14 KiB After Width: | Height: | Size: 14 KiB |
@@ -1,3 +1,16 @@
|
||||
<!--
|
||||
\begin{array}{l}
|
||||
E'_x = -sin(φ) \ , \ E'_y = cos(φ) \ , \ ||E'|| = \sqrt{ (-sin(φ))^2 + cos^2(φ)} = 1 \ , \\
|
||||
\left\{\begin{array}{l}
|
||||
C_2x = E_x - C_{1y} \cdot \frac{E_x'}{||E'||}
|
||||
= cos(φ) + C_{1y} \cdot sin(φ)
|
||||
= cos(φ) + \frac{4}{3} tan \left( \frac{φ}{4} \right) \cdot sin(φ) \\
|
||||
C_2y = E_y - C_{1y} \cdot \frac{E_y'}{||E'||}
|
||||
= sin(φ) - C_{1y} \cdot cos(φ)
|
||||
= sin(φ) - \frac{4}{3} tan \left( \frac{φ}{4} \right) \cdot cos(φ)
|
||||
\end{array}\right.
|
||||
\end{array}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="81.5ex" height="15.333ex" style="vertical-align: -7.167ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -3547.2 35114.3 6594.3" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D438" d="M763 653l-20 -173c-2 -19 -3 -25 -14 -25c-9 0 -12 7 -12 12s1 12 1 18c4 27 4 29 4 53c0 82 -30 111 -152 111h-141c-44 0 -45 -4 -54 -39l-60 -241h94c92 0 110 23 131 99c3 12 5 18 14 18c7 0 12 -5 12 -11l-57 -234c-4 -15 -7 -20 -15 -20c-9 0 -13 6 -13 11 c0 3 1 6 3 11c7 30 7 42 7 49c0 25 0 46 -85 46h-99l-68 -273c-5 -18 -5 -20 -5 -23c0 -8 3 -9 13 -10c6 -1 8 -1 22 -1h146c171 0 208 67 273 215c2 6 4 12 13 12c12 0 12 -11 12 -11s-3 -9 -5 -14l-92 -216c-7 -16 -8 -17 -31 -17h-519c-19 0 -28 0 -28 12 c0 19 11 19 28 19c79 0 81 8 91 47l132 529c5 18 5 20 5 24c0 18 -28 18 -65 18c-19 0 -28 0 -28 11c0 20 10 20 30 20h505c25 0 30 0 27 -27Z"></path>
|
||||
|
Before Width: | Height: | Size: 27 KiB After Width: | Height: | Size: 27 KiB |
@@ -1,3 +1,10 @@
|
||||
<!--
|
||||
\left\{\begin{array}{l}
|
||||
B_x - C_x = cos\left(\frac{φ}{2}\right) - cos^2\left(\frac{φ}{2}\right) \\
|
||||
B_y - C_y = sin\left(\frac{φ}{2}\right) - cos(\frac{φ}{2}) \cdot sin\left(\frac{φ}{2}\right)
|
||||
= sin\left(\frac{φ}{2}\right) - \frac{sin(φ)}{2}
|
||||
\end{array}\right.
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="61.5ex" height="8.167ex" style="vertical-align: -3.5ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2018.4 26498.1 3536.8" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-7B" d="M425 -238c0 -7 -5 -12 -12 -12c-105 0 -196 52 -196 125v250c0 58 -55 113 -130 113c-7 0 -12 5 -12 12s5 12 12 12c75 0 130 55 130 113v250c0 73 91 125 196 125c7 0 12 -5 12 -12s-5 -12 -12 -12c-75 0 -130 -49 -130 -101v-250c0 -58 -48 -104 -115 -125 c67 -21 115 -67 115 -125v-250c0 -52 55 -101 130 -101c7 0 12 -5 12 -12Z"></path>
|
||||
|
Before Width: | Height: | Size: 15 KiB After Width: | Height: | Size: 16 KiB |
@@ -1,3 +1,27 @@
|
||||
<!--
|
||||
B(t) =
|
||||
\begin{bmatrix}
|
||||
1 & t & t^2
|
||||
\end{bmatrix}
|
||||
\cdot M \cdot Q \cdot
|
||||
\begin{bmatrix}
|
||||
P_1 \\ P_2 \\ P_3
|
||||
\end{bmatrix}
|
||||
=
|
||||
\begin{bmatrix}
|
||||
1 & t & t^2
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
M
|
||||
\cdot
|
||||
\left (
|
||||
Q
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
P_1 \\ P_2 \\ P_3
|
||||
\end{bmatrix}
|
||||
\right )
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="67.667ex" height="8.833ex" style="vertical-align: -3.833ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2163.9 29120.3 3827.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D435" d="M756 545c0 -95 -105 -169 -209 -188c97 -11 155 -69 155 -141c0 -98 -118 -216 -276 -216h-357c-18 0 -27 0 -27 11c0 20 10 20 27 20c79 0 81 8 91 47l134 537c3 12 4 15 4 19c0 13 -9 14 -27 16c-17 2 -38 2 -38 2c-19 0 -28 0 -28 11c0 20 10 20 29 20h336 c120 0 186 -64 186 -138zM665 549c0 44 -21 103 -109 103h-129c-43 0 -45 -3 -54 -38l-62 -248h146c122 0 208 95 208 183zM609 227c0 43 -19 117 -115 117h-189l-69 -279c-5 -18 -5 -20 -5 -23c0 -8 3 -9 13 -10c6 -1 8 -1 22 -1h136c118 0 207 97 207 196Z"></path>
|
||||
|
Before Width: | Height: | Size: 12 KiB After Width: | Height: | Size: 13 KiB |
@@ -1,3 +1,6 @@
|
||||
<!--
|
||||
O(t) = B(t) + d \cdot N(t)
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="22.5ex" height="2.5ex" style="vertical-align: -0.667ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -771.9 9698.4 1043.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D442" d="M740 436c0 -239 -223 -458 -435 -458c-144 0 -256 101 -256 267c0 233 220 460 436 460c149 0 255 -108 255 -269zM651 475c0 149 -90 205 -172 205c-79 0 -177 -52 -246 -156c-77 -117 -91 -263 -91 -307c0 -132 70 -213 169 -213c84 0 166 59 214 120 c99 123 126 279 126 351Z"></path>
|
||||
|
Before Width: | Height: | Size: 4.9 KiB After Width: | Height: | Size: 5.0 KiB |
@@ -1,3 +1,11 @@
|
||||
<!--
|
||||
\begin{matrix}
|
||||
... & = & (1-t)^3 \\
|
||||
& + & 3 \cdot (1-t)^2 \cdot t \\
|
||||
& + & 3 \cdot (1-t) \cdot t^2 \\
|
||||
& + & t^3 \\
|
||||
\end{matrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="23.167ex" height="13ex" style="vertical-align: -5.833ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -3032.7 9958.3 5565.5" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-2E" d="M192 53c0 -29 -24 -53 -53 -53s-53 24 -53 53s24 53 53 53s53 -24 53 -53Z"></path>
|
||||
|
Before Width: | Height: | Size: 6.0 KiB After Width: | Height: | Size: 6.2 KiB |
@@ -1,3 +1,10 @@
|
||||
<!--
|
||||
\begin{array}{l}
|
||||
1 = cos(φ) + b \cdot -sin(φ) \ → \
|
||||
1 - cos(φ) = -b \cdot sin(φ) \ → \
|
||||
-1 + cos(φ) = b \cdot sin(φ)
|
||||
\end{array}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="86.833ex" height="2.5ex" style="vertical-align: -0.667ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -792.9 37360.4 1085.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-31" d="M419 0c-35 3 -122 3 -162 3s-127 0 -162 -3v31h32c90 0 93 12 93 48v518c-52 -26 -111 -26 -131 -26v31c32 0 120 0 182 64c23 0 23 -2 23 -26v-561c0 -37 3 -48 93 -48h32v-31Z"></path>
|
||||
|
Before Width: | Height: | Size: 9.3 KiB After Width: | Height: | Size: 9.5 KiB |
@@ -1,3 +1,13 @@
|
||||
<!--
|
||||
\begin{array}{l}
|
||||
... &= n \left (
|
||||
\frac{x!}{y!(x-y)!} t^{y} (1-t)^{x-y} - \frac{x!}{k!(x-k)!} t^k (1-t)^{x-k}
|
||||
\right )
|
||||
\ ,\ with\ x=n-1,\ y=k-1
|
||||
\\
|
||||
... &= n \left ( B_{(n-1),(k-1)}(t) - B_{(n-1),k}(t) \right )
|
||||
\end{array}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="83.167ex" height="8ex" style="vertical-align: -3.5ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1988.9 35801 3477.8" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-2E" d="M192 53c0 -29 -24 -53 -53 -53s-53 24 -53 53s24 53 53 53s53 -24 53 -53Z"></path>
|
||||
|
Before Width: | Height: | Size: 17 KiB After Width: | Height: | Size: 17 KiB |
@@ -1,3 +1,6 @@
|
||||
<!--
|
||||
Bézier'(n,t) = \sum_{i=0}^{n-1} Bézier(n-1,t)_i \cdot n \cdot (w_{i+1}-w_i)
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="53ex" height="7ex" style="vertical-align: -2.833ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1751.9 22822 2993.2" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D435" d="M756 545c0 -95 -105 -169 -209 -188c97 -11 155 -69 155 -141c0 -98 -118 -216 -276 -216h-357c-18 0 -27 0 -27 11c0 20 10 20 27 20c79 0 81 8 91 47l134 537c3 12 4 15 4 19c0 13 -9 14 -27 16c-17 2 -38 2 -38 2c-19 0 -28 0 -28 11c0 20 10 20 29 20h336 c120 0 186 -64 186 -138zM665 549c0 44 -21 103 -109 103h-129c-43 0 -45 -3 -54 -38l-62 -248h146c122 0 208 95 208 183zM609 227c0 43 -19 117 -115 117h-189l-69 -279c-5 -18 -5 -20 -5 -23c0 -8 3 -9 13 -10c6 -1 8 -1 22 -1h136c118 0 207 97 207 196Z"></path>
|
||||
|
Before Width: | Height: | Size: 11 KiB After Width: | Height: | Size: 11 KiB |
@@ -1,3 +1,6 @@
|
||||
<!--
|
||||
B'(1)_n = B'(0)_{n+1}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="18.667ex" height="2.833ex" style="vertical-align: -0.667ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -962.8 8065.8 1234.8" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D435" d="M756 545c0 -95 -105 -169 -209 -188c97 -11 155 -69 155 -141c0 -98 -118 -216 -276 -216h-357c-18 0 -27 0 -27 11c0 20 10 20 27 20c79 0 81 8 91 47l134 537c3 12 4 15 4 19c0 13 -9 14 -27 16c-17 2 -38 2 -38 2c-19 0 -28 0 -28 11c0 20 10 20 29 20h336 c120 0 186 -64 186 -138zM665 549c0 44 -21 103 -109 103h-129c-43 0 -45 -3 -54 -38l-62 -248h146c122 0 208 95 208 183zM609 227c0 43 -19 117 -115 117h-189l-69 -279c-5 -18 -5 -20 -5 -23c0 -8 3 -9 13 -10c6 -1 8 -1 22 -1h136c118 0 207 97 207 196Z"></path>
|
||||
|
Before Width: | Height: | Size: 4.6 KiB After Width: | Height: | Size: 4.6 KiB |
@@ -1,3 +1,27 @@
|
||||
<!--
|
||||
=
|
||||
\begin{bmatrix}
|
||||
1 & t & t^2
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 \\
|
||||
-2 & 2 & 0 \\
|
||||
1 & -2 & 1
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\left (
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 \\
|
||||
-(z-1) & z & 0 \\
|
||||
(z - 1)^2 & -2 \cdot (z-1) \cdot z & z^2
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
P_1 \\ P_2 \\ P_3
|
||||
\end{bmatrix}
|
||||
\right )
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="78.167ex" height="9.333ex" style="vertical-align: -4ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2242.4 33687 3984.8" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-3D" d="M722 347c0 -11 -9 -20 -20 -20h-626c-11 0 -20 9 -20 20s9 20 20 20h626c11 0 20 -9 20 -20zM722 153c0 -11 -9 -20 -20 -20h-626c-11 0 -20 9 -20 20s9 20 20 20h626c11 0 20 -9 20 -20Z"></path>
|
||||
|
Before Width: | Height: | Size: 14 KiB After Width: | Height: | Size: 14 KiB |
@@ -1,3 +1,9 @@
|
||||
<!--
|
||||
C_2 = \left [ \begin{matrix}
|
||||
cos(φ) + f \cdot sin(φ) \\
|
||||
sin(φ) - f \cdot cos(φ)
|
||||
\end{matrix} \right ],\ with\ f = \frac{4}{3} tan \left( \frac{φ}{4} \right)
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="51.167ex" height="5.833ex" style="vertical-align: -2.333ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1521.9 22056.6 2543.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D436" d="M760 695l-63 -255c-5 -18 -5 -20 -18 -20c-4 0 -15 0 -15 10s3 11 3 51c0 116 -59 193 -161 193c-89 0 -183 -50 -244 -121c-100 -117 -121 -279 -121 -336c0 -156 106 -208 196 -208c52 0 115 17 184 73c69 58 92 129 101 158c2 8 7 10 13 10c0 0 12 0 12 -10 c0 -3 -17 -94 -110 -176c-53 -46 -129 -86 -216 -86c-153 0 -271 109 -271 274c0 232 225 453 448 453c111 0 157 -75 166 -89l70 77c11 11 12 12 15 12c9 0 11 -7 11 -10Z"></path>
|
||||
|
Before Width: | Height: | Size: 14 KiB After Width: | Height: | Size: 14 KiB |
@@ -1,3 +1,6 @@
|
||||
<!--
|
||||
O(t) = B(t) + d
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="16.167ex" height="2.5ex" style="vertical-align: -0.667ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -771.9 6931 1043.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D442" d="M740 436c0 -239 -223 -458 -435 -458c-144 0 -256 101 -256 267c0 233 220 460 436 460c149 0 255 -108 255 -269zM651 475c0 149 -90 205 -172 205c-79 0 -177 -52 -246 -156c-77 -117 -91 -263 -91 -307c0 -132 70 -213 169 -213c84 0 166 59 214 120 c99 123 126 279 126 351Z"></path>
|
||||
|
Before Width: | Height: | Size: 3.9 KiB After Width: | Height: | Size: 3.9 KiB |
@@ -1,3 +1,6 @@
|
||||
<!--
|
||||
d = || tangent(t) || = \sqrt{B'_x(t)^2 + B'_y(t)^2}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="39.167ex" height="4.5ex" style="vertical-align: -1.667ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1205.9 16857.8 1907.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D451" d="M516 683l-144 -578c-4 -17 -6 -24 -6 -48c0 -20 3 -46 30 -46c41 0 59 59 76 124c3 14 4 18 14 18c3 0 12 0 12 -10c0 0 -13 -63 -30 -99c-16 -32 -39 -55 -74 -55c-48 0 -83 33 -91 75c-60 -71 -110 -75 -130 -75c-78 0 -133 66 -133 160c0 146 124 293 241 293 c45 0 74 -27 92 -64l60 237l3 20c0 10 -2 17 -50 17c-15 0 -24 0 -24 12c0 13 6 18 14 19c17 2 112 11 127 11c13 0 13 -11 13 -11zM361 332c0 6 -14 88 -79 88c-40 0 -85 -37 -116 -96c-23 -46 -55 -169 -55 -219c0 -39 14 -94 64 -94c28 0 69 16 113 71c15 17 15 19 20 37 l50 196c1 5 3 11 3 17Z"></path>
|
||||
|
Before Width: | Height: | Size: 9.6 KiB After Width: | Height: | Size: 9.7 KiB |
@@ -1,3 +1,6 @@
|
||||
<!--
|
||||
f(x) = a \cdot x^3 + b \cdot x^2 + c \cdot x + d
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="31.833ex" height="2.667ex" style="vertical-align: -0.667ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -904.8 13701.4 1176.8" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D453" d="M552 636c0 -38 -29 -60 -55 -60c-19 0 -37 12 -37 35c0 15 10 50 54 54c-19 18 -45 18 -49 18c-21 0 -38 -15 -47 -34c-6 -12 -20 -83 -24 -104c-11 -58 -10 -56 -21 -114h83c17 0 27 0 27 -11c0 -20 -10 -20 -30 -20h-86l-60 -317c-1 -7 -24 -128 -56 -191 c-18 -38 -58 -97 -113 -97c-41 0 -85 24 -85 69c0 38 29 60 55 60c19 0 37 -12 37 -35c0 -15 -9 -51 -55 -54c19 -18 44 -18 48 -18c52 0 69 91 87 188l75 395h-66c-19 0 -28 0 -28 12c0 19 11 19 30 19h69c24 126 27 136 33 157c30 99 93 117 127 117c41 0 87 -23 87 -69Z"></path>
|
||||
|
Before Width: | Height: | Size: 7.0 KiB After Width: | Height: | Size: 7.0 KiB |
@@ -1,3 +1,29 @@
|
||||
<!--
|
||||
\begin{bmatrix}
|
||||
V_1 \\ V_2 \\ V'_1 \\ V'_2
|
||||
\end{bmatrix}
|
||||
=
|
||||
T
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
P_1 \\ P_2 \\ P_3 \\ P_4
|
||||
\end{bmatrix}
|
||||
=
|
||||
\begin{bmatrix}
|
||||
P_2 \\ P_3 \\ \frac{P_3 - P_1}{2} \\ \frac{P_4 - P_2}{2}
|
||||
\end{bmatrix}
|
||||
\ \Rightarrow \
|
||||
T
|
||||
=
|
||||
\frac{1}{2}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
0 & 2 & 0 & 0 \\
|
||||
0 & 0 & 2 & 0 \\
|
||||
-1 & 0 & 1 & 0 \\
|
||||
0 & -1 & 0 & 1
|
||||
\end{bmatrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="65.5ex" height="14.5ex" style="vertical-align: -6.667ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -3387.9 28208.3 6275.7" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-5B" d="M256 -230c0 -11 -9 -20 -20 -20h-122v1000h122c11 0 20 -9 20 -20s-9 -20 -20 -20h-82v-920h82c11 0 20 -9 20 -20Z"></path>
|
||||
|
Before Width: | Height: | Size: 14 KiB After Width: | Height: | Size: 15 KiB |
@@ -1,3 +1,8 @@
|
||||
<!--
|
||||
Bézier_{n,k}(t) \frac{d}{dt} = \sum_{k=0}^{n-1} n \cdot B_{n-1,k}(t) \cdot (w_{k+1} - w_k)
|
||||
= \sum_{k=0}^{n-1} B_{n-1,k}(t) \cdot \underset{derivative\ weights}
|
||||
{\underbrace{n \cdot (w_{k+1} - w_k)}}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="81.167ex" height="8.167ex" style="vertical-align: -4.167ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1751.9 34976.4 3501.4" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D435" d="M756 545c0 -95 -105 -169 -209 -188c97 -11 155 -69 155 -141c0 -98 -118 -216 -276 -216h-357c-18 0 -27 0 -27 11c0 20 10 20 27 20c79 0 81 8 91 47l134 537c3 12 4 15 4 19c0 13 -9 14 -27 16c-17 2 -38 2 -38 2c-19 0 -28 0 -28 11c0 20 10 20 29 20h336 c120 0 186 -64 186 -138zM665 549c0 44 -21 103 -109 103h-129c-43 0 -45 -3 -54 -38l-62 -248h146c122 0 208 95 208 183zM609 227c0 43 -19 117 -115 117h-189l-69 -279c-5 -18 -5 -20 -5 -23c0 -8 3 -9 13 -10c6 -1 8 -1 22 -1h136c118 0 207 97 207 196Z"></path>
|
||||
|
Before Width: | Height: | Size: 21 KiB After Width: | Height: | Size: 21 KiB |
@@ -1,3 +1,11 @@
|
||||
<!--
|
||||
\begin{align*}
|
||||
linear &= \hskip{2.5em} 1 + 1 \\
|
||||
square &= \hskip{1.7em} 1 + 2 + 1\\
|
||||
cubic &= \hskip{0.85em} 1 + 3 + 3 + 1\\
|
||||
hypercubic &= 1 + 4 + 6 + 4 + 1
|
||||
\end{align*}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="32.167ex" height="11.5ex" style="vertical-align: -5.167ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2723.4 13844.9 4946.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D459" d="M258 683l-144 -578c-5 -19 -6 -24 -6 -48c0 -14 0 -46 30 -46c40 0 59 59 76 124c3 14 4 18 14 18c3 0 12 0 12 -10c0 0 -12 -60 -30 -98c-17 -36 -42 -56 -75 -56c-47 0 -91 35 -91 92c0 16 2 23 5 34l126 500l3 20c0 8 -1 17 -49 17c-15 0 -25 0 -25 11 c0 19 11 20 19 21c26 2 99 10 122 10c13 0 13 -11 13 -11Z"></path>
|
||||
|
Before Width: | Height: | Size: 14 KiB After Width: | Height: | Size: 14 KiB |
@@ -1,3 +1,22 @@
|
||||
<!--
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 & 0 \\
|
||||
-(z-1) & z & 0 & 0 \\
|
||||
(z-1)^2 & -2 \cdot (z-1) \cdot z & z^2 & 0 \\
|
||||
-(z-1)^3 & 3 \cdot (z-1)^2 \cdot z & -3 \cdot (z-1) \cdot z^2 & z^3
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
P_1 \\ P_2 \\ P_3 \\ P_4
|
||||
\end{bmatrix}
|
||||
=
|
||||
\begin{bmatrix}
|
||||
P_1 \\
|
||||
z \cdot P_2 - (z-1) \cdot P_1 \\
|
||||
z^2 \cdot P_3 - 2 \cdot z \cdot (z-1) \cdot P_2 + (z-1)^2 \cdot P_1 \\
|
||||
z^3 \cdot P_4 - 3 \cdot z^2 \cdot (z-1) \cdot P_3 + 3 \cdot z \cdot (z-1)^2 \cdot P_2 - (z-1)^3 \cdot P_1
|
||||
\end{bmatrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="130.833ex" height="12.667ex" style="vertical-align: -5.833ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2991.8 56358.6 5483.7" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-5B" d="M256 -230c0 -11 -9 -20 -20 -20h-122v1000h122c11 0 20 -9 20 -20s-9 -20 -20 -20h-82v-920h82c11 0 20 -9 20 -20Z"></path>
|
||||
|
Before Width: | Height: | Size: 20 KiB After Width: | Height: | Size: 20 KiB |
@@ -1,3 +1,19 @@
|
||||
<!--
|
||||
\begin{bmatrix}
|
||||
1 & t & t^2 & t^3
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 & 0 \\
|
||||
0 & 0 & 1 & 0 \\
|
||||
-3 & 3 & -2 & -1 \\
|
||||
2 & -2 & 1 & 1
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
V_1 \\ V_2 \\ V'_1 \\ V'_2
|
||||
\end{bmatrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="47.667ex" height="12.667ex" style="vertical-align: -5.833ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2984.6 20502 5469.1" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-5B" d="M256 -230c0 -11 -9 -20 -20 -20h-122v1000h122c11 0 20 -9 20 -20s-9 -20 -20 -20h-82v-920h82c11 0 20 -9 20 -20Z"></path>
|
||||
|
Before Width: | Height: | Size: 9.0 KiB After Width: | Height: | Size: 9.3 KiB |
@@ -1,3 +1,6 @@
|
||||
<!--
|
||||
C_1 = S + a \cdot \begin{pmatrix} 0 \\ 1 \end{pmatrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="18.5ex" height="5.667ex" style="vertical-align: -2.333ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1469.9 7965.1 2439.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D436" d="M760 695l-63 -255c-5 -18 -5 -20 -18 -20c-4 0 -15 0 -15 10s3 11 3 51c0 116 -59 193 -161 193c-89 0 -183 -50 -244 -121c-100 -117 -121 -279 -121 -336c0 -156 106 -208 196 -208c52 0 115 17 184 73c69 58 92 129 101 158c2 8 7 10 13 10c0 0 12 0 12 -10 c0 -3 -17 -94 -110 -176c-53 -46 -129 -86 -216 -86c-153 0 -271 109 -271 274c0 232 225 453 448 453c111 0 157 -75 166 -89l70 77c11 11 12 12 15 12c9 0 11 -7 11 -10Z"></path>
|
||||
|
Before Width: | Height: | Size: 5.2 KiB After Width: | Height: | Size: 5.2 KiB |
@@ -1,3 +1,11 @@
|
||||
<!--
|
||||
\begin{bmatrix}1 & t & t^2 & t^3\end{bmatrix} \cdot \begin{bmatrix}
|
||||
1 & 0 & 0 & 0 \\
|
||||
-3 & 3 & 0 & 0 \\
|
||||
3 & -6 & 3 & 0 \\
|
||||
-1 & 3 & -3 & 1
|
||||
\end{bmatrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="37.5ex" height="12.167ex" style="vertical-align: -5.5ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2863.9 16170.7 5227.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-5B" d="M256 -230c0 -11 -9 -20 -20 -20h-122v1000h122c11 0 20 -9 20 -20s-9 -20 -20 -20h-82v-920h82c11 0 20 -9 20 -20Z"></path>
|
||||
|
Before Width: | Height: | Size: 7.1 KiB After Width: | Height: | Size: 7.3 KiB |
@@ -1,3 +1,9 @@
|
||||
<!--
|
||||
\left \{ \begin{align}
|
||||
C1' &= v1 + \frac{v1 - start}{t} \\
|
||||
C2' &= v2 + \frac{v2 - end}{1 - t}
|
||||
\end{align} \right .
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="26ex" height="10.333ex" style="vertical-align: -4.667ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 0ex; margin-top: 1px;" viewBox="0 -2492.1 11163.4 4484.2" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-7B" d="M425 -238c0 -7 -5 -12 -12 -12c-105 0 -196 52 -196 125v250c0 58 -55 113 -130 113c-7 0 -12 5 -12 12s5 12 12 12c75 0 130 55 130 113v250c0 73 91 125 196 125c7 0 12 -5 12 -12s-5 -12 -12 -12c-75 0 -130 -49 -130 -101v-250c0 -58 -48 -104 -115 -125 c67 -21 115 -67 115 -125v-250c0 -52 55 -101 130 -101c7 0 12 -5 12 -12Z"></path>
|
||||
|
Before Width: | Height: | Size: 10 KiB After Width: | Height: | Size: 11 KiB |
@@ -1,3 +1,18 @@
|
||||
<!--
|
||||
\begin{bmatrix}
|
||||
P_1 \\
|
||||
P_2 \\
|
||||
P_3 \\
|
||||
P_4
|
||||
\end{bmatrix}_{Bézier}
|
||||
\Rightarrow
|
||||
\begin{bmatrix}
|
||||
P_4 + 6 \cdot (P_1 - P_2) \\
|
||||
P_1 \\
|
||||
P_4 \\
|
||||
P_1 + 6 \cdot (P_4 - P_3)
|
||||
\end{bmatrix}_{CatmullRom}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="47ex" height="12.5ex" style="vertical-align: -5.833ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2921.9 20231.1 5401.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-5B" d="M256 -230c0 -11 -9 -20 -20 -20h-122v1000h122c11 0 20 -9 20 -20s-9 -20 -20 -20h-82v-920h82c11 0 20 -9 20 -20Z"></path>
|
||||
|
Before Width: | Height: | Size: 18 KiB After Width: | Height: | Size: 19 KiB |
@@ -1,3 +1,6 @@
|
||||
<!--
|
||||
ratio(t)_{quadratic} = \left | \frac{2t^2 - 2t}{2t^2 - 2t + 1} \right |
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="32.167ex" height="6ex" style="vertical-align: -2.333ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1531.3 13869.5 2556.3" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D45F" d="M436 377c0 -36 -28 -59 -55 -59s-38 19 -38 35c0 26 22 50 52 55c0 0 -16 12 -42 12c-43 0 -72 -26 -80 -33c-24 -22 -52 -69 -56 -82l-32 -130c-4 -18 -38 -154 -40 -158c-7 -20 -25 -28 -37 -28c-15 0 -29 9 -29 27c0 5 6 28 9 43l58 231c13 52 16 63 16 84 c0 38 -14 46 -31 46c-36 0 -56 -48 -73 -119c-6 -22 -7 -23 -17 -23c0 0 -12 0 -12 10c0 3 13 63 31 97c9 18 28 57 74 57c47 0 83 -32 91 -77c19 28 63 77 128 77c51 0 83 -30 83 -65Z"></path>
|
||||
|
Before Width: | Height: | Size: 9.6 KiB After Width: | Height: | Size: 9.6 KiB |
@@ -1,3 +1,12 @@
|
||||
<!--
|
||||
Bézier'(n,t) = \sum_{i=0}^{k}
|
||||
\underset{binomial\ term}{\underbrace{\binom{k}{i}}}
|
||||
\cdot\
|
||||
\underset{polynomial\ term}{\underbrace{(1-t)^{k-i} \cdot t^{i}}}
|
||||
\cdot\
|
||||
\underset{derivative\ weight}{\underbrace{n \cdot (w_{i+1} - w_i)}}
|
||||
{\ , \ with \ k=n-1}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="81ex" height="9ex" style="vertical-align: -5ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1771.7 34892 3890" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D435" d="M756 545c0 -95 -105 -169 -209 -188c97 -11 155 -69 155 -141c0 -98 -118 -216 -276 -216h-357c-18 0 -27 0 -27 11c0 20 10 20 27 20c79 0 81 8 91 47l134 537c3 12 4 15 4 19c0 13 -9 14 -27 16c-17 2 -38 2 -38 2c-19 0 -28 0 -28 11c0 20 10 20 29 20h336 c120 0 186 -64 186 -138zM665 549c0 44 -21 103 -109 103h-129c-43 0 -45 -3 -54 -38l-62 -248h146c122 0 208 95 208 183zM609 227c0 43 -19 117 -115 117h-189l-69 -279c-5 -18 -5 -20 -5 -23c0 -8 3 -9 13 -10c6 -1 8 -1 22 -1h136c118 0 207 97 207 196Z"></path>
|
||||
|
Before Width: | Height: | Size: 26 KiB After Width: | Height: | Size: 26 KiB |
@@ -1,3 +1,6 @@
|
||||
<!--
|
||||
C = S + a \cdot \begin{pmatrix} 0 \\ 1 \end{pmatrix} \ , \ \ C = E + b \cdot \begin{pmatrix} -sin(φ) \\ cos(φ) \end{pmatrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="46.167ex" height="5.833ex" style="vertical-align: -2.333ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1521.9 19877.3 2543.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D436" d="M760 695l-63 -255c-5 -18 -5 -20 -18 -20c-4 0 -15 0 -15 10s3 11 3 51c0 116 -59 193 -161 193c-89 0 -183 -50 -244 -121c-100 -117 -121 -279 -121 -336c0 -156 106 -208 196 -208c52 0 115 17 184 73c69 58 92 129 101 158c2 8 7 10 13 10c0 0 12 0 12 -10 c0 -3 -17 -94 -110 -176c-53 -46 -129 -86 -216 -86c-153 0 -271 109 -271 274c0 232 225 453 448 453c111 0 157 -75 166 -89l70 77c11 11 12 12 15 12c9 0 11 -7 11 -10Z"></path>
|
||||
|
Before Width: | Height: | Size: 11 KiB After Width: | Height: | Size: 11 KiB |
@@ -1,3 +1,20 @@
|
||||
<!--
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 \\
|
||||
-(z-1) & z & 0 \\
|
||||
(z - 1)^2 & -2 \cdot (z-1) \cdot z & z^2
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
P_1 \\ P_2 \\ P_3
|
||||
\end{bmatrix}
|
||||
=
|
||||
\begin{bmatrix}
|
||||
P_1 \\
|
||||
z \cdot P_2 - (z-1) \cdot P_1 \\
|
||||
z^2 \cdot P_3 - 2 \cdot z \cdot (z-1) \cdot P_2 + (z - 1)^2 \cdot P_1
|
||||
\end{bmatrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="90.167ex" height="9.333ex" style="vertical-align: -4ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2242.4 38838.3 3984.8" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-5B" d="M256 -230c0 -11 -9 -20 -20 -20h-122v1000h122c11 0 20 -9 20 -20s-9 -20 -20 -20h-82v-920h82c11 0 20 -9 20 -20Z"></path>
|
||||
|
Before Width: | Height: | Size: 14 KiB After Width: | Height: | Size: 14 KiB |
@@ -1,3 +1,27 @@
|
||||
<!--
|
||||
B(t) =
|
||||
\begin{bmatrix}
|
||||
1 & t & t^2
|
||||
\end{bmatrix}
|
||||
\cdot M \cdot Q \cdot
|
||||
\begin{bmatrix}
|
||||
P_1 \\ P_2 \\ P_3
|
||||
\end{bmatrix}
|
||||
=
|
||||
\begin{bmatrix}
|
||||
1 & t & t^2
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
M
|
||||
\cdot
|
||||
\left (
|
||||
Q'
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
P_1 \\ P_2 \\ P_3
|
||||
\end{bmatrix}
|
||||
\right )
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="68.333ex" height="8.833ex" style="vertical-align: -3.833ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2163.9 29443.8 3827.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D435" d="M756 545c0 -95 -105 -169 -209 -188c97 -11 155 -69 155 -141c0 -98 -118 -216 -276 -216h-357c-18 0 -27 0 -27 11c0 20 10 20 27 20c79 0 81 8 91 47l134 537c3 12 4 15 4 19c0 13 -9 14 -27 16c-17 2 -38 2 -38 2c-19 0 -28 0 -28 11c0 20 10 20 29 20h336 c120 0 186 -64 186 -138zM665 549c0 44 -21 103 -109 103h-129c-43 0 -45 -3 -54 -38l-62 -248h146c122 0 208 95 208 183zM609 227c0 43 -19 117 -115 117h-189l-69 -279c-5 -18 -5 -20 -5 -23c0 -8 3 -9 13 -10c6 -1 8 -1 22 -1h136c118 0 207 97 207 196Z"></path>
|
||||
|
Before Width: | Height: | Size: 13 KiB After Width: | Height: | Size: 13 KiB |
@@ -1,3 +1,13 @@
|
||||
<!--
|
||||
T_2 =
|
||||
\left [
|
||||
\begin{matrix}
|
||||
1 & -\frac{ {U_2}_x }{ {U_2}_y } & 0 \\
|
||||
0 & 1 & 0 \\
|
||||
0 & 0 & 1
|
||||
\end{matrix}
|
||||
\right ]
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="22ex" height="10.833ex" style="vertical-align: -4.833ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2595.2 9454.2 4690.4" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D447" d="M704 666c0 -3 -1 -13 -2 -17l-27 -174c-2 -15 -4 -23 -15 -23c-9 0 -12 7 -12 13c0 3 2 15 3 19c4 26 8 65 8 80c0 78 -45 82 -146 82c-21 0 -54 0 -63 -2c-12 -3 -16 -9 -23 -37l-133 -531c-4 -15 -4 -21 -4 -21c0 -16 8 -19 37 -22c26 -2 39 -2 64 -2c26 0 34 0 34 -11 c0 -20 -12 -20 -22 -20c-28 0 -58 2 -87 2l-83 1l-85 -1c-27 0 -55 -2 -82 -2c-6 0 -17 0 -17 12c0 19 6 19 42 19c107 0 110 11 119 48l134 534c1 3 4 15 4 21c0 8 0 12 -28 12h-39c-148 0 -174 -18 -228 -173c-6 -16 -7 -21 -17 -21c-7 0 -12 5 -12 11c0 0 5 16 6 18 l60 176c7 19 8 20 32 20h555c17 0 27 0 27 -11Z"></path>
|
||||
|
Before Width: | Height: | Size: 7.6 KiB After Width: | Height: | Size: 7.8 KiB |
@@ -1,3 +1,19 @@
|
||||
<!--
|
||||
B(t) = \begin{bmatrix}
|
||||
1 & t & t^2 & t^3
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 & 0 \\
|
||||
-3 & 3 & 0 & 0 \\
|
||||
3 & -6 & 3 & 0 \\
|
||||
-1 & 3 & -3 & 1
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
P_1 \\ P_2 \\ P_3 \\ P_4
|
||||
\end{bmatrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="53.167ex" height="12.167ex" style="vertical-align: -5.5ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2863.9 22926.4 5227.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D435" d="M756 545c0 -95 -105 -169 -209 -188c97 -11 155 -69 155 -141c0 -98 -118 -216 -276 -216h-357c-18 0 -27 0 -27 11c0 20 10 20 27 20c79 0 81 8 91 47l134 537c3 12 4 15 4 19c0 13 -9 14 -27 16c-17 2 -38 2 -38 2c-19 0 -28 0 -28 11c0 20 10 20 29 20h336 c120 0 186 -64 186 -138zM665 549c0 44 -21 103 -109 103h-129c-43 0 -45 -3 -54 -38l-62 -248h146c122 0 208 95 208 183zM609 227c0 43 -19 117 -115 117h-189l-69 -279c-5 -18 -5 -20 -5 -23c0 -8 3 -9 13 -10c6 -1 8 -1 22 -1h136c118 0 207 97 207 196Z"></path>
|
||||
|
Before Width: | Height: | Size: 11 KiB After Width: | Height: | Size: 11 KiB |
74
images/latex/5ce7a2a21aa510441a04d1060754f2726f3a21bf.svg
Normal file
74
images/latex/5ce7a2a21aa510441a04d1060754f2726f3a21bf.svg
Normal file
@@ -0,0 +1,74 @@
|
||||
<!--
|
||||
m = a \cdot value_1 + f(a)=(C-a) \cdot value_2, C = constant
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="55.833ex" height="2.5ex" style="vertical-align: -0.667ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -771.9 24065.3 1043.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D45A" d="M848 143c0 -8 -37 -154 -131 -154c-47 0 -82 35 -82 82c0 20 4 31 13 55c20 53 62 167 62 224c0 36 -11 70 -54 70c-109 0 -162 -120 -165 -133l-60 -241c-8 -32 -14 -57 -45 -57c-15 0 -29 9 -29 27c0 5 9 39 13 59c9 33 10 39 20 76l28 116c8 30 15 58 15 83 c0 33 -9 70 -54 70c-95 0 -148 -91 -163 -122l-13 -50c-5 -23 -11 -45 -17 -67l-22 -90c-6 -25 -18 -72 -19 -74c-7 -20 -25 -28 -37 -28c-15 0 -29 9 -29 27c0 5 6 28 9 43l58 231c13 52 16 63 16 84c0 38 -15 46 -31 46c-36 0 -56 -48 -73 -119c-6 -22 -7 -23 -17 -23 c0 0 -12 0 -12 10c0 3 13 62 31 97c9 18 28 57 74 57c45 0 87 -30 92 -87c17 23 66 87 156 87c25 0 57 -5 82 -26c28 -24 31 -58 32 -71c37 53 88 97 163 97s115 -42 115 -107c0 -57 -42 -168 -61 -220c-9 -22 -18 -46 -18 -71c0 -23 7 -33 24 -33c55 0 87 71 102 124 c5 15 5 18 15 18c3 0 12 0 12 -10Z"></path>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-3D" d="M722 347c0 -11 -9 -20 -20 -20h-626c-11 0 -20 9 -20 20s9 20 20 20h626c11 0 20 -9 20 -20zM722 153c0 -11 -9 -20 -20 -20h-626c-11 0 -20 9 -20 20s9 20 20 20h626c11 0 20 -9 20 -20Z"></path>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D44E" d="M498 143c0 0 -13 -63 -30 -99c-16 -32 -39 -55 -74 -55c-48 0 -83 33 -91 75c-60 -71 -110 -75 -130 -75c-78 0 -133 66 -133 160c0 146 124 293 241 293c45 0 74 -27 92 -64c3 22 18 44 42 44c17 0 29 -10 29 -27c0 -4 0 -6 -7 -34l-36 -140l-22 -90 c-11 -44 -13 -52 -13 -74c0 -20 3 -46 30 -46c41 0 59 59 76 124c3 14 4 18 14 18c3 0 12 0 12 -10zM361 332c0 6 -14 88 -79 88c-40 0 -85 -37 -116 -96c-23 -46 -55 -169 -55 -219c0 -39 14 -94 64 -94c28 0 69 16 113 71c15 17 15 19 20 37l50 196c1 5 3 11 3 17Z"></path>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-22C5" d="M192 250c0 -29 -24 -53 -53 -53s-53 24 -53 53s24 53 53 53s53 -24 53 -53Z"></path>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D463" d="M468 372c0 -52 -57 -383 -225 -383c-46 0 -134 16 -134 124c0 43 13 89 57 205c7 18 17 45 17 70c0 32 -17 32 -25 32c-29 0 -72 -23 -101 -124c-5 -16 -6 -18 -16 -18c0 0 -12 0 -12 10c0 9 38 154 132 154c50 0 82 -37 82 -82c0 -19 -5 -33 -12 -50 c-31 -83 -58 -156 -58 -212c0 -52 23 -87 74 -87c117 0 178 229 178 271c0 36 -13 62 -34 82c-11 11 -16 17 -16 30c0 22 24 48 49 48c18 0 44 -16 44 -70Z"></path>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D459" d="M258 683l-144 -578c-5 -19 -6 -24 -6 -48c0 -14 0 -46 30 -46c40 0 59 59 76 124c3 14 4 18 14 18c3 0 12 0 12 -10c0 0 -12 -60 -30 -98c-17 -36 -42 -56 -75 -56c-47 0 -91 35 -91 92c0 16 2 23 5 34l126 500l3 20c0 8 -1 17 -49 17c-15 0 -25 0 -25 11 c0 19 11 20 19 21c26 2 99 10 122 10c13 0 13 -11 13 -11Z"></path>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D462" d="M543 143c0 0 -13 -63 -30 -99c-16 -32 -39 -55 -74 -55c-43 0 -78 26 -89 67c-17 -22 -53 -67 -119 -67c-54 0 -123 25 -123 120c0 49 21 111 58 210c6 15 17 44 17 68c0 32 -16 33 -25 33c-38 0 -76 -37 -101 -124c-5 -16 -6 -18 -16 -18c0 0 -12 0 -12 10 c0 9 37 154 132 154c50 0 82 -37 82 -82c0 -19 -5 -33 -17 -63c-26 -69 -54 -148 -54 -204c0 -37 10 -82 62 -82c73 0 113 80 114 84l75 301c8 34 34 35 39 35c15 0 29 -9 29 -27c0 -6 -10 -44 -15 -67c-4 -15 -14 -53 -17 -68l-28 -108c-8 -35 -20 -82 -20 -104 c0 -33 10 -46 31 -46c42 0 61 68 75 124c3 14 4 18 14 18c3 0 12 0 12 -10Z"></path>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D452" d="M430 107c0 -12 -84 -118 -227 -118c-98 0 -157 79 -157 181c0 175 151 272 262 272c69 0 107 -41 107 -85c0 -14 -5 -73 -75 -103c-50 -21 -124 -23 -153 -23h-53c-15 -61 -16 -92 -16 -104c0 -32 9 -116 87 -116c12 0 121 0 200 99c6 8 8 10 13 10c6 0 12 -7 12 -13z M382 357c0 34 -27 63 -74 63c-26 0 -129 -15 -168 -167h41c41 0 201 0 201 104Z"></path>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-31" d="M419 0c-35 3 -122 3 -162 3s-127 0 -162 -3v31h32c90 0 93 12 93 48v518c-52 -26 -111 -26 -131 -26v31c32 0 120 0 182 64c23 0 23 -2 23 -26v-561c0 -37 3 -48 93 -48h32v-31Z"></path>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-2B" d="M722 250c0 -11 -9 -20 -20 -20h-293v-293c0 -11 -9 -20 -20 -20s-20 9 -20 20v293h-293c-11 0 -20 9 -20 20s9 20 20 20h293v293c0 11 9 20 20 20s20 -9 20 -20v-293h293c11 0 20 -9 20 -20Z"></path>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D453" d="M552 636c0 -38 -29 -60 -55 -60c-19 0 -37 12 -37 35c0 15 10 50 54 54c-19 18 -45 18 -49 18c-21 0 -38 -15 -47 -34c-6 -12 -20 -83 -24 -104c-11 -58 -10 -56 -21 -114h83c17 0 27 0 27 -11c0 -20 -10 -20 -30 -20h-86l-60 -317c-1 -7 -24 -128 -56 -191 c-18 -38 -58 -97 -113 -97c-41 0 -85 24 -85 69c0 38 29 60 55 60c19 0 37 -12 37 -35c0 -15 -9 -51 -55 -54c19 -18 44 -18 48 -18c52 0 69 91 87 188l75 395h-66c-19 0 -28 0 -28 12c0 19 11 19 30 19h69c24 126 27 136 33 157c30 99 93 117 127 117c41 0 87 -23 87 -69Z"></path>
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After Width: | Height: | Size: 12 KiB |
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<!--
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||||
ratio(t)_{cubic} = \left | \frac{t^3 + (1-t)^3 - 1}{t^3 + (1-t)^3} \right |
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-->
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<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="33.5ex" height="6.167ex" style="vertical-align: -2.5ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1632.2 14422.9 2690.5" xmlns="http://www.w3.org/2000/svg">
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<!--
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CatmullRom(t) =
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\begin{bmatrix}
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1 & t & t^2 & t^3
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\end{bmatrix}
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\cdot
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\begin{bmatrix}
|
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1 & 0 & 0 & 0 \\
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0 & 0 & 1 & 0 \\
|
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-3 & 3 & -2 & -1 \\
|
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2 & -2 & 1 & 1
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\end{bmatrix}
|
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\cdot
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\begin{bmatrix}
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V_1 \\ V_2 \\ V'_1 \\ V'_2
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\end{bmatrix}
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-->
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<!--
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φ = 4 \cdot arccos \left(\frac{\sqrt{2+ε-\sqrt{ε(2+ε)}}}{\sqrt{2}}\right)
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-->
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<!--
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\begin{array}{l}
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\int_{0}^{z}\sqrt{ \left (dx/dt \right )^2+\left (dy/dt \right )^2} dt
|
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\\
|
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\simeq \
|
||||
\frac{z}{2} \cdot \left [ C_1 \cdot f\left(\frac{z}{2} \cdot t_1 + \frac{z}{2}\right)
|
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+ ...
|
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+ C_n \cdot f\left(\frac{z}{2} \cdot t_n + \frac{z}{2}\right)
|
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\right ]
|
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\\
|
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= \
|
||||
\frac{z}{2} \cdot \sum_{i=1}^{n}{C_i \cdot f\left(\frac{z}{2} \cdot t_i + \frac{z}{2}\right)}
|
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\end{array}
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-->
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<defs>
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Before Width: | Height: | Size: 19 KiB After Width: | Height: | Size: 19 KiB |
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<!--
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\begin{array}{l}
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S = (1, 0) \ , \
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C_1 = \left ( 1, 4 \frac{\sqrt{2}-1}{3} \right ) \ , \
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C_2 = \left ( 4 \frac{\sqrt{2}-1}{3} , 1 \right ) \ , \
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E = (0, 1)
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\end{array}
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-->
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<defs>
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|
Before Width: | Height: | Size: 9.7 KiB After Width: | Height: | Size: 9.8 KiB |
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<!--
|
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N(t) \perp \left ( \frac{B'(t)}{\left || B'(t) \right || } \right )
|
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-->
|
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<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="21ex" height="7ex" style="vertical-align: -3ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1768.9 9038.7 3037.9" xmlns="http://www.w3.org/2000/svg">
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<defs>
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Before Width: | Height: | Size: 5.3 KiB After Width: | Height: | Size: 5.3 KiB |
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<!--
|
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mapped_4 = \left (
|
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\begin{matrix}
|
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x = \left (
|
||||
\frac
|
||||
{
|
||||
-x_1 + x_4 - \frac{(-x_1+x_2)(-y_1+y_4)}{-y_1+y_2}
|
||||
}
|
||||
{
|
||||
-x_1+x_3-\frac{(-x_1+x_2)(-y_1+y_3)}{-y_1+y_2}
|
||||
}
|
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\right )
|
||||
\\
|
||||
y = \left (
|
||||
\frac{(-y_1+y_4)}{-y_1+y_2}
|
||||
+
|
||||
\frac
|
||||
{
|
||||
\left ( 1 - \frac{-y_1+y_3}{-y_1+y_2} \right )
|
||||
\left ( -x_1 + x_4 - \frac{(-x_1+x_2)(-y_1+y_4)}{-y_1+y_2} \right )
|
||||
}
|
||||
{
|
||||
-x_1+x_3-\frac{(-x_1+x_2)(-y_1+y_3)}{-y_1+y_2}
|
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}
|
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\right )
|
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\end{matrix}
|
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\right )
|
||||
-->
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<defs>
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After Width: | Height: | Size: 7.1 KiB |
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<!--
|
||||
\left \{ \begin{array}{l}
|
||||
normal_x(t) = \hat{x}(t) \cdot \cos{\frac{\pi}{2}} - \hat{y}(t) \cdot \sin{\frac{\pi}{2}} = - \hat{y}(t) \\
|
||||
normal_y(t) = \underset{quarter\ circle\ rotation} {\underbrace{ \hat{x}(t) \cdot \sin{\frac{\pi}{2}} + \hat{y}(t) \cdot \cos{\frac{\pi}{2}} }} = \hat{x}(t)
|
||||
\end{array} \right.
|
||||
-->
|
||||
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|
||||
ratio(t) = \frac{distance(B,C)}{distance(A,B)} = Constant
|
||||
-->
|
||||
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<!--
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\begin{array}{l}
|
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C_1 = 1 \\
|
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C_2 = 1 \\
|
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t_1 = - \frac{1}{\sqrt{3}} \\
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t_2 = + \frac{1}{\sqrt{3}}
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\end{array}
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-->
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<!--
|
||||
\begin{array}{l}
|
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B(n,t), & & w = \{A,B,C,D\} \\
|
||||
B'(n,t), & n = 3, & w' = \{A',B',C'\} &= \{3 \cdot (B-A), {\ } 3 \cdot (C-B), {\ } 3 \cdot (D-C)\} \\
|
||||
B''(n,t), & n = 2, & w'' = \{A'',B''\} &= \{2 \cdot (B'-A'), {\ } 2 \cdot (C'-B')\} \\
|
||||
B'''(n,t), & n = 1, & w''' = \{A'''\} &= \{1 \cdot (B''-A'')\}
|
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\end{array}
|
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-->
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Before Width: | Height: | Size: 19 KiB After Width: | Height: | Size: 19 KiB |
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<!--
|
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\begin{array}{l}
|
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\left\{\begin{align*}
|
||||
T_x &= \frac{1}{4}(3 + cos(φ))\\
|
||||
T_y &= \frac{1}{4}\left(\frac{2-2cos(φ)}{sin(φ)} + sin(φ)\right)
|
||||
= \frac{1}{4}\left(2tan\left(\frac{φ}{2}\right) + sin(φ)\right)
|
||||
\end{align*}\right.
|
||||
\end{array}
|
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-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="64.5ex" height="11.5ex" style="vertical-align: -5.167ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 0ex; margin-top: 1px;" viewBox="0 -2733.8 27745.2 4967.6" xmlns="http://www.w3.org/2000/svg">
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Before Width: | Height: | Size: 16 KiB After Width: | Height: | Size: 17 KiB |
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|
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<!--
|
||||
\begin{bmatrix}t^3 & t^2 & t & 1\end{bmatrix} \cdot \begin{bmatrix}
|
||||
-1 & 3 & -3 & 1 \\
|
||||
3 & -6 & 3 & 0 \\
|
||||
-3 & 3 & 0 & 0 \\
|
||||
1 & 0 & 0 & 0
|
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\end{bmatrix}
|
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-->
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<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="37.5ex" height="12.167ex" style="vertical-align: -5.5ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2863.9 16170.7 5227.9" xmlns="http://www.w3.org/2000/svg">
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<defs>
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Before Width: | Height: | Size: 7.1 KiB After Width: | Height: | Size: 7.3 KiB |
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<!--
|
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\begin{bmatrix}
|
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1 & t & t^2 & t^3
|
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\end{bmatrix}
|
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\cdot
|
||||
\frac{1}{2}
|
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\cdot
|
||||
\begin{bmatrix}
|
||||
0 & 2 & 0 & 0 \\
|
||||
-τ & 0 & τ & 0 \\
|
||||
2τ & τ-6 & -2(τ-3) & -τ \\
|
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-τ & 4-τ & τ-4 & τ
|
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\end{bmatrix}
|
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\cdot
|
||||
\begin{bmatrix}
|
||||
P_1 \\ P_2 \\ P_3 \\ P_4
|
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\end{bmatrix}
|
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=
|
||||
\begin{bmatrix}
|
||||
1 & t & t^2 & t^3
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 & 0 \\
|
||||
-3 & 3 & 0 & 0 \\
|
||||
3 & -6 & 3 & 0 \\
|
||||
-1 & 3 & -3 & 1
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
A
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
P_1 \\ P_2 \\ P_3 \\ P_4
|
||||
\end{bmatrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="113ex" height="12.333ex" style="vertical-align: -5.667ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2892.9 48630.9 5285.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-5B" d="M256 -230c0 -11 -9 -20 -20 -20h-122v1000h122c11 0 20 -9 20 -20s-9 -20 -20 -20h-82v-920h82c11 0 20 -9 20 -20Z"></path>
|
||||
|
Before Width: | Height: | Size: 17 KiB After Width: | Height: | Size: 18 KiB |
@@ -1,3 +1,13 @@
|
||||
<!--
|
||||
\left \{ \begin{matrix}
|
||||
\hat{x}(t) = || tangent_x(t) ||
|
||||
=\frac{tangent_x(t)}{ || tangent(t) || }
|
||||
= \frac{B'_x(t)}{d} \\
|
||||
\hat{y}(t) = || tangent_y(t) ||
|
||||
= \frac{tangent_y(t)}{ || tangent(t) || }
|
||||
= \frac{B'_y(t)}{d}
|
||||
\end{matrix} \right.
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="45.833ex" height="10.5ex" style="vertical-align: -4.667ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 0ex; margin-top: 1px;" viewBox="0 -2520.3 19719.5 4540.7" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-7B" d="M425 -238c0 -7 -5 -12 -12 -12c-105 0 -196 52 -196 125v250c0 58 -55 113 -130 113c-7 0 -12 5 -12 12s5 12 12 12c75 0 130 55 130 113v250c0 73 91 125 196 125c7 0 12 -5 12 -12s-5 -12 -12 -12c-75 0 -130 -49 -130 -101v-250c0 -58 -48 -104 -115 -125 c67 -21 115 -67 115 -125v-250c0 -52 55 -101 130 -101c7 0 12 -5 12 -12Z"></path>
|
||||
|
Before Width: | Height: | Size: 18 KiB After Width: | Height: | Size: 18 KiB |
@@ -1,3 +1,16 @@
|
||||
<!--
|
||||
\begin{bmatrix}
|
||||
x' \\ y'
|
||||
\end{bmatrix}
|
||||
=
|
||||
\begin{bmatrix}
|
||||
\cos(\phi) & -\sin(\phi) \\
|
||||
\sin(\phi) & \cos(\phi)
|
||||
\end{bmatrix}
|
||||
\begin{bmatrix}
|
||||
x \\ y
|
||||
\end{bmatrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="33.667ex" height="6.167ex" style="vertical-align: -2.5ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1570.3 14475 2640.6" xmlns="http://www.w3.org/2000/svg">
|
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<defs>
|
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<path stroke-width="10" id="E1-LATINMODERNMAIN-5B" d="M256 -230c0 -11 -9 -20 -20 -20h-122v1000h122c11 0 20 -9 20 -20s-9 -20 -20 -20h-82v-920h82c11 0 20 -9 20 -20Z"></path>
|
||||
|
Before Width: | Height: | Size: 8.6 KiB After Width: | Height: | Size: 8.8 KiB |
@@ -1,3 +1,13 @@
|
||||
<!--
|
||||
Given \left (
|
||||
\begin{align}
|
||||
p_1 &= some\ point \\
|
||||
p_2 &= some\ other\ point \\
|
||||
distance &= (p_2 - p_1) \\
|
||||
ratio &= \frac{percentage}{100} \\
|
||||
\end{align}
|
||||
\right ),\ our\ new\ point = p_1 + distance \cdot ratio
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="81.667ex" height="14.167ex" style="vertical-align: -6.5ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -3295.8 35192.6 6091.7" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D43A" d="M760 695l-63 -255c-5 -18 -5 -20 -18 -20c-4 0 -15 0 -15 10s3 11 3 51c0 116 -59 193 -161 193c-99 0 -196 -61 -250 -129c-105 -130 -115 -295 -115 -326c0 -153 105 -210 201 -210c35 0 165 11 193 121c10 37 21 82 21 91c0 13 -5 16 -31 19c-23 2 -53 2 -53 2 c-22 0 -30 0 -30 11c0 20 12 20 21 20l140 -3c23 0 82 3 105 3c8 0 13 -4 13 -11c0 -19 -11 -20 -16 -20c-57 -1 -58 -3 -69 -48c-4 -17 -9 -34 -13 -51l-19 -77c-5 -21 -15 -59 -17 -61c0 0 -2 -4 -7 -4c-10 0 -36 37 -45 62c-18 -20 -37 -41 -87 -61 c-36 -15 -81 -24 -125 -24c-162 0 -273 115 -273 274c0 232 225 453 448 453c111 0 157 -75 166 -89l70 77c11 11 12 12 15 12c9 0 11 -7 11 -10Z"></path>
|
||||
|
Before Width: | Height: | Size: 22 KiB After Width: | Height: | Size: 22 KiB |
@@ -1,3 +1,6 @@
|
||||
<!--
|
||||
f(x) = \cos(x)
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="13.833ex" height="2.5ex" style="vertical-align: -0.667ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -771.9 5978.6 1043.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D453" d="M552 636c0 -38 -29 -60 -55 -60c-19 0 -37 12 -37 35c0 15 10 50 54 54c-19 18 -45 18 -49 18c-21 0 -38 -15 -47 -34c-6 -12 -20 -83 -24 -104c-11 -58 -10 -56 -21 -114h83c17 0 27 0 27 -11c0 -20 -10 -20 -30 -20h-86l-60 -317c-1 -7 -24 -128 -56 -191 c-18 -38 -58 -97 -113 -97c-41 0 -85 24 -85 69c0 38 29 60 55 60c19 0 37 -12 37 -35c0 -15 -9 -51 -55 -54c19 -18 44 -18 48 -18c52 0 69 91 87 188l75 395h-66c-19 0 -28 0 -28 12c0 19 11 19 30 19h69c24 126 27 136 33 157c30 99 93 117 127 117c41 0 87 -23 87 -69Z"></path>
|
||||
|
Before Width: | Height: | Size: 4.3 KiB After Width: | Height: | Size: 4.3 KiB |
@@ -1,3 +1,25 @@
|
||||
<!--
|
||||
T
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
P_1 \\ P_2 \\ P_3 \\ P_4
|
||||
\end{bmatrix}
|
||||
=
|
||||
\begin{bmatrix}
|
||||
P_2 \\ P_3 \\ \frac{P_3 - P_1}{2 \cdot τ} \\ \frac{P_4 - P_2}{2 \cdot τ}
|
||||
\end{bmatrix}
|
||||
\Rightarrow \
|
||||
T
|
||||
=
|
||||
\frac{1}{2}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
0 & 2 & 0 & 0 \\
|
||||
0 & 0 & 2 & 0 \\
|
||||
-τ & 0 & τ & 0 \\
|
||||
0 & -τ & 0 & τ
|
||||
\end{bmatrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="55ex" height="14.667ex" style="vertical-align: -6.833ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -3396.3 23670.2 6292.7" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D447" d="M704 666c0 -3 -1 -13 -2 -17l-27 -174c-2 -15 -4 -23 -15 -23c-9 0 -12 7 -12 13c0 3 2 15 3 19c4 26 8 65 8 80c0 78 -45 82 -146 82c-21 0 -54 0 -63 -2c-12 -3 -16 -9 -23 -37l-133 -531c-4 -15 -4 -21 -4 -21c0 -16 8 -19 37 -22c26 -2 39 -2 64 -2c26 0 34 0 34 -11 c0 -20 -12 -20 -22 -20c-28 0 -58 2 -87 2l-83 1l-85 -1c-27 0 -55 -2 -82 -2c-6 0 -17 0 -17 12c0 19 6 19 42 19c107 0 110 11 119 48l134 534c1 3 4 15 4 21c0 8 0 12 -28 12h-39c-148 0 -174 -18 -228 -173c-6 -16 -7 -21 -17 -21c-7 0 -12 5 -12 11c0 0 5 16 6 18 l60 176c7 19 8 20 32 20h555c17 0 27 0 27 -11Z"></path>
|
||||
|
Before Width: | Height: | Size: 13 KiB After Width: | Height: | Size: 13 KiB |
@@ -1,3 +1,11 @@
|
||||
<!--
|
||||
\begin{matrix}
|
||||
... & = & (1-t) \cdot (1-t) \cdot (1-t) & = & -t^3 + 3 \cdot t^2 - 3 \cdot t + 1 \\
|
||||
& + & 3 \cdot (1-t) \cdot (1-t) \cdot t & = & 3 \cdot t^3 - 6 \cdot t^2 + 3 \cdot t \\
|
||||
& + & 3 \cdot (1-t) \cdot t \cdot t & = & -3 \cdot t^3 + 3 \cdot t^2 \\
|
||||
& + & t \cdot t \cdot t & = & t^3 \\
|
||||
\end{matrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="61.833ex" height="13ex" style="vertical-align: -5.833ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -3032.7 26633.5 5565.5" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-2E" d="M192 53c0 -29 -24 -53 -53 -53s-53 24 -53 53s24 53 53 53s53 -24 53 -53Z"></path>
|
||||
|
Before Width: | Height: | Size: 11 KiB After Width: | Height: | Size: 11 KiB |
@@ -1,3 +1,9 @@
|
||||
<!--
|
||||
Bézier_{n,k}(t) \frac{d}{dt} = n \cdot B_{(n-1),{\color{blue}0}}(t) \cdot (w_1 - w_0)
|
||||
+ n \cdot B_{(n-1),{\color{red}1}}(t) \cdot (w_2 - w_1)
|
||||
+ n \cdot B_{(n-1),{\color{magenta}2}}(t) \cdot (w_3 - w_2)
|
||||
\ + \ ...
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="107ex" height="5ex" style="vertical-align: -1.833ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1394.4 46041.5 2152.8" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D435" d="M756 545c0 -95 -105 -169 -209 -188c97 -11 155 -69 155 -141c0 -98 -118 -216 -276 -216h-357c-18 0 -27 0 -27 11c0 20 10 20 27 20c79 0 81 8 91 47l134 537c3 12 4 15 4 19c0 13 -9 14 -27 16c-17 2 -38 2 -38 2c-19 0 -28 0 -28 11c0 20 10 20 29 20h336 c120 0 186 -64 186 -138zM665 549c0 44 -21 103 -109 103h-129c-43 0 -45 -3 -54 -38l-62 -248h146c122 0 208 95 208 183zM609 227c0 43 -19 117 -115 117h-189l-69 -279c-5 -18 -5 -20 -5 -23c0 -8 3 -9 13 -10c6 -1 8 -1 22 -1h136c118 0 207 97 207 196Z"></path>
|
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|
Before Width: | Height: | Size: 17 KiB After Width: | Height: | Size: 17 KiB |
54
images/latex/7f5ebb8489a8d04beb28f47c8aac2632b78ae764.svg
Normal file
54
images/latex/7f5ebb8489a8d04beb28f47c8aac2632b78ae764.svg
Normal file
@@ -0,0 +1,54 @@
|
||||
<!--
|
||||
mixture = a \cdot value_1 + b \cdot value_2
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="33.333ex" height="2ex" style="vertical-align: -0.5ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -717.9 14333.1 888.9" xmlns="http://www.w3.org/2000/svg">
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<defs>
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</defs>
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<!--
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\begin{array}{l}
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n \cdot B_{n-1,-1}(t) \cdot w_0 &+& & \\
|
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n \cdot B_{n-1,{\color{blue}0}}(t) \cdot w_1 &-& n \cdot B_{n-1,{\color{blue}0}}(t) \cdot w_0 & + \\
|
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n \cdot B_{n-1,{\color{red}1}}(t) \cdot w_2 &-& n \cdot B_{n-1,{\color{red}1}}(t) \cdot w_1 & + \\
|
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n \cdot B_{n-1,{\color{magenta}2}}(t) \cdot w_3 &-& n \cdot B_{n-1,{\color{magenta}2}}(t) \cdot w_2 & + \\
|
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... &-& n \cdot B_{n-1,3}(t) \cdot w_3 & + \\
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... & & &
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\end{array}
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-->
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\left \{ \begin{matrix}
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x = {\color{blue}120} \cdot (1-t)^3 + {\color{blue}35} \cdot 3 \cdot (1-t)^2 \cdot t + {\color{blue}220} \cdot 3 \cdot (1-t) \cdot t^2 + {\color{blue}220} \cdot t^3 \\
|
||||
y = {\color{blue}160} \cdot (1-t)^3 + {\color{blue}200} \cdot 3 \cdot (1-t)^2 \cdot t + {\color{blue}260} \cdot 3 \cdot (1-t) \cdot t^2 + {\color{blue}40} \cdot t^3
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\end{matrix} \right.
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-->
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<!--
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\begin{align*}
|
||||
linear &= {\color{blue}a} + {\color{red}b} \\
|
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square &= {\color{blue}a} \cdot {\color{blue}a} + {\color{blue}a} \cdot {\color{red}b} + {\color{red}b} \cdot {\color{red}b} \\
|
||||
cubic &= {\color{blue}a} \cdot {\color{blue}a} \cdot {\color{blue}a} + {\color{blue}a} \cdot {\color{blue}a} \cdot {\color{red}b} + {\color{blue}a} \cdot {\color{red}b} \cdot {\color{red}b} + {\color{red}b} \cdot {\color{red}b} \cdot {\color{red}b}\\
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\end{align*}
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-->
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<!--
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\begin{array}{l}
|
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Bézier_{n,k}(t) &=& B_{n,0}(t) \cdot w_0 + B_{n,1}(t) \cdot w_1 + B_{n,2}(t) \cdot w_2 + B_{n,3}(t) \cdot w_3 + ... \\
|
||||
Bézier_{n,k}(t) \frac{d}{dt} &=& n \cdot (B_{n-1,-1}(t) - B_{n-1,0}(t)) \cdot w_0 + \\
|
||||
& & n \cdot (B_{n-1,0}(t) - B_{n-1,1}(t)) \cdot w_1 + \\
|
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& & n \cdot (B_{n-1,1}(t) - B_{n-1,2}(t)) \cdot w_2 + \\
|
||||
& & n \cdot (B_{n-1,2}(t) - B_{n-1,3}(t)) \cdot w_3 + \\
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& & ...
|
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\end{array}
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-->
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<!--
|
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\frac{1}{2}
|
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\cdot
|
||||
\begin{bmatrix}
|
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0 & 2 & 0 & 0 \\
|
||||
-τ & 0 & τ & 0 \\
|
||||
2τ & τ-6 & -2(τ-3) & -τ \\
|
||||
-τ & 4-τ & τ-4 & τ
|
||||
\end{bmatrix}
|
||||
=
|
||||
\begin{bmatrix}
|
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1 & 0 & 0 & 0 \\
|
||||
-3 & 3 & 0 & 0 \\
|
||||
3 & -6 & 3 & 0 \\
|
||||
-1 & 3 & -3 & 1
|
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\end{bmatrix}
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\cdot
|
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A
|
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-->
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49
images/latex/8c934a53204814a89bf8777c9289a12b9b23f577.svg
Normal file
49
images/latex/8c934a53204814a89bf8777c9289a12b9b23f577.svg
Normal file
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<!--
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m = a \cdot value_1 + f(a) \cdot value_2
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-->
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<use xlink:href="#E1-LATINMODERNMAIN-2B" x="6537" y="0"></use>
|
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<use xlink:href="#E1-LATINMODERNNORMAL-1D453" x="7542" y="0"></use>
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<use xlink:href="#E1-LATINMODERNMAIN-28" x="8099" y="0"></use>
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<use xlink:href="#E1-LATINMODERNNORMAL-1D44E" x="8493" y="0"></use>
|
||||
<use xlink:href="#E1-LATINMODERNMAIN-29" x="9027" y="0"></use>
|
||||
<use xlink:href="#E1-LATINMODERNMAIN-22C5" x="9643" y="0"></use>
|
||||
<use xlink:href="#E1-LATINMODERNNORMAL-1D463" x="10148" y="0"></use>
|
||||
<use xlink:href="#E1-LATINMODERNNORMAL-1D44E" x="10638" y="0"></use>
|
||||
<use xlink:href="#E1-LATINMODERNNORMAL-1D459" x="11172" y="0"></use>
|
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<use xlink:href="#E1-LATINMODERNNORMAL-1D462" x="11475" y="0"></use>
|
||||
<g transform="translate(12052,0)">
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||||
<use xlink:href="#E1-LATINMODERNNORMAL-1D452" x="0" y="0"></use>
|
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<use transform="scale(0.707)" xlink:href="#E1-LATINMODERNMAIN-32" x="666" y="-213"></use>
|
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</g>
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</g>
|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 7.4 KiB |
@@ -1,3 +1,6 @@
|
||||
<!--
|
||||
length = \int_{0}^{z}\sqrt{ \left (dx/dt \right )^2+\left (dy/dt \right )^2} dt
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="38ex" height="5.5ex" style="vertical-align: -2.167ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1431.5 16333.3 2374.4" xmlns="http://www.w3.org/2000/svg">
|
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<defs>
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<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D459" d="M258 683l-144 -578c-5 -19 -6 -24 -6 -48c0 -14 0 -46 30 -46c40 0 59 59 76 124c3 14 4 18 14 18c3 0 12 0 12 -10c0 0 -12 -60 -30 -98c-17 -36 -42 -56 -75 -56c-47 0 -91 35 -91 92c0 16 2 23 5 34l126 500l3 20c0 8 -1 17 -49 17c-15 0 -25 0 -25 11 c0 19 11 20 19 21c26 2 99 10 122 10c13 0 13 -11 13 -11Z"></path>
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|
Before Width: | Height: | Size: 11 KiB After Width: | Height: | Size: 11 KiB |
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|
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<!--
|
||||
\left [
|
||||
\begin{matrix}
|
||||
1 & S & 0 \\
|
||||
0 & 1 & 0 \\
|
||||
0 & 0 & 1
|
||||
\end{matrix}
|
||||
\right ]
|
||||
\cdot
|
||||
\left [
|
||||
\begin{matrix}
|
||||
x \\
|
||||
y \\
|
||||
1
|
||||
\end{matrix}
|
||||
\right ]
|
||||
=
|
||||
\left [
|
||||
\begin{matrix}
|
||||
x + S \cdot y \\
|
||||
y \\
|
||||
1
|
||||
\end{matrix}
|
||||
\right ]
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="34.833ex" height="9ex" style="vertical-align: -4ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2178.9 14982.5 3857.9" xmlns="http://www.w3.org/2000/svg">
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<defs>
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<path stroke-width="10" id="E1-LATINMODERNMAIN-5B" d="M256 -230c0 -11 -9 -20 -20 -20h-122v1000h122c11 0 20 -9 20 -20s-9 -20 -20 -20h-82v-920h82c11 0 20 -9 20 -20Z"></path>
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|
Before Width: | Height: | Size: 8.2 KiB After Width: | Height: | Size: 8.4 KiB |
@@ -1,3 +1,11 @@
|
||||
<!--
|
||||
\begin{align}
|
||||
l(x) = ax + b &= 0,\\
|
||||
ax + b &= 0,\\
|
||||
ax &= -b \\
|
||||
x &= \frac{-b}{a}
|
||||
\end{align}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="21ex" height="14.167ex" style="vertical-align: -6.5ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 0ex; margin-top: 1px;" viewBox="0 -3288.2 9018.1 6076.3" xmlns="http://www.w3.org/2000/svg">
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<defs>
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<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D459" d="M258 683l-144 -578c-5 -19 -6 -24 -6 -48c0 -14 0 -46 30 -46c40 0 59 59 76 124c3 14 4 18 14 18c3 0 12 0 12 -10c0 0 -12 -60 -30 -98c-17 -36 -42 -56 -75 -56c-47 0 -91 35 -91 92c0 16 2 23 5 34l126 500l3 20c0 8 -1 17 -49 17c-15 0 -25 0 -25 11 c0 19 11 20 19 21c26 2 99 10 122 10c13 0 13 -11 13 -11Z"></path>
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||||
|
Before Width: | Height: | Size: 6.6 KiB After Width: | Height: | Size: 6.7 KiB |
@@ -1,3 +1,12 @@
|
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<!--
|
||||
\begin{array}{l}
|
||||
l = cos(\frac{φ}{2}) \ , \\
|
||||
\left\{\begin{array}{l}
|
||||
C_x = l \cdot cos\left(\frac{φ}{2}\right) = cos^2\left(\frac{φ}{2}\right)\ , \\
|
||||
C_y = l \cdot sin\left(\frac{φ}{2}\right) = cos(\frac{φ}{2}) \cdot sin\left(\frac{φ}{2}\right)\ , \\
|
||||
\end{array}\right.
|
||||
\end{array}
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||||
-->
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||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="41.5ex" height="11.833ex" style="vertical-align: -5.333ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2805.4 17884.5 5110.9" xmlns="http://www.w3.org/2000/svg">
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<defs>
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<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D459" d="M258 683l-144 -578c-5 -19 -6 -24 -6 -48c0 -14 0 -46 30 -46c40 0 59 59 76 124c3 14 4 18 14 18c3 0 12 0 12 -10c0 0 -12 -60 -30 -98c-17 -36 -42 -56 -75 -56c-47 0 -91 35 -91 92c0 16 2 23 5 34l126 500l3 20c0 8 -1 17 -49 17c-15 0 -25 0 -25 11 c0 19 11 20 19 21c26 2 99 10 122 10c13 0 13 -11 13 -11Z"></path>
|
||||
|
Before Width: | Height: | Size: 14 KiB After Width: | Height: | Size: 15 KiB |
@@ -1,3 +1,23 @@
|
||||
<!--
|
||||
=
|
||||
\begin{bmatrix}
|
||||
1 & t & t^2 & t^3
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 & 0 \\
|
||||
-3 & 3 & 0 & 0 \\
|
||||
3 & -6 & 3 & 0 \\
|
||||
-1 & 3 & -3 & 1
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
P_2 \\
|
||||
P_2 + \frac{P_3-P_1}{6 \cdot τ} \\
|
||||
P_3 - \frac{P_4-P_2}{6 \cdot τ} \\
|
||||
P_3
|
||||
\end{bmatrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="57ex" height="14.667ex" style="vertical-align: -6.833ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -3403.4 24507.9 6306.8" xmlns="http://www.w3.org/2000/svg">
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<defs>
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<path stroke-width="10" id="E1-LATINMODERNMAIN-3D" d="M722 347c0 -11 -9 -20 -20 -20h-626c-11 0 -20 9 -20 20s9 20 20 20h626c11 0 20 -9 20 -20zM722 153c0 -11 -9 -20 -20 -20h-626c-11 0 -20 9 -20 20s9 20 20 20h626c11 0 20 -9 20 -20Z"></path>
|
||||
|
Before Width: | Height: | Size: 12 KiB After Width: | Height: | Size: 13 KiB |
@@ -1,3 +1,7 @@
|
||||
<!--
|
||||
very\ hard:\ solve\ at^3 + bt^2 + ct + d = 0\\
|
||||
easier:\ solve\ t^3 + pt + q = 0
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="100ex" height="6.167ex" style="vertical-align: -4.167ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -904.8 43055.4 2659.2" xmlns="http://www.w3.org/2000/svg">
|
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<defs>
|
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<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D463" d="M468 372c0 -52 -57 -383 -225 -383c-46 0 -134 16 -134 124c0 43 13 89 57 205c7 18 17 45 17 70c0 32 -17 32 -25 32c-29 0 -72 -23 -101 -124c-5 -16 -6 -18 -16 -18c0 0 -12 0 -12 10c0 9 38 154 132 154c50 0 82 -37 82 -82c0 -19 -5 -33 -12 -50 c-31 -83 -58 -156 -58 -212c0 -52 23 -87 74 -87c117 0 178 229 178 271c0 36 -13 62 -34 82c-11 11 -16 17 -16 30c0 22 24 48 49 48c18 0 44 -16 44 -70Z"></path>
|
||||
|
Before Width: | Height: | Size: 14 KiB After Width: | Height: | Size: 14 KiB |
@@ -1,3 +1,29 @@
|
||||
<!--
|
||||
Q' = M^{-1} \cdot Z' \cdot M =
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 \\
|
||||
1 & \frac{1}{2} & 0 \\
|
||||
1 & 1 & 1
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
1 & z & z^2 \\
|
||||
0 & 1-z & 2 \cdot z \cdot (1-z) \\
|
||||
0 & 0 & (1-z)^2
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 \\
|
||||
-2 & 2 & 0 \\
|
||||
1 & -2 & 1
|
||||
\end{bmatrix}
|
||||
=
|
||||
\begin{bmatrix}
|
||||
(z-1)^2 & -2 \cdot z \cdot (z-1) & z^2 \\
|
||||
0 & -(z-1) & z \\
|
||||
0 & 0 & 1
|
||||
\end{bmatrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="117.167ex" height="9.667ex" style="vertical-align: -4.333ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2343.6 50438.1 4187.1" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D444" d="M740 436c0 -193 -147 -371 -302 -430c10 -76 25 -103 71 -103c35 0 93 25 117 96c2 6 4 11 12 11c4 0 11 -3 11 -10c0 -11 -48 -194 -167 -194c-83 0 -83 78 -83 110c0 13 0 15 4 77c-39 -11 -73 -15 -98 -15c-144 0 -256 101 -256 267c0 233 220 460 436 460 c149 0 255 -108 255 -269zM652 468c0 134 -73 212 -173 212c-73 0 -167 -46 -240 -148c-76 -108 -102 -250 -102 -319c0 -90 34 -168 112 -199c0 0 -6 12 -6 32c0 52 49 102 102 102c73 0 83 -73 88 -108c168 94 219 328 219 428zM406 41c0 61 -19 85 -61 85 s-80 -40 -80 -80c0 -43 32 -43 46 -43c28 0 58 7 84 18c10 4 11 5 11 20Z"></path>
|
||||
|
Before Width: | Height: | Size: 16 KiB After Width: | Height: | Size: 16 KiB |
@@ -1,3 +1,19 @@
|
||||
<!--
|
||||
B(t) =
|
||||
\begin{bmatrix}
|
||||
1 & ( 0 + z \cdot t) & ( 0 + z \cdot t)^2
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 \\
|
||||
-2 & 2 & 0 \\
|
||||
1 & -2 & 1
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\begin{bmatrix}
|
||||
P_1 \\ P_2 \\ P_3
|
||||
\end{bmatrix}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="61ex" height="8.833ex" style="vertical-align: -3.833ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2163.9 26255 3827.9" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D435" d="M756 545c0 -95 -105 -169 -209 -188c97 -11 155 -69 155 -141c0 -98 -118 -216 -276 -216h-357c-18 0 -27 0 -27 11c0 20 10 20 27 20c79 0 81 8 91 47l134 537c3 12 4 15 4 19c0 13 -9 14 -27 16c-17 2 -38 2 -38 2c-19 0 -28 0 -28 11c0 20 10 20 29 20h336 c120 0 186 -64 186 -138zM665 549c0 44 -21 103 -109 103h-129c-43 0 -45 -3 -54 -38l-62 -248h146c122 0 208 95 208 183zM609 227c0 43 -19 117 -115 117h-189l-69 -279c-5 -18 -5 -20 -5 -23c0 -8 3 -9 13 -10c6 -1 8 -1 22 -1h136c118 0 207 97 207 196Z"></path>
|
||||
|
Before Width: | Height: | Size: 11 KiB After Width: | Height: | Size: 11 KiB |
@@ -1,3 +1,6 @@
|
||||
<!--
|
||||
y = \frac{-x^2 + 2x + 3}{4}, \{ x \leq 1 \}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="27.667ex" height="5.333ex" style="vertical-align: -1.667ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1531.3 11932.8 2261.7" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D466" d="M490 404c0 -7 0 -9 -4 -23l-96 -382c-28 -113 -131 -204 -234 -204c-62 0 -106 37 -106 87c0 49 33 65 56 65c10 0 37 -4 37 -35c0 -19 -10 -32 -20 -41c-14 -12 -27 -12 -43 -12c17 -39 62 -42 76 -42c46 0 84 29 110 63c40 53 52 102 65 154c-28 -28 -62 -45 -101 -45 c-59 0 -122 30 -122 119c0 47 18 104 58 210c7 19 17 45 17 70c0 32 -17 32 -25 32c-34 0 -74 -30 -101 -124c-5 -16 -6 -18 -16 -18c0 0 -12 0 -12 10c0 9 37 154 132 154c50 0 82 -37 82 -82c0 -20 -4 -31 -20 -72c-34 -88 -51 -150 -51 -196c0 -37 11 -81 62 -81 c66 0 109 70 113 85l45 180l20 80c4 18 12 49 14 54c9 15 25 21 35 21c15 0 29 -9 29 -27Z"></path>
|
||||
|
Before Width: | Height: | Size: 6.2 KiB After Width: | Height: | Size: 6.2 KiB |
@@ -1,3 +1,13 @@
|
||||
<!--
|
||||
T_4 =
|
||||
\left [
|
||||
\begin{matrix}
|
||||
1 & 0 & 0 \\
|
||||
\frac{1 - {W_3}_y}{ {W_3}_x } & 1 & 0 \\
|
||||
0 & 0 & 1
|
||||
\end{matrix}
|
||||
\right ]
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="22.5ex" height="11ex" style="vertical-align: -5ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2607.8 9719.5 4715.7" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D447" d="M704 666c0 -3 -1 -13 -2 -17l-27 -174c-2 -15 -4 -23 -15 -23c-9 0 -12 7 -12 13c0 3 2 15 3 19c4 26 8 65 8 80c0 78 -45 82 -146 82c-21 0 -54 0 -63 -2c-12 -3 -16 -9 -23 -37l-133 -531c-4 -15 -4 -21 -4 -21c0 -16 8 -19 37 -22c26 -2 39 -2 64 -2c26 0 34 0 34 -11 c0 -20 -12 -20 -22 -20c-28 0 -58 2 -87 2l-83 1l-85 -1c-27 0 -55 -2 -82 -2c-6 0 -17 0 -17 12c0 19 6 19 42 19c107 0 110 11 119 48l134 534c1 3 4 15 4 21c0 8 0 12 -28 12h-39c-148 0 -174 -18 -228 -173c-6 -16 -7 -21 -17 -21c-7 0 -12 5 -12 11c0 0 5 16 6 18 l60 176c7 19 8 20 32 20h555c17 0 27 0 27 -11Z"></path>
|
||||
|
Before Width: | Height: | Size: 8.3 KiB After Width: | Height: | Size: 8.4 KiB |
@@ -1,3 +1,6 @@
|
||||
<!--
|
||||
||{A,C}|| = d_2 + d_1 = d_2 + d_2 \cdot ratio_3 \left(\frac{1}{2}\right) = d_2 + \frac{1}{3}d_2 = \frac{4}{3}d_2
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="61.5ex" height="5.167ex" style="vertical-align: -2ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1377.4 26491 2197.4" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-7C" d="M159 -230c0 -11 -9 -20 -20 -20s-20 9 -20 20v960c0 11 9 20 20 20s20 -9 20 -20v-960Z"></path>
|
||||
|
Before Width: | Height: | Size: 11 KiB After Width: | Height: | Size: 11 KiB |
@@ -1,3 +1,9 @@
|
||||
<!--
|
||||
\begin{align}
|
||||
& u(t)_{quadratic} = \frac{(t-1)^2}{2t^2 - 2t + 1} \\
|
||||
& u(t)_{cubic} = \frac{(1-t)^3}{t^3 + (1-t)^3}
|
||||
\end{align}
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="27.833ex" height="12.667ex" style="vertical-align: -5.833ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -2994 12008.1 5488" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNNORMAL-1D462" d="M543 143c0 0 -13 -63 -30 -99c-16 -32 -39 -55 -74 -55c-43 0 -78 26 -89 67c-17 -22 -53 -67 -119 -67c-54 0 -123 25 -123 120c0 49 21 111 58 210c6 15 17 44 17 68c0 32 -16 33 -25 33c-38 0 -76 -37 -101 -124c-5 -16 -6 -18 -16 -18c0 0 -12 0 -12 10 c0 9 37 154 132 154c50 0 82 -37 82 -82c0 -19 -5 -33 -17 -63c-26 -69 -54 -148 -54 -204c0 -37 10 -82 62 -82c73 0 113 80 114 84l75 301c8 34 34 35 39 35c15 0 29 -9 29 -27c0 -6 -10 -44 -15 -67c-4 -15 -14 -53 -17 -68l-28 -108c-8 -35 -20 -82 -20 -104 c0 -33 10 -46 31 -46c42 0 61 68 75 124c3 14 4 18 14 18c3 0 12 0 12 -10Z"></path>
|
||||
|
Before Width: | Height: | Size: 12 KiB After Width: | Height: | Size: 12 KiB |
@@ -1,3 +1,9 @@
|
||||
<!--
|
||||
\left \{ \begin{matrix}
|
||||
x = {\color{blue}0} \cdot (1-t)^3 {\color{blue}\ -\ 85} \cdot 3 \cdot (1-t)^2 \cdot t {\color{blue}\ +\ 100} \cdot 3 \cdot (1-t) \cdot t^2 {\color{blue}\ +\ 100} \cdot t^3 \\
|
||||
y = {\color{blue}0} \cdot (1-t)^3 {\color{blue}\ +\ 40} \cdot 3 \cdot (1-t)^2 \cdot t {\color{blue}\ +\ 100} \cdot 3 \cdot (1-t) \cdot t^2 {\color{blue}\ -\ 120} \cdot t^3
|
||||
\end{matrix} \right.
|
||||
-->
|
||||
<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="73.5ex" height="6.167ex" style="vertical-align: -2.5ex; margin-left: 0ex; margin-right: 0ex; margin-bottom: 1px; margin-top: 1px;" viewBox="0 -1562.8 31628.7 2625.7" xmlns="http://www.w3.org/2000/svg">
|
||||
<defs>
|
||||
<path stroke-width="10" id="E1-LATINMODERNMAIN-7B" d="M425 -238c0 -7 -5 -12 -12 -12c-105 0 -196 52 -196 125v250c0 58 -55 113 -130 113c-7 0 -12 5 -12 12s5 12 12 12c75 0 130 55 130 113v250c0 73 91 125 196 125c7 0 12 -5 12 -12s-5 -12 -12 -12c-75 0 -130 -49 -130 -101v-250c0 -58 -48 -104 -115 -125 c67 -21 115 -67 115 -125v-250c0 -52 55 -101 130 -101c7 0 12 -5 12 -12Z"></path>
|
||||
|
Before Width: | Height: | Size: 15 KiB After Width: | Height: | Size: 16 KiB |
@@ -1,3 +1,9 @@
|
||||
<!--
|
||||
\left \{ \begin{array}{l}
|
||||
x = {\color{blue}85} \cdot 3 \cdot (1-t)^2 \cdot t {\color{blue}\ +\ 13} \cdot 3 \cdot (1-t) \cdot t^2 {\color{blue}\ -\ 156} \cdot t^3 \\
|
||||
y = {\color{blue}40} \cdot 3 \cdot (1-t)^2 \cdot t {\color{blue}\ -\ 141} \cdot 3 \cdot (1-t) \cdot t^2
|
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\end{array} \right.
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-->
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Before Width: | Height: | Size: 13 KiB After Width: | Height: | Size: 14 KiB |
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t_{n+1} = t_n - \frac{f_y(t_n)}{f'_y(t_n)}
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-->
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\underset{binomial\ term}{\underbrace{\binom{n}{i}}}
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\cdot\
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\cdot\
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Before Width: | Height: | Size: 8.0 KiB |
Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user