mirror of
https://github.com/Pomax/BezierInfo-2.git
synced 2025-08-30 03:30:34 +02:00
no more LaTeX component.
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@@ -1,7 +1,6 @@
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var React = require("react");
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var Graphic = require("../../Graphic.jsx");
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var SectionHeader = require("../../SectionHeader.jsx");
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var LaTeX = require("../../LaTeX.jsx");
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var Control = React.createClass({
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statics: {
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@@ -211,14 +210,14 @@ var Control = React.createClass({
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point with a value that changes its strength. These values are conventionally called "Weights", and
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we can add them to our original Bézier function:</p>
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<LaTeX>\[
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<p>\[
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Bézier(n,t) = \sum_{i=0}^{n}
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\underset{binomial\ term}{\underbrace{\binom{n}{i}}}
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\cdot\
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\underset{polynomial\ term}{\underbrace{(1-t)^{n-i} \cdot t^{i}}}
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\cdot\
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\underset{weight}{\underbrace{w_i}}
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\]</LaTeX>
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\]</p>
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<p>That looks complicated, but as it so happens, the "weights" are actually just the coordinate values
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we want our curve to have: for an <i>n<sup>th</sup></i> order curve, w<sub>0</sub> is our start coordinate,
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@@ -226,11 +225,11 @@ var Control = React.createClass({
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a cubic curve that starts at (120,160), is controlled by (35,200) and (220,260) and ends at (220,40),
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we use this Bézier curve:</p>
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<LaTeX>\[
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<p>\[
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\left \{ \begin{matrix}
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x = BLUE[120] \cdot (1-t)^3 + BLUE[35] \cdot 3 \cdot (1-t)^2 \cdot t + BLUE[220] \cdot 3 \cdot (1-t) \cdot t^2 + BLUE[220] \cdot t^3 \\
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y = BLUE[160] \cdot (1-t)^3 + BLUE[200] \cdot 3 \cdot (1-t)^2 \cdot t + BLUE[260] \cdot 3 \cdot (1-t) \cdot t^2 + BLUE[40] \cdot t^3
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\end{matrix} \right. \]</LaTeX>
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\end{matrix} \right. \]</p>
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<p>Which gives us the curve we saw at the top of the article:</p>
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