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Pomax
2020-10-18 14:27:57 -07:00
parent 133105d44e
commit 0f6683ca6d
314 changed files with 11182 additions and 266 deletions
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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
3 2 2 3
B =a(1-t) + 3b(1-t) t + 3c(1-t)t + dt
cubic

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ d = 0
D = ┌ d d ... d ┐, where ╡ 1
└ 1 2 n ┘ │ d = d + length(p , p )
╰ i i-1 i-1 i

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
2 2
B = a (1-t) + 2 b (1-t) t + c t
quadratic
2 2 2
= a - 2at + at + 2bt - 2bt + ct

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
┌ 1 0 ... 0 0 ┐
│ n-2 n-1 │
│ 1 s s s │
│ 2 2 2 │
𝕋 = │ \vdots ... \vdots │
│ n-2 n-1 │
│ 1 s s s │
│ n-1 n-1 n-1 │
└ 1 1 ... 1 1 ┘

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
┌ 1 0 0 0 0 ┐ ┌ a ┐
│ -4 4 0 0 0 │ │ b │
B = T · M · C = ┌ 2 3 4 ┐ · │ 6 -12 6 0 0 │ · │ c │
quartic └ 1 t t t t ┘ │ -4 12 -12 4 0 │ │ d │
└ 1 -4 6 -4 1 ┘ └ e ┘

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
2
E(C) = (p - Bézier(s ))
i i i

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
┌ 0 1 n-2 n-1 ┐
│ s s ... s s │
│ 1 1 1 1 │
│ │
𝕋 = │ \vdots ... \vdots │
│ │
│ 0 1 n-2 n-1 │
│ s s ... s s │
└ n n n n ┘

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
┌ a 0 0 ┐ ┌ 1 0 0 ┐ ┌ a ┐
B = T · M · C = ┌ 2 ┐ · │ -2a 2b 0 │ = ┌ 2 ┐ · │ -2 2 0 │ · │ b │
quadratic └ 1 t t ┘ └ a -2b c ┘ └ 1 t t ┘ └ 1 -2 1 ┘ └ c ┘

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ s = 0
│ 1
S = ┌ s s ... s ┐, where ╡ s = d / d
└ 1 2 n ┘ │ i i n
│ s = 1
╰ n

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
2
E(C) = (P - TMC)

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
B =a
cubic
- 3at + 3bt
2 2 2
+ 3at - 6bt +3ct
3 3 3 3
- at + 3bt -3ct + dt

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
T
E(C) = (P - TMC) (P - TMC)

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
__ n 2
E(C) = ❯ (p - Bézier(s ))
‾‾ i=1 i i

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
┌ 1 0 0 0 ┐ ┌ a ┐
B = T · M · C = ┌ 2 3 ┐ · │ -3 3 0 0 │ · │ b │
cubic └ 1 t t t ┘ │ 3 -6 3 0 │ │ c │
└ -1 3 -3 1 ┘ └ d ┘

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
T
E(C) = (P - 𝕋MC) (P - 𝕋MC)

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
-1 T -1 T
C = M (𝕋 𝕋) 𝕋 P

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
B =a
quadratic
- 2at+ 2bt
2 2 2
+ at - 2bt + ct

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
┌ p ┐
│ 1 │
│ p │
P = │ 2 │
│ ... │
│ p │
└ n ┘

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
∂E T
── = 0 = -2𝕋 (P - 𝕋MC)
∂C