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Pomax
2020-10-18 14:27:57 -07:00
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commit 0f6683ca6d
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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
__ n+1 n __ n+1 n
Bézier(n,t)= ❯ w (1 - t) B (t) + ❯ w t B (t)
‾‾ i=0 i i ‾‾ i=0 i i
__ n+1 k-i k __ n+1 i+1 k
= ❯ w ─── B (t) + ❯ w ─── B (t), where k = n + 1
‾‾ i=0 i k i ‾‾ i=0 i k i+1
__ n+1 k-i k __ n+1 i k
= ❯ w ─── B (t) + ❯ p ─ B (t)
‾‾ i=0 i k i ‾‾ i=0 i-1 k i
__ n+1 ╭ k-i i ╮ k
= ❯ │ w ─── + p ─ │ B (t)
‾‾ i=0 ╰ i k i-1 k ╯ i
__ n+1 k i
= ❯ (w (1-s) + p s) B (t), where s = ─
‾‾ i=0 i i-1 i k