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17 lines
999 B
Plaintext
17 lines
999 B
Plaintext
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__ n+1 n __ n+1 n
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Bézier(n,t)= ❯ w (1 - t) B (t) + ❯ w t B (t)
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‾‾ i=0 i i ‾‾ i=0 i i
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__ n+1 k-i k __ n+1 i+1 k
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= ❯ w ─── B (t) + ❯ w ─── B (t), where k = n + 1
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‾‾ i=0 i k i ‾‾ i=0 i k i+1
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__ n+1 k-i k __ n+1 i k
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= ❯ w ─── B (t) + ❯ p ─ B (t)
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‾‾ i=0 i k i ‾‾ i=0 i-1 k i
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__ n+1 ╭ k-i i ╮ k
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= ❯ │ w ─── + p ─ │ B (t)
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‾‾ i=0 ╰ i k i-1 k ╯ i
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__ n+1 k i
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= ❯ (w (1-s) + p s) B (t), where s = ─
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‾‾ i=0 i i-1 i k
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