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- The Bézier curve bi(t) for four noncollinear points bo, b₁, b, b, in R³ is defined by the following algorithm (going from the left column to the right): b(t) = (1-t)b²(t) + tb²(t) b(t)=(1-t)bo b}(t)=(1-t)b, + tb, + tb₂ b(t) = (1-t)b₂ + tb3 b(t)=(1-t)b (t) + tb}(t) bi(t)=(1-t)b (t) + tb (t)

- The Bézier curve bi(t) for four noncollinear points bo, b₁, b, b, in R³ is defined by the following algorithm (going from the left column to the right): b(t) = (1-t)b²(t) + tb²(t) b(t)=(1-t)bo b}(t)=(1-t)b, + tb, + tb₂ b(t) = (1-t)b₂ + tb3 b(t)=(1-t)b (t) + tb}(t) bi(t)=(1-t)b (t) + tb (t)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 29E
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段階的に解決し、 人工知能を使用せず、 優れた仕事を行います ご支援ありがとうございました SOLVE STEP BY STEP IN DIGITAL FORMAT DONT USE CHATGPT 14. The Bézier curve bi(t) for four noncollinear points bo, b₁, b, b, in R3 is defined by the following algorithm (going from the left column to the right): b(t) = (1-t)b (t) + tb²(t) b(t)=(1-t)bo + tb, b (t)=(1-t)b, + tb₂ b(t)=(1-t)b₂ + tb3 b(t)= (1-t)b (t) + tb (t) bi(t)=(1-t)b (t) + tb (t) (a) Show that b(t) = (1-t)³b, +3t(1-t)²b, +3t²(1-t)b₂ +t³b3. (b) Write the explicit formula (as in Example 1.40) for the Bézier curve for the points bo = (0,0,0), b₁ = (0, 1, 1), b₂ = (2,3,0), b3 = (4,5,2).
Transcribed Image Text:段階的に解決し、 人工知能を使用せず、 優れた仕事を行います ご支援ありがとうございました SOLVE STEP BY STEP IN DIGITAL FORMAT DONT USE CHATGPT 14. The Bézier curve bi(t) for four noncollinear points bo, b₁, b, b, in R3 is defined by the following algorithm (going from the left column to the right): b(t) = (1-t)b (t) + tb²(t) b(t)=(1-t)bo + tb, b (t)=(1-t)b, + tb₂ b(t)=(1-t)b₂ + tb3 b(t)= (1-t)b (t) + tb (t) bi(t)=(1-t)b (t) + tb (t) (a) Show that b(t) = (1-t)³b, +3t(1-t)²b, +3t²(1-t)b₂ +t³b3. (b) Write the explicit formula (as in Example 1.40) for the Bézier curve for the points bo = (0,0,0), b₁ = (0, 1, 1), b₂ = (2,3,0), b3 = (4,5,2).
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