Given six control points on the xy-plane of Bezier curve (0, 2), (-2,-2), (- 2, 2), (2, 2), (2, -2) and (0, -2), find the following using computational geometry based solution. a) Compute the partition of unity at u = 0.5 b) Use de Casteljau's algorithm to find the point on the curve that corresponds to u = 0.5 in triangular form. c) List all the control points of the resulting segments after subdivide the Bezier curve at u = 0.5.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Given six control points on the xy-plane of Bezier curve (0, 2), (-2,-2), (-
2, 2), (2, 2), (2, -2) and (0, -2), find the following using computational geometry
based solution.
a) Compute the partition of unity at u = 0.5
b) Use de Casteljau's algorithm to find the point on the curve that corresponds to
u = 0.5 in triangular form.
c) List all the control points of the resulting segments after subdivide the Bezier
curve at u = 0.5.
Transcribed Image Text:Given six control points on the xy-plane of Bezier curve (0, 2), (-2,-2), (- 2, 2), (2, 2), (2, -2) and (0, -2), find the following using computational geometry based solution. a) Compute the partition of unity at u = 0.5 b) Use de Casteljau's algorithm to find the point on the curve that corresponds to u = 0.5 in triangular form. c) List all the control points of the resulting segments after subdivide the Bezier curve at u = 0.5.
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