Ex. 6.2 Bzier patch evaluation A bi-cubic Bzier patch is defined by the following control points....

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Ex. 6.2 Bzier patch evaluation A bi-cubic Bzier patch is defined by the following control points. tp_patch1 [ = 1.5000 0 2.4000 1.7500 1.8750 2.0000 0 1.3500 2.0000 0 0.9000 1.5000 -0.8400 2.4000 1.7500 -0.9800 1.8750 2.0000 -1.1200 1.3500 2.0000 -1.1200 0.9000 0.8400 -1.5000 2.4000 0.9800 -1.7500 1.8750 1.1200 -2.0000 1.3500 1.1200 -2.0000 0.9000 0 -1.5000 2.4000 0 -1.7500 1.8750 0 -2.0000 1.3500 0 -2.0000 0.900 ] ; It follows the v-first convention. a. What are the polynomial form of blending functions for control points po,3, P1,3, P2,3 and P3,3? What are their values at (, )? b. Compute the surface point s(, 1) Os 1 1 c. Compute the partial derivatives 22 as 1 1 d. Compute the twist vector and Os 1 1 Judy 2' 2 e. Identify the tangent plan and the surface normal at the point s(, ) f. Render this patch and its control net. Ex. 6.2 Bzier patch evaluation A bi-cubic Bzier patch is defined by the following control points. tp_patch1 [ = 1.5000 0 2.4000 1.7500 1.8750 2.0000 0 1.3500 2.0000 0 0.9000 1.5000 -0.8400 2.4000 1.7500 -0.9800 1.8750 2.0000 -1.1200 1.3500 2.0000 -1.1200 0.9000 0.8400 -1.5000 2.4000 0.9800 -1.7500 1.8750 1.1200 -2.0000 1.3500 1.1200 -2.0000 0.9000 0 -1.5000 2.4000 0 -1.7500 1.8750 0 -2.0000 1.3500 0 -2.0000 0.900 ] ; It follows the v-first convention. a. What are the polynomial form of blending functions for control points po,3, P1,3, P2,3 and P3,3? What are their values at (, )? b. Compute the surface point s(, 1) Os 1 1 c. Compute the partial derivatives 22 as 1 1 d. Compute the twist vector and Os 1 1 Judy 2' 2 e. Identify the tangent plan and the surface normal at the point s(, ) f. Render this patch and its control net.