# Anupam Saxena Associate Professor Indian Institute of Technology KANPUR 208016.

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Anupam Saxena Associate Professor Indian Institute of Technology KANPUR 208016

Let each interval be subdivided as [0, 1/3, 2/3, 1] Need to find this matrix

r(0, 0) r(1/3, 0)r(2/3, 0) r(1, 0) r(0, 1/3) r(1/3, 1/3)r(2/3, 1/3) r(1, 1/3) r(0, 2/3) r(1/3, 2/3)r(2/3, 2/3) r(1, 2/3) r(0, 1) r(1/3, 1)r(2/3, 1) r(1, 1)

r ij, i = 0, …, m, j = 0, …, n are the control points Bernstein polynomials in parameters u and v In matrix form

Bézier matrix Geometric matrix

r 00 r 01 r 02 r 03 r 10 r 11 r 12 r 13 r 20 r 21 r 22 r 23 r 30 r 31 r 32 r 33 Fuse these points to get a triangular patch

control points for a Quadratic-Cubic Bézier Patch

For control points r 10 changed as (5, 2, 10)

control points for a bi-Cubic Bézier patch {2, 3, 2} {4, 7, 4}

Collapsing the data points for any boundary curve can create a triangular bi-cubic Bézier surface patch if r 00 = r 10 = r 20 = r 30 = {1, 0, 0}

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