Construct the Bezier curve with the following polygon vertices (contro | Computer Graphics 2081

Computer Graphics20815 marksNumerical: Bezier curve constructionRepresenting Curves

Construct the Bezier curve with the following polygon vertices (control points): A(1,1), B(2,3), C(4,3), and D(6,4). [5]

Control points (4 points → cubic Bezier, degree $n = 3$ ): - $P0 = A(1, 1)$ - $P1 = B(2, 3)$ - $P2 = C(4, 3)$ - $P3 = D(6, 4)$ $P(u) = \sum{k=0}^{3} Pk \, BEZ{k,3}(u), \quad 0 \le u \le 1$ $BEZ{k,3}(u) = \binom{3}{k} u^k (1-u)^{3-k}$ $k$ Blending Function ------ 0 $(1-u)^3$ 1 $3u(1-u)^2$ 2

Control points (4 points → cubic Bezier, degree $n = 3$): - $P0 = A(1, 1)$ - $P1 = B(2, 3)$ - $P2 = C(4, 3)$ - $P3 = D(6, 4)$ $$P(u) = \sum{k=0}^{3} Pk , BEZ{k,3}(u), \quad 0 \le u \le 1$$ $$BEZ{k,3}(u) = \binom{3}{k} u^k (1-u)^{3-k}$$ $k$ Blending Function ------ 0 $(1-u)^3$ 1 $3u(1-u)^2$ 2

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