The Coordinates of Four control points to a current WCS are given by $– P_0 = [2 \ 2 \ 0]^T , P_1 = [2 3 0]^T , P_2 = [3 3 0]^T , \ and \ P_3 = [3 2 0]^T.$ Find the equation of the resulting Bezier curve. Also find points on the curve for u = 0, ¼, ½, ¾ and 1.

Mumbai University > Mechanical Engineering > Sem 7 > CAD/CAM/CAE

Marks: 8 M

Year: Dec 2012

Number of points i.e. k=4,

Hence, we know that the degree of the Bezier curve is n= k-1= 4-1= 3.

Now, to obtain the equation of the Bezier curve in parametric format with parameter ‘u’, we know that

$P(u) = \sum_{i=0}^n P_i \ B_{i,n}(u)$

where, $n = 3$ and $P_i$ …