Second Bezier curve segment: Practical Assignment 3 Generate a Matlab program to blend two Bezier curves of given degrees with both C0 and C1 continuities at the blend point. n4{2}{2}[2}P5={{5}5}r6={{12}{1} Verify your program for the sample data given below. Solution: C0 continuity: Let us keep the Bezier curve segment -1 unchanged and modify the Bezier curve segment- 2 to achieve C0 continuity. The P4 must coincide with P3 to achieve C0 continuity at blend point. For this purpose, we translate the entire control polygon (that means all control points) of segement- 2 . Translation vector d=P3P4=xdi+ydj+zdk [P4]=[T]Trr[P4] where the [T]Tr is the required translational transformation matrix given by: [T]Tr=100001000010xdydzd1 The transformation vector must be used to translate the other control points of segment-2: [P5]=[T]Tr[P5] [P6]=[T]Tr[P6] C1 continuity: For C1 continuity at the blend point, the tangent vectors of the two curve segments must be collinear. To simplify, we impose equality of tangent vectors. [P(u=1)]segment-1 and [P(u=0)]seguent2 must be equal. That means, 3[P3P2] and 2[P5P4] must be equal. After C0 imposition, P4 has already become same as P3. Hence we can modify either P2 or P5 to achieve the above equality. Let us say, we cannot modify the segment-1 from application point of view. Then we can move P5* to, say, P5 to achieve the equality of tangent vector. Use the above equation to solve for P58. 3[P3P2] and 2[P58P3] P5=(3/2)[P3P2]+P3 Use the P0, P1, P2, P3, and P3, P5**, P6* to plot the two segments in Matlab and test with the sample data given. First Bezier curve segment