Assignments for Geometric Modeling and CAD

Assignment 3
• (Roll nos. 1 to 10) Compute Rational B-spline surface for arbitrary number of control points on either parameter surface and plot the surface for any order and knot-vector type.

• (Roll nos. 11 to 20) Using Rational B-spline curve (any number of control points, order and knot-vector type) and translational sweep, plot the surface.

• (Roll nos. 21 to 30) Using Rational B-spline curve (any number of control points, order and knot-vector type) and rotation trasformtion matrix, plot the surface.

• (Roll nos. 31 to 44) Using Rational B-spline curve (any number of control points, order and knot-vector type) and homogeneous trasformtion matrix, show the scaling of the curve in h=1 plane.

• (Rest of the students) Compute Rational B-spline curve and plot the same for any number of control point, order and knot-vector type. Bring another curve and assuming C1 continuity, plot both curves.

Assignment 2
• (Roll nos. 1 to 10) Given algberaic coefficiet matrix A, find geometric coefficient matrix B and plot the surface. Do the vice versa as well. Determine B2, given B1, assuming G1 continuity. Plot both surfaces.

• (Roll nos. 11 to 20) Given sixteen points, find geometric coefficient matrix B and plot the surface. Determine B2, given B1, assuming G1 continuity. Plot both surfaces.

• (Roll nos. 21 to 30) Using Hermite curve and trasformtion matrix, plot the surface. Determine transformation matrices that satisfy G1 continuity and plot the two surface.

• (Roll nos. 31 to 44) Plot the Bezier surface using polynomial form. Determine the control polyhedron of surface 2, given the same for surface 1, assuming G1 continuity. Plot both surfaces.

• (Rest of the students) Plot the Bezier surface using deCasteljau method of the Bezier curve. Raise the degree of the surface in both directions and plot the surface.

Assignment 1

1(a) Given algberaic coefficiet matrix A, find geometric coefficient matrix B and plot the curve. Do the vice versa as well.

1(b) Using the variables K0 and K1, and a matrix B, plot the curves for different K0 and K1 values.

1(c) Assuming two parameter values u1 and u2 (u1 < u2), truncate the curve between them and do a reparameterization of [u1,u2] to [0,1] of the truncated curve. Plot the reparameterized curve.

1(d) Given two curves B1 and B3, find the geometric coefficient matrix B2 of the intermediate curve satisfying G1/C1 continuity with B1 and B3. Plot all the three curves in differet colors!

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