11th practicals, 9. 12. 2021, Rational Bezier & NURBS curves

1. Plot a rational Bezier curve (Subscript[c, 1]) with control points pts1 and some weight vector. Plot the curve in space and its projection onto plane.

pts1= {{-3,-1},{-2,-(3/2)},{-1,-(4/3)},{0,-(1/2)},{1,(1/2)},{(1/2),(7/6)},{-(1/2),2}};

2. Plot a quarter of a circle (Subscript[c, 2]) using a rational Bezier curve with control points pts2.
a) Find a reparametrization of the curve (Subscript[c, 2]) so that (Subscript[c, 2])((1/2)) ={(3/5),(4/5)}.
b) Find a reparametrization of the quarter of the circle (Subscript[c, 2]) so that the weight for the second control point is (Sqrt[2]).

pts2={{0,1}, {1,1}, {1,0}};

3. Using a NURBS curve of degree 2 inscribe a circle into equilateral triangle.

4. Interpolate the data (Subscript[P, 1]) = [0,0], (Subscript[t, 1]) = (1,2), (Subscript[P, 2]) = [1,1], (Subscript[t, 2]) = (2,-3) by biarcs.