Chapter 1: The Bare Basics

3. The desired ratio is 1/3.

5. The barycentric coordinates of the points are as follows.

6. The triangle area is 9.

Chapter 2: Lines and Planes

2. The explicit form is given by y = ? x + 1.

4. The explicit form is given by z = x + y. Hence, the implicit form is x + y ? z = 0.

7. If there are no "?1" entries, every edge is an interior edge. Thus the corresponding mesh is closed. An example would be four triangles forming a tetrahedron.

Chapter 3: Cubic B zier Curves

1. If all B zier points are the same point, then the whole curve is confined to that point.

3. The desired sketch is Sketch 104. The point on the curve is and the derivative is .

5. The curve [ t, B ³ ₀] ^T is given by the B zier points

The curve [ t, B ³ ₁] ^T is given by the B zier points

The other two follow similarly.

Sketch 104: Solution to Exercise 3 in Section 3.8.

7. The desired B zier points are given by

Chapter 4: B zier Curves Cubic and Beyond

1. The solution is shown in Figure A.1

Figure A.1: The trajectory of the points b ¹ ₁( t) together with the points b ⁴ ₀( t)

3. The computation count depends on how the algorithm is organized.