Surfaces

- What is an implicit surface? Give a simple example.
- Which of the following are true for implicit surfaces: a) easy to draw, b) easy to test intersections, c) hard to describe complex shapes, d) local control?
- What is an parametric surface? Give a simple example.
- Which of the following are true for parametric surfaces: a) easy to draw, b) easy to test intersections, c) hard to describe complex shapes, d) local control?
- Which of the following are true for a cubic Bezier tensor product surface: a) interpolates the four corner control points, b) interpolates the centroid of the control points, c) lies within the convex hull of the control points, d) provides local control, e) has at most one point with positive curvature.
- Show that a point at parameter values (u,v) on a bicubic Bezier patch is the same as the point at parameter value u on a cubic Bezier curve defined by the four control points B1-B4 found by evaluating four Bezier curves through a group of four patch control points at parameter value v.
- What is a subdivision surface? Give a simple example.
- Which of the following are true for subdivision surfaces: a) easy to draw, b) easy to test intersections, c) hard to describe complex shapes, d) local control?
- For each of the following properties, list the surface representations (mesh, implicit, parametric, subdivision) that provide it best and worst: a) high accuracy, b) conciseness, c) local support, d) C2 continuity, e) efficient display, f) efficient intersections.