## COS 526 - Advanced Computer Graphics |
## Fall 2003 |

Course home | Outline and lecture notes | Assignments |

- B-Splines and continuity:
- Why do computer graphics applications use piecewise polynomial curves of degree 3 rather than single curves of higher order?
- What is C
^{2}continuity? How does it differ from C^{1}? - What is the degree of continuity at an interior point of a B-spline patch? What is the degree of continuity at a point on the boundary between two B-spline patches?

- As we saw, a single cubic Bézier curve can be defined as
Q(t) = b

where the P_{0}(t) P_{0}+ b_{1}(t) P_{1}+ b_{2}(t) P_{2}+ b_{3}(t) P_{3}_{i}are the control points and the b_{i}(t) are the Bernstein polynomials.- Extend this definition to a bicubic Bézier patch. That is, write
down the equation for Q(s,t) in terms of the Bernstein polynomials and the
sixteen control points P
_{ij}, i=0..3, j=0..3. - How would you go about computing the surface normal at an arbitrary point on a Bézier patch? That is, given some s and t, find the surface normal at Q(s,t). (Explain how you would derive the answer - it is not necessary to write out the full expression explicitly.)

- Extend this definition to a bicubic Bézier patch. That is, write
down the equation for Q(s,t) in terms of the Bernstein polynomials and the
sixteen control points P
- The basic operation in hierarchical frustum culling is testing whether some primitive shape lies completely inside, lies completely outside, or crosses the view frustum. Describe how to perform this test for a sphere and an AABB (axis-aligned bounding box). Assume the equations for the planes that make up the view frustum are given.

Please submit the answers to these questions in writing, or in an email to
`smr@cs.princeton.edu`, with "CS526" in the subject line.
Plain text email is preferred.

Please see the general notes on submitting your assignments, as well as the late policy and the collaboration policy.

Last update 29-Dec-2010 12:02:55 smr@cs.princeton.edu