Midterm Study Topics

Math 155B - Spring 2001

This is an outline of possible topics for the midterm exam.  The midterm may cover any topic covered in lecture up through the Monday, May 7 lecture.   I have tried to make list of topics complete, but it is possible a few topics have been omitted.   The exam will not cover any technical details about 3D Studio Max, nor will it cover the command syntax of OpenGL..

1. Basics of Splines.  B-splines.  Blending functions and their properties..  The Cox - de Boor definition. Piecewise polynomial curves.  Local control.  Continuous derivatives.  Knot vectors and non-uniformly spaced  knots.  How repeated knots affect continuity properties.   Converting between Bézier curves and B-splines.  Böhm knot insertion.   (You do not need to memorise the formula for knot insertion.)  You are also expected to know the Bézier curve material from last quarter.

2. Rational Splines & NURBS.  Equivalence with weighting.  Uses with points at infinity.  Conic sections, especially circular arcs, defined with degree 2 rational B-splines or rational Bézier curves.

3. Interpolation with splines.  Catmull-Rom interpolation.  Overhauser splines.  Interpolating many points with a B-spline curve.

4. Color.  RGB and CMY primaries.  Additive versus subtractive primaries.  The trichromatic theory of light and the opponent theory of light.  Conversion from RGB to HSL.

5. Recursive ray tracing.  Reflection,   refraction.   Angles of reflection and refraction.  Index of refraction. Local lighting model and new terms for reflection and transmission.  Shadow feelers.  Global light calculations.  What can and cannot be handled well with recursive ray tracing.

6. Distributed ray tracing. From viewpoint: antialising, depth of field, motion blur.  Soft shadows and penumbra.  Jitter.  Soft reflections.  Wavelength dependent refraction/reflection angles.

7. Backwards ray tracing.

8. Cheats to avoid raytracing.  Environment maps, accumulation buffer, mipmapping, transparencies with alpha value, shadows via perspective transformations.

Midterm date: Friday, May 11, in class.  No notes or textbook permitted.   Calculators are permitted but not particularly required.

Review session, Wednesday evening, 7:00pm, APM 7421.