1. Assignment 1 Motion Interpolation Date: 2006/9/28 TA: 彭任右 alvin@caig.cs.nctu.edu.tw EC 229B Ext: 56676

2. Framework Load the sampled motion Read the “ offset.txt ” file Create a new motion for interpolation Copy keyframes from sampled motion to the new motion Interpolate with different schemes Writes back the interpolated motion

3. Requirements Catmull-Rom interpolation. Spherical linear interpolation. Bezier interpolation. A Report –Comparison of linear and spline interpolation –Comparison of different representation

4. Graph 1

5. Graph 2

6. Graph 3

7. Crucial Techniques Catmull-rom Interpolation –q(t) = 0.5 *[ t^3 t^2 t 1 ] * [ -1 3 -3 1] *[ p1 ] [ 2 -5 4 -1] [ p2 ] [ -1 0 1 0] [ p3 ] [ 0 2 0 0] [ p4 ] –For the segment between the first and second keyframe, we let the p0 = p1 = the first keyframe.

8. Crucial Techniques Degree to Radius Transformation –Be careful when transforming between representation. Vector & Quaternion Normalization Handle for Root Translation De Casteljau Construction for Bezier Curves

9. Crucial Techniques Shorter Path Check –If q1q2 > 0, the path from q1 to q2 is shorter. –If q1q2 < 0, the path from q1 to –q2 is shorter. Speed Control for Bezier Interpolation –Truncating the end segments to one third their original length A n = Slerp(q n, a n, 1/3); B n+1 = Slerp(q n+1, b n+1, 1/3); –a n will closer to q n and b n+1 closer to q n+l

10. Grading Catmull-Rom interpolation –20% Spherical linear interpolation –20% Bezier interpolation –30% Report –30% Bonus –Speed Control(Section 3.2.2) : Ease-in, Ease-out 10% –Embed your code in Amc viewer 5%