Mar 21, 2007 - animation, we introduce a new evaluation technique, called Ringing. ..... equations using a matrix whose rows contain shifts of the limit mask ... For example, a single anticipation Jr step, with r = -33/26, followed by a series of ...
Tech Report GIT-GVU-07-06
3/21/07
March 21, 2007
Ringing Js refinements Jarek Rossignac School of Interactive Computing, College of Computing, GVU Center Georgia Institute of Technology, Atlanta, GA http://www.gvu.gatech.edu/~jarek
Scott Schaefer Department of Computer Science, 3112 Texas A&M University, College Station, TX 77843-3112 http://faculty.cs.tamu.edu/schaefer Abstract Both the four-point and the uniform cubic B-spline refinement (i.e. subdivision) schemes double the number of vertices of a closed-loop polygonal curve jP and respectively produce sequences of vertices fk and bk. The Js refinement proposed here produces vertices vk =(1–s)fk+sbk. Iterative applications of Js yield a family of curves parameterized by s. It includes the four-point curve (J0), the uniform cubic B-spline (J8/8), and the quintic B-spline (J12/8). Iterating Js converges to a C2 curve for 0
