Applying the distance function between two B-spline curves with respect to the L 2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the algorithm.
We propose a method for procedural modeling and animation of cartoon water effects such as water caustics,foamy wake,and longshore currents.In our method we emulate the visual abstraction of these cartoon effects by the use of Voronoi diagrams and the motion abstraction by designing relevant controlling mechanisms corresponding to each effect.Our system enables the creation of cartoon effects withminimal intervention from the animator.Through high-level initial specification,the effects are animated procedurally in the style of hand-drawn cartoons.
Jing LIAO 1,Jin-hui YU 1,Long JIA 2 (1 State Key Laboratory of CAD & CG,Zhejiang University,Hangzhou 310027,China) (2 School of Information Technology and Mathematical Sciences,University of Ballarat,Ballarat 3350,Australia)
