Physics-Based B-spline Morphing

This paper presents a new method for automatically generating a transition between two given B-spline curves or surfaces. Rather than treating the curves or surfaces as purely geometric objects, we distribute mass, damping, elasticity onto them. For elastic objects, morphing can be formulated as a boundary-valued problem of ordinary differential equations. By using Modal Analysis, the boundary-valued problem can be solved analytically. As a result, we can create a morphing that simulates the shape transition with respect to physical properties or by appropriately choosing the physics parameter values we may create a visually pleasing morphing that has no self-intersection or unwanted wiggles. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations; I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism—Animation