Anisotropic convolution surfaces

Abstract

Convolution surfaces with 1D skeletons have been limited to close-to-circular normal sections. The new formalism presented here allows for ellipsoidal normal sections. Anisotropy is prescribed on G1 skeletal curves, chosen as circular splines, by a rotation angle and the three radii of an ellipsoid at each extremity. This lightweight model creates smooth shapes that previously required tweaking the skeleton or supplementing it with 2D pieces. The scale invariance of our formalism achieves excellent radii control and thus lends itself to approximate a variety of shapes. The construction of a scaffold is extended to skeletons with G1 branches. It projects onto the convolution surface as a quad mesh with skeleton bound edge-flow.