Controllable blending of line and polygon skeleton-based convolution surfaces with finite support kernels

Abstract

We present a novel approach to control the blending of line and polygon skeleton-based convolution surfaces using locally varying Ratio of Support radius and Thickness (RST). With our method, solutions for local convolution surface approximation with prescribed surface thickness and support radii can be derived analytically. In addition, iso-surface shrinkage can be avoided by offsetting the endpoints of line skeletons and the edges of polygon skeletons. Our RST-based blending for convolution surfaces is local and can generate desired blending effects while approximating shapes with a specified thickness. Moreover, our method is intuitive and users can control the blending by adjusting the skeletal radius or the support radius of the finite support kernel independently. As our blending utilizes convolution integration only without requiring any extra composition operators, it allows for successive convolution blending operations to create complex shapes.