Barycentric convolution surfaces based on general planar polygon skeletons

© 2020 Elsevier Inc. Using barycentric coordinates for thickness interpolation, we present a novel polygonal skeleton based convolution surface approximation method with varying radii. Given the prescribed radii of an arbitrary planar polygonal skeleton, we first employ a smooth interior mean value coordinate interpolation approach to calculate the thickness at each projection position in the polygonal plane. Then a local thickness approximation method based on finite-support kernels is introduced to create an implicit surface with smoothly varying thickness. In addition, a polygon offset with different distances by winding numbers is employed to create local approximation at polygon boundaries. Our experiments show that the proposed uniform smooth thickness interpolation and local convolution approximation method can not only avoid surface wrinkles but also reduce computation cost. Moreover, our approach is insensitive to exterior thickness interpolation. Therefore smooth barycentric coordinates within a polygon can all be easily integrated into our approach.