Analytical solutions for tree‐like structure modelling using subdivision surfaces

Abstract

We present a novel approach to efficiently modelling branch structures with high-quality meshes. Our approach has the following advantages. First, the limit surface can fit the target skeleton models as tightly as possible by reversely calculating the control vertices of subdivision surfaces. Second, high performance is achieved through our proposed analytical solutions and the parallel subdivision scheme on a graphics processing unit. Third, a smooth manifold quad-only mesh is produced from the adopted Catmull-Clark scheme. A number of examples are given to demonstrate applications of our approach in various branch structures, such as tree branches, animal torsos, and vasculatures.

Extraction of the Quad Layout of a Triangle Mesh Guided by Its Curve Skeleton

“…In the Dinosaur dataset (middle of Fig. 14), although the histogram bell of [Zhu et al 2015] is slightly narrower, their mesh has a number of quite sharp angles, resulting in a higher RSD (15.83% against our 7.78%). Only in the Vessel dataset shown in the bottom part of Fig. 14, the method of [Zhu et al 2015] achieves a slightly better distribution of angles, but our layout contains about half a number of domains and they appear to be much better distributed on the surface of the object.…”

“…Fertility [Bommes et al 2009] 89.86 9.29 % [Tarini et al 2011] 89.92 12.21 % 89.91 18.22 % 89.98 19.22 % [Huang et al 2014] 89.95 10.91 % Ours 89.97 6.96 % Rocker arm [Bommes et al 2009] 89.95 8.79 % [Tarini et al 2011] 89.97 7.50 % 89.92 18.57 % [Ebke et al 2013] 89.74 9.21 % 89.98 16.24 % [Huang et al 2014] 89.96 10.82 % Ours 89.96 8.45 % Fig. 14. Visual and numerical comparisons with and [Zhu et al 2015]. Images on the right side are mirrored to better show correspondences.…”