Geometric Algorithms

Flow complex based shape reconstruction from 3D curves

Bardia Sadri and Karan Singh

We address the problem of shape reconstruction from a sparse unorganized collection of 3D curves, typically generated by increasingly popular 3D curve sketching applications. Experimentally, we observe that human understanding of shape from connected 3D curves is largely consistent, and informed by both topological connectivity and geometry of the curves. We thus employ the flow complex, a structure that captures aspects of input topology and geometry, in a novel algorithm to produce an intersection-free 3D triangulated shape that interpolates the input 3D curves. Our approach is able to triangulate highly non-planar and concave curve cycles, providing a robust 3D mesh and parametric embedding for challenging 3D curve input. Our evaluation is four-fold: we show our algorithm to match designer selected curve cycles for surfacing; we produce user acceptable shapes for a wide range of curve inputs; we show our approach to be predictable and robust to curve addition and deletion; we compare our results to prior art.

ACM Transactions on Graphics (TOG), to appear [

Untangling Triangulations Through Local Explorations

Pankaj K. Agarwal, Bardia Sadri, and Hai Yu
Symposium on Computational Geometry (SoCG), 2008 [PDF]