Fast Swept Volume Approximation of Complex Polyhedral Models
Young J. Kim youngkim [at] cs [dot] unc [dot] edu
Gokul Varadhan varadhan [at] cs [dot] unc [dot] edu
Ming C. Lin lin [at] cs [dot] unc [dot] edu
Dinesh Manocha dm [at] cs [dot] unc [dot] edu

Abstract:  We present an efficient algorithm to approximate the swept volume (SV) of a complex polyhedron along a given trajectory. Given the boundary description of the polyhedron and a path specified as a parametric curve, our algorithm enumerates a superset of the boundary surfaces of SV. It consists of ruled and developable surface primitives, and the SV corresponds to the outer boundary of their arrangement. We approximate this boundary by using a five-stage pipeline. This includes computing a bounded-error approximation of each surface primitive, computing unsigned distance fields on a uniform grid, classifying all grid points using fast marching front propagation, iso-surface reconstruction, and topological refinement. We also present a novel and fast algorithm for computing the signed distance of surface primitives as well as a number of techniques based on surface culling, fast marching level-set methods and rasterization hardware to improve the performance of the overall algorithm. We analyze different sources of error in our approximation algorithm and highlight its performance on complex models composed of thousands of polygons. In practice, it is able to compute a bounded-error approximation in tens of seconds for models composed of thousands of polygons sweeping along a complex trajectory.
Fast Swept Volume Approximation of Complex Polyhedral Models

Young J. Kim, Gokul Varadhan, Ming C. Lin, and Dinesh Manocha, ACM Symposium on Solid Modeling and Applications, June 16-20, 2003.

(Awarded the best paper at the ACM Symposium on Solid Modeling and Applications 2003)  

Acrobat (3.45 Mb)


In each column, from left to right, each figure shows a generator model, sweeping trajectory, and two views of the resulting SV approximation reconstructed by our SV algorithm, respectively. In each row, each figure shows different benchmarking model, from top to bottom, X-Wing, Air Cylinder, Swing Clamps, Hammer, Input Clutch, Pipe, and Pivoting Arms, respectively.


SV Reading List

Maintained by Young Kim

last updated: 07/19/2003