"Meshsweeper": dynamic point-to-polygonal mesh distance and applications

We introduce a new algorithm for computing the distance from a point to an arbitrary polygonal mesh. Our algorithm uses a multiresolution hierarchy of bounding volumes generated by geometric simplification. Our algorithm is dynamic, exploiting coherence between subsequent queries using a priority process and achieving constant time queries in some cases. It can be applied to meshes that transform rigidly or deform nonrigidly. We illustrate our algorithm with a simulation of particle dynamics and collisions with a deformable mesh, the computation of distance maps and offset surfaces, the computation of an approximation to the expensive Hausdorff distance between two shapes, and the detection of self-intersections. We also report comparison results between our algorithm and an alternative algorithm using an octree, upon which our method permits an order-of-magnitude speed-up.

[1]  Philip M. Hubbard,et al.  Interactive collision detection , 1993, Proceedings of 1993 IEEE Research Properties in Virtual Reality Symposium.

[2]  Lee Markosian,et al.  Skin: a constructive approach to modeling free-form shapes , 1999, SIGGRAPH.

[3]  André Guéziec,et al.  Locally Toleranced Surface Simplification , 1999, IEEE Trans. Vis. Comput. Graph..

[4]  Dinesh Manocha,et al.  Appearance-preserving simplification , 1998, SIGGRAPH.

[5]  P. Danielsson.  Euclidean distance mapping , 1980 .

[6]  Franz Aurenhammer,et al.  Voronoi diagrams—a survey of a fundamental geometric data structure , 1991, CSUR.

[7]  Hanan Samet,et al.  The Design and Analysis of Spatial Data Structures , 1989 .

[8]  Michael Garland,et al.  Surface simplification using quadric error metrics , 1997, SIGGRAPH.

[9]  Hugues Hoppe,et al.  View-dependent refinement of progressive meshes , 1997, SIGGRAPH.

[10]  Pat Morin,et al.  Progressive TINs: algorithms and applications , 1997, GIS '97.

[11]  Hugues Hoppe,et al.  Progressive meshes , 1996, SIGGRAPH.

[12]  Dinesh Manocha,et al.  Fast computation of generalized Voronoi diagrams using graphics hardware , 1999, SIGGRAPH.

[13]  Elaine Cohen,et al.  Bound coherence for minimum distance computations , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[14]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[15]  Chandrajit L. Bajaj,et al.  Error-bounded reduction of triangle meshes with multivariate data , 1996, Electronic Imaging.

[16]  Elaine Cohen,et al.  A framework for efficient minimum distance computations , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[17]  Hans-Peter Seidel,et al.  Multiresolution hierarchies on unstructured triangle meshes , 1999, Comput. Geom..

[18]  Gabriel Taubin,et al.  Geometry coding and VRML , 1998, Proc. IEEE.

[19]  Arie E. Kaufman,et al.  Efficient algorithms for 3D scan-conversion of parametric curves, surfaces, and volumes , 1987, SIGGRAPH.

[20]  Dinesh Manocha,et al.  I-COLLIDE: an interactive and exact collision detection system for large-scale environments , 1995, I3D '95.

[21]  Dinesh Manocha,et al.  OBBTree: a hierarchical structure for rapid interference detection , 1996, SIGGRAPH.

[22]  Tomas Möller,et al.  A fast triangle-triangle intersection test , 1997 .

[23]  Rémi Ronfard,et al.  Full‐range approximation of triangulated polyhedra. , 1996, Comput. Graph. Forum.

[24]  Enrico Puppo,et al.  Building and traversing a surface at variable resolution , 1997 .

[25]  Amitabh Varshney,et al.  Dynamic view-dependent simplification for polygonal models , 1996, Proceedings of Seventh Annual IEEE Visualization '96.

[26]  Joseph S. B. Mitchell,et al.  Efficient Collision Detection Using Bounding Volume Hierarchies of k-DOPs , 1998, IEEE Trans. Vis. Comput. Graph..

[27]  S. Sathiya Keerthi,et al.  A fast procedure for computing the distance between complex objects in three-dimensional space , 1988, IEEE J. Robotics Autom..

[28]  David H. Douglas,et al.  ALGORITHMS FOR THE REDUCTION OF THE NUMBER OF POINTS REQUIRED TO REPRESENT A DIGITIZED LINE OR ITS CARICATURE , 1973 .

[29]  Mike M. Chow.  Optimized geometry compression for real-time rendering , 1997 .

[30]  Urs Ramer,et al.  An iterative procedure for the polygonal approximation of plane curves , 1972, Comput. Graph. Image Process..

[31]  David Baraff,et al.  Curved surfaces and coherence for non-penetrating rigid body simulation , 1990, SIGGRAPH.

[32]  Gabriel Taubin,et al.  A Framework for Streaming Geometry in VRML , 1999, IEEE Computer Graphics and Applications.

[33]  Oliver Günther,et al.  Efficient Structures for Geometric Data Management , 1988, Lecture Notes in Computer Science.

[34]  Hanan Samet,et al.  Applications of spatial data structures , 1989 .

[35]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[36]  Nelson Max.  Visualizing Hilbert curves , 1998 .

[37]  Daniel Cohen-Or,et al.  Context‐based Space Filling Curves , 2000, Comput. Graph. Forum.

[38]  Sean Quinlan,et al.  Efficient distance computation between non-convex objects , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[39]  Takeo Kanade,et al.  Fast and accurate shape-based registration , 1996 .

[40]  Ming C. Lin,et al.  Efficient collision detection for animation and robotics , 1993 .

[41]  P. Volino,et al.  Efficient self‐collision detection on smoothly discretized surface animations using geometrical shape regularity , 1994 .

[42]  Hugues Hoppe,et al.  New quadric metric for simplifying meshes with appearance attributes , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).