Robust generation of signed distance fields from triangle meshes

A new method for robust generation of distance fields from triangle meshes is presented. Graphics hardware is used to accelerate a technique for generating layered depth images. From multiple layered depth images, a binary volume and a point representation are extracted. The point information is then used to convert the binary volume into a distance field. The method is robust and handles holes, spurious triangles and ambiguities. Moreover, the method lends itself to Boolean operations between solids. Since a point cloud as well as a signed distance is generated, it is possible to extract an iso-surface of the distance field and fit it to the point set. Using this method, one may recover sharp edge information. Examples are given where the method for generating distance fields coupled with mesh fitting is used to perform Boolean and morphological operations on triangle meshes.

[1]  Andreas Kolb,et al.  Volumetric Model Repair for Virtual Reality Applications , 2001, Eurographics.

[2]  Daniel Cohen-Or,et al.  3D Line Voxelization and Connectivity Control , 1997, IEEE Computer Graphics and Applications.

[3]  Mark W. Jones,et al.  Shape representation using space filled sub-voxel distance fields , 2001, Proceedings International Conference on Shape Modeling and Applications.

[4]  Shiaofen Fang,et al.  Fast volumetric CSG modeling using standard graphics system , 2002, SMA '02.

[5]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods , 1999 .

[6]  Greg Turk,et al.  Simplification and Repair of Polygonal Models Using Volumetric Techniques , 2003, IEEE Trans. Vis. Comput. Graph..

[7]  Markus H. Gross,et al.  Signed distance transform using graphics hardware , 2003, IEEE Visualization, 2003. VIS 2003..

[8]  Ronald N. Perry,et al.  Efficient estimation of 3D Euclidean distance fields from 2D range images , 2002, Symposium on Volume Visualization and Graphics, 2002. Proceedings. IEEE / ACM SIGGRAPH.

[9]  Dinesh Manocha,et al.  DiFi: Fast 3D Distance Field Computation Using Graphics Hardware , 2004, Comput. Graph. Forum.

[10]  Sarah F. Frisken Using Distance Maps for Accurate Surface Representation in Sampled Volumes , 1998, VVS.

[11]  Niels Jørgen Christensen,et al.  Interactive Modelling of Shapes Using the Level-Set Method , 2002, Int. J. Shape Model..

[12]  Ronald Fedkiw,et al.  Nonconvex rigid bodies with stacking , 2003, ACM Trans. Graph..

[13]  James F. O'Brien,et al.  Interpolating and approximating implicit surfaces from polygon soup , 2005, SIGGRAPH Courses.

[14]  Leif Kobbelt,et al.  A Robust Procedure to Eliminate Degenerate Faces from Triangle Meshes , 2001, VMV.

[15]  Ron Kimmel,et al.  Fast Marching Methods , 2004 .

[16]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.