Calculation and visualisation of the thickness of 3D CAD models

We present an algorithm for computing the thickness of a trimmed non-uniform rational B-Spline (NURBS) model, by finding the radius of maximal spheres contained within the modelled object. This information can then be visualised as a colour coded thickness map on the object's surface, allowing intuitive interpretation by designers and engineers. By making use of surface normal information the task of finding maximal spheres can be reduced to a simple minimisation problem, avoiding the calculation of Delaunay tetrahedra or Voronoi diagrams. Also our method allows the thickness to be evaluated one point at a time, so computation can be focused on a localised region of the model. The simplicity of this method makes implementation straightforward allowing it to be rapidly integrated into existing CAD/CAM packages.

[1]  Paul A. Yushkevich,et al.  Continuous medial representations for geometric object modeling in 2D and 3D , 2003, Image Vis. Comput..

[2]  Nicholas M. Patrikalakis,et al.  Computation of the Medial Axis Transform of 3-D polyhedra , 1995, Symposium on Solid Modeling and Applications.

[3]  Cecil G. Armstrong,et al.  Adaptive Shape-Sensitive Meshing of the Medial Axis , 2002, Engineering with Computers.

[4]  H. Blum.  Biological shape and visual science (part I) , 1973 .

[5]  Grégoire Malandain,et al.  Euclidean skeletons , 1998, Image Vis. Comput..

[6]  L. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communications.

[7]  Cecil Armstrong,et al.  MEDIALS FOR MESHING AND MORE , 2006 .

[8]  William L. Luken,et al.  Tessellation of trimmed NURB surfaces , 1996, Comput. Aided Geom. Des..

[9]  V. Ralph Algazi,et al.  Continuous skeleton computation by Voronoi diagram , 1991, CVGIP Image Underst..

[10]  Donald V. Rosato,et al.  Injection Molding Handbook , 1985 .

[11]  Damian J. Sheehy,et al.  Computing the medial surface of a solid from a domain Delaunay triangulation , 1995, Symposium on Solid Modeling and Applications.

[12]  Sunghee Choi,et al.  The power crust, unions of balls, and the medial axis transform , 2001, Comput. Geom..

[13]  Olivier Faugeras,et al.  Reconciling Distance Functions and Level Sets , 2000, J. Vis. Commun. Image Represent..

[14]  Damian J. Sheehy,et al.  Shape Description By Medial Surface Construction , 1996, IEEE Trans. Vis. Comput. Graph..

[15]  Nicholas M. Patrikalakis,et al.  Differential and Topological Properties of Medial Axis Transforms , 1996, CVGIP Graph. Model. Image Process..

[16]  Jon Louis Bentley,et al.  An Algorithm for Finding Best Matches in Logarithmic Expected Time , 1977, TOMS.

[17]  Tosiyasu L. Kunii,et al.  A Skeleton‐based Approach for Detection of Perceptually Salient Features on Polygonal Surfaces , 2002, Comput. Graph. Forum.

[18]  Li Xu,et al.  Plastic injection molding process optimisation using software tools , 2001 .

[19]  Edmond Boyer,et al.  Regular and non-regular point sets: Properties and reconstruction , 2001, Comput. Geom..

[20]  Wayne Tiller,et al.  Geometry-based triangulation of trimmed NURBS surfaces , 1998, Comput. Aided Des..

[21]  William H. Press,et al.  Numerical recipes in C , 2002 .

[22]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[23]  Peter Sampl.  Semi-Structured Mesh Generation Based on Medial Axis , 2000, IMR.

[24]  H. Blum.  Biological shape and visual science. I. , 1973, Journal of theoretical biology.

[25]  Pierre Soille,et al.  Morphological Image Analysis , 1999 .