Thickening freeform surfaces for solid fabrication

Purpose – Given an intersection-free mesh surface S, the paper introduces a method to thicken S into a solid H located at one side of S. By such a surface-to-solid conversion operation, industrial users are able to fabricate a designed (or reconstructed) surface by rapid prototyping. Design/methodology/approach – The paper first investigates an implicit representation of the thickened solid H according to an extension of signed distance function. After that, a partial surface reconstruction algorithm is proposed to generate the boundary surface of H, which retains the given surface S on the resultant surface. Findings – Experimental tests show that the thickening results generated by the method give nearly uniform thickness and meanwhile do not present shape approximation error at the region of input surface S. These two good properties are important to the industrial applications of solid fabrication. Research limitations/implications – The input polygonal model is assumed to be intersection-free, where ...

[1]  Aristides A. G. Requicha,et al.  Offsetting operations in solid modelling , 1986, Comput. Aided Geom. Des..

[2]  Charlie C. L. Wang,et al.  From Designing Products to Fabricating Them from Planar Materials , 2010, IEEE Computer Graphics and Applications.

[3]  R.T. Whitaker,et al.  3D scan conversion of CSG models into distance volumes , 1998, IEEE Symposium on Volume Visualization (Cat. No.989EX300).

[4]  Dinesh Manocha,et al.  Reliable sweeps , 2009, Symposium on Solid and Physical Modeling.

[5]  Charlie C. L. Wang,et al.  Uniform offsetting of polygonal model based on Layered Depth-Normal Images , 2011, Comput. Aided Des..

[6]  Sara McMains,et al.  A GPU-based voxelization approach to 3D Minkowski sum computation , 2010, SPM '10.

[7]  Tao Ju,et al.  Dual contouring of hermite data , 2002, ACM Trans. Graph..

[8]  Rida T. Farouki,et al.  Exact offset procedures for simple solids , 1985, Comput. Aided Geom. Des..

[9]  Jyh-Ming Lien,et al.  Covering Minkowski sum boundary using points with applications , 2008, Comput. Aided Geom. Des..

[10]  Sanha Lee,et al.  Surface embedding narrow volume reconstruction from unorganized points , 2014, Comput. Vis. Image Underst..

[11]  Mark E. Forsyth,et al.  Shelling and offsetting bodies , 1995, SMA '95.

[12]  Dinesh Manocha,et al.  Accurate Minkowski sum approximation of polyhedral models , 2004, 12th Pacific Conference on Computer Graphics and Applications, 2004. PG 2004. Proceedings..

[13]  Jakob Andreas Bærentzen,et al.  Signed Distance Computation Using the Angle Weighted Pseudonormal , 2005, IEEE Trans. Vis. Comput. Graph..

[14]  Charlie C. L. Wang,et al.  Computing on rays: A parallel approach for surface mesh modeling from multi-material volumetric data , 2011, Comput. Ind..

[15]  Charlie C. L. Wang,et al.  Fast Intersection-Free Offset Surface Generation From Freeform Models With Triangular Meshes , 2011, IEEE Transactions on Automation Science and Engineering.

[16]  Dinesh Manocha,et al.  Fast distance queries with rectangular swept sphere volumes , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[17]  Gershon Elber,et al.  Self-intersection detection and elimination in freeform curves and surfaces , 2008, Comput. Aided Des..

[18]  Micha Sharir,et al.  Filling gaps in the boundary of a polyhedron , 1995, Comput. Aided Geom. Des..

[19]  Gershon Elber,et al.  Trimming local and global self-intersections in offset curves/surfaces using distance maps , 2006, Comput. Aided Des..

[20]  Bert Jüttler,et al.  Computing exact rational offsets of quadratic triangular Bézier surface patches , 2008, Comput. Aided Des..

[21]  Dinesh Manocha,et al.  Fast swept volume approximation of complex polyhedral models , 2003, SM '03.

[22]  Dinesh Manocha,et al.  Fast Proximity Queries with Swept Sphere Volumes , 1999 .

[23]  Charlie C. L. Wang Approximate Boolean Operations on Large Polyhedral Solids with Partial Mesh Reconstruction , 2011, IEEE Transactions on Visualization and Computer Graphics.

[24]  Leif Kobbelt,et al.  High‐Resolution Volumetric Computation of Offset Surfaces with Feature Preservation , 2008, Comput. Graph. Forum.

[25]  Michael E. Mortenson,et al.  Geometric Modeling , 2008, Encyclopedia of GIS.

[26]  S. T. Tan,et al.  Using dexels to make hollow models for rapid prototyping , 1998, Comput. Aided Des..

[27]  Christoph M. Hoffmann,et al.  Robustness in Geometric Computations , 2001, J. Comput. Inf. Sci. Eng..

[28]  J. Baerentzen,et al.  Signed distance computation using the angle weighted pseudonormal , 2005, IEEE Transactions on Visualization and Computer Graphics.

[29]  Tushar Udeshi,et al.  Intersection-free Contouring on An Octree Grid , 2006 .

[30]  Yong Chen Non-Uniform Offsetting and its Applications in Laser Path Planning of Sterolithography Machine , 2007 .

[31]  Marcel Campen,et al.  Polygonal Boundary Evaluation of Minkowski Sums and Swept Volumes , 2010, Comput. Graph. Forum.

[32]  Binh Pham,et al.  Offset curves and surfaces: a brief survey , 1992, Comput. Aided Des..

[33]  Takashi Maekawa,et al.  An overview of offset curves and surfaces , 1999, Comput. Aided Des..

[34]  Tao Ju,et al.  Manifold Dual Contouring , 2007, IEEE Transactions on Visualization and Computer Graphics.