Radial Supershapes for Solid Modeling

In the previous work, an efficient method has been proposed to represent solid objects as multiple combinations of globally deformed supershapes. In this paper, this framework is applied with a new supershape implicit function that is based on the notion of radial distance and results are presented on realistic models composed of hundreds of hierarchically globally deformed supershapes. An implicit equation with guaranteed differential properties is obtained by simple combinations of the primitives’ implicit representations using R-function theory. The surface corresponding to the zero-set of the implicit equation is efficiently and directly polygonized using the primitives’ parametric forms. Moreover, hierarchical global deformations are considered to increase the range of shapes that can be modeled. The potential of the approach is illustrated by representing complex models composed of several hundreds of primitives inspired from CAD models of mechanical parts.

[1]  Alexei Sourin,et al.  Function representation in geometric modeling: concepts, implementation and applications , 1995, The Visual Computer.

[2]  Jarek Rossignac,et al.  Active zones in CSG for accelerating boundary evaluation, redundancy elimination, interference detection, and shading algorithms , 1988, TOGS.

[3]  Alexander A. Pasko,et al.  Hybrid system architecture for volume modeling , 2000, Comput. Graph..

[4]  Brian Wyvill,et al.  Extending the CSG Tree. Warping, Blending and Boolean Operations in an Implicit Surface Modeling System , 1999, Comput. Graph. Forum.

[5]  Henning Biermann,et al.  Approximate Boolean operations on free-form solids , 2001, SIGGRAPH.

[6]  Dinesh Manocha,et al.  BOOLE: A Boundary Evaluation System for Boolean Combinations of Sculptured Solids , 2001, Int. J. Comput. Geom. Appl..

[7]  Frédéric Truchetet,et al.  Boolean operations with implicit and parametric representation of primitives using R-functions , 2005, IEEE Transactions on Visualization and Computer Graphics.

[8]  Samir Akkouche,et al.  A hybrid shape representation for free-form modeling , 2004, Proceedings Shape Modeling Applications, 2004..

[9]  Aristides A. G. Requicha,et al.  Constructive non-regularized geometry , 1991, Comput. Aided Des..

[10]  J. Gielis.  A generic geometric transformation that unifies a wide range of natural and abstract shapes. , 2003, American journal of botany.

[11]  Franc Solina,et al.  Segmentation and Recovery of Superquadrics , 2000, Computational Imaging and Vision.

[12]  A. Ricci,et al.  A Constructive Geometry for Computer Graphics , 1973, Computer/law journal.

[13]  Franc Solina,et al.  Moments of superellipsoids and their application to range image registration , 2003, IEEE Trans. Syst. Man Cybern. Part B.

[14]  Jarek Rossignac,et al.  Constraints in constructive solid geometry , 1987, I3D '86.

[15]  James F. Blinn,et al.  A Generalization of Algebraic Surface Drawing , 1982, TOGS.

[16]  Alan H. Barr,et al.  Global and local deformations of solid primitives , 1984, SIGGRAPH.

[17]  Vadim Shapiro,et al.  Theory of R-functions and Applications: A Primer , 1991 .

[18]  Christoph M. Hoffmann,et al.  Geometric and Solid Modeling: An Introduction , 1989 .

[19]  Barr,et al.  Superquadrics and Angle-Preserving Transformations , 1981, IEEE Computer Graphics and Applications.

[20]  Y. Ohtake,et al.  Dynamic mesh optimization for polygonized implicit surfaces with sharp features , 2003, The Visual Computer.

[21]  Brian Wyvill,et al.  Polygonization of Implicit Surfaces with Constructive solid Geometry , 1996, Int. J. Shape Model..

[22]  Ed Zaluska,et al.  Surface subdivision for generating superquadrics , 1998, The Visual Computer.

[23]  Vadim Shapiro,et al.  Implicit functions with guaranteed differential properties , 1999, SMA '99.

[24]  Johan Gielis,et al.  Superquadrics with rational and irrational symmetry , 2003, SM '03.