Different applications of two-dimensional potential fields for volume modeling

Current methods for building models using implicit volume techniques present problems defining accurate and controllable blend shapes between implicit primitives. We present new methods to extend the freedom and controllability of implicit volume modeling. The main idea is to use a free-form curve to define the profile of the blend region between implicit primitives. The use of a free-form implicit curve, controlled point-by-point in the Euclidean user space, allows us to group boolean composition operators with sharp transitions or smooth free-form transitions in a single modeling metaphor. This idea is generalized for the creation, sculpting and manipulation of volume objects, while providing the user with simplicity, controllability and freedom in volume modeling. Bounded volume objects, known as “Soft objects” or “Metaballs”, have specific properties. We also present binary Boolean composition operators that gives more control on the form of the transition when these objects are blended. To finish, we show how our free-form implicit curves can be used to build implicit sweep objects.

[1]  Marie-Paule Cani,et al.  Practical volumetric sculpting , 2000, The Visual Computer.

[2]  Christophe Schlick,et al.  Implicit Sweep Objects , 1996, Comput. Graph. Forum.

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

[4]  Cindy Grimm.  Implicit Generalized Cylinders using Profile Curves , 2003 .

[5]  Alexander Pasko,et al.  Implicit Curved Polygons , 1996 .

[6]  Benjamin Mora,et al.  Visualization of Isosurfaces with Parametric Cubes , 2001, Comput. Graph. Forum.

[7]  Alyn P. Rockwood,et al.  The displacement method for implicit blending surfaces in solid models , 1989, TOGS.

[8]  Alexei Sourin,et al.  Function representation for sweeping by a moving solid , 1995, SMA '95.

[9]  Ronald N. Perry,et al.  Adaptively sampled distance fields: a general representation of shape for computer graphics , 2000, SIGGRAPH.

[10]  Brian Wyvill,et al.  Interactive techniques for implicit modeling , 1990, I3D '90.

[11]  Mathieu Desbrun,et al.  Animating soft substances with implicit surfaces , 1995, SIGGRAPH.

[12]  Min Chen,et al.  Constructive Volume Geometry , 2000, Comput. Graph. Forum.

[13]  Loïc Barthe,et al.  Extrusion of 1D Implicit Profiles: Theory and First Application , 2001, Int. J. Shape Model..

[14]  Alan E. Middleditch,et al.  Blend surfaces for set theoretic volume modelling systems , 1985, SIGGRAPH '85.

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

[16]  Cornelius W. A. M. van Overveld,et al.  Combining CSG modeling with soft blending using Lipschitz-based implicit surfaces , 2002, The Visual Computer.

[17]  Sabine Coquillart,et al.  A Control-Point-Based Sweeping Technique , 1987, IEEE Computer Graphics and Applications.

[18]  Arthur W. Toga,et al.  Distance field manipulation of surface models , 1992, IEEE Computer Graphics and Applications.

[19]  Brian Wyvill,et al.  CONTROLLED BLENDING OF PROCEDURAL IMPLICIT SURFACES , 1990 .

[20]  V. Savchenko,et al.  Parametric Patches and Volumes in Function Representation of Geometric Solids , 1996 .

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

[22]  Mario Botsch,et al.  Feature sensitive surface extraction from volume data , 2001, SIGGRAPH.

[23]  Neil A. Dodgson,et al.  Triquadratic reconstruction for interactive modelling of potential fields , 2002, Proceedings SMI. Shape Modeling International 2002.

[24]  Christoph M. Hoffmann,et al.  Implicit curves and surfaces in CAGD , 1993, IEEE Computer Graphics and Applications.

[25]  Richard K. Beatson,et al.  Reconstruction and representation of 3D objects with radial basis functions , 2001, SIGGRAPH.

[26]  Brian Wyvill,et al.  Controlled Blending for Implicit Surfaces using a Graph , 1999 .

[27]  Ron Goldman,et al.  Vector elimination: A technique for the implicitization, inversion, and intersection of planar parametric rational polynomial curves , 1984, Comput. Aided Geom. Des..

[28]  Daniel Cohen-Or,et al.  Volume graphics , 1993, Computer.

[29]  Samir Akkouche,et al.  Incremental Polygonization of Implicit Surfaces , 2000, Graph. Model..

[30]  I. Faux,et al.  Computational Geometry for Design and Manufacture , 1979 .

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