Surface subdivision for generating superquadrics

Superquadrics have been considered as important models for part-level description in computer graphics and computer vision. The description power of these models resides in their parameterised nature, which allows the definition of a wide variety of shapes, yet maintains a compact characterisation. We present a subdivision technique for modelling and displaying superquadrics. The method defines the surface of a superquadric as a deformation of an ellipsoid. The linear arc-length parameterisation obtained provides a regular distribution of the parameters along the surface. Furthermore, the definition simplifies computations in scanning by avoiding the evaluation of rational exponents. We exploit the geometric properties of an ellipsoid during subdivision for additional simplification.

[1]  Jules Bloomenthal,et al.  Modeling the mighty maple , 1985, SIGGRAPH.

[2]  Alex Pentland,et al.  Perceptual Organization and the Representation of Natural Form , 1986, Artif. Intell..

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

[4]  Michael Shantz,et al.  Rendering cubic curves and surfaces with integer adaptive forward differencing , 1989, SIGGRAPH.

[5]  Dieter W. Fellner,et al.  Robust rendering of general ellipses and elliptical arcs , 1993, TOGS.

[6]  Barry I. Soroka,et al.  Generalized cones from serial sections , 1981 .

[7]  Barr,et al.  Faster Calculation of Superquadric Shapes , 1981, IEEE Computer Graphics and Applications.

[8]  X. Wu,et al.  Double-step generation of ellipses , 1989, IEEE Computer Graphics and Applications.

[9]  Song Han,et al.  On Recovering Hyperquadrics from Range Data , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Dan Field.  Algorithms for drawing anti-aliased circles and ellipses , 1986, Comput. Vis. Graph. Image Process..

[11]  Andrew J. Hanson,et al.  Hyperquadrics: Smoothly deformable shapes with convex polyhedral bounds , 1988, Comput. Vis. Graph. Image Process..

[12]  David Marr,et al.  Visual information processing: artificial intelligence and the sensorium of sight , 1987 .

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

[14]  Sudhir P. Mudur,et al.  Computational techniques for processing parametric surfaces , 1984, Comput. Vis. Graph. Image Process..

[15]  Vaughan R. Pratt,et al.  Adaptive forward differencing for rendering curves and surfaces , 1987, SIGGRAPH.

[16]  Franc Solina.  Volumetric models in computer vision—an overview , 1994 .

[17]  Alan Watt,et al.  Fundamentals of three-dimensional computer graphics , 1989 .

[18]  Mark Novak,et al.  Curve-drawing algorithms for Raster displays , 1985, TOGS.

[19]  Ruzena Bajcsy,et al.  Recovery of Parametric Models from Range Images: The Case for Superquadrics with Global Deformations , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  Sudhanshu Kumar Semwal,et al.  Biomechanical modeling: Implementing line-of-action algorithm for human muscles and bones using generalized cylinders , 1994, Comput. Graph..

[21]  Alyn P. Rockwood,et al.  A Generalized Scanning Technique for Display of Parametrically Defined Surfaces , 1987, IEEE Computer Graphics and Applications.

[22]  M. Douglas McIlroy,et al.  Getting raster ellipses right , 1992, TOGS.

[23]  V. Leitáo,et al.  Computer Graphics: Principles and Practice , 1995 .

[24]  Tom Lyche,et al.  Discrete B-splines and subdivision techniques in computer-aided geometric design and computer graphics , 1980 .

[25]  Richard F. Riesenfeld,et al.  A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[26]  Richard E. Parent,et al.  Layered construction for deformable animated characters , 1989, SIGGRAPH.