Hyperquadrics: smoothly deformable shapes with convex polyhedral bounds
Computer Vision, Graphics, and Image Processing
Shape Evolution With Structural and Topological Changes Using Blending
IEEE Transactions on Pattern Analysis and Machine Intelligence
Segmentation and recovery of superquadrics: computational imaging and vision
Segmentation and recovery of superquadrics: computational imaging and vision
Global and local deformations of solid primitives
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
Boolean Operations with Implicit and Parametric Representation of Primitives Using R-Functions
IEEE Transactions on Visualization and Computer Graphics
A procedural object distribution function
ACM Transactions on Graphics (TOG)
Variational superformula curves for 2D and 3D graphic arts
SIGGRAPH '04 ACM SIGGRAPH 2004 Posters
Tile-based methods for interactive applications
ACM SIGGRAPH 2008 classes
A robust evolutionary algorithm for the recovery of rational Gielis curves
Pattern Recognition
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Superquadrics are important models for part level-description in computer graphics and computer vision. Their power resides in their compact characterization. To further extend the representational power of superquadrics several methods have been proposed for local and global deformations. This notwithstanding, it is very difficult, for example, to represent polygons or polyhedrons using classical superquadrics. In this paper we present a new approach to model natural and abstract shapes for computer graphics, using a Generalized Superellipse Equation, which solves the problem of symmetries. Our approach provides an elegant analytical way to fold or unfold the coordinate axis systems like a fan, thereby generalizing superquadrics and superellipses (and hyperspheres in general) to supershapes for any symmetry, rational or irrational. Very compact representations of various shapes with different symmetries are possible and this provides opportunities for CAD at the level of graphics kernels, CAD-users and their clients. For example, parts and assemblies can be represented in very small file sizes allowing to use the 3-D solid model throughout the design and manufacturing process. Our approach presents an elegant way to use 3-D models both for solid modeling and boundary representations, for rigid as well as soft models.