Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
ACM Transactions on Graphics (TOG)
Polygonization of implicit surfaces
Computer Aided Geometric Design
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Constructive non-regularized geometry
Computer-Aided Design - Beyond solid modelling
The NURBS book
Interactive Boolean operations for conceptual design of 3-D solids
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Computational geometry in C (2nd ed.)
Computational geometry in C (2nd ed.)
Shape Evolution With Structural and Topological Changes Using Blending
IEEE Transactions on Pattern Analysis and Machine Intelligence
Implicit functions with guaranteed differential properties
Proceedings of the fifth ACM symposium on Solid modeling and applications
Constraints in constructive solid geometry
I3D '86 Proceedings of the 1986 workshop on Interactive 3D graphics
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Segmentation and recovery of superquadrics: computational imaging and vision
Segmentation and recovery of superquadrics: computational imaging and vision
Approximate Boolean operations on free-form solids
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Superquadrics and Free-Form Deformations: A Global Model to Fit and Track 3D Medical Data
CVRMed '95 Proceedings of the First International Conference on Computer Vision, Virtual Reality and Robotics in Medicine
Superquadrics with rational and irrational symmetry
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Global and local deformations of solid primitives
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
A Hybrid Shape Representation for Free-Form Modelling
SMI '04 Proceedings of the Shape Modeling International 2004
Moments of superellipsoids and their application to range image registration
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
An implicit complexes framework for heterogeneous objects modelling
Heterogeneous objects modelling and applications
Solid modelling based on sixth order partial differential equations
Computer-Aided Design
A robust evolutionary algorithm for the recovery of rational Gielis curves
Pattern Recognition
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We present a new and efficient algorithm to accurately polygonize an implicit surface generated by multiple Boolean operations with globally deformed primitives. Our algorithm is special in the sense that it can be applied to objects with both an implicit and a parametric representation, such as superquadrics, supershapes, and Dupin cyclides. The input is a Constructive Solid Geometry tree (CSG tree) that contains the Boolean operations, the parameters of the primitives, and the global deformations. At each node of the CSG tree, the implicit formulations of the subtrees are used to quickly determine the parts to be transmitted to the parent node, while the primitives' parametric definition are used to refine an intermediary mesh around the intersection curves. The output is both an implicit equation and a mesh representing its solution. For the resulting object, an implicit equation with guaranteed differential properties is obtained by simple combinations of the primitives' implicit equations using R-functions. Depending on the chosen R--function, this equation is continuous and can be differentiable everywhere. The primitives' parametric representations are used to directly polygonize the resulting surface by generating vertices that belong exactly to the zero-set of the resulting implicit equation. The proposed approach has many potential applications, ranging from mechanical engineering to shape recognition and data compression. Examples of complex objects are presented and commented on to show the potential of our approach for shape modeling.