Direct least-squares fitting of algebraic surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Polygonization of implicit surfaces
Computer Aided Geometric Design
Analytical methods for dynamic simulation of non-penetrating rigid bodies
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
I3D '90 Proceedings of the 1990 symposium on Interactive 3D graphics
Interactive techniques for implicit modeling
I3D '90 Proceedings of the 1990 symposium on Interactive 3D graphics
Curved surfaces and coherence for non-penetrating rigid body simulation
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Volumetric shape description of range data using “Blobby Model”
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Generating textures on arbitrary surfaces using reaction-diffusion
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Generative modeling for computer graphics and CAD: symbolic shape design using interval analysis
Generative modeling for computer graphics and CAD: symbolic shape design using interval analysis
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Functional optimization for fair surface design
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Surface modeling with oriented particle systems
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Dynamic simulation of non-penetrating flexible bodies
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Through-the-lens camera control
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Physically-based methods for polygonization of implicit surfaces
Proceedings of the conference on Graphics interface '92
Higher-order interpolation and least-squares approximation using implicit algebraic surfaces
ACM Transactions on Graphics (TOG)
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
An implicit surface polygonizer
Graphics gems IV
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
A modeling system based on dynamic constraints
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Fast animation and control of nonrigid structures
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
An Evaluation of Implicit Surface Tilers
IEEE Computer Graphics and Applications
Temporal Computational Objects: A Process for Dynamic Surface Generation
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
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We present a new particle-based approach to sampling and controlling implicit surfaces. A simple constraint locks a set of particles onto a surface while the particles and the surface move. We use the constraint to make surfaces follow particles, and to make particles follow surfaces. We implement control points for direct manipulation by specifying particle motions, then solving for surface motion that maintains the constraint. For sampling and rendering, we run the constraint in the other direction, creating floater particles that roam freely over the surface. Local repulsion is used to make floaters spread evenly across the surface. By varying the radius of repulsion adaptively, and fissioning or killing particles based on the local density, we can achieve good sampling distributions very rapidly, and maintain them even in the face of rapid and extreme deformations and changes in surface topology.