## Generative Modeling: A Symbolic System for Geometric Modeling (1992)

Venue: | Computer Graphics |

Citations: | 30 - 1 self |

### BibTeX

@ARTICLE{Snyder92generativemodeling:,

author = {John M. Snyder and James T. Kajiya},

title = {Generative Modeling: A Symbolic System for Geometric Modeling},

journal = {Computer Graphics},

year = {1992},

volume = {26},

pages = {369--378}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper discusses a new, symbolic approach to geometric modeling called generative modeling. The approach allows specification, rendering, and analysis of a wide variety of shapes including 3D curves, surfaces, and solids, as well as higher-dimensional shapes such as surfaces deforming in time, and volumes with a spatially varying mass density. The system also supports powerful operations on shapes such as "reparameterize this curve by arclength", "compute the volume, center of mass, and moments of inertia of the solid bounded by these surfaces", or "solve this constraint or ODE system". The system has been used for a wide variety of applications, including creating surfaces for computer graphics animations, modeling the fur and body shape of a teddy bear, constructing 3D solid models of elastic bodies, and extracting surfaces from magnetic resonance (MR) data. Shapes in the system are specified using a language which builds multidimensional parametric functions. The language is bas...

### Citations

537 |
An Image Synthesizer
- PERLIN
- 1985
(Show Context)
Citation Context ...ring and simulation. The approach specifies sweeps procedurally, in a fashion similar to other procedural specification methods in computer graphics: shade trees [COOK84], Perlin's texturing language =-=[PERL85]-=-, and the POSTSCRIPT language [ADOB85]. A prototype system called GENMOD has been developed implementing these ideas, which includes a C interpreter, a curve editor, methods for several dozen primitiv... |

209 | Rendering Fur with ThreeDimensional Textures
- Kajiya
- 1989
(Show Context)
Citation Context ... any number of dimensions. The ability of GENMOD to represent and visualize such multidimensional shapes has been indispensable in many projects, such as the modeling of combed teddy bear fur used in =-=[KAJI89] (Figure 1-=-1), the modeling of elastic volumes using networks of masses and springs, and the modeling of time-dependent surfaces used in the 1988 SIGGRAPH Film and Video Show animation "Going Bananas" ... |

175 |
Shade Trees
- Cook
- 1984
(Show Context)
Citation Context ...vides high-level tools for their rendering and simulation. The approach specifies sweeps procedurally, in a fashion similar to other procedural specification methods in computer graphics: shade trees =-=[COOK84]-=-, Perlin's texturing language [PERL85], and the POSTSCRIPT language [ADOB85]. A prototype system called GENMOD has been developed implementing these ideas, which includes a C interpreter, a curve edit... |

174 |
Visual perception by computer
- Binford
- 1971
(Show Context)
Citation Context ...evolution, which sweep 2D curves. Sweeps whose generator can change size, orientation, or shape are called general sweeps. General sweeps that use 2D curve generators are called generalized cylinders =-=[BINF71]-=-. Several researchers have studied sweeps [GOLD83,CARL82b,WANG86, COQU87]. Barr's spherical product [BARR81], is an example of a sweep that uses a constant 2D curve generator with translation and scal... |

132 | Interval analysis for computer graphics
- Snyder
- 1992
(Show Context)
Citation Context ... One method evaluates the parametric function at a point in its parameter space. Other methods include symbolic differentiation of the parametric function and evaluation of an inclusion function (see =-=[SNYD92a]-=- for a discussion of inclusion functions). Section 3.2 discusses methods in more detail. 3 Symbolic Operators 3.1 Specific Operators In this section, we examine specific operators that form a basis fo... |

46 | Superquadrics and angle preserving transformations
- Barr
- 1981
(Show Context)
Citation Context ...eneral sweeps. General sweeps that use 2D curve generators are called generalized cylinders [BINF71]. Several researchers have studied sweeps [GOLD83,CARL82b,WANG86, COQU87]. Barr's spherical product =-=[BARR81]-=-, is an example of a sweep that uses a constant 2D curve generator with translation and scaling. Carlson [CARL82b] introduced the idea of varying the sweep generator. Wang and Wang [WANG86] explored s... |

42 |
Geometric modeling for swept volume of moving solids
- Wang, Wang
- 1986
(Show Context)
Citation Context ...al product [BARR81], is an example of a sweep that uses a constant 2D curve generator with translation and scaling. Carlson [CARL82b] introduced the idea of varying the sweep generator. Wang and Wang =-=[WANG86]-=- explored sweeps of surfaces for use in manipulating numerically controlled milling machine cutter paths. Sweeps have been used in solid modeling systems for many years (e.g., GMSolid, ROMULUS). Lossi... |

25 |
Generative Modeling for Computer Graphics and CAD: Symbolic Shape Design using Interval Analysis
- Snyder
- 1992
(Show Context)
Citation Context ...the set of operators implies that an operator not arbitrarily prohibit any "reasonable" arguments, given the nature of the operator. 3 GENMOD contains many more simple operators like these, =-=listed in [SNYD92b]. ca-=-n be formed by the integration operator applied to three parametric functions, where s(v; �� ) is the integrand, a(u;v) the upper limit of integration, and b(u) the lower limit of integration. In ... |

16 | Tracing Deformed Surfaces - Barr, Ray - 1986 |

7 |
Some Mathematical Tools for a Modeler's Workbench
- Cohen
- 1983
(Show Context)
Citation Context ...). Lossing and Eshleman [LOSS74] developed a system using sweeps of constant 2D curves. Alpha 1, a modeling system developed at the University of Utah, has a much more sophisticated sweeping facility =-=[COHE83]-=-. One of the advantages of sweeps is their naturalness, compactness, and controllability in representing a large class of man-made objects. For example, an airplane wing is naturally viewed as an airf... |

7 | Generative Modeling: An Approach to High Level Shape Design for Computer Graphics and CAD - Snyder - 1991 |

6 | Control point based sweeping technique - Coquillart |

3 |
Techniques for the Generation of Three Dimensional Data for Use in Complex Image Synthesis
- Carlson
- 1982
(Show Context)
Citation Context ...earchers have studied sweeps [GOLD83,CARL82b,WANG86, COQU87]. Barr's spherical product [BARR81], is an example of a sweep that uses a constant 2D curve generator with translation and scaling. Carlson =-=[CARL82b]-=- introduced the idea of varying the sweep generator. Wang and Wang [WANG86] explored sweeps of surfaces for use in manipulating numerically controlled milling machine cutter paths. Sweeps have been us... |

3 | Quadrics of revolution - Goldman - 1983 |

3 |
Barr,"Accurate Sampling of Deformed, Intersecting Surfaces with Quadtrees
- Herzen, Alan
- 1987
(Show Context)
Citation Context ...h faster than simple evaluation at each point in the rectilinear lattice of domain points, as discussed in the Appendix. Adaptive sampling can be used to generate approximations that satisfy criteria =-=[VONH87], where th-=-e sampling density varies over the parameter space. Robust approximation techniques that use inclusion functions are discussed in [SNYD92b]. The simple "evaluation at a specified point" meth... |

1 | Faster Calculation of Superquadrics - Franklin, Barr - 1981 |

1 |
Model Extraction using Classification," manuscript in progress
- Laidlaw, Snyder, et al.
(Show Context)
Citation Context ...ng new primitive operators, with a few attendant methods. We have added operators many times in the development of GENMOD, most recently an operator which allows bicubic interpolation through 3D data =-=[LAID92]-=- (see Figure 13). Once an operator is defined, it can be combined with any of the other operators already in the system to make new shapes, because of the closure property of the generative modeling a... |

1 |
Planning a Common Data Base for Engineering and Manufacturing
- Lossing, Eshleman
- 1974
(Show Context)
Citation Context ... of surfaces for use in manipulating numerically controlled milling machine cutter paths. Sweeps have been used in solid modeling systems for many years (e.g., GMSolid, ROMULUS). Lossing and Eshleman =-=[LOSS74]-=- developed a system using sweeps of constant 2D curves. Alpha 1, a modeling system developed at the University of Utah, has a much more sophisticated sweeping facility [COHE83]. One of the advantages ... |