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Interval Analysis For Computer Graphics
 Computer Graphics
, 1992
"... This paper discusses how interval analysis can be used to solve a wide variety of problems in computer graphics. These problems include ray tracing, interference detection, polygonal decomposition of parametric surfaces, and CSG on solids bounded by parametric surfaces. Only two basic algorithms are ..."
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Cited by 132 (2 self)
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This paper discusses how interval analysis can be used to solve a wide variety of problems in computer graphics. These problems include ray tracing, interference detection, polygonal decomposition of parametric surfaces, and CSG on solids bounded by parametric surfaces. Only two basic algorithms are required: SOLVE, which computes solutions to a system of constraints, and MINIMIZE, which computes the global minimum of a function, subject to a system of constraints. We present algorithms for SOLVE and MINIMIZE using interval analysis as the conceptual framework. Crucial to the technique is the creation of "inclusion functions" for each constraint and function to be minimized. Inclusion functions compute a bound on the range of a function, given a similar bound on its domain, allowing a branch and bound approach to constraint solution and constrained minimization. Inclusion functions also allow the MINIMIZE algorithm to compute global rather than local minima, unlike many other numerica...
A Simulation Testbed for the Study of Multicellular Development: The Multiple Mechanisms of Morphogenesis
, 1993
"... This paper presents a simulation framework and computational testbed for studying multicellular pattern formation. The approach combines several developmental mechanisms (chemical, mechanical, genetic and electrical) known to be important for biological pattern formation. The mechanisms are present ..."
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Cited by 58 (4 self)
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This paper presents a simulation framework and computational testbed for studying multicellular pattern formation. The approach combines several developmental mechanisms (chemical, mechanical, genetic and electrical) known to be important for biological pattern formation. The mechanisms are present in an environment containing discrete cells which are capable of independent movement (cell migration). Experience with the testbed indicates that the interactions between the developmental mechanisms are important in determining multicellular and developmental patterns. Each simulated cell has an artificial genome whose expression is dependent only upon its internal state and its local environment. The changes of each cell's state and of the environment are determined by piecewise continuous differential equations. The current twodimensional simulation exhibits a variety of multicellular behaviors, including cell migration, cell differentiation, gradient following, clustering, lateral inhibition, and neurite outgrowth (see color plates). We plan to perform simulated evolution on developmental models as part of a long range goal to create artificial neural networks which solve problems in perception and control [Fleischer]. The testbed is a step on the path towards this goal. 1 Introduction
Generative Modeling: A Symbolic System for Geometric Modeling
 Computer Graphics
, 1992
"... 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 higherdimensional shapes such as surfaces deforming in time, a ..."
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Cited by 29 (1 self)
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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 higherdimensional 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...
Polygonizing Implicit Surfaces With Guaranteed Topology
, 1997
"... by Barton Talbot Stander, Ph.D. Washington State University May 1997 Chair: John C. Hart An interactive modeling system for implicit surfaces is presented. The display consists of a polygonal approximation which is guaranteed to have the same topology as the implicit surface. The current work focuse ..."
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Cited by 7 (1 self)
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by Barton Talbot Stander, Ph.D. Washington State University May 1997 Chair: John C. Hart An interactive modeling system for implicit surfaces is presented. The display consists of a polygonal approximation which is guaranteed to have the same topology as the implicit surface. The current work focuses on blended ellipsoids, but could be extended to include any smooth, bounded implicit surface. A polygonization algorithm and an incremental repolygonization algorithm are provided. Treating an implicit surface as a gradient system allows theorems from Morse theory to describe implicit surface topology. An implicit surface changes topology only when a critical value of its defining function changes sign. These critical points may be found using interval analysis. Techniques for modifying the polygonization to accommodate such changes in topology are given. iv Contents 1 Introduction 1 1.1 Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Implicit Surfaces...
Material Classification of Magnetic Resonance Volume Data
 Masterâ€™s thesis, Calif. Inst. Technol
, 1992
"... A major unsolved problem in computer graphics is that of making highquality models. Traditionally, models have consisted of interactively or algorithmically described collections of graphics primitives such as polygons. The process of constructing these models is painstaking and often misses featur ..."
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Cited by 4 (4 self)
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A major unsolved problem in computer graphics is that of making highquality models. Traditionally, models have consisted of interactively or algorithmically described collections of graphics primitives such as polygons. The process of constructing these models is painstaking and often misses features and behavior that we wish to model. Models extracted from volume data collected from real, physical objects have the potential to show features and behavior that are difficult to capture using these traditional modeling methods. We use vectorvalued magnetic resonance volume data in this thesis. The process of extracting models from such data involves four main steps: collecting the sampled volume data; preprocessing it to reduce artifacts from the collection process; classifying materials within the data; and creating either a rigid geometric model that is static, or a flexible, dynamic model that can be simulated. In this thesis we focus on the the first three steps. We present guidelin...
Implicit Surfaces for Geometric Modeling and Computer Graphics Speaker Biographies
, 1996
"... Implicit Surfaces for Geometric Modeling and Computer Graphics ..."