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Surface Modeling with Oriented Particle Systems
 COMPUTER GRAPHICS
, 1991
"... Splines and deformable surface models are widely used in computer graphics to describe freeform surfaces. These methods require manual preprocessing to discretize the surface into patches and to specify their connectivity. We present a new model of elastic surfaces based on interacting particle sys ..."
Abstract

Cited by 214 (6 self)
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Splines and deformable surface models are widely used in computer graphics to describe freeform surfaces. These methods require manual preprocessing to discretize the surface into patches and to specify their connectivity. We present a new model of elastic surfaces based on interacting particle systems, which, unlike previous techniques, can be used to split, join, or extend surfaces without the need for manual intervention. The particles we use have longrange attraction forces and shortrange repulsion forces and follow Newtonian dynamics, much like recent computational models of fluids and solids. To enable our particles to model surface elements instead of point masses or volume elements, we add an orientation to each particle's state. We devise new interaction potentials for our oriented particles which favor locally planar or spherical arrangements. We also develop techniques for adding new particles automatically, which enables our surfaces to stretch and grow. We demonstrate t...
Curvature and Continuity Control in ParticleBased Surface Models
 In SPIE Geometric Methods in Computer Vision II
, 1993
"... This paper develops techniques to locally control curvature and continuity in particlebased surface models. Such models are a generalization of traditional spline surfaces built out of triangular patches. Traditional splines require the topology of the triangular mesh to be specified ahead of time. ..."
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Cited by 11 (4 self)
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This paper develops techniques to locally control curvature and continuity in particlebased surface models. Such models are a generalization of traditional spline surfaces built out of triangular patches. Traditional splines require the topology of the triangular mesh to be specified ahead of time. In contrast, particlebased surface models compute the topology dynamically as a function of the relative node positions, and can add or delete nodes as required. Such models are particularly important in computer vision and other inverse problems, where the topology of the surface being reconstructed is usually not known a priori. We develop techniques for both locally controlling the curvature of the surface (through additional state at each node), and for adapting the triangulation to surface curvature (by concentrating more particles in areas of high curvature). We show how the same ideas can also be applied to 3D curves, which results in a flexible version of traditional dynamic contours (snakes). 1.
SUMMARY
"... We present a modification of the springembedder model of Eades [Congressus Numerantiurn, 42, 149160, (1984)) for drawing undirected graphs with straight edges. Our heuristic strives for uniform edge lengths, and we develop it in analogy to forces in natural systems, for a simple, elegant, conceptu ..."
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We present a modification of the springembedder model of Eades [Congressus Numerantiurn, 42, 149160, (1984)) for drawing undirected graphs with straight edges. Our heuristic strives for uniform edge lengths, and we develop it in analogy to forces in natural systems, for a simple, elegant, conceptuallyintuitive, and efficient algorithm. KEY WORDS Graph drawing Forcedirected placement Multilevel techniques Simulated annealing THE GRAPHDRAWING PROBLEM A graph G = ( V, E) is a set V of vertices and a set E of edges, in which an edge joins a pair of vertices. ’ Normally, graphs are depicted with their vertices as points in a plane and their edges as line or curve segments connecting those points. There are different styles of representation, suited to different types of graphs or different purposes of presentation. We concentrate on the most general class of graphs: undirected graphs, drawn with straight edges. In this paper, we introduce an algorithm that attempts to produce aestheticallypleasing, twodimensional pictures of graphs by doing simplified simulations of physical systems. We are concerned with drawing undirected graphs according to some generally