## Position-Based Physics: Simulating the Motion of Many Highly Interacting Spheres and Polyhedra (1996)

Venue: | In Computer Graphics |

Citations: | 16 - 4 self |

### BibTeX

@INPROCEEDINGS{Milenkovic96position-basedphysics:,

author = {Victor J. Milenkovic},

title = {Position-Based Physics: Simulating the Motion of Many Highly Interacting Spheres and Polyhedra},

booktitle = {In Computer Graphics},

year = {1996},

pages = {129--136},

publisher = {ACM Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper proposes a simplified position-based physics that allows us to rapidly generate "piles" or "clumps" of many objects: local energy minima under a variety of potential energy functions. We can also generate plausible motions for many highly interacting objects from arbitrary starting positions to a local energy minimum. We present an efficient and numerically stable algorithm for carrying out position-based physics on spheres and non-rotating polyhedra through the use of linear programming. This algorithm is a generalization of an algorithm for finding tight packings of (nonrotating) polygons in two dimensions. This work introduces linear programming as a useful tool for graphics animation. As its name implies, position-based physics does not contain a notion of velocity, and thus it is not suitable for simulating the motion of free-flying, unencumbered objects. However, it generates realistic motions of "crowded" sets of objects in confined spaces, and it does so at least two...

### Citations

230 | Collision detection and response for computer animation
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Citation Context ...on. Velocity-based methods are farther divorced from "reality" but are faster. Position-based methods are the farthest from reality and the fastest. Spring model methods (also called penalty=-= methods) [25]-=- [26] are typical acceleration-based methods. They allow the objects to overlap. For each pair of overlapping objects, there is a repulsive force proportional to the amount of overlap. The resulting r... |

224 | S.: Using particles to sample and control implicit surfaces
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- 1994
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Citation Context ...]. Finally, it is important to note the difference between positionbased physics and particle-based systems. Examples of particlebased systems are too numerous to note all of them. See [32] [17] [31] =-=[33]-=- [10] [9] [21] for recent work. In general, particlebased systems model moving particles with forces between them, not rigid colliding objects. Simulating rigid objects using particles requires a very... |

213 | Fast contact force computation for nonpenetrating rigid bodies
- Baraff
- 1994
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Citation Context ...ns of spheres and polyhedra, whereas Li's algorithm is restricted to two-dimensional polygons. Interestingly enough, some recent work has moved away from the use of large complex optimization systems =-=[5]-=-. Position-based physics reduces motion planning to linear programming. Instead of dealing with implementing optimization code ourselves, we simply use a commercial linear programming library. Goldsmi... |

213 |
Image Analysis and Mathematical Morphology, volume 2 : theoretical advances
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Citation Context ...d similar to Baraff's [1], but he found this to be very expensive computationally and also numerically unstable. He formulated a position-based model and algorithm. This algorithm uses Minkowski sums =-=[27, 13]-=- and a locality heuristic to calculate a maximum convex region of the configuration space visible to the current configuration. Linear programming finds the lowest energy configuration in this region,... |

200 | D.: Surface modeling with oriented particle systems
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Citation Context ...] [15]. Finally, it is important to note the difference between positionbased physics and particle-based systems. Examples of particlebased systems are too numerous to note all of them. See [32] [17] =-=[31]-=- [33] [10] [9] [21] for recent work. In general, particlebased systems model moving particles with forces between them, not rigid colliding objects. Simulating rigid objects using particles requires a... |

182 | Analytical methods for dynamic simulation of non-penetrating rigid bodies
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Citation Context ...orrect step size. Incorrect discretization of time can cause unusual numerical results such as nonconservation of energy or momentum. Contact force model methods (also called analytical methods) [14] =-=[1]-=- [8] are examples of velocity-based methods. See [4] for a discussion of the many issues involved in contact force models. Rigid bodies are allowed to contact but not overlap. Given the current set of... |

160 |
A Modeling System Based on Dynamic Constraints," (submitted to Computer Graphics
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Citation Context ...ct step size. Incorrect discretization of time can cause unusual numerical results such as nonconservation of energy or momentum. Contact force model methods (also called analytical methods) [14] [1] =-=[8]-=- are examples of velocity-based methods. See [4] for a discussion of the many issues involved in contact force models. Rigid bodies are allowed to contact but not overlap. Given the current set of con... |

159 | Realistic Animation of Rigid Bodies
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Citation Context ...the correct step size. Incorrect discretization of time can cause unusual numerical results such as nonconservation of energy or momentum. Contact force model methods (also called analytical methods) =-=[14]-=- [1] [8] are examples of velocity-based methods. See [4] for a discussion of the many issues involved in contact force models. Rigid bodies are allowed to contact but not overlap. Given the current se... |

136 | ªCurved Surfaces and Coherence for Non-Penetrating Rigid Body Simulation,º
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Citation Context ...t needed to accurately carry out numerical integration. Even though these methods do not simulate acceleration, they can handle increasingly sophisticated types of objects and forces: curved surfaces =-=[2]-=-, friction [3], and flexible bodies [7]. Unfortunately, the velocity-based method is subject to two problems which cause small time-steps and thus high computational cost. Local rattle occurs when one... |

128 |
Constraints methods for flexible models
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Citation Context ...elocity-based methods are farther divorced from "reality" but are faster. Position-based methods are the farthest from reality and the fastest. Spring model methods (also called penalty meth=-=ods) [25] [26]-=- are typical acceleration-based methods. They allow the objects to overlap. For each pair of overlapping objects, there is a repulsive force proportional to the amount of overlap. The resulting repuls... |

122 | Dynamics simulation of non-penetrating flexible bodies
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- 1992
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Citation Context ...cal integration. Even though these methods do not simulate acceleration, they can handle increasingly sophisticated types of objects and forces: curved surfaces [2], friction [3], and flexible bodies =-=[7]-=-. Unfortunately, the velocity-based method is subject to two problems which cause small time-steps and thus high computational cost. Local rattle occurs when one object bounces between two others (suc... |

95 |
A Kinetic Framework for Computational Geometry
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Citation Context ...d similar to Baraff's [1], but he found this to be very expensive computationally and also numerically unstable. He formulated a position-based model and algorithm. This algorithm uses Minkowski sums =-=[27, 13]-=- and a locality heuristic to calculate a maximum convex region of the configuration space visible to the current configuration. Linear programming finds the lowest energy configuration in this region,... |

93 |
Issues in computing contact forces for non-penetrating rigid bodies. Algorithmica 10(2–4):292–352
- Baraff
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Citation Context ...an cause unusual numerical results such as nonconservation of energy or momentum. Contact force model methods (also called analytical methods) [14] [1] [8] are examples of velocity-based methods. See =-=[4]-=- for a discussion of the many issues involved in contact force models. Rigid bodies are allowed to contact but not overlap. Given the current set of contacts, the method computes a set of consistent v... |

81 | Coping with friction for non-penetrating rigid body simulation
- Baraff
- 1991
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Citation Context ...curately carry out numerical integration. Even though these methods do not simulate acceleration, they can handle increasingly sophisticated types of objects and forces: curved surfaces [2], friction =-=[3]-=-, and flexible bodies [7]. Unfortunately, the velocity-based method is subject to two problems which cause small time-steps and thus high computational cost. Local rattle occurs when one object bounce... |

77 |
K.: Heating and melting deformable models (from goop to glop
- TERZOPOULOS, PLATT, et al.
- 1989
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Citation Context ... motion [6] [15]. Finally, it is important to note the difference between positionbased physics and particle-based systems. Examples of particlebased systems are too numerous to note all of them. See =-=[32]-=- [17] [31] [33] [10] [9] [21] for recent work. In general, particlebased systems model moving particles with forces between them, not rigid colliding objects. Simulating rigid objects using particles ... |

61 |
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Citation Context ..., it is important to note the difference between positionbased physics and particle-based systems. Examples of particlebased systems are too numerous to note all of them. See [32] [17] [31] [33] [10] =-=[9]-=- [21] for recent work. In general, particlebased systems model moving particles with forces between them, not rigid colliding objects. Simulating rigid objects using particles requires a very steep re... |

54 |
stable fluid dynamics for computer graphics
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- 1990
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Citation Context ...on [6] [15]. Finally, it is important to note the difference between positionbased physics and particle-based systems. Examples of particlebased systems are too numerous to note all of them. See [32] =-=[17]-=- [31] [33] [10] [9] [21] for recent work. In general, particlebased systems model moving particles with forces between them, not rigid colliding objects. Simulating rigid objects using particles requi... |

31 |
Volumen und Oberfläche
- Minkowski
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Citation Context ... spaces. It is shown how to apply the algorithm of Section 3.2.2 to the problems of animating and generating "piles" of spheres and polyhedra under translation. 3.3.1 Minkowski Sum. The Mink=-=owski sum [24, 13, 27, 28]-=- of two point-sets (of R 3 in the case of this paper) is defined A \Phi B = fa + b j a 2 A; b 2 Bg: For a point-set A, let A denote the set complement of A and define \GammaA = f\Gammaa j a 2 Ag. For ... |

27 |
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Citation Context ...nable. However, even in situations for which position-based methods give an unrealistic motion, there may be other applications. Recent work on manipulation of models makes use of non-physical motion =-=[6]-=- [15]. Finally, it is important to note the difference between positionbased physics and particle-based systems. Examples of particlebased systems are too numerous to note all of them. See [32] [17] [... |

27 | Compaction Algorithms for Non-Convex Polygons and Their Applications
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Citation Context ...ount. Even if two objects in the model require only a small motion to come into contact, this does not prevent other objects in the model from moving farther, if they are able to. In his Ph.D. thesis =-=[19]-=- and in joint work with this author [22, 23], Li introduced the concept of position-based modeling. His application is compaction: finding tight packings of polygonal objects in the plane. As he and o... |

27 |
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Citation Context ...k with this author [22, 23], Li introduced the concept of position-based modeling. His application is compaction: finding tight packings of polygonal objects in the plane. As he and others have noted =-=[29, 30]-=-, for most layout applications the motion of the objects is immaterial, and only the final configuration matters. He attempted to carry out compaction using a velocity-based method similar to Baraff's... |

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24 | Interactive physically-based manipulation of discrete/continuous models
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Citation Context ...e. However, even in situations for which position-based methods give an unrealistic motion, there may be other applications. Recent work on manipulation of models makes use of non-physical motion [6] =-=[15]-=-. Finally, it is important to note the difference between positionbased physics and particle-based systems. Examples of particlebased systems are too numerous to note all of them. See [32] [17] [31] [... |

19 | Placement and Compaction of Nonconvex Polygons for Clothing Manufacture
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- 1992
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Citation Context ...equire only a small motion to come into contact, this does not prevent other objects in the model from moving farther, if they are able to. In his Ph.D. thesis [19] and in joint work with this author =-=[22, 23]-=-, Li introduced the concept of position-based modeling. His application is compaction: finding tight packings of polygonal objects in the plane. As he and others have noted [29, 30], for most layout a... |

16 | Implicitly searching convolutions and computing depth of collision - Dobkin, Hershberger, et al. - 1990 |

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Visual Simulation of Water Currents Using a Particle-based Behavioural Model
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Citation Context ...nally, it is important to note the difference between positionbased physics and particle-based systems. Examples of particlebased systems are too numerous to note all of them. See [32] [17] [31] [33] =-=[10]-=- [9] [21] for recent work. In general, particlebased systems model moving particles with forces between them, not rigid colliding objects. Simulating rigid objects using particles requires a very stee... |

2 | Applying constrained optimization to computer graphics
- Goldsmith, Barr
- 1993
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Citation Context ...-based physics reduces motion planning to linear programming. Instead of dealing with implementing optimization code ourselves, we simply use a commercial linear programming library. Goldsmith et al. =-=[12] discuss a-=- number of ways optimization is applied in the field of graphics. Most of these involve "either starting or finishing problems. " Furthermore, most are non-linear. We believe that positionba... |

2 |
Yasmine Ghallab. Efficient collision prediction among many moving objects
- Hayward, Aubry, et al.
- 1995
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Citation Context ...when there are many interacting objects. Since there are so many, it is inevitable that some pair will make contact in a short amount of time. Even systems which can rapidly detect the next collision =-=[16]-=- cannot reduce the number of collisions. Each new contact forces us to recalculate the velocities. Just as a velocity-based method eliminates accelerations, a position-based method eliminates velociti... |

2 |
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Citation Context ...break the set of spheres into "zones" and simulate within each zone. By switching between overlapping zones, one could still generate a good animation. Multi-scale techniques might also be a=-=pplicable [20]-=-. The issue of non-convex sets of valid directions arises for sets of translating polyhedra. However, we believe that this potential difficulty will not have a practical impact. A difficult practical ... |

2 |
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Citation Context ... is important to note the difference between positionbased physics and particle-based systems. Examples of particlebased systems are too numerous to note all of them. See [32] [17] [31] [33] [10] [9] =-=[21]-=- for recent work. In general, particlebased systems model moving particles with forces between them, not rigid colliding objects. Simulating rigid objects using particles requires a very steep repulsi... |