Baraff, D., "Rigid Body Simulation" in "An Introduction to Physically-Based Modeling", Course Notes 32, organizer: A. Witkin, Siggraph, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....contact forces and impulses required to guarantee that the simulated bodies never inter penetrate. These methods differ from penalty methods that introduce restoring forces, typically proportional to the amount of penetration, only after the objects have penetrated. The simulator Coriolis [1] [2] [3] developed by David Baraff constructs a system of simultaneous constraints, which is solved to find the exact contact forces and impulses required to prevent inter penetration. The simulator Impulse developed by Brian Mirtich and John Canny [8] models all inter object interaction as a series ....

D. Baraff, "Rigid Body Simulation", Lecture Notes for SIGGRAPH '92 Course, (1992).

....of a physics laboratory in which students are guided by their professor to perform simulated experiments that involve for example, kinematics and kinetic of rigid object translation and rotation, ballistic movement, friction, inertia, etc. There is relevant literature in this area. Baraff [1,2] has worked in the simulation of rigid objects. Some research has taken place in different improvements to this method [11,3,6] AERO (Animation Editor for Realistic Object Motion) is a 3D animation system based on rigid object dynamic, that allows the creation of virtual environments in which ....

....rigid object, which is equivalent to a resultant force applied to center of mass of the object [4] dt t dH ) rate of change of the angular momentum of a rigid object, which is equivalent to a resultant torque applied to the object. 4] Also: t w : omega star operator, in Baraff [2] relates dt t dR ) with ) t R , and is defined as: 0 ) 0 ) 0 ) t t t t t t t x y x z y z w w w w w w w Where: t t t z y x w w w : rigid object s angular velocity components at any time. Because ) t w r is not an object ....

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Baraff David, "Rigid Body Simulation", Robotic Insitutue, Carnegie Mellon University.

....direction of the vessel surface. Thus, when v n = x:n (where n is the normal to the contact surface pointing outwards) is negative, the mass point is advancing in the direction of the surface and collision has occured. In this case, impulse forces are calculated using the following equations [29]: F collision = Gamma(1 ) v n 1 m n: I Gamma1 : q Theta n) Theta q (6.34) where is the coefficient of restitution [0 1] which controls how elastic is the collision; q is the local position of the contact point relative to the material coordinates; I Gamma1 is the inverse ....

D. Baraff. Rigid body simulation. In SIGGRAPH'98: Course Notes, pages D1--D48, Florida, USA, July 1998. ACM.

....of detail. The collision detection algorithm uses the different levels of detail to reduce the number of components that are examined. Similarly, bounding representations approximately model an object with simple primitives such as rectangles. Efficient algorithms, such as described by Baraff [11], determine if collision has occurred between the bounding representation and only then are components of the original model examined. In this paper, we present an efficient algorithm for distance computation between non convex obstacles. The approach builds from the research on collision ....

D. Baraff, "Rigid Body Simulation," SIGGRAPH Course Notes 1992 19 (July 1992).

....y v z Gamma 2sv x 2v x v z Gamma 2sv y 2v y v z 2sv x 1 Gamma 2v x 2 Gamma 2v y 2 1 A ; where the three column vectors correspond to x body , y body , and z body , respectively. Additionally, to handle the submarine as a rigid To appear in the SIGGRAPH 97 conference proceedings object [1], we need to define its inertia tensor I body . We approximate I body with the inertia tensor of a cylinder as follows: 0 B 3r 2 h 2 12 0 0 0 3r 2 h 2 12 0 0 0 r 2 2 1 C A ; where r and h are the radius and the length of the submarine, respectively. Note that the values of r ....

D. Baraff. Rigid Body Simulation. SIGGRAPH 95 Course Note 34. ACM SIGGRAPH, August 1995.

....there is a DOF that induces no change in configuration. This is unacceptable for applications such as dynamic simulation (and some control algorithms) that invert a quantity known as the mass matrix, because the ineffectual DOF causes the mass matrix to become singular. Baraff and Witkin [1] take a different approach, discarding the quaternion parameters as the basis for differentially controlling a quaternion rotation. They reason as follows: given a current orientation represented by a quaternion q , the orientation can differentially change by acquiring an angular velocity w , ....

....the position and orientation correctly as the simulation moves forward in time, we need, in addition to the derivatives necessary for differential control, a formula for computing the time derivative of the orientation given the current orientation and the instantaneous angular velocity. Baraff [1] derives such a formula for a quaternion orientation: q q = 1 2 w o where w is the angular velocity vector w extended with a zero scalar component to make a quaternion. Since RQ does not possess an equivalent operation to quaternion multiplication, we cannot derive a similar formula for v ....

David Baraff. Rigid Body Simulation. In Andrew P. Witkin, organizer, Physically Based Modeling Course Notes (SIGGRAPH '95), pages G1-G68, July 1995.

....bypass further collision contact checking. Figure 4 shows two 6 DOF arm robots with appropriate bounding boxes around their links. A naive collision checking implementation, which checks all pairs of objects, produces O(n 2 ) performance, but a sort and sweep algorithm can solve it in O(n log n) [2]. Subsequent steps can use an insertion sort for more efficiency. Objects with overlapping bounding boxes require calculation of the minimum distance between them in order to determine inter penetrations. Orlowski [12] uses an algorithm with O(M log M ) performance where M is total number of ....

....Orlowski [12] uses an algorithm with O(M log M ) performance where M is total number of vertices in the two objects, M = M 1 M 2 . Baraff uses an algorithm which has O(M 1 M 2 ) performance initially, but uses temporal witnesses to reduce subsequent calculations to O(M ) performance [2]. We have implemented an algorithm developed by Gilbert [5] which is considered to be one of the most efficient algorithms for computing distance. Its computation times are O(M ) with a small coefficient of linear growth. 5.2 Impulse Force Resolution A collision between two objects a, and b ....

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D. Baraff, "Rigid Body Simulation", Lecture Notes for SIGGRAPH '92 Course, (1992).

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Baraff, D., "Rigid Body Simulation," An Introduction to Physically Based Modeling, SIGGRAPH '93 Course Notes, 1993.

....un produit scalaire positif avec cette facette et on propage ces informations r ecursivement (voir figure 1.12) Le temps n ecessaire pour trouver V est donc de l ordre de O(nlog 2 n) o u n est le cardinal de la famille initiale de vecteurs. 1.3. 5 Algorithme de Baraff Witkin Baraff [7, 6] a propos e un algorithme capable, en temps lin eaire, de d etecter le contact entre deux objets rigides. Nous n allons pas expliquer cet al..gorithme car il est moins efficace que les algorithmes de Gilbert (x1.3.1) ou Lin (x1.3.2) qui sont largement utilis es dans le domaine de la robotique. Pour ....

D. Baraff. Rigid body simulation. SIGGRAPH, 1992. Lecture notes.

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Baraff, D., "Rigid Body Simulation" in "An Introduction to Physically-Based Modeling", Course Notes 32, organizer: A. Witkin, Siggraph, 1994.

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D. Baraff. Rigid body simulation, SIGRPAPH '92 Course Notes), 19, 1992. 2

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Baraff, D., "Rigid Body Simulation" in "An Introduction to Physically-Based Modeling", Course Notes 32, organizer: A. Witkin, Siggraph, 1994.

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