An algorithm with linear complexity for interactive, physically-based modeling of large proteins

Surles, Mark C.

doi:10.1145/142920.134065

Cited by 16 publications

(10 citation statements)

References 15 publications

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“…[44], but departs from our focus on dynamic simulation. In the area of simulation, [45], [46] implemented recursive algorithms with [46] able to handle closed loops, [47] used a Lagrange multiplier approach for protein modeling, [48] proposed using impulses to treat collisions while inserting springs to model contact, and [7] used a mix of impulses, temporary joint constraints, and the method of [49] to model collision, contact and friction. [50], [51] proposed an O(n) method although it required loop decomposition, dealt with only a handful of rigid bodies, and presented no clear method for handling large numbers of unpredictable contact and collision events.…”

Section: Previous Workmentioning

confidence: 99%

Dynamic simulation of articulated rigid bodies with contact and collision

Weinstein

Teran

Fedkiw

2006

IEEE Trans. Visual. Comput. Graphics

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Abstract-We propose a novel approach for dynamically simulating articulated rigid bodies undergoing frequent and unpredictable contact and collision. In order to leverage existing algorithms for nonconvex bodies, multiple collisions, large contact groups, stacking, etc., we use maximal rather than generalized coordinates and take an impulse based approach that allows us to treat articulation, contact and collision in a unified manner. Traditional constraint handling methods are subject to drift, and we propose a novel pre-stabilization method that does not require tunable potentially stiff parameters as does Baumgarte stabilization. This differs from poststabilization in that we compute allowable trajectories before moving the rigid bodies to their new positions, instead of correcting them after the fact when it can be difficult to incorporate the effects of contact and collision. A post-stabilization technique is used for momentum and angular momentum. Our approach works with any black box method for specifying valid joint constraints, and no special considerations are required for arbitrary closed loops or branching. Moreover, our implementation is linear both in the number of bodies and in the number of auxiliary contact and collision constraints, unlike many other methods that are linear in the number of bodies but not in the number of auxiliary constraints.

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Section: Previous Workmentioning

confidence: 99%

Dynamic simulation of articulated rigid bodies with contact and collision

Weinstein

Teran

Fedkiw

2006

IEEE Trans. Visual. Comput. Graphics

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“…In constraint dynamics simulation, two different methods are frequently used: the reduced coordinate method 10 and Lagrange multiplier method. 11,12 Although the reduced coordinate method can also be used, symbolic knowledge of the body-space to world-space mapping is required to parameterize the system's degree of freedom. 12 Our system is based on the Lagrange multiplier method.…”

Section: Constraint Dynamicsmentioning

confidence: 99%

“…Many numerical techniques can be used to solve the above equation. [11][12][13] Among them, Baraff's extension method 12 gives linear time solutions for usual constraint functions. However, this method requires complicated algorithms for auxiliary constraints, which can frequently occur in the case of virtual mobiles.…”

Section: Constraint Dynamicsmentioning

confidence: 99%

Reproducing works of Calder

Lee¹,

Bae²,

Kim³

et al. 2001

J. Visual. Comput. Animat.

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Many fine art pieces have been reproduced in digital form. The digital reproductions have been used to store and transmit the original work. In contrast, mobiles, or moving sculptures, such as those designed by Alexander Calder cannot be reproduced realistically by photographs and/or static images. The real characteristics of mobiles come from the motions generated by interactive external forces applied to their structures. Hence people could not fully enjoy them through static images or even static three-dimensional models. We present a virtual mobile system where users can easily control the mobile and can feel the impressions that the artist originally intended to provide. Virtual winds are generated by blowing on a microphone which then exert external forces to the mobile. This microphone interface lets users control the mobile while they are watching it through a monitor. We introduce a linear time solution for the constraint dynamics and an improved impulse dynamics to speed up the simulation. Using these techniques, we achieve a realtime simulation of the mobile on personal computers. The techniques presented can easily be extended to simulate other interactive dynamics systems.

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“…Figure 7 summarizes the steps in our iterative constrained minimization algorithm. This method is presented in Gill et al (1981, p. 227), and its relative merits are described in Surles (1992a). The multipliers and variables converge to a constrained local minimum (Hestenes, 1975).…”

Section: Unconstrained Minimizationmentioning

confidence: 99%

Sculpting proteins interactively: Continual energy minimization embedded in a graphical modeling system

Surles

Richardson

et al. 1994

Protein Science

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We describe a new paradigm for modeling proteins in interactive computer graphics systems-continual maintenance of a physically valid representation, combined with direct user control and visualization. This is achieved by a fast algorithm for energy minimization, capable of real-time performance on all atoms of a small protein, plus graphically specified user tugs. The modeling system, called Sculpt, rigidly constrains bond lengths, bond angles, and planar groups (similar to existing interactive modeling programs), while it applies elastic restraints to minimize the potential energy due to torsions, hydrogen bonds, and van der Waals and electrostatic4 interactions (similar to existing batch minimization programs), and user-specified springs. The graphical interface can show bad and/or favorable contacts, and individual energy terms can be turned on or off to determine their effects and interactions.Sculpt finds a local minimum of the total energy that satisfies all the constraints using an augmented Lagrangemultiplier method; calculation time increases only linearly with the number of atoms because the matrix of constraint gradients is sparse and banded. On a 100-MHz MIPS R4000 processor (Silicon Graphics Indigo), Sculpt achieves 11 updates per second on a 20-residue fragment and 2 updates per second on an 80-residue protein, using all atoms except non-H-bonding hydrogens, and without electrostatic interactions. Applications of Sculpt are described: to reverse the direction of bundle packing in a designed 4-helix bundle protein, to fold up a 2-stranded @-ribbon into an approximate @-barrel, and to design the sequence and conformation of a 30-residue peptide that mimics one partner of a protein subunit interaction. Computer models that are both interactive and physically realistic (within the limitations of a given force field) have 2 significant advantages: (1) they make feasible the modeling of very large changes (such as needed for de novo design), and ( 2 ) they help the user understand how different energy terms interact to stabilize a given conformation. The Sculpt paradigm combines many of the best features of interactive graphical modeling, energy minimization, and actual physical models, and we propose it as an especially productive way to use current and future increases in computer speed. Keywords: energy minimization; interactive computer graphics; molecular modeling; protein structure.We describe a new paradigm for modeling proteins in interactive computer graphics systems -continual maintenance of a physically valid representation, combined with direct user control and visualization. A modeling system, called Sculpt, maintains valid bond lengths, bond angles, and van der Waals separations in a model as a user changes its structure by interactively moving atoms, peptides, and side chains. Like a phys- ical model, Sculpt prevents certain movements due to bond rigidity, propagates changes throughout a model due to coupling in secondary structure or packing, and changes local conformation when ...

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An algorithm with linear complexity for interactive, physically-based modeling of large proteins

Cited by 16 publications

References 15 publications

Dynamic simulation of articulated rigid bodies with contact and collision

Dynamic simulation of articulated rigid bodies with contact and collision

Reproducing works of Calder

Sculpting proteins interactively: Continual energy minimization embedded in a graphical modeling system

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