Geometrically‐Aware Interactive Object Manipulation

This paper describes formulation and management of constraints, and a nonlinear optimization algorithm that together enable interactive geometrically aware manipulation of articulated objects. Going beyond purely kinematic or dynamic approaches, our solution method directly employs geometric constraints to ensure non‐interpenetration during object manipulation. We present the formulation of the inequality constraints used to ensure nonpenetration, describe how to manage the set of active inequality constraints as objects move, and show how these results are combined with a nonlinear optimization algorithm to achieve interactive geometrically aware object manipulation. Our optimization algorithm handles equality and inequality constraints and does not restrict object topology. It is an efficient iterative algorithm, quadratically convergent, with each iteration bounded by O(nnz(L)), where nnz(L) is the number of non‐zeros in L, a Cholesky factor of a sparse matrix.

[1]  Michael Gleicher,et al.  Interactive dynamics , 1990, I3D '90.

[2]  Yinyu Ye,et al.  On a homogeneous algorithm for the monotone complementarity problem , 1999, Math. Program..

[3]  Patrick R. Amestoy,et al.  An Approximate Minimum Degree Ordering Algorithm , 1996, SIAM J. Matrix Anal. Appl..

[4]  L. A. Bardord.  A graphical, language-based editor for generic solid models represented by constraints , 1987 .

[5]  Roger Fletcher,et al.  Practical methods of optimization; (2nd ed.) , 1987 .

[6]  Brian Mirtich,et al.  V-Clip: fast and robust polyhedral collision detection , 1998, TOGS.

[7]  David Baraff,et al.  Linear-time dynamics using Lagrange multipliers , 1996, SIGGRAPH.

[8]  John M. Snyder,et al.  An interactive tool for placing curved surfaces without interpenetration , 1995, SIGGRAPH.

[9]  Jacek Gondzio,et al.  Implementation of Interior Point Methods for Large Scale Linear Programming , 1996 .

[10]  Knud D. Andersen.  A modified Schur-complement method for handling dense columns in interior-point methods for linear programming , 1996, TOMS.

[11]  Brian Mirtich.  Rigid Body Contact: Collision Detection to Force Computation , 1998 .

[12]  Norman I. Badler,et al.  Simulating humans: computer graphics animation and control , 1993 .

[13]  Knud D. Andersen,et al.  The APOS linear programming solver: an implementation of the homogeneous algorithm , 1997 .

[14]  Min-Hyung Choi,et al.  Geometric Awareness for Interactive Object Manipulation , 1999, Graphics Interface.

[15]  Knud D. Andersen,et al.  The Mosek Interior Point Optimizer for Linear Programming: An Implementation of the Homogeneous Algorithm , 2000 .

[16]  T Talaky,et al.  Interior Point Methods of Mathematical Programming , 1997 .

[17]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[18]  Dinesh Manocha,et al.  V-COLLIDE: accelerated collision detection for VRML , 1997, VRML '97.

[19]  Dinesh Manocha,et al.  I-COLLIDE: an interactive and exact collision detection system for large-scale environments , 1995, I3D '95.