Hierarchical spacetime control
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
ADIC: an extensible automatic differentiation tool for ANSI-C
Software—Practice & Experience
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
Interactive control for physically-based animation
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Dynamic Analysis of Robot Manipulators: A Cartesian Tensor Approach
Dynamic Analysis of Robot Manipulators: A Cartesian Tensor Approach
Adifor 2.0: Automatic Differentiation of Fortran 77 Programs
IEEE Computational Science & Engineering
Efficient synthesis of physically valid human motion
ACM SIGGRAPH 2003 Papers
Learning physics-based motion style with nonlinear inverse optimization
ACM SIGGRAPH 2005 Papers
Local, deformable precomputed radiance transfer
ACM SIGGRAPH 2005 Papers
Newton-Type Algorithms for Dynamics-Based Robot Movement Optimization
IEEE Transactions on Robotics
Optimal gait and form for animal locomotion
ACM SIGGRAPH 2009 papers
Mathematical equations as executable models of mechanical systems
Proceedings of the 1st ACM/IEEE International Conference on Cyber-Physical Systems
Linear-time dynamics for multibody systems with general joint models
Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Interactive spacetime control of deformable objects
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Hi-index | 0.00 |
Functions with densely interconnected expression graphs, which arise in computer graphics applications such as dynamics, space-time optimization, and PRT, can be difficult to efficiently differentiate using existing symbolic or automatic differentiation techniques. Our new algorithm, D*, computes efficient symbolic derivatives for these functions by symbolically executing the expression graph at compile time to eliminate common subexpressions and by exploiting the special nature of the graph that represents the derivative of a function. This graph has a sum of products form; the new algorithm computes a factorization of this derivative graph along with an efficient grouping of product terms into subexpressions. For the problems in our test suite D* generates symbolic derivatives which are up to 4.6 x 103 times faster than those computed by the symbolic math program Mathematica and up to 2.2x105 times faster than the non-symbolic automatic differentiation program CppAD. In some cases the D* derivatives rival the best manually derived solutions.