Analytical methods for dynamic simulation of non-penetrating rigid bodies
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Digital Signal Processing
Using partial differential equations to generate free-form surfaces: 91787
Computer-Aided Design
Deformable curve and surface finite-elements for free-form shape design
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Fast contact force computation for nonpenetrating rigid bodies
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Haptic sculpting of dynamic surfaces
I3D '99 Proceedings of the 1999 symposium on Interactive 3D graphics
Three dimensional freeform sculpting via zero sets of scalar trivariate functions
Proceedings of the fifth ACM symposium on Solid modeling and applications
Advanced Engineering Mathematics: Maple Computer Guide
Advanced Engineering Mathematics: Maple Computer Guide
D-NURBS: A Physics-Based Framework for Geometric Design
IEEE Transactions on Visualization and Computer Graphics
Impulse-based dynamic simulation of rigid body systems
Impulse-based dynamic simulation of rigid body systems
| Hi-index | 0.00 |
Physics-based modeling integrates dynamics and geometry. The standard methods to solve the Lagrangian equations use a direct approach in the spatial domain. Though extremely powerful, it requires time consuming discrete-time integration. In this paper, we propose to use an indirect approach using the Transformation Theory. In particular, we use z-transform from the digital signal processing theory, and formulate a general, novel, unified solver that is applicable for various models and behavior. The convergence and accuracy of the solver are guaranteed if the temporal sampling period is less than the critical sampling period, which is a function of the physical properties of the model. Our solver can seamlessly handle curves, surfaces and solids, and supports a wide range of dynamic behavior. The solver does not depend on the topology of the model, and hence supports nonmanifold and arbitrary topology. Our numerical techniques are simple, easy to use, stable, and efficient. We develop an algorithm and a prototype software simulating various models and behavior. Our solver preserves physical properties such as energy, linear momentum, and angular momentum. This approach will serve as a foundation for many applications in many fields.