Smooth interpolation of orientations with angular velocity constraints using quaternions
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Dynamic NURBS with geometric constraints for interactive sculpting
ACM Transactions on Graphics (TOG) - Special issue on interactive sculpting
A general construction scheme for unit quaternion curves with simple high order derivatives
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
A Lie group formulation of robot dynamics
International Journal of Robotics Research
Smooth invariant interpolation of rotations
ACM Transactions on Graphics (TOG)
Fast construction of accurate quaternion splines
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
A Mathematical Introduction to Robotic Manipulation
A Mathematical Introduction to Robotic Manipulation
Linear combination of transformations
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Robot Dynamics Algorithm
Continuous contact simulation for smooth surfaces
ACM Transactions on Graphics (TOG)
A general joint component framework for realistic articulation in human characters
I3D '03 Proceedings of the 2003 symposium on Interactive 3D graphics
Anatomy-Based Joint Models for Virtual Human Skeletons
CA '02 Proceedings of the Computer Animation
Fast frictional dynamics for rigid bodies
ACM SIGGRAPH 2005 Papers
Heads up!: biomechanical modeling and neuromuscular control of the neck
ACM SIGGRAPH 2006 Papers
Comprehensive biomechanical modeling and simulation of the upper body
ACM Transactions on Graphics (TOG)
Linear-time dynamics for multibody systems with general joint models
Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Large-scale dynamic simulation of highly constrained strands
ACM SIGGRAPH 2011 papers
Rod constraints for simplified ragdolls
Proceedings of the 12th ACM SIGGRAPH/Eurographics Symposium on Computer Animation
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Spline joints are a novel class of joints that can model general scleronomic constraints for multibody dynamics based on the minimal-coordinates formulation. The main idea is to introduce spline curves and surfaces in the modeling of joints: We model 1-DOF joints using splines on SE(3), and construct multi-DOF joints as the product of exponentials of splines in Euclidean space. We present efficient recursive algorithms to compute the derivatives of the spline joint, as well as geometric algorithms to determine optimal parameters in order to achieve the desired joint motion. Our spline joints can be used to create interesting new simulated mechanisms for computer animation and they can more accurately model complex biomechanical joints such as the knee and shoulder.