Smooth interpolation of orientations with angular velocity constraints using quaternions
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Through-the-lens camera control
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Graphics gems IV
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
Retargetting motion to new characters
Proceedings of the 25th 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
Fast animation and control of nonrigid structures
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Interactive manipulation of rigid body simulations
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
On-line locomotion generation based on motion blending
Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation
Linear combination of transformations
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Motion texture: a two-level statistical model for character motion synthesis
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
General Construction of Time-Domain Filters for Orientation Data
IEEE Transactions on Visualization and Computer Graphics
A general joint component framework for realistic articulation in human characters
I3D '03 Proceedings of the 2003 symposium on Interactive 3D graphics
Machine Vision and Applications - Special issue: Human modeling, analysis, and synthesis
Application of inverse kinematics for skeleton manipulation in real-time
SCCG '03 Proceedings of the 19th spring conference on Computer graphics
MuscleBuilder: a modeling tool for human anatomy
Journal of Computer Science and Technology - Special issue on computer graphics and computer-aided design
Learning physics-based motion style with nonlinear inverse optimization
ACM SIGGRAPH 2005 Papers
Style translation for human motion
ACM SIGGRAPH 2005 Papers
An efficient search algorithm for motion data using weighted PCA
Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation
Spatial keyframing for performance-driven animation
Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation
Trajectory synthesis by hierarchical spatio-temporal correspondence: comparison of different methods
APGV '05 Proceedings of the 2nd symposium on Applied perception in graphics and visualization
Hierarchical implicit surface joint limits for human body tracking
Computer Vision and Image Understanding
Hierarchical motion controllers for real-time autonomous virtual humans
Lecture Notes in Computer Science
GI '06 Proceedings of Graphics Interface 2006
Monocular model-based 3D tracking of rigid objects
Foundations and Trends® in Computer Graphics and Vision
Spatial keyframing for performance-driven animation
ACM SIGGRAPH 2006 Courses
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Learnt inverse kinematics for animation synthesis
Graphical Models - Special issue on the vision, video and graphics conference 2005
Interactive motion correction and object manipulation
Proceedings of the 2007 symposium on Interactive 3D graphics and games
Multifactor Gaussian process models for style-content separation
Proceedings of the 24th international conference on Machine learning
Many-worlds browsing for control of multibody dynamics
ACM SIGGRAPH 2007 papers
Embedded deformation for shape manipulation
ACM SIGGRAPH 2007 papers
Spatial keyframing for performance-driven animation
ACM SIGGRAPH 2007 courses
Visualizing quaternions: course notes for Siggraph 2007
ACM SIGGRAPH 2007 courses
Interactive motion correction and object manipulation
ACM SIGGRAPH 2008 classes
Planning collision-free reaching motions for interactive object manipulation and grasping
ACM SIGGRAPH 2008 classes
Haptic Interaction with Virtual Avatars
EuroHaptics '08 Proceedings of the 6th international conference on Haptics: Perception, Devices and Scenarios
Full-body performance animation with Sequential Inverse Kinematics
Graphical Models
Generalizing motion edits with Gaussian processes
ACM Transactions on Graphics (TOG)
Evaluating distance metrics for animation blending
Proceedings of the 4th International Conference on Foundations of Digital Games
Hierarchical implicit surface joint limits for human body tracking
Computer Vision and Image Understanding
Qualitative evaluation of quantitative dance motion data
ACM SIGGRAPH ASIA 2009 Posters
Motion Pattern Encapsulation for Data-Driven Constraint-Based Motion Editing
MIG '09 Proceedings of the 2nd International Workshop on Motion in Games
Integrated Analytic and Linearized Inverse Kinematics for Precise Full Body Interactions
MIG '09 Proceedings of the 2nd International Workshop on Motion in Games
Space-time curve analogies for motion editing
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Comparing and evaluating real time character engines for virtual environments
Presence: Teleoperators and Virtual Environments
Linear-time dynamics for multibody systems with general joint models
Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Expressive gait synthesis using PCA and Gaussian modeling
MIG'10 Proceedings of the Third international conference on Motion in games
Human 3D motion computation from a varying number of cameras
SCIA'11 Proceedings of the 17th Scandinavian conference on Image analysis
Steady affine motions and morphs
ACM Transactions on Graphics (TOG)
Two Distributed-State Models For Generating High-Dimensional Time Series
The Journal of Machine Learning Research
ICEC'06 Proceedings of the 5th international conference on Entertainment Computing
Motion editing with the state feedback dynamic model
CGI'06 Proceedings of the 24th international conference on Advances in Computer Graphics
Twists – an operational representation of shape
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
iSAM2: Incremental smoothing and mapping using the Bayes tree
International Journal of Robotics Research
Gaussian process motion graph models for smooth transitions among multiple actions
Computer Vision and Image Understanding
Footprint analysis and motion synthesis
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part III
Style animations generated from dynamic model
Edutainment'06 Proceedings of the First international conference on Technologies for E-Learning and Digital Entertainment
Discovery of complex behaviors through contact-invariant optimization
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Contact-invariant optimization for hand manipulation
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Component-based locomotion composition
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Simple data-driven control for simulated bipeds
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Contact-invariant optimization for hand manipulation
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Component-based locomotion composition
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Simple data-driven control for simulated bipeds
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Analyzing and evaluating markerless motion tracking using inertial sensors
ECCV'10 Proceedings of the 11th European conference on Trends and Topics in Computer Vision - Volume Part I
Real-time 6-DOF multi-session visual SLAM over large-scale environments
Robotics and Autonomous Systems
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Parameterizing three degree-of-freedom (DOF) rotations is difficult to do well. Many graphics applications demand that we be able to compute and differentiate positions and orientations of articulated figures with respect to their rotational (and other) parameters, as well as integrate differential equations, optimize rotation parameters, and interpolate orientations. Widely used parameterizations such as Euler angles and quaternions are well suited to only a few of these operations. The exponential map maps a vector in R 3 describing the axis and magnitude of a three-DOF rotation to the corresponding rotation. Several graphics researchers have applied it with limited success to interpolation of orientations, but it has been virtually ignored with respect to the other operations mentioned above. In this paper we present formulae for computing, differentiating, and integrating three-DOF rotations with the exponential map. We show that our formulation is numerically stable in the face of machine precision issues, and that for most applications all singularities in the map can be avoided through a simple technique of dynamic reparameterization. We demonstrate how to use the exponential map to solve both the "freely rotating body" problem, and the important ball-and-socket joint required to accurately model shoulder and hip joints in articulated figures. Examining several common graphics applications, we explain the benefits of our formulation of the exponential map over Euler angles and quaternions, including robustness, small state vectors, lack of explicit constraints, good modeling capabilities, simplicity of solving ordinary differential equations, and good interpolation behavior.