Topics in matrix analysis
An introduction to the use of splines in computer graphics
An introduction to the use of splines in computer graphics
Smooth interpolation of orientations with angular velocity constraints using quaternions
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Matrix animation and polar decomposition
Proceedings of the conference on Graphics interface '92
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
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
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
Compression of time-dependent geometry
I3D '99 Proceedings of the 1999 symposium on Interactive 3D graphics
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
SIAM Journal on Numerical Analysis
A Mathematical Introduction to Robotic Manipulation
A Mathematical Introduction to Robotic Manipulation
Geometric Algebra: A Computational Framework for Geometrical Applications (Part 2)
IEEE Computer Graphics and Applications
Practical parameterization of rotations using the exponential map
Journal of Graphics Tools
Continuous methods for motion planning
Continuous methods for motion planning
Ryan: rendering your animation nonlinearly projected
Proceedings of the 3rd international symposium on Non-photorealistic animation and rendering
Towards the next generation of 3D content creation
Proceedings of the working conference on Advanced visual interfaces
IEEE Transactions on Visualization and Computer Graphics
Spherical blend skinning: a real-time deformation of articulated models
Proceedings of the 2005 symposium on Interactive 3D graphics and games
Registration of point cloud data from a geometric optimization perspective
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Shape segmentation using local slippage analysis
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
ACM SIGGRAPH 2005 Papers
Physically based rigging for deformable characters
Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation
Sweepers: swept deformation defined by gesture
Graphical Models - Special issue on SMI 2004
Swirling-sweepers: constant-volume modeling
Graphical Models - Special issue on PG2004
Animation space: A truly linear framework for character animation
ACM Transactions on Graphics (TOG)
Space deformations and their application to shape modeling
ACM SIGGRAPH 2006 Courses
ACM SIGGRAPH 2006 Courses
Material aware mesh deformations
SIGGRAPH '05 ACM SIGGRAPH 2005 Posters
Keyframing using linear interpolation of matrices
SIGGRAPH '05 ACM SIGGRAPH 2005 Posters
Physically based rigging for deformable characters
Graphical Models
Skinning with dual quaternions
Proceedings of the 2007 symposium on Interactive 3D graphics and games
Kinodynamic skinning using volume-preserving deformations
SCA '07 Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation
Global registration of multiple 3D point sets via optimization-on-a-manifold
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Re-cinematography: improving the camera dynamics of casual video
Proceedings of the 15th international conference on Multimedia
A comparison of linear skinning techniques for character animation
AFRIGRAPH '07 Proceedings of the 5th international conference on Computer graphics, virtual reality, visualisation and interaction in Africa
Optimisation-on-a-manifold for global registration of multiple 3D point sets
International Journal of Intelligent Systems Technologies and Applications
Spline joints for multibody dynamics
ACM SIGGRAPH 2008 papers
Re-cinematography: Improving the camerawork of casual video
ACM Transactions on Multimedia Computing, Communications, and Applications (TOMCCAP)
Geometric skinning with approximate dual quaternion blending
ACM Transactions on Graphics (TOG)
Lie group integrators for animation and control of vehicles
ACM Transactions on Graphics (TOG)
Sensing, Acquisition, and Interactive Playback of Data-based Models for Elastic Deformable Objects
International Journal of Robotics Research
Exact volume preserving skinning with shape control
Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Interactive exploration of tensor fields in geosciences using volume rendering
Computers & Geosciences
Boneless pose editing and animation
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
Construction of a dynamic 4D probabilistic atlas for the developing brain
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
Interpolating 3D diffusion tensors in 2D planar domain by locating degenerate lines
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part I
Combining automated and interactive visual analysis of biomechanical motion data
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part II
Active geometry for game characters
MIG'10 Proceedings of the Third international conference on Motion in games
Steady affine motions and morphs
ACM Transactions on Graphics (TOG)
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part II
SAMBA: steadied choreographies
CAe '12 Proceedings of the Eighth Annual Symposium on Computational Aesthetics in Graphics, Visualization, and Imaging
Lie bodies: a manifold representation of 3D human shape
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
Automated skeleton based multi-modal deformable registration of head&neck datasets
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
Online real-time presentation of virtual experiences forexternal viewers
Proceedings of the 18th ACM symposium on Virtual reality software and technology
Mathematical analysis on affine maps for 2D shape interpolation
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Quaternion space sparse decomposition for motion compression and retrieval
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Mathematical analysis on affine maps for 2D shape interpolation
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Quaternion space sparse decomposition for motion compression and retrieval
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Profile Arthur S. Bland: high performance at Oak Ridge laboratory
XRDS: Crossroads, The ACM Magazine for Students - Scientific Computing
Matrix function: a "VIP" in linear algebra and its applications
XRDS: Crossroads, The ACM Magazine for Students - Scientific Computing
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Differential blending for expressive sketch-based posing
Proceedings of the 12th ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Technical Section: Planar shape interpolation using relative velocity fields
Computers and Graphics
Mathematical description of motion and deformation: from basics to graphics applications
SIGGRAPH Asia 2013 Courses
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Geometric transformations are most commonly represented as square matrices in computer graphics. Following simple geometric arguments we derive a natural and geometrically meaningful definition of scalar multiples and a commutative addition of transformations based on the matrix representation, given that the matrices have no negative real eigenvalues. Together, these operations allow the linear combination of transformations. This provides the ability to create weighted combination of transformations, interpolate between transformations, and to construct or use arbitrary transformations in a structure similar to a basis of a vector space. These basic techniques are useful for synthesis and analysis of motions or animations. Animations through a set of key transformations are generated using standard techniques such as subdivision curves. For analysis and progressive compression a PCA can be applied to sequences of transformations. We describe an implementation of the techniques that enables an easy-to-use and transparent way of dealing with geometric transformations in graphics software. We compare and relate our approach to other techniques such as matrix decomposition and quaternion interpolation.