Flocks, herds and schools: A distributed behavioral model
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Advanced animation and rendering techniques
Advanced animation and rendering techniques
Graphics gems IV
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
As-rigid-as-possible shape interpolation
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Pose space deformation: a unified approach to shape interpolation and skeleton-driven deformation
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Linear combination of transformations
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Approximating the Logarithm of a Matrix to Specified Accuracy
SIAM Journal on Matrix Analysis and Applications
Similarity and Affine Invariant Distances Between 2D Point Sets
IEEE Transactions on Pattern Analysis and Machine Intelligence
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Mean value coordinates for closed triangular meshes
ACM SIGGRAPH 2005 Papers
As-rigid-as-possible shape manipulation
ACM SIGGRAPH 2005 Papers
Rigid shape interpolation using normal equations
NPAR '08 Proceedings of the 6th international symposium on Non-photorealistic animation and rendering
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)
Compatible Embedding for 2D Shape Animation
IEEE Transactions on Visualization and Computer Graphics
Character Skin Deformation: A Survey
CGIV '10 Proceedings of the 2010 Seventh International Conference on Computer Graphics, Imaging and Visualization
Quaternions for Computer Graphics
Quaternions for Computer Graphics
Mathematical analysis on affine maps for 2D shape interpolation
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
| Hi-index | 0.00 |
While many technical terms, such as Euler angle, quaternion, and affine transformation, now become quite popular in computer graphics, their graphical meanings are sometimes a bit far from the original mathematical entities, which might cause misunderstanding or misuse of the mathematical techniques. This course presents an intuitive introduction to several mathematical concepts that are quite useful for describing motion and deformation of geometric objects. The concepts are inherited mostly from differential geometry and Lie theory, and now commonly used in various aspects of computer graphics, including curve/surface editing, deformation and animation of geometric objects. The objective of this course is to fill the gap between the original mathematical concepts and the practical meanings in computer graphics without assuming any prior knowledge of pure mathematics. We then illustrate practical usefulness of deep understanding of the mathematical concepts. Moreover this course demonstrates our current/ongoing research work, which is benefited from our mathematical formulation.