Joint triangulations and triangulation maps
SCG '87 Proceedings of the third annual symposium on Computational geometry
A physically based approach to 2–D shape blending
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Feature-based image metamorphosis
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
On compatible triangulations of simple polygons
Computational Geometry: Theory and Applications
2-D shape blending: an intrinsic solution to the vertex path problem
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
Three-dimensional distance field metamorphosis
ACM Transactions on Graphics (TOG)
Graphical Models and Image Processing
How to morph tilings injectively
Journal of Computational and Applied Mathematics
As-rigid-as-possible shape interpolation
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
On Compatible Star Decompositions of Simple Polygons
IEEE Transactions on Visualization and Computer Graphics
Morphing Stick Figures Using Optimized Compatible Triangulations
PG '01 Proceedings of the 9th Pacific Conference on Computer Graphics and Applications
Blending Multiple Polygonal Shapes
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
Proceedings of the 2004 ACM symposium on Applied computing
Designing a compelling user interface for morphing
Proceedings of the SIGCHI Conference on Human Factors in Computing Systems
Morphing orthogonal planar graph drawings
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Proceedings of the twenty-second annual symposium on Computational geometry
Compatible triangulations and point partitions by series-triangular graphs
Computational Geometry: Theory and Applications
Rigid shape interpolation using normal equations
NPAR '08 Proceedings of the 6th international symposium on Non-photorealistic animation and rendering
Morphing polyhedra with parallel faces: Counterexamples
Computational Geometry: Theory and Applications
Compatible triangulations and point partitions by series-triangular graphs
Computational Geometry: Theory and Applications
Reactive 2D/3D garment pattern design modification
Computer-Aided Design
Morphing planar graphs in spherical space
GD'06 Proceedings of the 14th international conference on Graph drawing
Embedding a triangular graph within a given boundary
Computer Aided Geometric Design
SAMBA: steadied choreographies
CAe '12 Proceedings of the Eighth Annual Symposium on Computational Aesthetics in Graphics, Visualization, and Imaging
Planar shape interpolation with bounded distortion
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Morphing orthogonal planar graph drawings
ACM Transactions on Algorithms (TALG)
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Two planar triangulations with a correspondence between the pair of vertex sets are compatible (isomorphic) if they are topologically equivalent. This work describes methods for morphing compatible planar triangulations with identical convex boundaries in a manner that guarantees compatibility throughout the morph. These methods are based on a fundamental representation of a planar triangulation as a matrix that unambiguously describes the triangulation. Morphing the triangulations corresponds to interpolations between these matrices.We show that this basic approach can be extended to obtain better control over the morph, resulting in valid morphs with various natural properties. Two schemes, which generate the linear trajectory morph if it is valid, or a morph with trajectories close to linear otherwise, are presented. An efficient method for verification of validity of the linear trajectory morph between two triangulations is proposed. We also demonstrate how to obtain a morph with a natural evolution of triangle areas and how to find a smooth morph through a given intermediate triangulation.