A physically based approach to 2–D shape blending
SIGGRAPH '92 Proceedings of the 19th 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
Controllable morphing of compatible planar triangulations
ACM Transactions on Graphics (TOG)
Shape Blending Using the Star-Skeleton Representation
IEEE Computer Graphics and Applications
Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pyramid Coordinates for Morphing and Deformation
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
Perceptually Based Approach for Planar Shape Morphing
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Linear rotation-invariant coordinates for meshes
ACM SIGGRAPH 2005 Papers
As-rigid-as-possible shape manipulation
ACM SIGGRAPH 2005 Papers
Physically based morphing of point-sampled surfaces: Animating Geometrical Models
Computer Animation and Virtual Worlds - CASA 2005
Graphical Models - Special issue on SPM 05
Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition (Studies in Advanced Mathematics)
Actual morphing: a physics-based approach to blending
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Geometric modeling in shape space
ACM SIGGRAPH 2007 papers
As-rigid-as-possible surface modeling
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
ACM Transactions on Graphics (TOG)
Conformal equivalence of triangle meshes
ACM SIGGRAPH 2008 papers
Rigid shape interpolation using normal equations
NPAR '08 Proceedings of the 6th international symposium on Non-photorealistic animation and rendering
As-rigid-as-possible image registration for hand-drawn cartoon animations
Proceedings of the 7th International Symposium on Non-Photorealistic Animation and Rendering
Surface Quasi-Conformal Mapping by Solving Beltrami Equations
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
A local/global approach to mesh parameterization
SGP '08 Proceedings of the Symposium on Geometry Processing
A simple geometric model for elastic deformations
ACM SIGGRAPH 2010 papers
Controllable conformal maps for shape deformation and interpolation
ACM SIGGRAPH 2010 papers
Spin transformations of discrete surfaces
ACM SIGGRAPH 2011 papers
Ball-Morph: Definition, Implementation, and Comparative Evaluation
IEEE Transactions on Visualization and Computer Graphics
Bounded distortion mapping spaces for triangular meshes
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Simple formulas for quasiconformal plane deformations
ACM Transactions on Graphics (TOG)
Computing Extremal Quasiconformal Maps
Computer Graphics Forum
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Planar shape interpolation is widely used in computer graphics applications. Despite a wealth of interpolation methods, there is currently no approach that produces shapes with a bounded amount of distortion with respect to the input. As a result, existing interpolation methods may produce shapes that are significantly different than the input and can suffer from fold-overs and other visual artifacts, making them less useful in many practical scenarios. We introduce a novel shape interpolation scheme designed specifically to produce results with a bounded amount of conformal (angular) distortion. Our method is based on an elegant continuous mathematical formulation and provides several appealing properties such as existence and uniqueness of the solution as well as smoothness in space and time domains. We further present a discretization and an efficient practical algorithm to compute the interpolant and demonstrate its usability and good convergence behavior on a wide variety of input shapes. The method is simple to implement and understand. We compare our method to state-of-the-art interpolation methods and demonstrate its superiority in various cases.