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
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Image metamorphosis using snakes and free-form deformations
SIGGRAPH '95 Proceedings of the 22nd 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
Preventing Self-Intersection under Free-Form Deformation
IEEE Transactions on Visualization and Computer Graphics
Image Warping with Scattered Data Interpolation
IEEE Computer Graphics and Applications
Computer Aided Geometric Design
Mean value coordinates for closed triangular meshes
ACM SIGGRAPH 2005 Papers
Image deformation using moving least squares
ACM SIGGRAPH 2006 Papers
Mean value coordinates for arbitrary planar polygons
ACM Transactions on Graphics (TOG)
Harmonic coordinates for character articulation
ACM SIGGRAPH 2007 papers
Spherical barycentric coordinates
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
GPU-assisted positive mean value coordinates for mesh deformations
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
ACM SIGGRAPH 2008 papers
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Maximum entropy coordinates for arbitrary polytopes
SGP '08 Proceedings of the Symposium on Geometry Processing
Controllable conformal maps for shape deformation and interpolation
ACM SIGGRAPH 2010 papers
Bounded biharmonic weights for real-time deformation
ACM SIGGRAPH 2011 papers
Interference-aware geometric modeling
Proceedings of the 2011 SIGGRAPH Asia Conference
Bounded distortion mapping spaces for triangular meshes
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Smooth Shape-Aware Functions with Controlled Extrema
Computer Graphics Forum
IEEE Transactions on Visualization and Computer Graphics
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We introduce the novel concept of composite barycentric mappings and give theoretical conditions under which they are guaranteed to be bijective. We then focus on mean value mappings and derive a simple procedure for computing their Jacobians, leading to an efficient GPU-assisted implementation for interactively designing composite mean value mappings which are bijective up to pixel resolution. We provide a number of examples of 2D image deformation and an example of 3D shape deformation based on a natural extension of the concept to spatial mappings.