Least squares conformal maps for automatic texture atlas generation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Computer Aided Geometric Design
As-rigid-as-possible shape manipulation
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
ACM SIGGRAPH 2008 papers
Bounded biharmonic weights for real-time deformation
ACM SIGGRAPH 2011 papers
Sketch based image deformation and editing with guaranteed feature correspondence
Proceedings of the 10th International Conference on Virtual Reality Continuum and Its Applications in Industry
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)
Computer Graphics Forum
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Planar shape interpolation with bounded distortion
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Technical Section: Planar shape interpolation using relative velocity fields
Computers and Graphics
Transmogrification: causal manipulation of visualizations
Proceedings of the 26th annual ACM symposium on User interface software and technology
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
Bijective composite mean value mappings
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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Conformal maps are considered very desirable for planar deformation applications, since they allow only local rotations and scale, avoiding shear and other visually disturbing distortions of local detail. Conformal maps are also orientation-preserving C∞ diffeomorphisms, meaning they are extremely smooth and prevent unacceptable "foldovers" in the plane. Unfortunately, these maps are also notoriously difficult to control, so working with them in an interactive animation scenario to achieve specific effects is a significant challenge, sometimes even impossible. We describe a novel 2D shape deformation system which generates conformal maps, yet provides the user a large degree of control over the result. For example, it allows discontinuities at user-specified boundary points, so true "bends" can be introduced into the deformation. It also allows the prescription of angular constraints at corners of the target image. Combining these provides for a very effective user experience. At the heart of our method is a very natural differential shape representation for conformal maps, using so-called "conformal factors" and "angular factors", which allow more intuitive control compared to representation in the usual spatial domain. Beyond deforming a given shape into a new one at each key frame, our method also provides the ability to interpolate between shapes in a very natural way, such that also the intermediate deformations are conformal. Our method is extremely efficient: it requires only the solution of a small dense linear system at preprocess time and a matrix-vector multiplication during runtime (which can be implemented on a modern GPU), thus the deformations, even on extremely large images, may be performed in real-time.