Principles of traditional animation applied to 3D computer animation
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Introduction to numerical linear algebra and optimisation
Introduction to numerical linear algebra and optimisation
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Area and Length Preserving Geometric Invariant Scale-Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
BLaC-Wavelets: a multiresolution analysis with non-nested spaces
Proceedings of the 7th conference on Visualization '96
Large steps in cloth simulation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Wavelets for computer graphics: theory and applications
Wavelets for computer graphics: theory and applications
Interactive animation of structured deformable objects
Proceedings of the 1999 conference on Graphics interface '99
Multiresolution curve editing with linear constraints
Proceedings of the sixth ACM symposium on Solid modeling and applications
Signal Analysis: Wavelets, Filter Banks, Time-Frequency Transforms and Applications
Signal Analysis: Wavelets, Filter Banks, Time-Frequency Transforms and Applications
Volume-Preserving Free-Form Solids
IEEE Transactions on Visualization and Computer Graphics
Adaptive Simulation of Soft Bodies in Real-Time
CA '00 Proceedings of the Computer Animation
Sparse geometric image representations with bandelets
IEEE Transactions on Image Processing
Detail preserving deformation of B-spline surfaces with volume constraint
Computer Aided Geometric Design
Technical Section: Smooth reverse subdivision
Computers and Graphics
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We describe a method for multiresolution deformation of closed planar curves that keeps the enclosed area constant. We use a wavelet based multiresolution representation of the curves that are represented by a finite number of control points at each level of resolution. A deformation can then be applied to the curve by modifying one or more control points at any level of resolution. This process is generally known as multiresolution editing to which we add the constraint of constant area. The key contribution of this paper is the efficient computation of the area in the wavelet decomposition form: the area is expressed through all levels of resolution as a bilinear form of the coarse and detail coefficients, and recursive formulas are developed to compute the matrix of this bilinear form. A similar result is also given for the bending energy of the curve. The area constraint is maintained through an optimization process. These contributions allow a real time multiresolution deformation with area constraint of complex curves.