SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Interpolating Subdivision for meshes with arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Multiresolution analysis for surfaces of arbitrary topological type
ACM Transactions on Graphics (TOG)
Interactive multiresolution mesh editing
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
MAPS: multiresolution adaptive parameterization of surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Displaced subdivision surfaces
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Globally smooth parameterizations with low distortion
ACM SIGGRAPH 2003 Papers
Geometry compression of normal meshes using rate-distortion algorithms
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
ACM SIGGRAPH 2004 Papers
Multilevel Solvers for Unstructured Surface Meshes
SIAM Journal on Scientific Computing
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Normal mesh based geometrical image compression
Image and Vision Computing
Globally convergent adaptive normal multi-scale transforms
Proceedings of the 7th international conference on Curves and Surfaces
Normal multi-scale transforms for surfaces
Proceedings of the 7th international conference on Curves and Surfaces
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Hierarchical representations of surfaces have many advantages for digital geometry processing applications. Normal meshes are particularly attractive since their level-to-level displacements are in the local normal direction only. Consequently, they only require scalar coefficients to specify. In this article, we propose a novel method to approximate a given mesh with a normal mesh. Instead of building an associated parameterization on the fly, we assume a globally smooth parameterization at the beginning and cast the problem as one of perturbing this parameterization. Controlling the magnitude of this perturbation gives us explicit control over the range between fully constrained (only scalar coefficients) and unconstrained (3-vector coefficients) approximations. With the unconstrained problem giving the lowest approximation error, we can thus characterize the error cost of normal meshes as a function of the number of nonnormal offsets---we find a significant gain for little (error) cost. Because the normal mesh construction creates a geometry driven approximation, we can replace the difficult geometric distance minimization problem with a much simpler least squares problem. This variational approach reduces magnitude and structure (aliasing) of the error further. Our method separates the parameterization construction into an initial setup followed only by subsequent perturbations, giving us an algorithm which is far simpler to implement, more robust, and significantly faster.