Martin Marinov, Mario Botsch, Leif Kobbelt
ACM Journal of Graphics Tools 12(1), 2007, pp. 27-46

Multiresolution shape editing performs global deformations while preserving fine surface details by modifying a smooth base surface and reconstructing the modified detailed surface as a normal displacement from it. Since two non-trivial operators (deformation and reconstruction) are involved, the computational complexity can become too high for real-time deformations of complex models. We present an efficient technique for evaluating multiresolution deformations of high-resolution triangle meshes directly on the GPU. By precomputing the deformation functions as well as their gradient information we can map both the deformation and the reconstruction operator to the GPU, which enables us to reconstruct the deformed positions and sufficiently close approximations of the normal vectors in the vertex shader in a single rendering pass. This allows us to render dynamically deforming 3D models several times faster than on the CPU. We demonstrate the application of our technique to two modern multiresolution approaches: one based on (irregular) displaced subdivision surfaces and the other one on volumetric space deformation using radial basis functions.

Mario Botsch, Mark Pauly, Markus Gross, Leif Kobbelt
Eurographics Symposium on Geometry Processing (SGP 2006), 11-20

We present a new method for 3D shape modeling that achieves intuitive and robust deformations by emulating physically plausible surface behavior inspired by thin shells and plates. The surface mesh is embedded in a layer of volumetric prisms, which are coupled through non-linear, elastic forces. To deform the mesh, prisms are rigidly transformed to satisfy user constraints while minimizing the elastic energy. The rigidity of the prisms prevents degenerations even under extreme deformations, making the method numerically stable. For the underlying geometric optimization we employ both local and global shape matching techniques. Our modeling framework allows for the specification of various geometrically intuitive parameters that provide control over the physical surface behavior. While computationally more involved than previous methods, our approach significantly improves robustness and simplifies user interaction for large, complex deformations.

Mario Botsch, Leif Kobbelt
ACM Transactions on Graphics (TOG), 23(3), 630-634, 2004 Proceedings of the 2004 SIGGRAPH Conference

We present a freeform modeling framework for unstructured triangle meshes which is based on constraint shape optimization. The goal is to simplify the user interaction even for quite complex freeform or multiresolution modifications. The user first sets various boundary constraints to define a custom tailored (abstract) basis function which is adjusted to a given design task. The actual modification is then controlled by moving one single 9-dof manipulator object. The technique can handle arbitrary support regions and piecewise boundary conditions with smoothness ranging continuously from C0 to C2. To more naturally adapt the modification to the shape of the support region, the deformed surface can be tuned to bend with anisotropic stiffness. We are able to achieve real-time response in an interactive design session even for complex meshes by precomputing a set of scalar-valued basis functions that correspond to the degrees of freedom of the manipulator by which the user controls the modification.

Leif Kobbelt, Swen Campagna, Jens Vorsatz, Hans-Peter Seidel
ACM SIGGRAPH '98 proceedings, 1998, pp. 105-114

During the last years the concept of multi-resolution modeling has gained special attention in many fields of computer graphics and geometric modeling. In this paper we generalize powerful multiresolution techniques to arbitrary triangle meshes without requiring subdivision connectivity. Our major observation is that the hierarchy of nested spaces which is the structural core element of most multi-resolution algorithms can be replaced by the sequence of intermediate meshes emerging from the application of incremental mesh decimation. Performing such schemes with local frame coding of the detail coefficients already provides effective and efficient algorithms to extract multi-resolution information from unstructured meshes. In combination with discrete fairing techniques, i.e., the constrained minimization of discrete energy functionals, we obtain very fast mesh smoothing algorithms which are able to reduce noise from a geometrically specified frequency band in a multiresolution decomposition. Putting mesh hierarchies, local frame coding and multi-level smoothing together allows us to propose a flexible and intuitive paradigm for interactive detail-preserving mesh modification. We show examples generated by our mesh modeling tool implementation to demonstrate its functionality.

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