Interactive multi-resolution modeling on arbitrary meshes

Leif Kobbelt, Swen Campagna, Jens Vorsatz, Hans-Peter Seidel
1998 Proceedings of the 25th annual conference on Computer graphics and interactive techniques - SIGGRAPH '98  
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
more » ... ication 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. meshes are already sufficiently close to the smooth limit after only a few refinement steps. Within a multi-resolution framework, subdivision schemes provide a set of basis functions φ i¢ j £ φ ¤ 2 i ¥ § ¦ j¨which are suitable to build a cascade of nested spaces V i £ span ¤ © © u¤ v¤ n plus an index i identifying the affine frame F i £ © © ˆu¤v¤ h takes about 20µS while the reconstruction © ˆu¤v¤ h q takes approximately 8µS. Since a progressive mesh representation introduces two triangles per vertex split, this means that for the reconstruction of a mesh with 10 5 triangles, the computational overhead due to the local frame representation is less than half a second. Suppose the original mesh model M k is transformed into the progressive mesh sequence © M k ¤ ¢ ¢ ¢ ¤ M 0 with M 0 being the coarsest base mesh. If the user picks the mesh M i and applies modifications then this invalidates the subsequence © M i¡ 1 ¤ ¢ ¢ ¢ ¤ M 0 . If the working resolution is to be reduced afterwards to M j ( j ¡ i) then the intermediate meshes have to be recomputed by online mesh decimation. The textural detail encoded in the subsequence © M k ¤ ¢ ¢ ¢ ¤ M i 1 however remains unchanged since it is stored with respect to local frames such that reconstruction starting from a modified mesh M i leads to the intended result M k . Fig. 9 shows an example of this procedure.
doi:10.1145/280814.280831 dblp:conf/siggraph/KobbeltCVS98 fatcat:zadxavkr4bdh5ml3ykkb7qww5y