## Sharp Features of Polygonized Implicit Surfaces

####

Ohtake Y.,
Belyaev A.,
Pasko A.,

Dynamic Mesh Optimization for Polygonized Implicit Surfaces
with Sharp Features,

The Visual Computer, vol. 19, No. 2-3, 2003, pp. 115-126.

Electronic version: zipped PDF (1.24 Mb) ,
PDF (5.2 Mb)

#### Abstract

The paper presents a novel approach to accurate polygonization
of implicit surfaces with sharp features. The approach is based on
mesh evolution towards a given implicit surface with simultaneous
control of the mesh vertex positions and mesh normals.
Given an initial polygonization of an implicit surface,
a mesh evolution process initialized by the polygonization
is used. The evolving mesh converges to a limit mesh
which delivers a high quality approximation of the
implicit surface. For analyzing how close the evolving mesh
approaches the implicit surface we use two error metrics.
The metrics measure deviations of the mesh vertices
from the implicit surface and deviations of mesh normals
from the normals of the implicit surface.
####
Ohtake Y.,
Belyaev A.,

Dual/Primal Mesh Optimization for Polygonized Implicit Surfaces,

ACM Solid Modeling Symposium (June 17-21, 2002, Saarbrucken, Germany),
ACM Press, K. Lee and N. Patrikalakis (Eds.), 2002, pp. 171-178.

Electronic version: PDF (1.5 Mb)

#### Abstract

A new method for improving polygonizations of implicit surfaces
with sharp features is proposed. The method is based on the observation
that, given an implicit surface with sharp features, a triangle
mesh whose triangles are tangent to the implicit surface at
certain inner triangle points gives a better approximation of the
implicit surface than the standard marching cubes mesh. First, given
an initial triangle mesh, its dual mesh composed of the triangle
centroids is considered. Then the dual mesh is modified such that
its vertices are placed on the implicit surface and the mesh dual
to the modified dual mesh is considered. Finally the vertex positions
of that “double dual” mesh are optimized by minimizing a
quadratic energy measuring a deviation of the mesh normals from
the implicit surface normals computed at the vertices of the modified
dual mesh. In order to achieve an accurate approximation of
fine surface features, these basic steps are combined with adaptive
mesh subdivision and curvature-weighted vertex resampling. The
proposed method outperforms approaches based on the mesh evolution
paradigm in speed and accuracy.

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