1,669 research outputs found
Constrained Texture Mapping And Foldover-free Condition
Texture mapping has been widely used in image
processing and graphics to enhance the realism of CG scenes.
However to perfectly match the feature points of a 3D model
with the corresponding pixels in texture images, the
parameterisation which maps a 3D mesh to the texture space
must satisfy the positional constraints. Despite numerous
research efforts, the construction of a mathematically robust
foldover-free parameterisation subject to internal constraints
is still a remaining issue. In this paper, we address this
challenge by developing a two-step parameterisation method.
First, we produce an initial parameterisation with a method
traditionally used to solve structural engineering problems,
called the bar-network. We then derive a mathematical
foldover-free condition, which is incorporated into a Radial
Basis Function based scheme. This method is therefore able to
guarantee that the resulting parameterization meets the hard
constraints without foldovers
Mesh parameterization by minimizing the synthesized distortion metric with the coefficient-optimizing algorithm
2005-2006 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe
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A Local/Global Approach to Mesh Parameterization
We present a novel approach to parameterize a mesh with disk topology to the plane in a shape-preserving manner. Our key contribution is a local/global algorithm, which combines a local mapping of each 3D triangle to the plane, using transformations taken from a restricted set, with a global "stitch" operation of all triangles, involving a sparse linear system. The local transformations can be taken from a variety of families, e.g. similarities or rotations, generating different types of parameterizations. In the first case, the parameterization tries to force each 2D triangle to be an as-similar-as-possible version of its 3D counterpart. This is shown to yield results identical to those of the LSCM algorithm. In the second case, the parameterization tries to force each 2D triangle to be an as-rigid-as-possible version of its 3D counterpart. This approach preserves shape as much as possible. It is simple, effective, and fast, due to pre-factoring of the linear system involved in the global phase. Experimental results show that our approach provides almost isometric parameterizations and obtains more shape-preserving results than other state-of-the-art approaches.
We present also a more general "hybrid" parameterization model which provides a continuous spectrum of possibilities, controlled by a single parameter. The two cases described above lie at the two ends of the spectrum. We generalize our local/global algorithm to compute these parameterizations. The local phase may also be accelerated by parallelizing the independent computations per triangle.Engineering and Applied Science
3D mesh metamorphosis from spherical parameterization for conceptual design
Engineering product design is an information intensive decision-making
process that consists of several phases including design specification
definition, design concepts generation, detailed design and analysis,
and manufacturing. Usually, generating geometry models for
visualization is a big challenge for early stage conceptual design.
Complexity of existing computer aided design packages constrains
participation of people with various backgrounds in the design
process. In addition, many design processes do not take advantage of
the rich amount of legacy information available for new concepts
creation.
The research presented here explores the use of advanced graphical
techniques to quickly and efficiently merge legacy information with
new design concepts to rapidly create new conceptual product designs.
3D mesh metamorphosis framework 3DMeshMorpher was created to
construct new models by navigating in a shape-space of registered
design models. The framework is composed of: i) a fast spherical
parameterization method to map a geometric model (genus-0) onto a unit
sphere; ii) a geometric feature identification and picking technique
based on 3D skeleton extraction; and iii) a LOD controllable 3D
remeshing scheme with spherical mesh subdivision based on the
developedspherical parameterization. This efficient software framework
enables designers to create numerous geometric concepts in real time
with a simple graphical user interface.
The spherical parameterization method is focused on closed genus-zero
meshes. It is based upon barycentric coordinates with convex boundary.
Unlike most existing similar approaches which deal with each vertex in
the mesh equally, the method developed in this research focuses
primarily on resolving overlapping areas, which helps speed the
parameterization process. The algorithm starts by normalizing the
source mesh onto a unit sphere and followed by some initial relaxation
via Gauss-Seidel iterations. Due to its emphasis on solving only
challenging overlapping regions, this parameterization process is much
faster than existing spherical mapping methods.
To ensure the correspondence of features from different models, we
introduce a skeleton based feature identification and picking method
for features alignment. Unlike traditional methods that align single
point for each feature, this method can provide alignments for
complete feature areas. This could help users to create more
reasonable intermediate morphing results with preserved topological
features. This skeleton featuring framework could potentially be
extended to automatic features alignment for geometries with similar
topologies. The skeleton extracted could also be applied for other
applications such as skeleton-based animations.
The 3D remeshing algorithm with spherical mesh subdivision is
developed to generate a common connectivity for different mesh models.
This method is derived from the concept of spherical mesh subdivision.
The local recursive subdivision can be set to match the desired LOD
(level of details) for source spherical mesh. Such LOD is controllable
and this allows various outputs with different resolutions. Such
recursive subdivision then follows by a triangular correction process
which ensures valid triangulations for the remeshing. And the final
mesh merging and reconstruction process produces the remeshing model
with desired LOD specified from user. Usually the final merged model
contains all the geometric details from each model with reasonable
amount of vertices, unlike other existing methods that result in big
amount of vertices in the merged model. Such multi-resolution outputs
with controllable LOD could also be applied in various other computer
graphics applications such as computer games
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