199 research outputs found
Morphing of Triangular Meshes in Shape Space
We present a novel approach to morph between two isometric poses of the same
non-rigid object given as triangular meshes. We model the morphs as linear
interpolations in a suitable shape space . For triangulated 3D
polygons, we prove that interpolating linearly in this shape space corresponds
to the most isometric morph in . We then extend this shape space
to arbitrary triangulations in 3D using a heuristic approach and show the
practical use of the approach using experiments. Furthermore, we discuss a
modified shape space that is useful for isometric skeleton morphing. All of the
newly presented approaches solve the morphing problem without the need to solve
a minimization problem.Comment: Improved experimental result
Analysis of and workarounds for element reversal for a finite element-based algorithm for warping triangular and tetrahedral meshes
We consider an algorithm called FEMWARP for warping triangular and
tetrahedral finite element meshes that computes the warping using the finite
element method itself. The algorithm takes as input a two- or three-dimensional
domain defined by a boundary mesh (segments in one dimension or triangles in
two dimensions) that has a volume mesh (triangles in two dimensions or
tetrahedra in three dimensions) in its interior. It also takes as input a
prescribed movement of the boundary mesh. It computes as output updated
positions of the vertices of the volume mesh. The first step of the algorithm
is to determine from the initial mesh a set of local weights for each interior
vertex that describes each interior vertex in terms of the positions of its
neighbors. These weights are computed using a finite element stiffness matrix.
After a boundary transformation is applied, a linear system of equations based
upon the weights is solved to determine the final positions of the interior
vertices. The FEMWARP algorithm has been considered in the previous literature
(e.g., in a 2001 paper by Baker). FEMWARP has been succesful in computing
deformed meshes for certain applications. However, sometimes FEMWARP reverses
elements; this is our main concern in this paper. We analyze the causes for
this undesirable behavior and propose several techniques to make the method
more robust against reversals. The most successful of the proposed methods
includes combining FEMWARP with an optimization-based untangler.Comment: Revision of earlier version of paper. Submitted for publication in
BIT Numerical Mathematics on 27 April 2010. Accepted for publication on 7
September 2010. Published online on 9 October 2010. The final publication is
available at http://www.springerlink.co
A Revisit of Shape Editing Techniques: from the Geometric to the Neural Viewpoint
3D shape editing is widely used in a range of applications such as movie
production, computer games and computer aided design. It is also a popular
research topic in computer graphics and computer vision. In past decades,
researchers have developed a series of editing methods to make the editing
process faster, more robust, and more reliable. Traditionally, the deformed
shape is determined by the optimal transformation and weights for an energy
term. With increasing availability of 3D shapes on the Internet, data-driven
methods were proposed to improve the editing results. More recently as the deep
neural networks became popular, many deep learning based editing methods have
been developed in this field, which is naturally data-driven. We mainly survey
recent research works from the geometric viewpoint to those emerging neural
deformation techniques and categorize them into organic shape editing methods
and man-made model editing methods. Both traditional methods and recent neural
network based methods are reviewed
High-Order Mesh Morphing for Boundary and Interface Fitting to Implicit Geometries
We propose a method that morphs high-orger meshes such that their boundaries
and interfaces coincide/align with implicitly defined geometries. Our focus is
particularly on the case when the target surface is prescribed as the zero
isocontour of a smooth discrete function. Common examples of this scenario
include using level set functions to represent material interfaces in
multimaterial configurations, and evolving geometries in shape and topology
optimization. The proposed method formulates the mesh optimization problem as a
variational minimization of the sum of a chosen mesh-quality metric using the
Target-Matrix Optimization Paradigm (TMOP) and a penalty term that weakly
forces the selected faces of the mesh to align with the target surface. The
distinct features of the method are use of a source mesh to represent the level
set function with sufficient accuracy, and adaptive strategies for setting the
penalization weight and selecting the faces of the mesh to be fit to the target
isocontour of the level set field. We demonstrate that the proposed method is
robust for generating boundary- and interface-fitted meshes for curvilinear
domains using different element types in 2D and 3D.Comment: 30 pages, 16 figure
A new surface joining technique for the design of shoe lasts
The footwear industry is a traditional craft sector, where technological advances are difficult to implement owing to the complexity of the processes being carried out, and the level of precision demanded by most of them. The shoe last joining operation is one clear example, where two halves from different lasts are put together, following a specifically traditional process, to create a new one. Existing surface joining techniques analysed in this paper are not well adapted to shoe last design and production processes, which makes their implementation in the industry difficult. This paper presents an alternative surface joining technique, inspired by the traditional work of lastmakers. This way, lastmakers will be able to easily adapt to the new tool and make the most out of their know-how. The technique is based on the use of curve networks that are created on the surfaces to be joined, instead of using discrete data. Finally, a series of joining tests are presented, in which real lasts were successfully joined using a commercial last design software. The method has shown to be valid, efficient, and feasible within the sector
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