330 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
Surface parameterization over regular domains
Surface parameterization has been widely studied and it has been playing a critical role in many geometric processing tasks in graphics, computer-aided design, visualization, vision, physical simulation and etc. Regular domains, such as polycubes, are favored due to their structural regularity and geometric simplicity. This thesis focuses on studying the surface parameterization over regular domains, i.e. polycubes, and develops effective computation algorithms. Firstly, the motivation for surface parameterization and polycube mapping is introduced. Secondly, we briefly review existing surface parameterization techniques, especially for extensively studied parameterization algorithms for topological disk surfaces and parameterizations over regular domains for closed surfaces. Then we propose a polycube parameterization algorithm for closed surfaces with general topology. We develop an efficient optimization framework to minimize the angle and area distortion of the mapping. Its applications on surface meshing, inter-shape morphing and volumetric polycube mapping are also discussed
Analysis of Farthest Point Sampling for Approximating Geodesics in a Graph
A standard way to approximate the distance between any two vertices and
on a mesh is to compute, in the associated graph, a shortest path from
to that goes through one of sources, which are well-chosen vertices.
Precomputing the distance between each of the sources to all vertices of
the graph yields an efficient computation of approximate distances between any
two vertices. One standard method for choosing sources, which has been used
extensively and successfully for isometry-invariant surface processing, is the
so-called Farthest Point Sampling (FPS), which starts with a random vertex as
the first source, and iteratively selects the farthest vertex from the already
selected sources.
In this paper, we analyze the stretch factor of
approximate geodesics computed using FPS, which is the maximum, over all pairs
of distinct vertices, of their approximated distance over their geodesic
distance in the graph. We show that can be bounded in terms
of the minimal value of the stretch factor obtained using an
optimal placement of sources as , where is the ratio of the lengths of
the longest and the shortest edges of the graph. This provides some evidence
explaining why farthest point sampling has been used successfully for
isometry-invariant shape processing. Furthermore, we show that it is
NP-complete to find sources that minimize the stretch factor.Comment: 13 pages, 4 figure
Smooth 2D Coordinate Systems on Discrete Surfaces
International audienceWe introduce a new method to compute conformal param- eterizations using a recent definition of discrete conformity, and estab- lish a discrete version of the Riemann mapping theorem. Our algorithm can parameterize triangular, quadrangular and digital meshes. It can be adapted to preserve metric properties. To demonstrate the efficiency of our method, many examples are shown in the experiment section
A Survey of Developable Surfaces: From Shape Modeling to Manufacturing
Developable surfaces are commonly observed in various applications such as
architecture, product design, manufacturing, and mechanical materials, as well
as in the development of tangible interaction and deformable robots, with the
characteristics of easy-to-product, low-cost, transport-friendly, and
deformable. Transforming shapes into developable surfaces is a complex and
comprehensive task, which forms a variety of methods of segmentation,
unfolding, and manufacturing for shapes with different geometry and topology,
resulting in the complexity of developable surfaces. In this paper, we reviewed
relevant methods and techniques for the study of developable surfaces,
characterize them with our proposed pipeline, and categorize them based on
digital modeling, physical modeling, interaction, and application. Through the
analysis to the relevant literature, we also discussed some of the research
challenges and future research opportunities.Comment: 20 pages, 24 figures, Author submitted manuscrip
different numerical approaches for the analysis of a single screw expander
Abstract Positive displacement machines (e.g. scroll, twin screw, reciprocating, etc.) are proven to be suitable as expanders for organic Rankine cycle (ORC) applications, especially in the medium to low power range. However, in order to increase their performance, detailed simulation models are required to optimize the design and reduce the internal losses. In recent years, computational fluid dynamics (CFD) has been applied for the design and analysis of positive displacement machines (both compressors and expanders) with numerous challenges due to the dynamics of the expansion (or compression) process and deforming working chambers. The majority of the studies reported in literature focused on scroll, twin screw and reciprocating machines. Furthermore, the limitation of such methodologies to be applied directly to complex multi-rotor machines has been highlighted in literature. In this paper, a single screw expander (SSE) is used as benchmark to evaluate the applicability of different grid generation methodologies (dynamic remeshing and Chimera strategy overlapping grid), in terms of computational resources required, accuracy of the results and limitations. Although, the low-order models have been applied to single screw machines, there is still a lack of CFD analyses due to the particular complexity of the machine geometry and of its working principle. The calculations have been performed with air to reduce the complexity of the problem. to the main results are two folds: (i) the assessment of a numerical strategy with respect to the most critical parameters of a dynamic mesh-based simulation and (ii) the comparison of the pressure field and internal flow features obtained by using different numerical approaches
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