Medial Axis Construction in Three Dimensions and its Application to Mesh Generation

Sampl, Peter

doi:10.1007/s003660170004

Cited by 12 publications

(10 citation statements)

References 17 publications

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“…(3) bounds each segment's length at d. s − f is the greatest value such that no intermediate path of length s − f departs from the region covered by these projections. For general shapes in R 2 , the GVD forms a set of curves meeting at branching points [23]. In this case, no GVD cusps or branching points occur in any intermediate path.…”

Section: Equivalence Relationmentioning

confidence: 99%

An Equivalence Relation for Local Path Sets

Knepper

Srinivasa

Mason

2010

Springer Tracts in Advanced Robotics

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We propose a novel enhancement to the task of collision-testing a set of local paths. Our approach circumvents expensive collision-tests, yet it declares a continuum of paths collision-free by exploiting both the structure of paths and the outcome of previous tests. We define a homotopy-like equivalence relation among local paths and provide algorithms to (1) classify paths based on equivalence, and (2) implicitly collision-test up to 90% of them. We then prove both correctness and completeness of these algorithms before providing experimental results showing a performance increase up to 300%.

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Section: Equivalence Relationmentioning

confidence: 99%

An Equivalence Relation for Local Path Sets

Knepper

Srinivasa

Mason

2010

Springer Tracts in Advanced Robotics

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“…The application of mesh-improvement operations in a manner that preserves the integrity of the boundary representation is greatly compounded in three dimensions. The construction of three-dimensional contrained Delaunay triangulations which properly restrict to a prescribed boundary is a difficult and largely open problem, Amenta and Bern [1999]; Radovitzky and Ortiz [2000]; Sampl [2001]; Amenta et al [2002]. In the problem under consideration, the main difficulty resides in ensuring that the mesh operations preserve the geometry of the crack front.…”

Section: Three-dimensional Linear Elastic Crackmentioning

confidence: 99%

A variational r‐adaption and shape‐optimization method for finite‐deformation elasticity

Thoutireddy

Ortiz

2004

Numerical Meth Engineering

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This paper is concerned with the formulation of a variational r-adaption method for finite-deformation elastostatic problems. The distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution, the optimal mesh and, in problems of shape optimization, the equilibrium shapes of the system. This is accomplished by minimizing the energy functional with respect to the nodal field values as well as with respect to the triangulation of the domain of analysis. Energy minimization with respect to the referential nodal positions has the effect of equilibrating the energetic or configurational forces acting on the nodes. We derive general expressions for the configuration forces for isoparametric elements and nonlinear, possibly anisotropic, materials under general loading. We illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications, including the problem of a semi-infinite crack in linear and nonlinear elastic bodies; and the optimization of the shape of elastic inclusions.

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“…The 2-surface s(u, v) in IR 3,1 has the MOS property if its PILT vector simultaneously satisfies the MOS condition (22) and the Plücker condition (12). Consequently, in order to characterize MOS surfaces, we have to solve a system of two quadratic equations.…”

Section: Characterizing the Pilt Vectors Of Mos Surfacesmentioning

confidence: 99%

“…Consequently, in order to characterize MOS surfaces, we have to solve a system of two quadratic equations. First, we use a central (or inverse stereographic) projection to solve (22). Let…”

Section: Characterizing the Pilt Vectors Of Mos Surfacesmentioning

confidence: 99%

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MOS Surfaces: Medial Surface Transforms with Rational Domain Boundaries

Kosinka

Jüttler

Mathematics of Surfaces XII

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Abstract. We consider rational surface patches s (u, v) in the fourdimensional Minkowski space IR 3,1 , which describe parts of the medial surface (or medial axis) transform of spatial domains. The corresponding segments of the domain boundary are then obtained as the envelopes of the associated two-parameter family of spheres. If the Plücker coordinates of the line at infinity of the (two-dimensional) tangent plane of s satisfy a sum-of-squares condition, then the two envelope surfaces are shown to be rational surfaces. We characterize these Plücker coordinates and analyze the case, where the medial surface transform is contained in a hyperplane of the four-dimensional Minkowski space.

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Medial Axis Construction in Three Dimensions and its Application to Mesh Generation

Cited by 12 publications

References 17 publications

An Equivalence Relation for Local Path Sets

An Equivalence Relation for Local Path Sets

A variational r‐adaption and shape‐optimization method for finite‐deformation elasticity

MOS Surfaces: Medial Surface Transforms with Rational Domain Boundaries

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