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Title:

Geometric computing for freeform architecture

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Abstract Geometric computing has recently found a new field of applications, namely the various geometric problems which lie at the heart of rationalization and construction-aware design processes of freeform architecture. We report on our work in this area, dealing with meshes with planar faces and meshes which allow multilayer constructions (w...

Abstract Geometric computing has recently found a new field of applications, namely the various geometric problems which lie at the heart of rationalization and construction-aware design processes of freeform architecture. We report on our work in this area, dealing with meshes with planar faces and meshes which allow multilayer constructions (which is related to discrete surfaces and their curvatures), triangles meshes with circle-packing properties (which is related to conformal uniformization), and with the paneling problem. We emphasize the combination of numerical optimization and geometric knowledge. 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-09-21

Source:

http://www.mathematicsinindustry.com/content/pdf/2190-5983-1-4.pdf

http://www.mathematicsinindustry.com/content/pdf/2190-5983-1-4.pdf Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Title:

IVORY’S THEOREM IN HYPERBOLIC SPACES

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Abstract. According to the planar version of Ivory’s Theorem the family of confocal conics has the property that in each quadrangle formed by two pairs of conics the diagonals are of equal length. It turned out that this theorem is closely related to self-adjoint affine transformations. This point of view is capable of generalization to hyperbol...

Abstract. According to the planar version of Ivory’s Theorem the family of confocal conics has the property that in each quadrangle formed by two pairs of conics the diagonals are of equal length. It turned out that this theorem is closely related to self-adjoint affine transformations. This point of view is capable of generalization to hyperbolic and other spaces. 1. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

Source:

http://www.geometrie.tuwien.ac.at/stachel/h_ivory.pdf

http://www.geometrie.tuwien.ac.at/stachel/h_ivory.pdf Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Title:

Infinitesimally flexible meshes and . . .

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-06-08

Source:

http://www.geometrie.tugraz.at/wallner/cmin.pdf

http://www.geometrie.tugraz.at/wallner/cmin.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Key words ; conical meshes ; discrete minimal surfaces ; reciprocal-parallel

Key words ; conical meshes ; discrete minimal surfaces ; reciprocal-parallel Minimize

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Title:

Configuration Space of Surface-Surface contact

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: We consider a space X of constant curvature (Euclidean, elliptic, and hyperbolic space, and the sphere). The set of isometries of X transforming a surface such that it touches a second surface is called the configuration space of surface-surface contact. We investigate when this subset of Isom(X) is an immersed submanifold, and characterize th...

: We consider a space X of constant curvature (Euclidean, elliptic, and hyperbolic space, and the sphere). The set of isometries of X transforming a surface such that it touches a second surface is called the configuration space of surface-surface contact. We investigate when this subset of Isom(X) is an immersed submanifold, and characterize the absence of singularities by the principal curvatures of the surfaces involved. 1 Introduction The set of positions of one object such that it touches another, has been studied from various different points of view. From the side of mechanical engineering comes the problem of milling a sculptured surface by a cutter, which is, geometrically, a convex surface of revolution. It moves such that it always touches a given surface, and it should touch only in one point in order to avoid undercuttings. Geometric aspects of the restricted problem of translational motions, which include self-intersections of generalized offset surfaces and special ca. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-12

Source:

http://www.geometrie.tuwien.ac.at/wallner/konfraum.ps.gz

http://www.geometrie.tuwien.ac.at/wallner/konfraum.ps.gz Minimize

Document Type:

text

Language:

en

DDC:

516 Geometry *(computed)*

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Title:

INDUSTRIAL GEOMETRY Computer Aided Geometric Design Computer Vision Abstract Voronoi Diagrams for Oriented Spheres ∗

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We consider finite sets of oriented spheres inÊk−1 and, by interpreting such spheres as points inÊk, study the Voronoi diagrams they induce for several variants of distance between spheres. Our results are motivated by applications to special relativity theory. 1

We consider finite sets of oriented spheres inÊk−1 and, by interpreting such spheres as points inÊk, study the Voronoi diagrams they induce for several variants of distance between spheres. Our results are motivated by applications to special relativity theory. 1 Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

Source:

http://www.ig.jku.at/uploads/appw-vdos-06-report.pdf

http://www.ig.jku.at/uploads/appw-vdos-06-report.pdf Minimize

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text

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en

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Title:

Viscous Resuspension of a sediment caused by oscillating stratified flows

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It is known that a sediment of settled particles can resuspend under the action of shear. In this paper, based on a mathematical model given by Leighton & Acrivos [6], we study theoretically the viscous resuspension of a sediment in a Couette channel with harmonically oscillating walls. Numerical experiments reveal that the resuspension height a...

It is known that a sediment of settled particles can resuspend under the action of shear. In this paper, based on a mathematical model given by Leighton & Acrivos [6], we study theoretically the viscous resuspension of a sediment in a Couette channel with harmonically oscillating walls. Numerical experiments reveal that the resuspension height and the particle volume concentration at the bottom of the channel depend on the frequency of the oscillation. While oscillation of the top wall has nearly no influence on the sediment, a moving bottom wall causes the settled particles to completely resuspend if the frequency is large enough. 1 Introduction A settled bed of negatively buoyant particles can resuspend when in comes in contact with a clear fluid, even if Brownian motion or turbulence at very small Reynolds numbers are absent. This phenomenon, called viscous resuspension, was first observed by Gadala -Maria [3] and Gadala-Maria & Acrivos [4], and has been the subject of several exp. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-11

Source:

http://www.geometrie.tuwien.ac.at/wallner/resusp.ps.gz

http://www.geometrie.tuwien.ac.at/wallner/resusp.ps.gz Minimize

Document Type:

text

Language:

en

DDC:

532 Fluid mechanics; liquid mechanics *(computed)*

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Title:

Line Element Geometry for 3D Shape Understanding and Reconstruction

Author:

M. Hofer ; H. Pottmann ; J. Wallner ; B. Odehnal ; T. Steiner ; M. Hofer ; H. Pottmann ; J. Wallner ; B. Odehnal ; T. Steiner ; ...

M. Hofer ; H. Pottmann ; J. Wallner ; B. Odehnal ; T. Steiner ; M. Hofer ; H. Pottmann ; J. Wallner ; B. Odehnal ; T. Steiner ; Line Element ; Geometry Task ; M. Hofer ; B. Odehnal ; H. Pottmann ; T. Steiner ; J. Wallner D ; M. Hofer ; B. Odehnal ; H. Pottmann ; T. Steiner ; J. Wallner D ; M. Hofer ; B. Odehnal ; H. Pottmann ; T. Steiner ; J. Wallner D ; M. Hofer ; B. Odehnal ; H. Pottmann ; T. Steiner ; J. Wallner D Minimize authors

Description:

◮ Given: data set of a 3D shape ◮ Goal: understand and reconstruct the special geometry ◮ Tools: line elements and their relation to equiform kinematics

◮ Given: data set of a 3D shape ◮ Goal: understand and reconstruct the special geometry ◮ Tools: line elements and their relation to equiform kinematics Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-12-17

Source:

http://www.industrial-geometry.at/events/stmartin2005/mhofer_wien.pdf

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text

Language:

en

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Title:

Agenesis of the dorsal pancreas

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During the last 100 years in medical literature, there are only 54 reports, including the report of Pasaoglu et al (World J Gastroenterol 2008; 14: 2915-2916), with clinical descriptions of agenesis of the dorsal pancreas in humans. Agenesis of the dorsal pancreas, a rare congenital pancreatic malformation, is associated with some other medical ...

During the last 100 years in medical literature, there are only 54 reports, including the report of Pasaoglu et al (World J Gastroenterol 2008; 14: 2915-2916), with clinical descriptions of agenesis of the dorsal pancreas in humans. Agenesis of the dorsal pancreas, a rare congenital pancreatic malformation, is associated with some other medical conditions such as hyperglycemia, abdominal pain, pancreatitis and a few other diseases. In approximately 50% of reported patients with this congenital malformation, hyperglycemia was demonstrated. Evaluation of hyperglycemia and diabetes mellitus in all patients with agenesis of the dorsal pancreas including description of fasting blood glucose, oral glucose tolerance test, glycated hemoglobin and medical treatment would be a future goal. Since autosomal dominant transmission has been suggested in single families, more family studies including imaging technologies with demonstration of the pancreatic duct system are needed for evaluation of this disease. With this letter to the editor, we aim to increase available information for the better understanding of this rare disease. Minimize

Publisher:

Baishideng Publishing Group Co. Limited

Year of Publication:

2009-01-01T00:00:00Z

Source:

World Journal of Gastroenterology, Vol 15, Iss 3, Pp 376-377 (2009)

World Journal of Gastroenterology, Vol 15, Iss 3, Pp 376-377 (2009) Minimize

Document Type:

article

Language:

English

Subjects:

Agenesis of dorsal pancreas ; Diabetes mellitus ; Glucose intolerance ; Abdominal pain ; Pancreatitis ; LCC:Diseases of the digestive system. Gastroenterology ; LCC:RC799-869 ; LCC:Specialties of internal medicine ; LCC:RC581-951 ; LCC:Internal medicine ; LCC:RC31-1245 ; LCC:Medicine ; LCC:R ; DOAJ:Gastroenterology ; DOAJ:Medicine (General) ; DO...

Agenesis of dorsal pancreas ; Diabetes mellitus ; Glucose intolerance ; Abdominal pain ; Pancreatitis ; LCC:Diseases of the digestive system. Gastroenterology ; LCC:RC799-869 ; LCC:Specialties of internal medicine ; LCC:RC581-951 ; LCC:Internal medicine ; LCC:RC31-1245 ; LCC:Medicine ; LCC:R ; DOAJ:Gastroenterology ; DOAJ:Medicine (General) ; DOAJ:Health Sciences ; LCC:Diseases of the digestive system. Gastroenterology ; LCC:RC799-869 ; LCC:Specialties of internal medicine ; LCC:RC581-951 ; LCC:Internal medicine ; LCC:RC31-1245 ; LCC:Medicine ; LCC:R ; DOAJ:Gastroenterology ; DOAJ:Medicine (General) ; DOAJ:Health Sciences ; LCC:Diseases of the digestive system. Gastroenterology ; LCC:RC799-869 ; LCC:Specialties of internal medicine ; LCC:RC581-951 ; LCC:Internal medicine ; LCC:RC31-1245 ; LCC:Medicine ; LCC:R ; LCC:Diseases of the digestive system. Gastroenterology ; LCC:RC799-869 ; LCC:Specialties of internal medicine ; LCC:RC581-951 ; LCC:Internal medicine ; LCC:RC31-1245 ; LCC:Medicine ; LCC:R ; LCC:Diseases of the digestive system. Gastroenterology ; LCC:RC799-869 ; LCC:Specialties of internal medicine ; LCC:RC581-951 ; LCC:Internal medicine ; LCC:RC31-1245 ; LCC:Medicine ; LCC:R Minimize

DDC:

610 Medicine & health *(computed)*

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Title:

Circular Arc Snakes and Kinematic Surface Generation

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Figure 1: Non-static architecture: A flexing structure composed of many instances of the same flexible 6-snake of circular arcs, each of which in turn is composed of equal pieces. This fact is very relevant for the cost of manufacturing. In the center column one can see two stages of this flexion: two different snakes which happen to be at the s...

Figure 1: Non-static architecture: A flexing structure composed of many instances of the same flexible 6-snake of circular arcs, each of which in turn is composed of equal pieces. This fact is very relevant for the cost of manufacturing. In the center column one can see two stages of this flexion: two different snakes which happen to be at the same instant of their own respective flexion are highlighted. Right: The motion of the flexible kinematic chain of arcs which this structure is based on (see Section 4.2). We discuss the theory, discretization, and numerics of curves which are evolving such that part of their shape, or at least their curvature as a function of arc length, remains unchanged. The discretization of a curve as a smooth sequence of circular arcs is well suited for such purposes, and allows us to reduce evolution of curves to the evolution of a control point collection in a certain finite-dimensional shape space. We approach this evolution by a 2-step process: linearized evolution via optimized velocity fields, followed by optimization in order to exactly fulfill all geometric side conditions. We give applications to freeform architecture, including “rationalization ” of a surface by congruent arcs, form finding and, most interestingly, non-static architecture. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-07-17

Source:

http://www.geometrie.tuwien.ac.at/pottmann/2013/snakes/ccc-final.pdf

http://www.geometrie.tuwien.ac.at/pottmann/2013/snakes/ccc-final.pdf Minimize

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text

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en

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Title:

Error Propagation in Geometric Constructions

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In this paper we consider error propagation in geometric constructions from a geometric viewpoint. First we study affine combinations of convex bodies: This has numerous examples in splines curves and surfaces defined by control points. Second, we study in detail the circumcircle of three points in the Euclidean plane. It turns out that the righ...

In this paper we consider error propagation in geometric constructions from a geometric viewpoint. First we study affine combinations of convex bodies: This has numerous examples in splines curves and surfaces defined by control points. Second, we study in detail the circumcircle of three points in the Euclidean plane. It turns out that the right geometric setting for this problem is Laguerre geometry and the cyclographic mapping, which provides a point model for sets of circles or spheres. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

Source:

http://www.geometrie.tuwien.ac.at/geom/ig/papers/pot106.pdf

http://www.geometrie.tuwien.ac.at/geom/ig/papers/pot106.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Error propagation ; convex combination ; spline curve ; Apollonius problem

Error propagation ; convex combination ; spline curve ; Apollonius problem Minimize

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