An introduction to line geometry with applications

Pottmann, Helmut; Peternell, Martín; Ravani, Bahram

doi:10.1016/s0010-4485(98)00076-1

Cited by 96 publications

(56 citation statements)

References 13 publications

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“…In this work, in order to estimate the axis, two methods are implemented: the normal intersections method (Pottmann et al 1999) (henceforth denoted as Π 1 ) and the curvature centres method (Cao and Mumford 2002) (from now on denoted as Π 2 ). These rules must be stated in the tolerance specification.…”

Section: The Intrinsic Derived Reference Association: the Case Of Thementioning

confidence: 99%

Automatic evaluation of form errors in high-density acquired surfaces

Angelo¹,

Stefano²,

Morabito³

2011

International Journal of Production Research

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International audienceIn this paper the authors present an original methodology aiming at the automation of the geometric inspection, starting from a high-density acquired surface. The concept of intrinsic nominal reference is herein introduced in order to evaluate geometric errors. Starting from these concepts, a new specification language, which is based on recognizable geometric entities, is defined. This work also proposes some surface differential properties, such as the intrinsic nominal references, from which new categories of form errors can be introduced. Well-defined rules are then necessary for the unambiguous identification of these intrinsic nominal references. These rules are an integral part of the tolerance specification. This new approach requires that a recognition process be performed on the acquired model so as to automatically identify the already-mentioned intrinsic nominal references. The assessable errors refer to recognizable geometric entities and their evaluation leaves the nominal reference specification aside since they can be intrinsically associated with a recognized geometric shape. Tolerance specification is defined based on the error categories which can be automatically evaluated and which are an integral part of the specification language

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Section: The Intrinsic Derived Reference Association: the Case Of Thementioning

confidence: 99%

Automatic evaluation of form errors in high-density acquired surfaces

Angelo¹,

Stefano²,

Morabito³

2011

International Journal of Production Research

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“…Thus, the question is whether the lines on the objects near their realization are close -within some tolerance -to the lines of a linear complex. This is an approximation or regression problem in line space (Helmut et al, 1999 The topic about the Klein mapping and special sets of lines can refer to the paper written by Pottmann et al (Pottmann et al, 1999). lines and are associated with a line at infinity.…”

Section: Line Geometry and Plücker Coordinatesmentioning

confidence: 99%

“…The singularity of this matrix therefore means that there will be a linear dependence between these vectors. Grassmann showed that linear dependence of Plücker vectors induced www.intechopen.com geometric relations between the associated lines, so that a set of n Plücker vectors creates a variety with dimension m<n. A thorough introduction to Grassmann geometry please refers to (Pottmann et al, 1999). The applications of Grassmann geometry can be found in references (Collins & Long, 1995;Hao & McCarthy, 1998;Wu et al, 2006).…”

Section: Line Geometry and Plücker Coordinatesmentioning

confidence: 99%

“…This singularity arises from deficiency of constraints, so we call this singularity as "constraint singularity". In order to investigate the instantaneous motion the robot tends to perform while in singular configurations, the LCAA which was presented at (Pottmann et al, 1999) and further used for robotic analysis in (Wolf & Shoham, 2003) is adopted. The LCAA is based on determining the linear complex…”

mentioning

confidence: 99%

“…Equation (59) is equivalent to minimizing the positive semi-definite quadratic form given by (Pottmann et al, 1999):…”

mentioning

confidence: 99%

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An automated pottery archival and reconstruction system

Kampel¹,

Sablatnig²

2003

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Motivated by the current requirements of archaeologists, we are developing an automated archival system for archaeological classification and reconstruction of ceramics. Our system uses the profile of an archaeological fragment, which is the cross‐section of the fragment in the direction of the rotational axis of symmetry, to classify and reconstruct it virtually. Ceramic fragments are recorded automatically by a 3D measurement system based on structured (coded) light. The input data for the estimation of the profile is a set of points produced by the acquisition system. By registering the front and the back views of the fragment the profile is computed and measurements like diameter, area percentage of the complete vessel, height and width are derived automatically. We demonstrate the method and give results on synthetic and real data. Copyright © 2003 John Wiley & Sons, Ltd.

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An introduction to line geometry with applications

Cited by 96 publications

References 13 publications

Automatic evaluation of form errors in high-density acquired surfaces

Automatic evaluation of form errors in high-density acquired surfaces

A Novel 4-DOF Parallel Manipulator H4

An automated pottery archival and reconstruction system

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