Error propagation in geometric constructions

J. Wallner; R. Krasauskas; H. Pottmann

doi:10.1016/S0010-4485(00)00053-1

Error propagation in geometric constructions

J. Wallner^*, R. Krasauskas, H. Pottmann

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

In this paper we consider error propagation in geometric constructions from a geometric viewpoint. First we study affine combinations of convex bodies: this has many applications concerning spline 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.

Original language	English (US)
Pages (from-to)	631-641
Number of pages	11
Journal	CAD Computer Aided Design
Volume	32
Issue number	11
DOIs	https://doi.org/10.1016/S0010-4485(00)00053-1
State	Published - Sep 15 2000
Externally published	Yes

ASJC Scopus subject areas

Computer Science Applications
Computer Graphics and Computer-Aided Design
Industrial and Manufacturing Engineering

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10.1016/S0010-4485(00)00053-1

Cite this

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title = "Error propagation in geometric constructions",

abstract = "In this paper we consider error propagation in geometric constructions from a geometric viewpoint. First we study affine combinations of convex bodies: this has many applications concerning spline 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.",

author = "J. Wallner and R. Krasauskas and H. Pottmann",

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AU - Krasauskas, R.

AU - Pottmann, H.

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AB - In this paper we consider error propagation in geometric constructions from a geometric viewpoint. First we study affine combinations of convex bodies: this has many applications concerning spline 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.

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DO - 10.1016/S0010-4485(00)00053-1

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JO - CAD Computer Aided Design

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ER -

Error propagation in geometric constructions

Abstract

ASJC Scopus subject areas

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