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Journal for Geometry and Graphics 7 (2003), No. 2, 221--236
Copyright Heldermann Verlag 2003

Planar Grouping for Fast Affine Transformation and Clipping

Jonathan Dinerstein
Computer Science Department, Brigham Young University, 3366 TMCB, Provo, Utah 84602, U.S.A., jondinerstein@yahoo.com

Miklos Hoffmann
Inst. of Mathematics and Informatics, Karoly Eszterhazy College, 3300 Eger, Hungary, hofi@ektf.hu

Parris Egbert
Computer Science Department, Brigham Young University, 3366 TMCB, Provo, Utah 84602, U.S.A., egbert@cs.byu.edu

Kathryn Turner
Mathematics Dept., Utah State University, U.S.A., kturner@math.usu.edu

We introduce planar grouping, a technique where planar relationship information is gathered for a set of rigid points. This information is used to accelerate affine transformations and clipping. The planar grouping technique is an optimization problem, implemented in a best-first greedy search. We present two error metrics, one simple and fast, one based on the quadric error metric (QEM) to achieve higher quality planar grouping. We also apply the quadric error metric to linear grouping.

Keywords: linear grouping, planar grouping, quadratic error metric.

MSC: 68U05.

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