TY - JOUR

T1 - An efficient algorithm for the computation of the metric average of two intersecting convex polygons, with application to morphing

AU - Lipovetsky, Evgeny

AU - Dyn, Nira

PY - 2007/1

Y1 - 2007/1

N2 - Motivated by the method for the reconstruction of 3D objects from a set of parallel cross sections, based on the binary operation between 2D sets termed "metric average", we developed an algorithm for the computation of the metric average between two intersecting convex polygons in 2D. For two 1D sets there is an algorithm for the computation of the metric average, with linear time in the number of intervals in the two 1D sets. The proposed algorithm has linear computation time in the number of vertices of the two polygons. As an application of this algorithm, a new technique for morphing between two convex polygons is developed. The new algorithm performs morphing in a non-intuitive way.

AB - Motivated by the method for the reconstruction of 3D objects from a set of parallel cross sections, based on the binary operation between 2D sets termed "metric average", we developed an algorithm for the computation of the metric average between two intersecting convex polygons in 2D. For two 1D sets there is an algorithm for the computation of the metric average, with linear time in the number of intervals in the two 1D sets. The proposed algorithm has linear computation time in the number of vertices of the two polygons. As an application of this algorithm, a new technique for morphing between two convex polygons is developed. The new algorithm performs morphing in a non-intuitive way.

KW - Convex polygons

KW - Linear time complexity

KW - Metric average

KW - Morphing

UR - http://www.scopus.com/inward/record.url?scp=33847671445&partnerID=8YFLogxK

U2 - 10.1007/s10444-005-7473-6

DO - 10.1007/s10444-005-7473-6

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AN - SCOPUS:33847671445

SN - 1019-7168

VL - 26

SP - 269

EP - 282

JO - Advances in Computational Mathematics

JF - Advances in Computational Mathematics

IS - 1-3

ER -