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Kinematic measures for sets of support figures
- Part of
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- Journal:
- Mathematika / Volume 21 / Issue 2 / December 1974
- Published online by Cambridge University Press:
- 26 February 2010, pp. 270-281
- Print publication:
- December 1974
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- Article
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1. W. Blaschke's kinematic formula in the integral geometry of Euclidean n-dimensional space gives a weighted measure to the set of positions in which a mobile figure K1 overlaps a fixed figure K0. In the simplest case, K0 and K1 are compact convex sets and all positions are equally weighted; we give this in more detail. Let Wq denote the q-th Quermassintegral of K1: Steiner's formula for the volume V of the vector sum K1 + λB of K1 and a ball of radius λ defines these set functions by the equation
see [4; p. 214]. Blaschke's formula [4; p. 243] gives
as the measure, to within a normalization, of overlapping positions of K1 relative to K0.
