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https://en.wikipedia.org/wiki/Support_function
The support function is a convex function on . Any non-empty closed convex set A is uniquely determined by h A . Furthermore, the support function, as a function of the set A is compatible with many natural geometric operations, like scaling, translation, rotation and Minkowski addition .
https://math.stackexchange.com/questions/2277721/how-to-prove-that-the-support-function-of-a-convex-body-can-be-written-hk-u
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https://pdfs.semanticscholar.org/e373/7858dd3338a926d7f53a2b0708e704e64d50.pdf
scheme for convex bodies is the support function representation [3, 13, 29]. It was introduced by Minkowski in 1903, and has been extensively studied by mathematicians thereafter. The representation scheme goes as follows. Let A‰Rd be a convex body (i.e., nonempty compact convex set) in the real Euclidean d-dimensional spaceRd. The support ...
https://www.sciencedirect.com/science/article/pii/S1077314298906749
The importance of thesupport functionin representation, manipulation, and analysis of convex bodies can indeed be compared with that of the Fourier transform in signal processing.The support function, in intuitive terms, is the signed distance of a supporting plane of a convex body from the origin point.Cited by: 56
https://encyclopedia2.thefreedictionary.com/Convex+Body
Convex bodies can be defined by a support function expressing the distance from the origin of coordinates to the support surface as a function of the outer normal to the convex body (that is, of a unit vector that is perpendicular to the support surface and directed toward that one of two half-spaces that is defined by this surface...
https://www.encyclopediaofmath.org/index.php/Convex_set
A convex body has associated with it its support function, defined by the equation , where is the scalar product. The function is positively homogeneous of the first degree: for , and is convex: (1) H u v H u H v All functions with these two properties are support functions for some unique convex body.
http://www.math.kit.edu/stoch/~hug/media/11.pdf
special functions related to a convex body, like the distance function, the support function and the convex characteristic function. Moreover, an additional interesting and unexpected feature in the theory of Hessian measures, as presented here, is a notion of duality related to the conjugation of convex functions, for which no correspondence ...
https://perso.math.u-pem.fr/fradelizi.matthieu/pdf/hyperplane.pdf
sections of a convex body in isotropic position through its centroid, as well as those of maximal volume in a fixed direction, does not depend much of the hyperplane. ... For p ≥ 1, the p-th centroid body ΓpK of K is the convex body whose support function is h ...
https://math.stackexchange.com/questions/235926/what-is-a-support-function-sup-z-in-k-langle-z-x-rangle
Do you have knowledge about the norms can be represented as support functions? So, let us take $\x\_p$. ... Some intuition on the support function of a convex set. Related. 0. The support function of two sets are equal iff the sets are equal. 0. Achieving equality in the definition of the support function…
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