Sampling Projected Spherical Caps in Real Time
نویسندگان
چکیده
منابع مشابه
Codes in spherical caps
We consider bounds on codes in spherical caps and related problems in geometry and coding theory. An extension of the Delsarte method is presented that relates upper bounds on the size of spherical codes to upper bounds on codes in caps. Several new upper bounds on codes in caps are derived. Applications of these bounds to estimates of the kissing numbers and one-sided kissing numbers are consi...
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Halfspaces or linear threshold functions are widely studied in complexity theory, learning theory and algorithm design. In this work we study the natural problem of constructing pseudorandom generators (PRGs) for halfspaces over the sphere, aka spherical caps, which besides being interesting and basic geometric objects, also arise frequently in the analysis of various randomized algorithms (e.g...
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It is proved that given H ≥ 0 and an embedded compact orientable constant mean curvature H surface M included in the half space z ≥ 0, not everywhere tangent to z = 0 along its boundary ∂M = γ ⊂ {z = 0}, the inequality H ≤ (min κ) ( min √ 1 − (κg/κ) ) is satisfied, where κ and κg are the geodesic curvatures of γ on z = 0 and on the surface M , respectively, if and only if M is a spherical cap o...
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We prove an useful upper bound for the measure of spherical caps. Consider the uniformly distributed measure σn−1 on the Euclidean unit sphere Sn−1 ⊂ R. On the sphere, as among only a handful other spaces, the isoperimetric problem is completely solved. This goes back to Lévy [Lé] and Schmidt [Sch] and states that caps have the minimal measure of a boundary among all sets with a fixed mass. For...
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ژورنال
عنوان ژورنال: Proceedings of the ACM on Computer Graphics and Interactive Techniques
سال: 2019
ISSN: 2577-6193
DOI: 10.1145/3320282