Geometric algorithms

Bounding volume

In computer graphics and computational geometry, a bounding volume for a set of objects is a closed volume that completely contains the union of the objects in the set. Bounding volumes are used to improve the efficiency of geometrical operations by using simple volumes to contain more complex objects. Normally, simpler volumes have simpler ways to test for overlap. A bounding volume for a set of objects is also a bounding volume for the single object consisting of their union, and the other way around. Therefore, it is possible to confine the description to the case of a single object, which is assumed to be non-empty and bounded (finite). (Wikipedia).

Bounding volume
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A. Song - What is the (essential) minimal volume? 4

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From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

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More resources available at www.misterwootube.com

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A. Song - What is the (essential) minimal volume? 3

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From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

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From playlist Volume and Surface Area (Geometry)

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A. Song - What is the (essential) minimal volume? 4 (version temporaire)

I will discuss the notion of minimal volume and some of its variants. The minimal volume of a manifold is defined as the infimum of the volume over all metrics with sectional curvature between -1 and 1. Such an invariant is closely related to "collapsing theory", a far reaching set of resu

From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

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A. Song - What is the (essential) minimal volume? 2 (version temporaire)

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From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

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From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

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A. Song - On the essential minimal volume of Einstein 4-manifolds

Given a positive epsilon, a closed Einstein 4-manifold admits a natural thick-thin decomposition. I will explain how, for any delta, one can modify the Einstein metric to a bounded sectional curvature metric so that the thick part has volume linearly bounded by the Euler characteristic and

From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

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A. Song - What is the (essential) minimal volume? 1 (version temporaire)

I will discuss the notion of minimal volume and some of its variants. The minimal volume of a manifold is defined as the infimum of the volume over all metrics with sectional curvature between -1 and 1. Such an invariant is closely related to "collapsing theory", a far reaching set of resu

From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

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A. Song - What is the (essential) minimal volume? 1

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From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

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From playlist GCSE Maths Videos

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From playlist Vietoris-Rips Seminar

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From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022

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Related pages

Polytope | Scene graph | Minimum bounding rectangle | Ray tracing (graphics) | Convex hull | Cuboid | Ellipsoid | Unit sphere | Bounding sphere | Principal axis theorem | Bounding volume hierarchy | Rectangle | Collision detection | Clipping (computer graphics) | Minimum bounding box | Slab (geometry) | Visual hull | Polyhedron | Polygon | Sphere | R-tree | Computer stereo vision | Convex hull algorithms | Computational geometry | Circle | Convex set | Multiplicative inverse