Convex geometry | Geometric algorithms
The Minkowski Portal Refinement collision detection algorithm is a technique for determining whether two convex shapes overlap. The algorithm was created by in 2006 and was first published in Game Programming Gems 7. The algorithm was used in Tomb Raider: Underworld and other games created by Crystal Dynamics and its sister studios within Eidos Interactive. MPR, like its cousin GJK, relies on shapes that are defined using support mappings. This allows the algorithm to support a limitless variety of shapes that are problematic for other algorithms. Support mappings require only a single mathematical function to represent a point, line segment, disc, cylinder, cone, ellipsoid, football, bullet, frustum or most any other common convex shape. Once a set of basic primitives have been created, they can easily be combined with one another using operations such as sweep, shrink-wrap and affine transformation. Unlike GJK, MPR does not provide the shortest distance between separated shapes. However, according to its author, MPR is simpler, more numerically robust and handles translational sweeping with very little modification. This makes it well-suited for games and other real-time applications. (Wikipedia).
What is an enlargement dilation
👉 Learn about dilations. Dilation is the transformation of a shape by a scale factor to produce an image that is similar to the original shape but is different in size from the original shape. A dilation that creates a larger image is called an enlargement or a stretch while a dilation tha
From playlist Transformations
How to determine the scale factor of a dilation for enlargement
👉 Learn about dilations. Dilation is the transformation of a shape by a scale factor to produce an image that is similar to the original shape but is different in size from the original shape. A dilation that creates a larger image is called an enlargement or a stretch while a dilation tha
From playlist Transformations
Code - Seminar 28 - Ince on Robust and Fast Collision Detection in Games
Ince (https://twitter.com/Ince_FS) presents his new algorithm for fast and robust collision detection, using Minkowski differences. The webpage for this seminar is https://metauni.org/code/ You can join this seminar from anywhere, on any device, at https://www.metauni.org. This video wa
From playlist Code seminar
Determining the scale factor of the enlargement of a triangle
👉 Learn about dilations. Dilation is the transformation of a shape by a scale factor to produce an image that is similar to the original shape but is different in size from the original shape. A dilation that creates a larger image is called an enlargement or a stretch while a dilation tha
From playlist Transformations
In this video from The Physics Classroom's Concept Builder series, Mr. H explains how to use the direction that light refracts to make a claim regarding the relative optical density of, light speed within, and index of refraction of the two media. Put your learning to practice with our Re
From playlist Concept Builder Series - Reflection and Refraction
👉 Learn about dilations. Dilation is the transformation of a shape by a scale factor to produce an image that is similar to the original shape but is different in size from the original shape. A dilation that creates a larger image is called an enlargement or a stretch while a dilation tha
From playlist Transformations
Refraction (1 of 5) What is Refraction? An Explanation
Refraction, A conceptual qualitative explanation. Refraction is the change in direction of a ray of light as it passes from one medium to another. The amount of refraction is determined by the index of refraction of the media and the angle of incidence. For light, refraction follows Snell
From playlist Optics: Ray Diagrams, Reflection, Refraction, Thin Lens Equation
What are dilations, similarity and scale factors
👉 Learn about dilations. Dilation is the transformation of a shape by a scale factor to produce an image that is similar to the original shape but is different in size from the original shape. A dilation that creates a larger image is called an enlargement or a stretch while a dilation tha
From playlist Transformations
Determining the scale factor of two quadrilaterals
👉 Learn about dilations. Dilation is the transformation of a shape by a scale factor to produce an image that is similar to the original shape but is different in size from the original shape. A dilation that creates a larger image is called an enlargement or a stretch while a dilation tha
From playlist Transformations
Peter Pivovarov: Random s-concave functions and isoperimetry
I will discuss stochastic geometry of s-concave functions. In particular, I will explain how a ”local” stochastic isoperimetry underlies several functional inequalities. A new ingredient is a notion of shadow systems for s-concave functions. Based on joint works with J. Rebollo Bueno.
From playlist Workshop: High dimensional spatial random systems
What is Time? Can We Travel through It? | Wondrium Perspectives
People have always kept a close eye on the time. First, we looked to the heavenly bodies, and now we look at digital displays. While our methods of timekeeping have gotten more sophisticated, the question remains: What exactly is time? In this episode of Wondrium Perspectives, four exper
From playlist Wondrium Perspectives
👉 Learn about dilations. Dilation is the transformation of a shape by a scale factor to produce an image that is similar to the original shape but is different in size from the original shape. A dilation that creates a larger image is called an enlargement or a stretch while a dilation tha
From playlist Transformations
Christian Bär: Local index theory for Lorentzian manifolds
HYBRID EVENT We prove a local version of the index theorem for Dirac-type operators on globally hyperbolic Lorentzian manifolds with Cauchy boundary. In case the Cauchy hypersurface is compact, we do not assume self-adjointness of the Dirac operator on the spacetime or of the associated el
From playlist Mathematical Physics
Franz Schuster: Blaschke–Santaló Inequalities for Minkowski and Asplund Endomorphisms
The Blaschke–Santaló inequality is one of the best known and most powerful affine isoperimetric inequalities in convex geometric analysis. In particular, it is significantly stronger than the classical Euclidean Urysohn inequality. In this talk, we present new isoperimetric inequalities fo
From playlist Workshop: High dimensional measures: geometric and probabilistic aspects
4D galaxy simulation [research]
Broadcasted live on Twitch -- Watch live at https://www.twitch.tv/leioslabs
From playlist research
Nathaël Gozlan : Ehrard’s inequality and hypercontractivity of Ornstein-Ulheinbeck semigroup
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 28, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Geometry
[ANT05] Minkowski's geometry of numbers
Unsurprisingly, many of the pictures we've drawn are honest geometric objects, leaving them open to geometric attacks.
From playlist [ANT] An unorthodox introduction to algebraic number theory
Gautam Mandal - Introduction to Hawking radiation (1)
PROGRAM: THE 8TH ASIAN WINTER SCHOOL ON STRINGS, PARTICLES AND COSMOLOGY DATES: Thursday 09 Jan, 2014 - Saturday 18 Jan, 2014 VENUE: Blue Lily Hotel, Puri PROGRAM LINK: http://www.icts.res.in/program/asian8 The 8th Asian Winter School on Strings, Particles and Cosmology is part of a seri
From playlist The 8th Asian Winter School on Strings, Particles and Cosmology
Live CEOing Ep 686: Language Design in Wolfram Language [Numerical GR Framework Review]
In this episode of Live CEOing, Stephen Wolfram discusses upcoming improvements and features to the Wolfram Language. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or through the official Twitch channel of Stephen Wolfram
From playlist Behind the Scenes in Real-Life Software Design
How to determine the reduction scale factor for two parallelograms
👉 Learn about dilations. Dilation is the transformation of a shape by a scale factor to produce an image that is similar to the original shape but is different in size from the original shape. A dilation that creates a larger image is called an enlargement or a stretch while a dilation tha
From playlist Transformations