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Möller–Trumbore Intersection Algorithm
The Möller–Trumbore ray-triangle intersection algorithm, named after its inventors Tomas Möller and Ben Trumbore, is a fast method for calculating the intersection of a ray and a triangle in three dimensions without needing precomputation of the plane equation of the plane containing the triangle. Among other uses, it can be used in computer graphics to implement ray tracing computations involving triangle meshes. Calculation Definitions The ray is defined by an origin point O and a direction vector \vec. Every point on the ray can be expressed by \vec(t) = O + t\vec, where the parameter t ranges from zero to infinity. The triangle is defined by three vertices, named v_1, v_2, v_3. The plane that the triangle is on, which is needed to calculate the ray-triangle intersection, is defined by a point on the plane, such as v_1, and a vector that is orthogonal to every point on that plane, such as the cross product between the vector from v_1 to v_2 and the vector from v_1 to v_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intersection (Euclidean Geometry)
In geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces). The simplest case in Euclidean geometry is the line–line intersection between two distinct lines, which either is one point or does not exist (if the lines are parallel). Other types of geometric intersection include: * Line–plane intersection * Line–sphere intersection * Intersection of a polyhedron with a line * Line segment intersection * Intersection curve Determination of the intersection of flats – linear geometric objects embedded in a higher-dimensional space – is a simple task of linear algebra, namely the solution of a system of linear equations. In general the determination of an intersection leads to non-linear equations, which can be solved numerically, for example using Newton iteration. Intersection problems between a line and a conic section (circle, ellipse, parabola, etc.) or a quadric (sphere, cylinder, hyperboloid, et ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Combination
In convex geometry and vector algebra, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points in an affine space) where all coefficients are non-negative and sum to 1. In other words, the operation is equivalent to a standard weighted average, but whose weights are expressed as a percent of the total weight, instead of as a fraction of the ''count'' of the weights as in a standard weighted average. More formally, given a finite number of points x_1, x_2, \dots, x_n in a real vector space, a convex combination of these points is a point of the form :\alpha_1x_1+\alpha_2x_2+\cdots+\alpha_nx_n where the real numbers \alpha_i satisfy \alpha_i\ge 0 and \alpha_1+\alpha_2+\cdots+\alpha_n=1. As a particular example, every convex combination of two points lies on the line segment between the points. A set is convex if it contains all convex combinations of its points. The convex hull of a given set of points is id ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Badouel Intersection Algorithm
The Badouel ray (geometry), ray-triangle intersection algorithm, named after its inventor Didier Badouel, is a fast method for calculating the Intersection (Euclidean geometry), intersection of a ray and a triangle in three dimensions without needing precomputation of the plane equation of the plane (geometry), plane containing the triangle. External links Ray-Polygon Intersection An Efficient Ray-Polygon Intersection by Didier Badouel from Graphics Gems I Computational geometry {{Algorithm-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
