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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. [1]
Take the intersection point C of the ray OA with the circle P. Connect the point C with an arbitrary point B on the circle P (different from C and from the point on P antipodal to C) Let h be the reflection of ray BA in line BC. Then h cuts ray OC in a point A '. A ' is the inverse point of A with respect to circle P. [4]: § 3.2
Cell is the intersection of all of these half-spaces, and hence it is a convex polygon. [6] When two cells in the Voronoi diagram share a boundary, it is a line segment , ray , or line, consisting of all the points in the plane that are equidistant to their two nearest sites.
This equation is known as Euler's polyhedron formula. Thus the number of vertices is 2 more than the excess of the number of edges over the number of faces. For example, since a cube has 12 edges and 6 faces, the formula implies that it has eight vertices.
The visual hull of a three-dimensional object, with respect to a set of viewpoints, consists of the points such that every ray from a viewpoint through intersects the object. Equivalently it is the intersection of the (non-convex) cones generated by the outline of the object with respect to each viewpoint.
The Badouel ray-triangle intersection algorithm, named after its inventor Didier Badouel, 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.
An improved algorithm to calculate the winding number was developed by Dan Sunday in 2001. [6] It does not use angles in calculations, nor any trigonometry, and functions exactly the same as the ray casting algorithms described above. Sunday's algorithm works by considering an infinite horizontal ray cast from the point being checked.
No intersection at all; Intersection in exactly one point; Intersection in two points. Methods for distinguishing these cases, and determining the coordinates for the points in the latter cases, are useful in a number of circumstances. For example, it is a common calculation to perform during ray tracing. [1]