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Trilinear coordinates are an example of homogeneous coordinates. The ratio x : y is the ratio of the perpendicular distances from the point to the sides (extended if necessary) opposite vertices A and B respectively; the ratio y : z is the ratio of the perpendicular distances from the point to the sidelines opposite vertices B and C ...
Trilinear form, a type of mathematical function from a vector space to the underlying field; Trilinear interpolation, an extension of linear interpolation for interpolating functions of three variables on a rectilinear 3D grid; Trilinear map, a type of mathematical function between vector spaces; Trilinear coordinates; Trilinear polarity, in ...
In the context of a triangle, barycentric coordinates are also known as area coordinates or areal coordinates, because the coordinates of P with respect to triangle ABC are equivalent to the (signed) ratios of the areas of PBC, PCA and PAB to the area of the reference triangle ABC. Areal and trilinear coordinates are used for similar purposes ...
Trilinear coordinate diagram: Date: 16 May 2008: Source: Own work: Author: Adoniscik: Permission (Reusing this file) Attribution appreciated but not required. Licensing.
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, ... Trilinear coordinates are used in the context of triangles.
Trilinear interpolation is a method of multivariate interpolation on a 3-dimensional regular grid. It approximates the value of a function at an intermediate point ( x , y , z ) {\displaystyle (x,y,z)} within the local axial rectangular prism linearly, using function data on the lattice points.
Let ABC be a plane triangle and let x : y : z be the trilinear coordinates of an arbitrary point in the plane of triangle ABC.. A straight line in the plane of ABC whose equation in trilinear coordinates has the form (,,) + (,,) + (,,) = where the point with trilinear coordinates (,,): (,,): (,,) is a triangle center, is a central line in the plane of ABC relative to ABC.
Animation illustrating the fact that the locus of the trilinear poles of a pencil of lines passing through a fixed point K is a circumconic of the reference triangle. Let P with trilinear coordinates X : Y : Z be the pole of a line passing through a fixed point K with trilinear coordinates x 0 : y 0 : z 0. Equation of the line is