Definition of Trilinear coordinates. Meaning of Trilinear coordinates. Synonyms of Trilinear coordinates

Here you will find one or more explanations in English for the word Trilinear coordinates. Also in the bottom left of the page several parts of wikipedia pages related to the word Trilinear coordinates and, of course, Trilinear coordinates synonyms and on the right images related to the word Trilinear coordinates.

Definition of Trilinear coordinates

Trilinear coordinates
Note: Co["o]rdinates are of several kinds, consisting in some of the different cases, of the following elements, namely: (a) (Geom. of Two Dimensions) The abscissa and ordinate of any point, taken together; as the abscissa PY and ordinate PX of the point P (Fig. 2, referred to the co["o]rdinate axes AY and AX. (b) Any radius vector PA (Fig. 1), together with its angle of inclination to a fixed line, APX, by which any point A in the same plane is referred to that fixed line, and a fixed point in it, called the pole, P. (c) (Geom. of Three Dimensions) Any three lines, or distances, PB, PC, PD (Fig. 3), taken parallel to three co["o]rdinate axes, AX, AY, AZ, and measured from the corresponding co["o]rdinate fixed planes, YAZ, XAZ, XAY, to any point in space, P, whose position is thereby determined with respect to these planes and axes. (d) A radius vector, the angle which it makes with a fixed plane, and the angle which its projection on the plane makes with a fixed line line in the plane, by which means any point in space at the free extremity of the radius vector is referred to that fixed plane and fixed line, and a fixed point in that line, the pole of the radius vector. Cartesian co["o]rdinates. See under Cartesian. Geographical co["o]rdinates, the latitude and longitude of a place, by which its relative situation on the globe is known. The height of the above the sea level constitutes a third co["o]rdinate. Polar co["o]rdinates, co["o]rdinates made up of a radius vector and its angle of inclination to another line, or a line and plane; as those defined in (b) and (d) above. Rectangular co["o]rdinates, co["o]rdinates the axes of which intersect at right angles. Rectilinear co["o]rdinates, co["o]rdinates made up of right lines. Those defined in (a) and (c) above are called also Cartesian co["o]rdinates. Trigonometrical or Spherical co["o]rdinates, elements of reference, by means of which the position of a point on the surface of a sphere may be determined with respect to two great circles of the sphere. Trilinear co["o]rdinates, co["o]rdinates of a point in a plane, consisting of the three ratios which the three distances of the point from three fixed lines have one to another.

Meaning of Trilinear coordinates from wikipedia

- In geometry, the trilinear coordinates x : y : z of a point relative to a given triangle describe the relative directed distances from the three sidelines...
- p {\displaystyle p} to these three lines. These are called the trilinear coordinates of p {\displaystyle p} with respect to the triangle whose vertices...
- and trilinear coordinates, the various other equations given in Trilinear coordinates#Formulas can be rewritten in terms of barycentric coordinates. The...
- of the triangle, the trilinear coordinates for the incenter are   1 : 1 : 1. {\displaystyle \ 1:1:1.} The barycentric coordinates for a point in a triangle...
- line at infinity, given in trilinear coordinates by a x + b y + c z = 0 {\displaystyle ax+by+cz=0} and in barycentric coordinates by x + y + z = 0. {\displaystyle...
- bisector line. The trilinear coordinates for a point in the triangle give the ratio of distances to the triangle sides. Trilinear coordinates for the incenter...
- Centers the circle E is the called the Apollonius circle of △ABC. The trilinear coordinates of the Apollonius point are a ( b + c ) 2 b + c − a : b ( c + a...
- on a rectilinear 3D grid Trilinear map, a type of mathematical function between vector spaces Trilinear coordinates Trilinear polarity, in geometry This...
- |AN|^{2}+|BL|^{2}+|CM|^{2}=|NB|^{2}+|LC|^{2}+|MA|^{2}.} If P has trilinear coordinates p : q : r, then the vertices L, M, N of the pedal triangle of P...
- analysis of triangles. Trilinear coordinates are used in the context of triangles. There are ways of describing curves without coordinates, using intrinsic...