## PlaneByOriginAndVectors4d Class

A Plane4dByOriginAndVectors is a 4d origin and pair of 4d "vectors" defining a 4d plane.

• The parameterization of the plane is `X = origin + vectorU*u + vectorV * v`
• With particular weight values `origin.w === 1, vectorU.w === 0, vectorV.w === 0` this is like `Plane3dByOriginAndVectors`
• With other weights, the deweighted xyz coordinates of points on the 4d plane still form a 3d plane.

### Methods

Name Description
clone(result?: PlaneByOriginAndVectors4d): Return a clone of this plane
fractionToPoint(u: number, v: number, result?: Point4d): evaluate plane point (full 3d) at given (u,v) coordinate.
isAlmostEqual(): boolean Return true if origin, vectorU, and vectorV pass isAlmostEqual.
setFrom(): void copy all content from other plane
setOriginAndVectors(origin: Point4d, vectorU: Point4d, vectorV: Point4d): Copy the contents of origin, vectorU, vectorV parameters to respective member variables
setOriginAndVectorsXYZW(x0: number, y0: number, z0: number, w0: number, ux: number, uy: number, uz: number, uw: number, vx: number, vy: number, vz: number, vw: number): Set all numeric data from complete list of (x,y,z,w) in origin, vectorU, and vectorV
createOriginAndTargets3d(origin: Point3d, targetU: Point3d, targetV: Point3d, result?: PlaneByOriginAndVectors4d): Static create from origin point, (u=1,v=0) point, and (u=0,v=1) point.
createOriginAndVectors(origin: Point4d, vectorU: Point4d, vectorV: Point4d, result?: PlaneByOriginAndVectors4d): Static Create a plane with (copies of) origin, vectorU, vectorV parameters, all given as full 4d points.
createOriginAndVectorsXYZW(x0: number, y0: number, z0: number, w0: number, ux: number, uy: number, uz: number, uw: number, vx: number, vy: number, vz: number, vw: number, result?: PlaneByOriginAndVectors4d): Static Create from complete list of (x,y,z,w) in origin, vectorU, and vectorV
createXYPlane(result?: PlaneByOriginAndVectors4d): Static create a new plane which maps to the cartesian xy plane.

### Properties

Name Type Description
origin Point4d homogeneous origin
vectorU Point4d homogeneous u-direction vector
vectorV Point4d homogeneous v-direction vector

### Defined in

Last Updated: 10 September, 2019