## Transform Class

A transform is an origin and a Matrix3d.

• This describes a coordinate frame with this origin, with the columns of the Matrix3d being the local x,y,z axis directions.
• Beware that for common transformations (e.g. scale about point, rotate around line, mirror across a plane) the "fixed point" that is used when describing the transform is NOT the "origin" stored in the transform. Setup methods (e.g createFixedPointAndMatrix, createScaleAboutPoint) take care of determining the appropriate origin coordinates.

### Methods

Name Description
clone(result?: Transform): Copy the contents of this transform into a new Transform (or to the result, if specified).
cloneRigid(axisOrder: AxisOrder.XYZ = AxisOrder.XYZ): Transform | undefined Return a copy of this Transform, modified so that its axes are rigid
computeCachedInverse(useCached: boolean = true): boolean * Compute (if needed) the inverse of the matrix part, thereby ensuring inverse operations can complete.
freeze(): Readonly<this> Freeze this instance (and its members) so it is read-only
getOrigin(): return a (clone of) the origin part of the transform, as a Point3d
getTranslation(): return a (clone of) the origin part of the transform, as a Vector3d
inverse(): Transform | undefined * Return a Transform which is the inverse of this transform.
isAlmostEqual(other: Transform): boolean Test for near equality with other Transform.
isAlmostEqualAllowZRotation(other: Transform): boolean Test for near equality with other Transform.
multiplyComponentXYZ(componentIndex: number, x: number, y: number, z: number = 0): number Multiply a specific row of the transform times xyz.
multiplyComponentXYZW(componentIndex: number, x: number, y: number, z: number, w: number): number Multiply a specific row of the transform times (weighted!) xyzw.
multiplyInversePoint3d(point: XYAndZ, result?: Point3d): Point3d | undefined Return product of the transform's inverse times a point.
multiplyInversePoint3dArray(source: Point3d[], result?: Point3d[]): Point3d[] | undefined * for each point: multiply transform * point
multiplyInversePoint3dArrayInPlace(source: Point3d[]): boolean * for each point in source: multiply transformInverse * point in place in the point.
multiplyInversePoint4d(weightedPoint: Point4d, result?: Point4d): Point4d | undefined Inverse transform the input homogeneous point.
multiplyInverseXYZ(x: number, y: number, z: number, result?: Point3d): Point3d | undefined Return product of the transform's inverse times a point (point given as x,y,z)
multiplyPoint2d(source: XAndY, result?: Point2d): Transform the input 2d point.
multiplyPoint2dArray(source: Point2d[], result?: Point2d[]): Point2d[] * for each point: multiply transform * point
multiplyPoint3d(point: XYAndZ, result?: Point3d): Transform the input 3d point.
multiplyPoint3dArray(source: Point3d[], result?: Point3d[]): Point3d[] * for each point: multiply transform * point
multiplyPoint3dArrayArrayInPlace(chains: Point3d[][]): void for each point: replace point by Transform*point
multiplyPoint3dArrayInPlace(points: Point3d[]): void for each point: replace point by Transform*point
multiplyRange(range: Range3d.createNull, result?: Range3d.createNull): Return the range of the transformed corners.
multiplyTransformMatrix3d(other: Matrix3d, result?: Transform): multiply this Transform times other Matrix3d, with other considered to be a Transform with 0 translation.
multiplyTransformTransform(other: Transform, result?: Transform): multiply this Transform times other Transform.
multiplyTransposeXYZW(x: number, y: number, z: number, w: number, result?: Point4d): Multiply the transposed transform (as 4x4 with 0001 row) by Point4d given as xyzw..
multiplyVector(vector: Vector3d, result?: Vector3d): Multiply the vector by the Matrix3d part of the transform.
multiplyVectorXYZ(x: number, y: number, z: number, result?: Vector3d): Multiply the vector (x,y,z) by the Matrix3d part of the transform.
multiplyXYAndZInPlace(point: XYAndZ): void Transform the input object with x,y,z members
multiplyXYZ(x: number, y: number, z: number = 0, result?: Point3d): Transform the input point.
multiplyXYZToFloat64Array(x: number, y: number, z: number, result?: Float64Array): Float64Array Transform the input homogeneous point.
multiplyXYZW(x: number, y: number, z: number, w: number, result?: Point4d): Transform the input homogeneous point.
multiplyXYZWToFloat64Array(x: number, y: number, z: number, w: number, result?: Float64Array): Float64Array Transform the input homogeneous point.
setFrom(other: Transform): void Copy contents from other Transform into this Transform
setFromJSON(json?: TransformProps | Transform): void Set this Transform instance from flexible inputs:
setIdentity(): void Set this Transform to be an identity.
setMultiplyTransformTransform(transformA: Transform, transformB: Transform): void multiply transformA * transformB, store to calling instance.
setOriginAndMatrixColumns(origin: XYZ | undefined, vectorX: Vector3d | undefined, vectorY: Vector3d | undefined, vectorZ: Vector3d | undefined): void Reinitialize by directly installing origin and columns of the matrix
toJSON(): Return a 3 by 4 matrix containing the rows of this Transform
toRows(): number[][] Return a 3 by 4 matrix containing the rows of this Transform
createFixedPointAndMatrix(fixedPoint: XYAndZ | undefined, matrix: Matrix3d, result?: Transform): Static Create a transform with the specified matrix.
createIdentity(result?: Transform): Static Return an identity transform, optionally filling existing transform.
createMatrixPickupPutdown(matrix: Matrix3d, pointA: Point3d, pointB: Point3d, result?: Transform): Static Create a transform with the specified matrix, acting on any pointXvia
createOriginAndMatrix(origin: XYZ | undefined, matrix: Matrix3d | undefined, result?: Transform): Static Create by directly installing origin and matrix
createOriginAndMatrixColumns(origin: XYZ, vectorX: Vector3d, vectorY: Vector3d, vectorZ: Vector3d, result?: Transform): Static Create by directly installing origin and columns of the matrix
createRefs(origin: XYZ | undefined, matrix: Matrix3d, result?: Transform): Static Create a copy with the given origin and matrix captured as the Transform origin and Matrix3d.
createRigidFromOriginAndColumns(origin: XYZ | undefined, vectorX: Vector3d, vectorY: Vector3d, axisOrder: AxisOrder.XYZ, result?: Transform): Transform | undefined Static Create by with matrix from Matrix3d.createRigidFromColumns.
createRowValues(qxx: number, qxy: number, qxz: number, ax: number, qyx: number, qyy: number, qyz: number, ay: number, qzx: number, qzy: number, qzz: number, az: number, result?: Transform): Static Create a transform with complete contents given
createScaleAboutPoint(fixedPoint: Point3d, scale: number, result?: Transform): Static Create a Transform which leaves the fixedPoint unchanged and
createTranslation(translation: XYZ, result?: Transform): Static Create a matrix with specified translation part.
createTranslationXYZ(x: number = 0, y: number = 0, z: number = 0, result?: Transform): Static create a Transform with translation provided by x,y,z parts.
createZero(result?: Transform): Static Create a transform with all zeros.
fromJSON(json?: TransformProps): Static Return a new Transform initialized by setFromJSON (json)
initFromRange(min: Point3d, max: Point3d, npcToGlobal?: Transform, globalToNpc?: Transform): void Static Initialize transforms that map each direction of a box (axis aligned) to [0,1].
matchArrayLengths(source: any[], dest: any[], constructionFunction: () => any): number Static * If destination has more values than source, remove the extras.

### Properties

Name Type Description
identity Accessor StaticReadOnly The identity Transform.
isIdentity Accessor ReadOnly boolean test if the transform has 000 origin and identity Matrix3d
matrix Accessor ReadOnly Return a reference to the matrix within the transform.
origin Accessor ReadOnly Return a reference to the origin within the transform.

### Defined in

Last Updated: 06 October, 2021