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.

Implements

Methods

Name Description
clone(result?: Transform): Transform Copy the contents of this transform into a new Transform (or to the result, if specified).  
cloneRigid(axisOrder: AxisOrder = AxisOrder.XYZ): Transform | undefined Return a copy of this Transform, modified so that its axes are rigid
The first axis direction named in axisOrder is preserved
The plane of the first and second directions is preserved, and its vector in the rigid matrix has positive dot product with the corresponding vector if the instance
* The third named column is the cross product of the first and second.
 
computeCachedInverse(useCached: boolean = true): boolean * Compute (if needed) the inverse of the matrix part, thereby ensuring inverse operations can complete.  
freeze(): void Freeze this instance (and its deep content) so it can be considered read-only  
getOrigin(): Point3d return a (clone of) the origin part of the transform, as a Point3d  
getTranslation(): Vector3d 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.  
multiplyComponentXYZ(componentIndex: number, x: number, y: number, z: number): 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
if result is given, resize to match source and replace each corresponding pi
if result is not given, return a new array.
 
multiplyInversePoint3dArrayInPlace(source: Point3d[]): boolean for each point in source: multiply transformInverse point in place in the 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): Point2d Transform the input 2d point.  
multiplyPoint2dArray(source: Point2d[], result?: Point2d[]): Point2d[] for each point: multiply transform point
if result is given, resize to match source and replace each corresponding pi
if result is not given, return a new array.
 
multiplyPoint3d(point: XYAndZ, result?: Point3d): Point3d Transform the input 3d point.  
multiplyPoint3dArray(source: Point3d[], result?: Point3d[]): Point3d[] for each point: multiply transform point
if result is given, resize to match source and replace each corresponding pi
if result is not given, return a new array.
 
multiplyPoint3dArrayInPlace(points: Point3d[]): void for each point: replace point by Transform*point  
multiplyRange(range: Range3d, result?: Range3d): Range3d transform each of the 8 corners of a range.  
multiplyTransformMatrix3d(other: Matrix3d, result?: Transform): Transform multiply this Transform times other Matrix3d, with other considered to be a Transform with 0 translation.  
multiplyTransformTransform(other: Transform, result?: Transform): Transform multiply this Transform times other Transform.  
multiplyTransposeXYZW(x: number, y: number, z: number, w: number, result?: Point4d): Point4d Multiply the transposed transform (as 4x4 with 0001 row) by Point4d given as xyzw..  
multiplyVector(vector: Vector3d, result?: Vector3d): Vector3d Multiply the vector by the Matrix3d part of the transform.  
multiplyVectorXYZ(x: number, y: number, z: number, result?: Vector3d): Vector3d Multiply the vector (x,y,z) by the Matrix3d part of the transform.  
multiplyXYZ(x: number, y: number, z: number, result?: Point3d): 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): 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): void Set this Transform instance from flexible inputs:
Any object (such as another Transform) that has origin and matrix members accepted by Point3d.setFromJSON and Matrix3d.setFromJSON
An array of 3 number arrays, each with 4 entries which are rows in a 3x4 matrix.
 
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, vectorX: Vector3d, vectorY: Vector3d, vectorZ: Vector3d): void Reinitialize by directly installing origin and columns of the matrix  
toJSON(): TransformProps Return a 3 by 4 matrix containing the rows of this Transform
* This transform's origin is the [3] entry of the json arrays
 
createFixedPointAndMatrix(fixedPoint: XYAndZ, matrix: Matrix3d, result?: Transform): Transform Static Create a transform with the specified matrix.  
createIdentity(result?: Transform): Transform Static Return an identity transform, optionally filling existing transform.  
createMatrixPickupPutdown(matrix: Matrix3d, pointA: Point3d, pointB: Point3d, result?: Transform): Transform Static Create a transform with the specified matrix, acting on any pointXvia
pointY = matrix * (pointX - pointA) + pointB
so that the fixedPoint maps back to itself.
 
createOriginAndMatrix(origin: XYZ | undefined, matrix: Matrix3d | undefined, result?: Transform): Transform Static Create by directly installing origin and matrix
this is a the appropriate construction when the columns of the matrix are coordinate axes of a local-to-global mapping
Note there is a closely related createFixedPointAndMatrix whose point input is the fixed point of the global-to-global transformation.
 
createOriginAndMatrixColumns(origin: XYZ, vectorX: Vector3d, vectorY: Vector3d, vectorZ: Vector3d, result?: Transform): Transform Static Create by directly installing origin and columns of the matrix  
createRefs(origin: XYZ, matrix: Matrix3d, result?: Transform): Transform Static Create a copy with the given origin and matrix captured as the Transform origin and Matrix3d.  
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): Transform Static Create a transform with complete contents given  
createScaleAboutPoint(fixedPoint: Point3d, scale: number, result?: Transform): Transform Static Create a Transform which leaves the fixedPoint unchanged and
scales everything else around it by a single scale factor.
 
createTranslation(translation: XYZ, result?: Transform): Transform Static Create a matrix with specified translation part.  
createTranslationXYZ(x: number = 0, y: number = 0, z: number = 0, result?: Transform): Transform Static create a Transform with translation provided by x,y,z parts.  
createZero(result?: Transform): Transform Static Create a transform with all zeros.  
fromJSON(json?: TransformProps): Transform 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 Transform The identity Transform.  
isIdentity Accessor ReadOnly boolean test if the transform has 000 origin and identity Matrix3d  
matrix Accessor ReadOnly Matrix3d Return a reference to the matrix within the transform.  
origin Accessor ReadOnly XYZ Return a reference to the origin within the transform.  

Defined in

Last Updated: 03 June, 2019