﻿Transform Methods

# Transform Methods

The Transform type exposes the following members. Methods
NameDescription Affineize
Replaces the last row with (0 0 0 1), discarding any perspective part of this transform  ChangeBasis(Plane, Plane)
Computes a change of basis transformation. A basis change is essentially a remapping of geometry from one coordinate system to another.  ChangeBasis(Vector3d, Vector3d, Vector3d, Vector3d, Vector3d, Vector3d)
Computes a change of basis transformation. A basis change is essentially a remapping of geometry from one coordinate system to another. Clone
Returns a deep copy of the transform. For languages that treat structures as value types, this can be accomplished by a simple assignment. CompareTo
Compares this transform with another transform.

M33 has highest value, then M32, etc.. DecomposeAffine(Transform, Vector3d)
Decomposes an affine transformation. A transformation is affine if it is valid and its last row is [0, 0, 0, 1]. An affine transformation can be broken into a linear transformation and a translation. Note, a perspective transformation is not affine. DecomposeAffine(Vector3d, Transform)
Decomposes an affine transformation. A transformation is affine if it is valid and its last row is [0, 0, 0, 1]. An affine transformation can be broken into a linear transformation and a translation. Note, a perspective transformation is not affine. DecomposeAffine(Vector3d, Transform, Transform, Vector3d)
An affine transformation can be decomposed into a Symmetric, Rotation and Translation. Then the Symmetric component may be further decomposed as non-uniform scale in an orthonormal coordinate system. DecomposeRigid
Decomposes a rigid transformation. The transformation must be affine. DecomposeSimilarity
Decomposes a similarity transformation. The transformation must be affine. A similarity transformation can be broken into a sequence of a dilation, translation, rotation, and a reflection. DecomposeSymmetric
A Symmetric linear transformation can be decomposed A = Q * Diag * Q ^ T, where Diag is a diagonal transformation. Diag[i][i] is an eigenvalue of A and the i-th column of Q is a corresponding unit length eigenvector. Note, this transformation must be Linear and Symmetric.  Diagonal(Vector3d)
Constructs a new transformation with diagonal (d0,d1,d2,1.0).  Diagonal(Double, Double, Double)
Constructs a new transformation with diagonal (d0,d1,d2,1.0). Equals(Object)
Determines if another object is a transform and its value equals this transform value.
(Overrides ValueTypeEquals(Object).) Equals(Transform)
Determines if another transform equals this transform value. GetEulerZYZ
Find the Euler angles for a rotation transformation. GetHashCode
Gets a non-unique hashing code for this transform.
(Overrides ValueTypeGetHashCode.) GetQuaternion
If this transform is a proper rotation, then find the eqivalent quaternion. GetType
Gets the Type of the current instance.
(Inherited from Object.) GetYawPitchRoll
Find the Tait-Byran angles (also loosely called Euler angles) for a rotation transformation. IsRigid
Gets a value indicating whether or not the Transform is rigid. A rigid transformation can be broken into a proper rotation and a translation, while an isometry transformation could also include a reflection. IsSimilarity
Gets a value indicating whether or not the Transform maintains similarity. A similarity transformation can be broken into a sequence of a dilation, translation, rotation, and a reflection. IsZeroTransformationWithTolerance
True if all values are 0 within tolerance, except for M33 which is exactly 1. Linearize
Affinitize() and replaces the last column with (0 0 0 1)^T, discarding any translation part of this transform.  Mirror(Plane)
Constructs a new Mirror transformation.  Mirror(Point3d, Vector3d)
Create mirror transformation matrix The mirror transform maps a point Q to Q - (2*(Q-P)oN)*N, where P = pointOnMirrorPlane and N = normalToMirrorPlane.  Multiply
Multiplies (combines) two transformations.

This is the same as the * operator between two transformations. Orthogonalize
Force the linear part of this transformation to be a rotation (or a rotation with reflection). Use DecomposeRigid(T,R) to find the nearest rotation.  PlanarProjection
Constructs a projection transformation.  PlaneToPlane
Create a rotation transformation that orients plane0 to plane1. If you want to orient objects from one plane to another, use this form of transformation.  ProjectAlong
Construct a projection onto a plane along a specific direction.  Rotation(Double, Point3d)
Constructs a new rotation transformation with specified angle and rotation center. The axis of rotation is ZAxis.  Rotation(Double, Vector3d, Point3d)
Constructs a new rotation transformation with specified angle, rotation center and rotation axis.  Rotation(Vector3d, Vector3d, Point3d)
Constructs a new rotation transformation with start and end directions and rotation center.  Rotation(Double, Double, Vector3d, Point3d)
Constructs a new rotation transformation with specified angle, rotation center and rotation axis.  Rotation(Vector3d, Vector3d, Vector3d, Vector3d, Vector3d, Vector3d)
Constructs a transformation that maps X0 to X1, Y0 to Y1, Z0 to Z1. The frames should be right hand orthonormal frames (unit vectors with Z = X x Y). The resulting rotation fixes the origin (0,0,0), maps initial X to final X, initial Y to final Y, and initial Z to final Z.  RotationZYX
Create rotation transformation From Tait-Byran angles (also loosely known as Euler angles).  RotationZYZ
Create rotation transformation From Euler angles.  Scale(Point3d, Double)
Constructs a new uniform scaling transformation with a specified scaling anchor point.  Scale(Plane, Double, Double, Double)
Constructs a new non-uniform scaling transformation with a specified scaling anchor point.  Shear
Constructs a Shear transformation. ToFloatArray
Return the matrix as a linear array of 16 float values ToString
Returns a string representation of this transform.
(Overrides ValueTypeToString.) TransformBoundingBox
Computes a new bounding box that is the smallest axis aligned bounding box that contains the transformed result of its 8 original corner points. TransformList
Given a list, an array or any enumerable set of points, computes a new array of transformed points.   Translation(Vector3d)
Constructs a new translation (move) transformation.   Translation(Double, Double, Double)
Constructs a new translation (move) transformation. Right column is (dx, dy, dz, 1.0). Transpose
Flip row/column values TryGetInverse
Attempts to get the inverse transform of this transform.
Top See Also