ChangeBasis(Vector3d initialBasisX, Vector3d initialBasisY, Vector3d initialBasisZ, Vector3d finalBasisX, Vector3d finalBasisY, Vector3d finalBasisZ)

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(Transform other)

Compares this transform with another transform.
M33 has highest value, then M32, etc..

DecomposeAffine(out Transform linear, out Vector3d translation)

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(out Vector3d translation, out Transform linear)

DecomposeAffine(out Vector3d translation, out Transform rotation, out Transform orthogonal, out Vector3d diagonal)

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(out Vector3d translation, out Transform rotation, double tolerance)

Decomposes a rigid transformation. The transformation must be affine.

DecomposeSimilarity(out Vector3d translation, out double dilation, out Transform rotation, double tolerance)

DecomposeSymmetric(out Transform matrix, out Vector3d diagonal)

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.

DecomposeTextureMapping(out Vector3d offset, out Vector3d repeat, out Vector3d rotation)

Decomposition of a uvw transform into components

Diagonal(double d0, double d1, double d2)

Constructs a new transformation with diagonal (d0,d1,d2,1.0).

Diagonal(Vector3d diagonal)

Constructs a new transformation with diagonal (d0,d1,d2,1.0).

Equals(object obj)

Determines if another object is a transform and its value equals this transform value.

Equals(Transform other)

Determines if another transform equals this transform value.

GetEulerZYZ(out double alpha, out double beta, out double gamma)

Find the Euler angles for a rotation transformation.

GetHashCode()

Gets a non-unique hashing code for this transform.

GetQuaternion(out Quaternion quaternion)

If this transform is a proper rotation, then find the equivalent quaternion.

GetYawPitchRoll(out double yaw, out double pitch, out double roll)

Find the Tait-Byran angles (also loosely called Euler angles) for a rotation transformation.

IsRigid(double tolerance)

IsSimilarity(double tolerance)

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(double zeroTolerance)

True if all values are 0 within tolerance, except for M33 which is exactly 1.

IsZeroTransformaton(double zeroTolerance)

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 mirrorPlane)

Constructs a new Mirror transformation.

Mirror(Point3d pointOnMirrorPlane, Vector3d normalToMirrorPlane)

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(Transform a, Transform b)

Multiplies (combines) two transformations.
This is the same as the * operator between two transformations.

Orthogonalize(double tolerance)

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(Plane plane)

Constructs a projection transformation.

PlaneToPlane(Plane plane0, Plane plane1)

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(Plane plane, Vector3d direction)

Construct a projection onto a plane along a specific direction.

Rotation(double angleRadians, Point3d rotationCenter)

Constructs a new rotation transformation with specified angle and rotation center. The axis of rotation is <b>Vector3d.ZAxis</b> .

Rotation(double angleRadians, Vector3d rotationAxis, Point3d rotationCenter)

Constructs a new rotation transformation with specified angle, rotation center and rotation axis.

Rotation(double sinAngle, double cosAngle, Vector3d rotationAxis, Point3d rotationCenter)

Constructs a new rotation transformation with specified angle, rotation center and rotation axis.

Rotation(Vector3d startDirection, Vector3d endDirection, Point3d rotationCenter)

Constructs a new rotation transformation with start and end directions and rotation center.

Rotation(Vector3d x0, Vector3d y0, Vector3d z0, Vector3d x1, Vector3d y1, Vector3d z1)

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(double yaw, double pitch, double roll)

Create rotation transformation From Tait-Byran angles (also loosely known as Euler angles).

RotationZYZ(double alpha, double beta, double gamma)

Create rotation transformation From Euler angles.

Scale(Plane plane, double xScaleFactor, double yScaleFactor, double zScaleFactor)

Constructs a new non-uniform scaling transformation with a specified scaling anchor point.

Scale(Point3d anchor, double scaleFactor)

Constructs a new uniform scaling transformation with a specified scaling anchor point.

Shear(Plane plane, Vector3d x, Vector3d y, Vector3d z)

Constructs a Shear transformation.

TextureMapping(Vector3d offset, Vector3d repeat, Vector3d rotation)

Construct a UVW Transform from components.

ToDoubleArray(bool rowDominant)

Return the matrix as a linear array of 16 double values.

ToFloatArray(bool rowDominant)

Return the matrix as a linear array of 16 float values.

ToString()

Returns a string representation of this transform.

TransformBoundingBox(BoundingBox bbox)

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(IEnumerable<Point3d> points)

Given a list, an array or any enumerable set of points, computes a new array of transformed points.

Translation(double dx, double dy, double dz)

Constructs a new translation (move) transformation. Right column is (dx, dy, dz, 1.0).

Translation(Vector3d motion)

Constructs a new translation (move) transformation.

Transpose()

Flip row/column values

TryGetInverse(out Transform inverseTransform)

Attempts to get the inverse transform of this transform.

Operators (5)

Determines if two transformations are different in value.

Multiplies a transformation by a point and gets a new point.

Multiplies (combines) two transformations.

Multiplies a transformation by a vector and gets a new vector.

Determines if two transformations are equal in value.

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