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,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(Double alpha,Double beta,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(Double yaw,Double pitch,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(Boolean rowDominant)

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

ToFloatArray(Boolean 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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