Transform Structure |
Represents the values in a 4x4 transform matrix.
This is parallel to C++ ON_Xform.
Namespace: Rhino.Geometry
Assembly: RhinoCommon (in RhinoCommon.dll)
SyntaxThe Transform type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | Transform(Double) |
Initializes a new transform matrix with a specified value along the diagonal.
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| Transform(Transform) |
Initializes a new transform matrix with a specified value.
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Properties| Name | Description | |
|---|---|---|
 | Determinant |
The determinant of this 4x4 matrix.
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 | Identity |
Gets a new identity transform matrix. An identity matrix defines no transformation.
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| IsAffine |
Tests for 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.
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| IsIdentity | Return true if this Transform is the identity transform |
| IsLinear |
Tests for a linear transformation.
A transformation is affine if it is valid and its last row is [0, 0, 0, 1].
If in addition its last column is ( 0, 0, 0, 1)^T then it is linear.
An affine transformation can be broken into a linear transformation and a translation.
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| IsRotation |
Returns true if this is a proper rotation.
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| IsValid |
Gets a value indicating whether or not this Transform is a valid matrix.
A valid transform matrix is not allowed to have any invalid numbers.
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| IsZero |
True if matrix is Zero4x4, ZeroTransformation, or some other type of
zero. The value xform[3][3] can be anything.
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| IsZero4x4 |
True if all values are 0
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| IsZeroTransformation |
True if all values are 0, except for M33 which is 1.
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| Item |
Gets or sets the matrix value at the given row and column indices.
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| M00 | Gets or sets this[0,0]. |
| M01 | Gets or sets this[0,1]. |
| M02 | Gets or sets this[0,2]. |
| M03 | Gets or sets this[0,3]. |
| M10 | Gets or sets this[1,0]. |
| M11 | Gets or sets this[1,1]. |
| M12 | Gets or sets this[1,2]. |
| M13 | Gets or sets this[1,3]. |
| M20 | Gets or sets this[2,0]. |
| M21 | Gets or sets this[2,1]. |
| M22 | Gets or sets this[2,2]. |
| M23 | Gets or sets this[2,3]. |
| M30 | Gets or sets this[3,0]. |
| M31 | Gets or sets this[3,1]. |
| M32 | Gets or sets this[3,2]. |
| M33 | Gets or sets this[3,3]. |
| RigidType |
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.
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| SimilarityType |
Gets a value indicating whether or not the Transform maintains similarity.
The easiest way to think of Similarity is that any circle, when transformed,
remains a circle. Whereas a non-similarity Transform deforms circles into ellipses.
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| Unset |
Gets an XForm filled with RhinoMath.UnsetValue.
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| ZeroTransformation |
ZeroTransformation diagonal = (0,0,0,1)
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Methods| Name | Description | |
|---|---|---|
| Affineize |
Replaces the last row with (0 0 0 1), discarding any perspective part of this transform
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| ChangeBasis(Plane, Plane) |
Computes a change of basis transformation. A basis change is essentially a remapping
of geometry from one coordinate system to another.
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| 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.
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| Clone |
Returns a deep copy of the transform. For languages that treat structures as value types, this can
be accomplished by a simple assignment.
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| 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.
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| 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.
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| 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.
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| DecomposeRigid |
Decomposes a rigid transformation. The transformation must be affine.
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| 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.
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| 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.
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| DecomposeTextureMapping |
Decomposition of a uvw transform into components
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| Diagonal(Vector3d) |
Constructs a new transformation with diagonal (d0,d1,d2,1.0).
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| Diagonal(Double, Double, Double) |
Constructs a new transformation with diagonal (d0,d1,d2,1.0).
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| 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.
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| GetEulerZYZ |
Find the Euler angles for a rotation transformation.
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| GetHashCode |
Gets a non-unique hashing code for this transform.
(Overrides ValueTypeGetHashCode.) |
| GetQuaternion |
If this transform is a proper rotation, then find the equivalent quaternion.
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| 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.
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| 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.
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| 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.
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| IsZeroTransformationWithTolerance |
True if all values are 0 within tolerance, except for M33 which is exactly 1.
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| Linearize |
Affinitize() and replaces the last column with (0 0 0 1)^T, discarding any translation part of this transform.
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| Mirror(Plane) |
Constructs a new Mirror transformation.
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| 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.
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| 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.
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| PlanarProjection |
Constructs a projection transformation.
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| 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.
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| ProjectAlong |
Construct a projection onto a plane along a specific direction.
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| Rotation(Double, Point3d) |
Constructs a new rotation transformation with specified angle and rotation center. The axis of rotation is ZAxis.
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| Rotation(Double, Vector3d, Point3d) |
Constructs a new rotation transformation with specified angle, rotation center and rotation axis.
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| Rotation(Vector3d, Vector3d, Point3d) |
Constructs a new rotation transformation with start and end directions and rotation center.
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| Rotation(Double, Double, Vector3d, Point3d) |
Constructs a new rotation transformation with specified angle, rotation center and rotation axis.
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| 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.
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| RotationZYX |
Create rotation transformation From Tait-Byran angles (also loosely known as Euler angles).
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| RotationZYZ |
Create rotation transformation From Euler angles.
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| Scale(Point3d, Double) |
Constructs a new uniform scaling transformation with a specified scaling anchor point.
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| Scale(Plane, Double, Double, Double) |
Constructs a new non-uniform scaling transformation with a specified scaling anchor point.
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| Shear |
Constructs a Shear transformation.
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| TextureMapping |
Construct a UVW Transform from components.
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| ToDoubleArray |
Return the matrix as a linear array of 16 double values.
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| ToFloatArray |
Return the matrix as a linear array of 16 float values.
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| 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.
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| TransformList |
Given a list, an array or any enumerable set of points, computes a new array of transformed points.
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 | Translation(Vector3d) |
Constructs a new translation (move) transformation.
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| Translation(Double, Double, Double) |
Constructs a new translation (move) transformation.
Right column is (dx, dy, dz, 1.0).
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| Transpose |
Flip row/column values
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| TryGetInverse |
Attempts to get the inverse transform of this transform.
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Operators| Name | Description | |
|---|---|---|
 | Equality |
Determines if two transformations are equal in value.
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| Inequality |
Determines if two transformations are different in value.
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| Multiply(Transform, Point3d) |
Multiplies a transformation by a point and gets a new point.
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| Multiply(Transform, Transform) |
Multiplies (combines) two transformations.
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| Multiply(Transform, Vector3d) |
Multiplies a transformation by a vector and gets a new vector.
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See Also