Struct Transform3D

Represents a 3D transformation.

[DataContract]
[AvailableSinceVersion(7, 6, 0, 0)]
public struct Transform3D

The transformation is defined by a 4x4 matrix that operates as multiplier on column vectors containing homogeneous coordinates:

[ R00 R01 R02 Tx ]

[ R10 R11 R12 Ty ]

[ R20 R21 R22 Tz ]

[ Px Py Pz Si ]

That transforms (X, Y, Z, H) into (X', Y', Z', H') as follows:

X' = R00 * X + R01 * Y + R02 * Z + Tx * H

Y' = R10 * X + R11 * Y + R12 * Z + Ty * H

Z' = R20 * X + R21 * Y + R22 * Z + Tz * H

H' = Px * X + Py * Y + Pz * Z + Si * H

R is a non singular transformation matrix, that contains the rotation, reflection, non-uniform scaling and shearing components.

T is a translation vector.

P represents the perspective terms in viewing transformations. It must be zero in transformations used for modeling.

Si is the inverse of the global scale factor, it has to be greater than zero.

In the case of conventional coordinates, H is equal to one, and the coordinates of the transformed point are (X'/H', Y'/H', Z'/H').

For instance here is the transformation matrix corresponding to the rotation of angle "a" around the Z axis:

[ cos(a) -sin(a) 0 0 ]

[ sin(a) cos(a) 0 0 ]

[ 0 0 1 0 ]

[ 0 0 0 1 ]

This structure is available since v7.6.

Name	Description
Transform3D(double, double, double, double, double, double, double, double, double, double, double, double, double, double, double, double)	Initializes a new instance of the Transform3D structure.

Name	Description
Identity	Indentity transformation.
Px	Perspective factor along X.
Py	Perspective factor along Y.
Pz	Perspective factor along Z.
R00	Rotation[0,0].
R01	Rotation[0,1].
R02	Rotation[0,2].
R10	Rotation[1,0].
R11	Rotation[1,1].
R12	Rotation[1,2].
R20	Rotation[2,0].
R21	Rotation[2,1].
R22	Rotation[2,2].
Si	Inverse of the global scale factor.
Tx	Translation along X.
Ty	Translation along Y.
Tz	Translation along Z.

Name	Description
SetRotation(Axis3D, double)	Sets the transformation as the rotation about a specified axis with a specified angle.
SetTranslation(Vector3D)	Sets the transformation as the translation along a specified vector.