3DAffiner

Performs a 3D affine transformation (such as offset, rotate, or scale) on the coordinates of the feature.

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Typical Uses

• Moving, scaling, and rotating 3D geometry.

How does it work?

The 3DAffiner receives features with any geometry type and moves their x, y and z coordinates according to a specified affine transformation.

A 3D affine transformation is a mathematical method of modifying geometry that:

• Preserves lines and collinearity: all points on a straight line or plane are still on a straight line or plane after transformation.

• Preserves parallelism: lines and planes that are initially parallel are still parallel after transformation.

• May not preserve angles, lengths, or areas, depending on the type of transformation performed.

Scaling, mirroring, rotating, shearing, and translating (relocating or offsetting) are all affine transformations. They can be performed singly or in combination.

The 3DAffiner performs 3D transformations, using this formula:

x' = Ax + By + Cz + D

y' = Ex + Fy + Gz + H

z' = Ix + Jy + Kz + L

Where (x,y,z) are the input coordinates and (x',y',z') are the transformed output coordinates.

	Description	Formula/Coefficients	Example
Original 3D Object	This 3D building model is centered at the origin (0,0,0) and its units are meters. It is not georeferenced.
Translate	Move the geometry a fixed distance.	x' = 1x + 0y + 0z + D y' = 0x + 1y + 0z + H z' = 0x + 0y + 1z + L Simplified: x' = x + D y' = y + H z' = z + L D = X offset H = Y offset L = Z offset	Move object 22 meters along all axes: x' = 1x + 0y + 0z + 22 y' = 0x + 1y + 0z + 22 z' = 0x + 0y + 1z + 22
Scale	Shrink or enlarge the geometry.	x' = Ax + 0y + 0z + 0 y' = 0x + Fy + 0z + 0 z' = 0x + 0y + Kz + 0 Simplified: x' = Ax y' = Fy z' = Kz A = X scale factor F = Y scale factor K = Z scale factor	Enlarge object by a scale factor of 1.5: x' = 1.5x + 0y + 0z + 0 y' = 0x + 1.5y + 0z + 0 z' = 0x + 0y + 1.5z + 0
Rotate about X	Rotate the geometry around the X axis.	x' = 1x + 0y + 0z + 0 y' = 0x + cos(ϴ)y + −sin(ϴ)z + 0 z' = 0x + sin(ϴ)y + cos(ϴ)z + 0 Simplified: x' = x y' = cos(ϴ)y − sin(ϴ)z z' = sin(ϴ)y + cos(ϴ)z ϴ = Angle in degrees F = cos(ϴ) G = −sin(ϴ) (Note negative value) J = sin(ϴ) K = cos(ϴ)	Rotate object by 45 degrees around the X axis: x' = 1x + 0y + 0z + 0 y' = 0x + 0.70711y + −0.70711z + 0 z' = 0x + 0.70711y + 0.70711z + 0
Rotate about Y	Rotate the geometry around the Y axis.	x' = cos(ϴ)x + 0y + sin(ϴ)z + 0 y' = 0x + 1y + 0z + 0 z' = −sin(ϴ)x + 0y + cos(ϴ)z + 0 Simplified: x' = cos(ϴ)x + sin(ϴ)z y' = y z' = -sin(ϴ)x + cos(ϴ)z ϴ = Angle in degrees A = cos(ϴ) C = sin(ϴ) I = −sin(ϴ) (Note negative value) K = cos(ϴ)	Rotate object by 45 degrees around the Y axis: x' = 0.70711x + 0y + 0.70711z + 0 y' = 0x + 1y + 0z + 0 z' = -0.70711x + 0y + 0.70711z + 0
Rotate about Z	Rotate the geometry around the Z axis.	x' = cos(ϴ)x + −sin(ϴ)y + 0z + 0 y' = sin(ϴ)x + cos(ϴ)y + 0z + 0 z' = 0x + 0y + 1z + 0 Simplified: x' = cos(ϴ)x − sin(ϴ)z y' = sin(ϴ)x + cos(ϴ)y z' = z ϴ = Angle in degrees A = cos(ϴ) B = −sin(ϴ) (Note negative value) E = sin(ϴ) F = cos(ϴ)	Rotate object by 45 degrees around the Z axis: x' = 0.70711x + −0.70711y + 0z + 0 y' = 0.70711x + 0.70711y + 0z + 0 z' = 0x + 0y + 1z + 0

Usage Notes

• To perform affine transformations in place on geographic features, consider temporary reprojection (Reprojector) to a local coordinate system or using the CommonLocalReprojector.

• The Scaler performs 2D and 3D scaling affine transformations, with additional options for specific geometry types and origin handling.

• The Offsetter performs 2D and 3D translation affine transformations, with additional coordinate space options (polar and spherical coordinates, in addition to cartesian).

• The Rotator and 3DRotator perform rotation affine transformations, with a simplified interface for rotation value, origin (2D) and axis choice (3D).

Configuration

Input Ports

Output Ports

Parameters

Editing Transformer Parameters

Using a set of menu options, transformer parameters can be assigned by referencing other elements in the workspace. More advanced functions, such as an advanced editor and an arithmetic editor, are also available in some transformers. To access a menu of these options, click beside the applicable parameter. For more information, see Transformer Parameter Menu Options.

Defining Values

There are several ways to define a value for use in a Transformer. The simplest is to simply type in a value or string, which can include functions of various types such as attribute references, math and string functions, and workspace parameters. There are a number of tools and shortcuts that can assist in constructing values, generally available from the drop-down context menu adjacent to the value field.

Dialog Options - Tables

Transformers with table-style parameters have additional tools for populating and manipulating values.

Reference

Processing Behavior	Feature-Based
Feature Holding	No
Dependencies	None
Aliases
History

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Examples may contain information licensed under the Open Government Licence – Vancouver and/or the Open Government Licence – Canada.

3D building model by Berlin Partner für Wirtschaft und Technologie GmbH.