FME Transformers: 2024.1

Categories
3D
Coordinates
Related Transformers
3DRotator
Affiner
AffineWarper
Offsetter
PointCloudTransformationApplier
Rotator
Scaler
SecondOrderConformer

# 3DAffiner

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

### 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).

## Editing Transformer Parameters

Transformer parameters can be set by directly entering values, using expressions, or referencing other elements in the workspace such as attribute values or user parameters. Various editors and context menus are available to assist. To see what is available, click beside the applicable parameter.

For more information, see Transformer Parameter Menu Options.

## Reference

 Processing Behavior Feature Holding No Dependencies None Aliases History

## FME Community

The FME Community is the place for demos, how-tos, articles, FAQs, and more. Get answers to your questions, learn from other users, and suggest, vote, and comment on new features.

Search for all results about the 3DAffiner on the FME Community.

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

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