GeometricTransformation [g,tfun]
represents the result of applying the transformation function tfun to the geometric objects corresponding to the primitives g.
GeometricTransformation [g,m]
transforms geometric objects in g by effectively replacing every point r by m.r.
GeometricTransformation [g,{m,v}]
effectively replaces every point r by m.r+v.
GeometricTransformation [g,{t1,t2,…}]
represents multiple copies of g transformed by a collection of transformations.
GeometricTransformation
GeometricTransformation [g,tfun]
represents the result of applying the transformation function tfun to the geometric objects corresponding to the primitives g.
GeometricTransformation [g,m]
transforms geometric objects in g by effectively replacing every point r by m.r.
GeometricTransformation [g,{m,v}]
effectively replaces every point r by m.r+v.
GeometricTransformation [g,{t1,t2,…}]
represents multiple copies of g transformed by a collection of transformations.
Details and Options
- GeometricTransformation [g,…] remains unchanged under evaluation, but affects how g is rendered.
- GeometricTransformation works on lists of graphics primitives and directives in 2D and 3D.
- GeometricTransformation [g,{m,v}] effectively applies an affine transform to g.
- GeometricTransformation [g,{{mxx,myx},{mxy,myy}}] transforms the unit vectors and to {mxx,mxy} and {myx,myy}, respectively.
- For different spec, GeometricTransformation [g,{m,spec}] leaves fixed the following special points on the bounding box of g:
-
Center centerLeft midpoint of the left sideRight midpoint of the right sideTop midpoint of the topBottom midpoint of the bottomFront midpoint of the frontBack midpoint of the back
- For objects specified with scaled coordinates Scaled [{x,y}], GeometricTransformation effectively applies its transformation to the corresponding ordinary coordinates.
- Normal [expr] if possible replaces all GeometricTransformation [gi,…] constructs by versions of the gi in which the coordinates have explicitly been transformed.
- The following option can be given:
-
- For matrices m1 and m2, GeometricTransformation [GeometricTransformation[g,m1],m2] is equivalent to GeometricTransformation [g,m2.m1].
Examples
open all close allBasic Examples (3)
Transform a 2D object:
Transform a 3D object:
Multiple transforms can be applied to the same object:
Scope (5)
Transformation applied to a 2D shape:
Transformation applied to a 3D shape:
Objects with scaled coordinates:
Keep the rightmost point of the circle fixed:
Create nested transformations:
Properties & Relations (2)
Using {m,v} as the second argument is the same as using AffineTransform [{m,v}]:
When possible, Normal will perform the transformations explicitly:
Neat Examples (1)
Rotating and moving a cuboid along a space curve:
Related Guides
Related Workflows
- Rotate, Pan, and Zoom 3D Graphics
History
Introduced in 2007 (6.0) | Updated in 2008 (7.0) ▪ 2010 (8.0)
Text
Wolfram Research (2007), GeometricTransformation, Wolfram Language function, https://reference.wolfram.com/language/ref/GeometricTransformation.html (updated 2010).
CMS
Wolfram Language. 2007. "GeometricTransformation." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2010. https://reference.wolfram.com/language/ref/GeometricTransformation.html.
APA
Wolfram Language. (2007). GeometricTransformation. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeometricTransformation.html
BibTeX
@misc{reference.wolfram_2025_geometrictransformation, author="Wolfram Research", title="{GeometricTransformation}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/GeometricTransformation.html}", note=[Accessed: 16-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_geometrictransformation, organization={Wolfram Research}, title={GeometricTransformation}, year={2010}, url={https://reference.wolfram.com/language/ref/GeometricTransformation.html}, note=[Accessed: 16-November-2025]}