This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# FindGeometricTransform

 FindGeometricTransform finds a geometric transformation between two geometries and , returning the alignment error together with the transformation function.
• FindGeometricTransform returns an expression of the form , where err is an estimate of the average alignment error, and trfun is a transformation function. The function trfun can be applied to the positions to align them with the positions .
• The geometries and can be given as lists of position coordinates or Mathematica graphics objects.
• FindGeometricTransform works with points in any dimensions as well as with built-in 2D and 3D graphics primitives.
• FindGeometricTransform takes a option. By default it automatically finds the most suitable geometric transformation for the given sets of positions.
• Possible settings for the option include:
 "Translation" translation only "Rigid" translation and rotation "Similarity" translation, rotation, and scaling "Affine" linear transformation and translation "Perspective" linear fractional transformation
• Available fitting methods:
 "Linear" linear solver based on SVD "RANSAC" random sample consensus method "FindFit" uses FindFit
• With the setting , some positions may be considered as outliers and may not be used to determine the geometric transformation.
Determine the spatial transformation between two sets of positions:
Find the similarity transformation between two sets of two points:
Determine the spatial transformation between two sets of positions:
 Out[1]=

Find the similarity transformation between two sets of two points:
 Out[1]=
 Scope   (2)
Transformation between graphic primitives:
Apply the transformation and display the result:
A three-dimensional geometric transformation:
 Options   (2)
The method is typically faster than :
The method works best if there are outliers or erroneous correspondences:
 Applications   (2)
Use an estimated transformation of the corresponding points for aligning two images:
A basic image-stitching method:
Find a 3D transformation, and apply it using GeometricTransformation:
Find the parameters of an affine transformation:
New in 8