Linked from

The 37 pages that link to Affine transformation, each with the reason it gives.

• Function compositionBroader topic: Composing affine transformations combines geometric actions into one map.

• Rotation matrixCompared with: Unlike general affine transformations, rotation matrices preserve Euclidean distances and angles.

• Barycentric coordinatesRelated: Barycentric coordinates remain unchanged under affine transformations of the entire configuration.

• Conversion of unitsRelated: Temperature-scale changes include an offset and therefore are not pure scaling.

• Congruence (geometry)Compared with: Affine maps can stretch a figure, so they do not generally preserve congruence.

• Point groupCompared with: General affine transformations need not preserve the metric structure of point-group symmetries.

• Affine spaceRelated: Such maps preserve the structure defining an affine space.

• Coordinate transformationBroader topic: It captures coordinate changes that include both rotation or scaling and an origin shift.

• Affine geometryBroader topic: These transformations define which geometric properties affine geometry preserves.

• Linear mapCompared with: A nonzero translation breaks preservation of vector addition, unlike a linear map.

• Linear operatorCompared with: Translations generally break linearity by moving the zero vector.

• Projective transformationCompared with: It is a more restrictive map: projective transformations need not preserve parallelism.

• Vector graphicsRelated: Affine transforms move, rotate, and resize vector objects without changing their basic structure.

• Möbius transformationBroader topic: When c=0, a Möbius transformation reduces to an affine map.

• Cross-ratioCompared with: Affine maps preserve more structure than projective maps, but the cross-ratio remains invariant under both.

• Similarity (geometry)Compared with: Unlike similarity transformations, general affine transformations need not preserve shape.

• Affine combinationRelated: Preservation of these combinations characterizes affine maps.

• Change of variablesCompared with: Affine substitutions shift or rescale coordinates without the curvature of nonlinear maps.

• Euclidean planeRelated: It describes many plane transformations used in graphics and geometry.

• ParallelogramRelated: Affine maps send parallelograms to parallelograms, even when lengths and angles change.

• Similarity transformationNarrower topic: Every similarity is affine, while general affine maps can distort shape.

• Point (geometry)Related: It moves points while preserving affine relations such as collinearity.

• Sierpiński triangleRelated: Each recursive step uses scaled and translated copies of the original triangle.

• Inverse elementRelated: Invertible affine maps can be undone by their inverse transformations.

• Linear functionRelated: In one dimension, such transformations have the form x ↦ mx + b.

• Rigid motionCompared with: It preserves less geometric structure than a rigid motion.

• Affine subspaceRelated: Affine transformations send affine subspaces to affine subspaces.

• Inversive geometryCompared with: Affine maps preserve lines and parallelism; inversion generally bends lines into circles.

• Mazur–Ulam theoremBroader topic: The theorem concludes that every surjective isometry has this form.

• Von Neumann–Morgenstern utility theoremRelated: Positive affine changes preserve expected-utility rankings and explain the representation’s uniqueness.

• D'Arcy Wentworth ThompsonRelated: Thompson’s transformation grids show how such mappings can relate animal forms.

• 2D computer graphicsRelated: It provides the standard operations for positioning and reshaping 2D graphics.

• Dittert conjectureRelated: Affine changes of coordinates relate simplex shapes while changing volume by a determinant factor.

• Geometry (configuration)Related: It describes stretching, shearing, and other changes that preserve affine structure.

• Monsky's theoremRelated: Affine changes of coordinates preserve the equal-area condition up to a common factor.

• Pohlke's theoremRelated: Parallel projection is affine, which explains why spatial frames can yield planar segment triples.

• Ryll-Nardzewski fixed-point theoremNarrower topic: The theorem requires every map in the semigroup to preserve convex structure.