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The 28 pages that link to Homogeneous coordinates, each with the reason it gives.

• Coordinate systemRelated: They let computer graphics represent perspective projection with matrix operations.

• Projective geometryRelated: They encode projective points and transformations with linear algebra.

• Cartesian coordinate systemRelated: Computer vision and projective geometry augment Cartesian coordinates to represent perspective transformations.

• Affine transformationRelated: They combine the linear part and translation into one matrix multiplication.

• Projective planeRelated: Triples encode both ordinary points and ideal points uniformly.

• Identity matrixRelated: The identity matrix represents doing no transformation in homogeneous coordinates.

• Coordinate transformationRelated: They let computer graphics combine coordinate changes in a single matrix calculation.

• Affine geometryRelated: They package translations and linear changes into a single matrix operation.

• CollinearityRelated: In the projective plane, three points are collinear when their coordinate determinant vanishes.

• Projective spaceRelated: They encode each line through the origin as a coordinate tuple.

• Invertible matrixRelated: Invertible matrices encode reversible projective and affine transformations in these coordinates.

• Cross-ratioRelated: They express points on a projective line and make the invariant formula independent of coordinate choice.

• Scalar multiplicationRelated: Equivalent coordinate tuples can encode the same projective point after scaling.

• Point (geometry)Related: They represent points at infinity alongside ordinary points in projective geometry.

• Rational pointRelated: They describe projective rational points without privileging an affine chart.

• August Ferdinand MöbiusRelated: They provide a coordinate framework for projective geometry closely associated with Möbius’s methods.

• Homogeneous polynomialRelated: Homogeneous polynomials provide equations that remain well-defined under coordinate rescaling.

• Robot kinematicsRelated: They let rotation and translation combine in one pose matrix.

• Rotation (geometry)Related: They let rotations about centers other than the origin use matrix multiplication.

• Chasles' theoremRelated: They encode the displacement as one matrix whose rotation and translation reveal the screw motion.

• CoplanarityRelated: They let projective geometry express incidence, including whether points share a plane.

• Desargues's theoremRelated: They encode the theorem's joins and intersections with concise algebraic equations.

• Steiner conicRelated: They express projective correspondences and the resulting conic without choosing a preferred affine chart.