Linked from

The 27 pages that link to Barycentric coordinates, each with the reason it gives.

• Affine transformationRelated: They encode points using precisely the combinations an affine map preserves.

• Equilateral triangleRelated: Its center has equal barycentric weights for all three vertices.

• Homogeneous coordinatesCompared with: Barycentric coordinates depend on a chosen simplex, while homogeneous coordinates describe projective incidence.

• Affine spaceBroader topic: They describe affine points while keeping the weights’ sum equal to one.

• Affine geometryRelated: Affine combinations describe points without making distance or angle fundamental.

• Ceva's theoremRelated: They encode each cevian's side division and reveal the concurrency condition algebraically.

• Triangle geometryRelated: They encode triangle centers and incidence relations through vertex weights.

• RasterizationRelated: They interpolate colors, texture coordinates, and depth across rasterized triangles.

• Texture mappingRelated: They support interpolation of texture coordinates across each triangle.

• Affine combinationRelated: They encode affine combinations as coordinates relative to chosen points.

• Carathéodory's theoremRelated: They encode the nonnegative coefficients in the theorem's finite representation.

• Convex combinationRelated: Nonnegative barycentric coordinates characterize points inside a simplex.

• Nine-point circleRelated: They provide an algebraic way to express the nine-point circle relative to the triangle.

• Point (geometry)Related: They locate points relative to a triangle or other simplex without selecting axes.

• TetrahedronRelated: They describe points inside a tetrahedron through four vertex weights.

• August Ferdinand MöbiusRelated: Möbius introduced these coordinates as a systematic way to describe points in geometric figures.

• Vector geometryRelated: They use weighted vertex vectors to describe positions inside and around triangles and higher-dimensional simplices.

• Triangle centersRelated: They provide a compact way to specify many triangle centers.

• Radon's theoremRelated: The shared point is expressed as a convex combination from each side of the partition.

• Viviani's theoremRelated: In an equilateral triangle, normalized barycentric coordinates encode the three side distances as fractions of the altitude.

• Tverberg's theoremRelated: They describe the convex combinations that place one point in every group’s hull.

• Barrow's inequalityRelated: They provide an algebraic way to describe the interior point in triangle inequalities.

• Incenter–excenter lemmaRelated: They give compact coordinates for the incenter and excenters.

• Lester's theoremRelated: Triangle centers can be expressed in barycentric coordinates to verify the collinearity and concyclicity relations involved.

• Marden's theoremRelated: They provide a convenient framework for expressing the triangle's median-centered ellipse.

• Monsky's theoremRelated: They express triangle areas through determinants of vertex coordinates.

• Van Lamoen circleRelated: Barycentric coordinates make the six subtriangle centroids and their common circumradius easy to calculate.