在数学里，齐次坐标（homogeneous coordinates），或投影坐标（projective coordinates）是指一个用于投影几何里的坐标系统，如同用于欧氏几何里的笛卡儿坐标一般。该词由奥古斯特·费迪南德·莫比乌斯于1827年在其著作《Der barycentrische Calcul》一书内引入。齐次坐标可让包括无穷远点的点坐标以有限坐标表示。使用齐次坐标的公式通常会比用笛卡儿坐标表示更为简单，且更为对称。齐次坐标有着广泛的应用，包括电脑图形及3D电脑视觉。使用齐次坐标可让电脑进行仿射变换，并通常，其投影变换能简单地使用矩阵来表示。

In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcül, are a system of coordinates used in projective geometry, as Cartesian coordinates are used in Euclidean geometry. They have the advantage that the coordinates of points, including points at infinity, can be represented using finite coordinates. Formulas involving homogeneous coordinates are often simpler and more symmetric than their Cartesian counterparts. Homogeneous coordinates have a range of applications, including computer graphics and 3D computer vision, where they allow affine transformations and, in general, projective transformations to be easily represented by a matrix.