First, many graphics applications involve geometric transformation, mainly including translation, rotation and scaling. When calculating these transformations with matrix expressions, translation is matrix addition, rotation and scaling are matrix multiplication, which can be expressed as p' = p *m 1+ m2(m 1 rotation scaling matrix, m2 is translation matrix, p is original vector and p' is transformation vector). The purpose of introducing homogeneous coordinates is mainly to combine multiplication and addition in matrix operation, which is expressed in the form of p' = p * m, that is, matrix operation provides an effective method to transform point sets in two-dimensional, three-dimensional and even high-dimensional space from one coordinate system to another.

Secondly, it can represent a point at infinity. If h=0 in n+ 1 Vezi secondary coordinate, it actually represents an infinite point in n-dimensional space. For homogeneous coordinates (a, b, h), keeping a and b unchanged, |V|=(x 1*x 1, y 1 * y 1, z1* z/kloc-0.