The dubblerate from 4 collinear points shows how the points are located relative to each other.

Properties
The dubblerate of 4 collinear is invariable to the projective axes

How to calculate the dubblerate?

  • A (x1,y1,z1), B(x2,y2,z2), C(x3,y3,z3), D(x4,y4,z4) and P Q R arbitrary but not all 0



  • Let's say that A1, A2, A3 and A4 are real collinear points not equal to each other and their dubblerate is (A1 A2 A3 A4) = (A1 A2 A3) / (A1 A2 A4)

  • A1 A2 A3 A4 zijn collineair
    => Kies eigen projectieve ijk met A1 en A2 als basispunten
    => parameter of the line A1 A2:
            x = A1(x) k + A2(x) l
            y = A1(y) k + A2(y) l
            z = A1(z) k + A2(z) l
    => (devide by k who is not 0)
            x = A1(x) + A2(x) h
            y = A1(y) + A2(y) h
            z = A1(z) + A2(z) h
    =>
    (A1 A2 A3 A4) = [h with A3 substituted in the parameter equation (Left Side)]  /  [h with A4 substituted in the parameter equation(Left Side)]
The dubblerate with 4 rival lines shows how the points are located relative to each other.

Properties
Because of duality the same properties apply as apply to the dubblerate of 4 collinear points

How to calculate the dubblerate?

Use line-coordinates
example: ux + vy +wz= 0 has line coordinates: (u,v,w)