1 | initial version |
The function GetPerspectiveTransform calculates the matrix of perspective transformation between srcQuad points and dstQuad points. In other words it calculates coefficients of perspective transformation which maps (xi,yi) to (ui,vi), (i=1,2,3,4):
c00*xi + c01*yi + c02
ui = ---------------------
c20*xi + c21*yi + c22
c10*xi + c11*yi + c12
vi = ---------------------
c20*xi + c21*yi + c22
Coefficients are calculated by solving linear system:
/ x0 y0 1 0 0 0 -x0*u0 -y0*u0 \ /c00\ /u0\
| x1 y1 1 0 0 0 -x1*u1 -y1*u1 | |c01| |u1|
| x2 y2 1 0 0 0 -x2*u2 -y2*u2 | |c02| |u2|
| x3 y3 1 0 0 0 -x3*u3 -y3*u3 |.|c10| = |u3|
| 0 0 0 x0 y0 1 -x0*v0 -y0*v0 | |c11| |v0|
| 0 0 0 x1 y1 1 -x1*v1 -y1*v1 | |c12| |v1|
| 0 0 0 x2 y2 1 -x2*v2 -y2*v2 | |c20| |v2|
\ 0 0 0 x3 y3 1 -x3*v3 -y3*v3 / \c21/ \v3/
where: cij - matrix coefficients, c22 = 1
2 | fixed formatting |
The function GetPerspectiveTransform calculates the matrix of perspective transformation between srcQuad points and dstQuad points. In other words it calculates coefficients of perspective transformation which maps (xi,yi) to (ui,vi), (i=1,2,3,4):
c00*xi + c01*yi + c02
ui = ---------------------
c20*xi + c21*yi + c22
c10*xi + c11*yi + c12
vi = ---------------------
c20*xi + c21*yi + c22
Coefficients are calculated by solving linear system:
/ x0 y0 1 0 0 0 -x0*u0 -y0*u0 \ /c00\ /u0\
| x1 y1 1 0 0 0 -x1*u1 -y1*u1 | |c01| |u1|
| x2 y2 1 0 0 0 -x2*u2 -y2*u2 | |c02| |u2|
| x3 y3 1 0 0 0 -x3*u3 -y3*u3 |.|c10| = |u3|
| 0 0 0 x0 y0 1 -x0*v0 -y0*v0 | |c11| |v0|
| 0 0 0 x1 y1 1 -x1*v1 -y1*v1 | |c12| |v1|
| 0 0 0 x2 y2 1 -x2*v2 -y2*v2 | |c20| |v2|
\ 0 0 0 x3 y3 1 -x3*v3 -y3*v3 / \c21/ \v3/
where: cij - matrix coefficients, c22 = 1