What is the surface condition equation?

If these points are all on a line, then they must be plane, and all planes passing through this line are the results;

If they are not all on a line , then three points that are not on a straight line can determine a plane, and a plane equation can be obtained through the undetermined coefficient method: aX + bY + cZ = k. All points satisfy this equation, which means these points*** noodle.

In the case of intersection, the determinant value = 0, which means (x-x1, y-y1,z-z1) can be (m1,n1,p1) and (m2,n2, p2) Linear expression, this is established. Because the two vectors (m1, n1, p1) and (m2, n2, p2) derived from the intersection determine the plane O, where these two straight lines are on the plane.

Extended information:

Suppose the image space coordinates of a certain image point are x, у, -f, its auxiliary space coordinates are X, Y, Z, and the projection center S is The origin of the two coordinate systems, then the coordinate transformation relationship (expressed in matrix form) is:

where f is the main distance of the camera; R is the rotation matrix, which is the sum of the corresponding coordinate axes of the two coordinate systems. They are all functions of the three angular elements of the image in the spatial coordinate system.

Baidu Encyclopedia-Analytical Photogrammetry