Plane construction from 3D Points in OpenCV

Question

I would like to construct a plane from a list of 3D points in OpenCV. I would like to obtain the result by finding the four parameters in the following form: Ax+By+Cz+

Answer 1

Answer by leveraging OpenCV

If you want to have equation solved by 3 points, just like follows:

ax + by + cz = 1

Example

you have three points: cv::Point3f p1, p2 and p3, and here is the code:

cv::Matx33f M(p1.x, p1.y, p1.z,
              p2.x, p2.y, p2.z,
              p3.x, p3.y, p3.z);
cv::Vec3f d(1, 1, 1);
cv::Vec3f coef = M.inv() * d;

Then, a, b, c are coef(0), coef(1), coef(2) sequentially.