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. This algorithm is based on an optimization of the Proximity ratio, a measure of similarity between two segments of a line. You can have a look at the following code for further explanations: // *** Define the starting point of the line in the plane. // *** The lines are computed in the same direction (if not, there is a slight mistake). Vector3d startingPoint = Vector3d(-4.0, -2.0, 0.0); // *** The last point of the line is the starting point of the next line. Vector3d endPoint = Vector3d(-4.0, -2.0, 3.0); // *** The normal of the plane is computed: the plane is perpendicular to the plane norm. // *** The plane norm is the vector perpendicular to the plane norm pointing in the positive direction. Vector3d planeNorm = Vector3d::CrossProduct(Vector3d::VectorNegative(endPoint) - startingPoint, Vector3d::VectorNegative(endPoint)); Vector3d planeNorm_new = planeNorm.Normalized(); // *** The vector that points in the opposite direction of the plane norm is computed. // *** The angle of the vector with the plane norm must be in the range of -Pi to Pi. Vector3d planeNorm2 = Vector3d::CrossProduct(planeNorm, planeNorm_new); Vector3d planeNorm_new2 = planeNorm2.Normalized(); // *** The norm of the plane norm is computed and its angle with the normal of the plane is calculated. // *** The vector that points in the opposite direction of the normal must be computed. Vector3d normPlaneNorm = planeNorm_new2.CrossProduct(planeNorm_new); // *** The vector that points in the opposite direction of the norm vector must be computed. // *** The angle of the vector with the norm vector must be in the range of -Pi to Pi. Vector3d normNorm = planeNorm_new2.CrossProduct(normPlaneNorm); Vector3d normNorm_new = normNorm.Normalized(); // *** The vector that points in the opposite direction of the norm vector is computed.

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