GLM plane to plane trasformation - c++

Question

I am trying to use plane to plane transformation method in glm.
But rotations are wrong, I use this code in Eigen, also in CGAL libraries. Everything was working correctly. But something off is in GLM.
Can someone tell me why this orientation code produces wrong results?
inline glm::mat4 plane_to_plane(
const std::array<glm::vec3, 4>& plane_0,
const std::array<glm::vec3, 4>& plane_1
//IK::Vector_3 O1, IK::Vector_3 X1, IK::Vector_3 Y1, IK::Vector_3 Z1
) {
// transformation maps P0 to P1, P0+X0 to P1+X1, ...
//Move to origin -> T0 translates point P0 to (0,0,0)
glm::mat4 T0 = glm::translate(glm::vec3(0 - plane_0[0].x, 0 - plane_0[0].y, 0 - plane_0[0].z));
//Rotate ->
glm::mat3 F0(
plane_0[1].x, plane_0[1].y, plane_0[1].z,
plane_0[2].x, plane_0[2].y, plane_0[2].z,
plane_0[3].x, plane_0[3].y, plane_0[3].z
);
glm::mat3 F1(
plane_1[1].x, plane_1[2].x, plane_1[3].x,
plane_1[1].y, plane_1[2].y, plane_1[3].y,
plane_1[1].z, plane_1[2].z, plane_1[3].z
);
glm::mat3 R = F1 * F0;
glm::mat4 R_ = glm::mat4(R);
//Move to 3d -> T1 translates (0,0,0) to point P1
glm::mat4 T1 = glm::translate(glm::vec3(plane_1[0].x - 0, plane_1[0].y - 0, plane_1[0].z - 0));
return T1 * R_ * T0;
}
I use two planes for the transformation:
std::vector<float> plines_v = {
-0.5, -0.5, 0, 0.5, -0.5, 0, 0.5, 0, 0, 0.307011, 0.5, 0, 0.307011, 0.5, 0.136471, 0.5, 0, 0.136471, 0.5, -0.5, 0.136471, -0.5, -0.5, 0.136471, -0.5, 0.5, 0.136471, -0.5, 0.5, 0, -0.5, -0.5, 0
};
auto plane_0 = std::array<glm::vec3, 4>{
glm::vec3(-0.5, -0.5, 0),
glm::vec3(1, 0, 0),
glm::vec3(0, 1, 0),
glm::vec3(0, 0, 1),
};
auto plane_1 = std::array<glm::vec3, 4>{
glm::vec3(-0.5, -0.5, 0),
glm::vec3(0.912851, 0.035424, -0.406752),
glm::vec3(0.225204, -0.874665, 0.429238),
glm::vec3(-0.340566, -0.483432, -0.806417),
};
auto xform = opengl_transform::plane_to_plane(plane_0, plane_1);
for (int i = 0; i < plines_v.size(); i += 3) {
glm::vec4 v(plines_v[i + 0], plines_v[i + 1], plines_v[i + 2], 1);
v = xform*v;
plines_v[i + 0] = v.x;
plines_v[i + 1] = v.y;
plines_v[i + 2] = v.z;
}
Long story short, I tried to inverse R matrix with the following code that seems to work.
Any ideas how to write F0 and F1 matrices without inverting them afterwards?
inline glm::mat4 plane_to_plane(
const std::array<glm::vec3, 4>& plane_0,
const std::array<glm::vec3, 4>& plane_1
//IK::Vector_3 O1, IK::Vector_3 X1, IK::Vector_3 Y1, IK::Vector_3 Z1
) {
// transformation maps P0 to P1, P0+X0 to P1+X1, ...
//Move to origin -> T0 translates point P0 to (0,0,0)
glm::mat4 T0 = glm::translate(glm::vec3(0 - plane_0[0].x, 0 - plane_0[0].y, 0 - plane_0[0].z));
//Rotate ->
glm::mat3 F0(
plane_0[1].x, plane_0[1].y, plane_0[1].z,
plane_0[2].x, plane_0[2].y, plane_0[2].z,
plane_0[3].x, plane_0[3].y, plane_0[3].z
);
glm::mat3 F1(
plane_1[1].x, plane_1[2].x, plane_1[3].x,
plane_1[1].y, plane_1[2].y, plane_1[3].y,
plane_1[1].z, plane_1[2].z, plane_1[3].z
);
glm::mat3 R = F1 * F0;
glm::mat3 R_inv(1.0);
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
R_inv[j][i] = R[i][j];
}
}
glm::mat4 R_ = glm::mat4(R_inv);
//Move to 3d -> T1 translates (0,0,0) to point P1
glm::mat4 T1 = glm::translate(glm::vec3(plane_1[0].x, plane_1[0].y, plane_1[0].z));
return T1 * R_ * T0;
}