# Thread: can't extract correct Euler angles from Euler Angle transformation matrix

1. ## can't extract correct Euler angles from Euler Angle transformation matrix

I successfully combined all (3) Euler angle rotations into one single matrix. It was a learning process as I had to convert it from a 3x3 matrix to a 4x4, a row-major format to a column-major format, then convert it once more by a -1 offset since matrices in computers consider 0,0 the origin. I also checked my work with ::GLM, and with custom written rotations for each axis and their results multiplied together. All the matrices agree with each other.

Now I need some help. You should be able to extract all 3 Euler angles from the matrix, but my numbers aren't coming up right.
example:
Yaw angle:
atan2(r21,r11)

This uses the Euler product matrix below (labeled). But all the matrices agree anyway, custom and GLM. When I plug r21 and r11 in I should get a 30 degree angle from which the matrix was generated. I used 3 - 30 degree angles for the Euler product generation. The example extraction here isn't even close (81 degrees).

Output at very bottom.

Code :
using namespace glm;

glm::mat4 Euler_product(float u, float v, float w){
float cu = std::cos(u), cv = std::cos(v), cw = std::cos(w);
float su = std::sin(u), sv = std::sin(v), sw = std::sin(w);
return glm::mat4(
cv * cw, cv * sw, -1 * sv, 0.0f,
(su* sv * cw-cu * sw), (cu * cw) + (su * sv * sw) , su * cv, 0.0f,
(su * sw) + (cu * sv * cw), (cu * sv * sw) - (su * cw), cu*cv, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f);
}

glm::mat4 rotx(float a){
float s = std::sin(a);
float c = std::cos(a);
return glm::mat4(
1.0f,0.0f,0.0f,0.0f,
0.0f,c,s, 0.0f,
0.0f, -s,  c, 0.0f,
0.0f,0.0f,0.0f,1.0f );
};
glm::mat4 roty(float a) {
float s = std::sin(a);
float c = std::cos(a);
return glm::mat4(
c, 0.0f,   -s, 0.0f,
0.0f, 1.0f, 0.0f, 0.0f,
s, 0.0f,    c, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f);
};

glm::mat4 rotz(float a) {
float s = std::sin(a);
float c = std::cos(a);
return glm::mat4(
c,s,0.0f,0.0f,
-s,c,0.0f,0.0f,
0.0f,0.0f,1.0f,0.0f,
0.0f,0.0f,0.0f,1.0f );
};

void print_mat_4x4(glm::mat4 &matrix, std::string input_string);
//void print_vector(glm::vec3 & _vector)
//{
//	std::cout<<glm::to_string(_vector)<<std::endl;
//}
void print_vector(glm::vec4 & _vector);
::GLM rotation product z * y * x
Code :
int main()
{			//GLM

glm::mat4 glm_rotx = glm::mat4(1.0f);
glm_rotx = glm::rotate(glm_rotx, 30.0f, glm::vec3(1,0,0));
glm::mat4 glm_roty = glm::mat4(1.0f);
glm_roty = glm::rotate(glm_roty, 30.0f, glm::vec3(0,1,0));
glm::mat4 glm_rotz = glm::mat4(1.0f);
glm_rotz = glm::rotate(glm_rotz, 30.0f, glm::vec3(0,0,1));
glm::mat4 prod_xyz_glm = glm::mat4(1.0f);
prod_xyz_glm = glm_rotz * glm_roty * glm_rotx;
print_mat_4x4(prod_xyz_glm, "GLM calculated xyz Euler product");
custom code : individual rotations multiplied by each other
Code :
//custom
glm::mat4 _trans_rotx = glm::mat4(1.0f);
_trans_rotx = rotx(30.0f);

glm::mat4 _trans_roty = glm::mat4(1.0f);
_trans_roty = roty(30.0f);

glm::mat4 _trans_rotz = glm::mat4(1.0f);
_trans_rotz = rotz(30.0f);

mat4 trans_product = glm::mat4(1.0f);
trans_product = _trans_rotz * _trans_roty * _trans_rotx;

print_mat_4x4(trans_product, "Custom code calculated rotational xyz product");
custom mat "Euler product"
Code :
mat4 trans_xyz_custom = glm::mat4(1.0f);
trans_xyz_custom = Euler_product(30.0, 30.0, 30.0);

print_mat_4x4(trans_xyz_custom, "Single rotational xyz matrix custom");

//float yaw_angle = 0.0f, pitch_angle = 0.0f, roll_angle = 0.0f;
std::cout<<"Euler angle extraction:"<<std::endl;
//x angle
float r21 = trans_xyz_custom[1][0];
float r11 = trans_xyz_custom[0][0];
float rad_angle_x =atan2(r21,r11) ; //swapped i,j->shifted -1x -1y
float r31 = trans_xyz_custom[0][2]; //this was: 02 rj swap, then applied -1x -y1 offset for computer mat tol computer =0,0
//tol matrix in question = 1,1
//z angle degrees
float r32 = trans_xyz_custom[1][2]; //this was: 02 rj swap, then applied -1x -y1 offset for computer mat tol computer =0,0
float r33 = trans_xyz_custom[2][2];

Custom code calculated rotational xyz product
Code :
0.0237935	-0.152405	0.988032	0
0.302987	-0.940729	-0.152405	0
0.952698	0.302987	0.0237935	0
0	0	0	1
Single rotational xyz matrix custom
Code :
0.0237935	-0.152405	0.988032	0
0.302987	-0.940729	-0.152405	0
0.952698	0.302987	0.0237935	0
0	0	0	1
Euler angle extraction:
Code :
y angle radians: -1.41593	degs: -81.1266
z angle radians: -1.41593	degs: -81.1266

2. Originally Posted by technologist
Code :
return glm::mat4(
cv * cw, cv * sw, -1 * sv, 0.0f,
(su* sv * cw-cu * sw), (cu * cw) + (su * sv * sw) , su * cv, 0.0f,
(su * sw) + (cu * sv * cw), (cu * sv * sw) - (su * cw), cu*cv, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f);

Code :
float r21 = trans_xyz_custom[1][0];
float r11 = trans_xyz_custom[0][0];
float rad_angle_x =atan2(r21,r11) ; //swapped i,j->shifted -1x -1y
Note that [1][0] is column 1, row 0. From the code for Euler_product(), this would give you r21=(su* sv * cw-cu * sw). If you had used [0][1], then you'd end up with r21=cv * sw, r11=cv * cw, r21/r11=sw/cw=tan(w).

3. ## followup on GLM:: rotation mat z*x*y and ::custom Euler mat angle1,angle2,angle3

Originally Posted by GClements
Note that [1][0] is column 1, row 0. From the code for Euler_product(), this would give you r21=(su* sv * cw-cu * sw). If you had used [0][1], then you'd end up with r21=cv * sw, r11=cv * cw, r21/r11=sw/cw=tan(w).
I've tried using those values. lAlso have gotten little desperate and am trying adjacent values picked from the matrix. Its only a 3x3 and with some random picking I should eventually hit 30 degrees but I am not coming close. The matrices created by ::GLM, and myself, are in agreement so I am at a loss to reconcile.

4. ## something i need to know

Originally Posted by technologist
I've tried using those values. lAlso have gotten little desperate and am trying adjacent values picked from the matrix. Its only a 3x3 and with some random picking I should eventually hit 30 degrees but I am not coming close. The matrices created by ::GLM, and myself, are in agreement so I am at a loss to reconcile.
(su* sv * cw-cu * sw), << was this intended as is or ((su*sv*(cw-cu)*sw))?

5. ## Euler matrix question

Originally Posted by didydriver
(su* sv * cw-cu * sw), << was this intended as is or ((su*sv*(cw-cu)*sw))?
Hi,

This was intended as (su* sv * cw)-(cu * sw) by me, but I reviewed the original matrix and the author(s) didn't bother to include the grouping braces, so I took them off as well.
Still runs the same though.

Code :
lm::mat4 Euler_product(float u, float v, float w){
float cu = std::cos(u), cv = std::cos(v), cw = std::cos(w);
float su = std::sin(u), sv = std::sin(v), sw = std::sin(w);
return glm::mat4(
cv * cw, cv * sw, -1 * sv, 0.0f,
su* sv * cw-cu * sw, cu * cw + su * sv * sw , su * cv, 0.0f,
su * sw + cu * sv * cw, cu * sv * sw - su * cw, cu*cv, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f);