How to create billboard matrix in glm

Question

How to create a billboard translation matrix from a point in space using glm?

Answer 1

mat4 billboard(vec3 position, vec3 cameraPos, vec3 cameraUp) {
    vec3 look = normalize(cameraPos - position);
    vec3 right = cross(cameraUp, look);
    vec3 up2 = cross(look, right);
    mat4 transform;
    transform[0] = vec4(right, 0);
    transform[1] = vec4(up2, 0);
    transform[2] = vec4(look, 0);
    // Uncomment this line to translate the position as well
    // (without it, it's just a rotation)
    //transform[3] = vec4(position, 0);
    return transform;
}

Answer 2

Just set the upper left 3×3 submatrix of the transformation to identity.

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Update: Fixed function OpenGL variant:

void makebillboard_mat4x4(double *BM, double const * const MV)
{
    for(size_t i = 0; i < 3; i++) {
    
        for(size_t j = 0; j < 3; j++) {
            BM[4*i + j] = i==j ? 1 : 0;
        }
        BM[4*i + 3] = MV[4*i + 3];
    }

    for(size_t i = 0; i < 4; i++) {
        BM[12 + i] = MV[12 + i];
    }
}

void mygltoolMakeMVBillboard(void)
{
    GLenum active_matrix;
    double MV[16];

    glGetIntegerv(GL_MATRIX_MODE, &active_matrix);

    glMatrixMode(GL_MODELVIEW);
    glGetDoublev(GL_MODELVIEW_MATRIX, MV);
    makebillboard_mat4x4(MV, MV);
    glLoadMatrixd(MV);
    glMatrixMode(active_matrix);
}