Now that I’ve started to do some OpenGL I needed to determine where in my 3D world a user had touched. In order to do this you can use a function called gluUnProject, which isn’t part of the standard framework. I’ve converted the code (so have many others) and posted it here in case it might help someone else.
I used the following article to then use this methods.
/* implementation de gluProject et gluUnproject */
/* M. Buffat 17/2/95 */
/*
* Transform a point (column vector) by a 4x4 matrix. I.e. out = m * in
* Input: m - the 4x4 matrix
* in - the 4x1 vector
* Output: out - the resulting 4x1 vector.
*/
static void
transform_point(GLfloat out[4], const GLfloat m[16], const GLfloat in[4])
{
#define M(row,col) m[col*4+row]
out[0] = M(0, 0) * in[0] + M(0, 1) * in[1] + M(0, 2) * in[2] + M(0, 3) * in[3];
out[1] = M(1, 0) * in[0] + M(1, 1) * in[1] + M(1, 2) * in[2] + M(1, 3) * in[3];
out[2] = M(2, 0) * in[0] + M(2, 1) * in[1] + M(2, 2) * in[2] + M(2, 3) * in[3];
out[3] = M(3, 0) * in[0] + M(3, 1) * in[1] + M(3, 2) * in[2] + M(3, 3) * in[3];
#undef M
}
/*
* Perform a 4x4 matrix multiplication (product = a x b).
* Input: a, b - matrices to multiply
* Output: product - product of a and b
*/
static void
matmul(GLfloat * product, const GLfloat * a, const GLfloat * b)
{
/* This matmul was contributed by Thomas Malik */
GLfloat temp[16];
GLint i;
#define A(row,col) a[(col<<2)+row]
#define B(row,col) b[(col<<2)+row]
#define T(row,col) temp[(col<<2)+row]
/* i-te Zeile */
for (i = 0; i < 4; i++) {
T(i, 0) = A(i, 0) * B(0, 0) + A(i, 1) * B(1, 0) + A(i, 2) * B(2, 0) + A(i, 3) * B(3, 0);
T(i, 1) = A(i, 0) * B(0, 1) + A(i, 1) * B(1, 1) + A(i, 2) * B(2, 1) + A(i, 3) * B(3, 1);
T(i, 2) = A(i, 0) * B(0, 2) + A(i, 1) * B(1, 2) + A(i, 2) * B(2, 2) + A(i, 3) * B(3, 2);
T(i, 3) = A(i, 0) * B(0, 3) + A(i, 1) * B(1, 3) + A(i, 2) * B(2, 3) + A(i, 3) * B(3, 3);
}
#undef A
#undef B
#undef T
memcpy(product, temp, 16 * sizeof(GLfloat));
}
/*
* Compute inverse of 4x4 transformation matrix.
* Code contributed by Jacques Leroy jle@star.be
* Return GL_TRUE for success, GL_FALSE for failure (singular matrix)
*/
static GLboolean
invert_matrix(const GLfloat * m, GLfloat * out)
{
/* NB. OpenGL Matrices are COLUMN major. */
#define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; }
#define MAT(m,r,c) (m)[(c)*4+(r)]
GLfloat wtmp[4][8];
GLfloat m0, m1, m2, m3, s;
GLfloat *r0, *r1, *r2, *r3;
r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
r0[0] = MAT(m, 0, 0), r0[1] = MAT(m, 0, 1),
r0[2] = MAT(m, 0, 2), r0[3] = MAT(m, 0, 3),
r0[4] = 1.0f, r0[5] = r0[6] = r0[7] = 0.0f,
r1[0] = MAT(m, 1, 0), r1[1] = MAT(m, 1, 1),
r1[2] = MAT(m, 1, 2), r1[3] = MAT(m, 1, 3),
r1[5] = 1.0f, r1[4] = r1[6] = r1[7] = 0.0f,
r2[0] = MAT(m, 2, 0), r2[1] = MAT(m, 2, 1),
r2[2] = MAT(m, 2, 2), r2[3] = MAT(m, 2, 3),
r2[6] = 1.0f, r2[4] = r2[5] = r2[7] = 0.0f,
r3[0] = MAT(m, 3, 0), r3[1] = MAT(m, 3, 1),
r3[2] = MAT(m, 3, 2), r3[3] = MAT(m, 3, 3),
r3[7] = 1.0f, r3[4] = r3[5] = r3[6] = 0.0f;
/* choose pivot - or die */
if (fabsf(r3[0]) > fabsf(r2[0]))
SWAP_ROWS(r3, r2);
if (fabsf(r2[0]) > fabsf(r1[0]))
SWAP_ROWS(r2, r1);
if (fabsf(r1[0]) > fabsf(r0[0]))
SWAP_ROWS(r1, r0);
if (0.0f == r0[0])
return GL_FALSE;
/* eliminate first variable */
m1 = r1[0] / r0[0];
m2 = r2[0] / r0[0];
m3 = r3[0] / r0[0];
s = r0[1];
r1[1] -= m1 * s;
r2[1] -= m2 * s;
r3[1] -= m3 * s;
s = r0[2];
r1[2] -= m1 * s;
r2[2] -= m2 * s;
r3[2] -= m3 * s;
s = r0[3];
r1[3] -= m1 * s;
r2[3] -= m2 * s;
r3[3] -= m3 * s;
s = r0[4];
if (s != 0.0f) {
r1[4] -= m1 * s;
r2[4] -= m2 * s;
r3[4] -= m3 * s;
}
s = r0[5];
if (s != 0.0f) {
r1[5] -= m1 * s;
r2[5] -= m2 * s;
r3[5] -= m3 * s;
}
s = r0[6];
if (s != 0.0f) {
r1[6] -= m1 * s;
r2[6] -= m2 * s;
r3[6] -= m3 * s;
}
s = r0[7];
if (s != 0.0f) {
r1[7] -= m1 * s;
r2[7] -= m2 * s;
r3[7] -= m3 * s;
}
/* choose pivot - or die */
if (fabsf(r3[1]) > fabsf(r2[1]))
SWAP_ROWS(r3, r2);
if (fabsf(r2[1]) > fabsf(r1[1]))
SWAP_ROWS(r2, r1);
if (0.0f == r1[1])
return GL_FALSE;
/* eliminate second variable */
m2 = r2[1] / r1[1];
m3 = r3[1] / r1[1];
r2[2] -= m2 * r1[2];
r3[2] -= m3 * r1[2];
r2[3] -= m2 * r1[3];
r3[3] -= m3 * r1[3];
s = r1[4];
if (0.0f != s) {
r2[4] -= m2 * s;
r3[4] -= m3 * s;
}
s = r1[5];
if (0.0f != s) {
r2[5] -= m2 * s;
r3[5] -= m3 * s;
}
s = r1[6];
if (0.0f != s) {
r2[6] -= m2 * s;
r3[6] -= m3 * s;
}
s = r1[7];
if (0.0f != s) {
r2[7] -= m2 * s;
r3[7] -= m3 * s;
}
/* choose pivot - or die */
if (fabsf(r3[2]) > fabsf(r2[2]))
SWAP_ROWS(r3, r2);
if (0.0f == r2[2])
return GL_FALSE;
/* eliminate third variable */
m3 = r3[2] / r2[2];
r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4],
r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6], r3[7] -= m3 * r2[7];
/* last check */
if (0.0f == r3[3])
return GL_FALSE;
s = 1.0f / r3[3]; /* now back substitute row 3 */
r3[4] *= s;
r3[5] *= s;
r3[6] *= s;
r3[7] *= s;
m2 = r2[3]; /* now back substitute row 2 */
s = 1.0f / r2[2];
r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
m1 = r1[3];
r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1,
r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
m0 = r0[3];
r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;
m1 = r1[2]; /* now back substitute row 1 */
s = 1.0f / r1[1];
r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
m0 = r0[2];
r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0,
r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;
m0 = r0[1]; /* now back substitute row 0 */
s = 1.0f / r0[0];
r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);
MAT(out, 0, 0) = r0[4];
MAT(out, 0, 1) = r0[5], MAT(out, 0, 2) = r0[6];
MAT(out, 0, 3) = r0[7], MAT(out, 1, 0) = r1[4];
MAT(out, 1, 1) = r1[5], MAT(out, 1, 2) = r1[6];
MAT(out, 1, 3) = r1[7], MAT(out, 2, 0) = r2[4];
MAT(out, 2, 1) = r2[5], MAT(out, 2, 2) = r2[6];
MAT(out, 2, 3) = r2[7], MAT(out, 3, 0) = r3[4];
MAT(out, 3, 1) = r3[5], MAT(out, 3, 2) = r3[6];
MAT(out, 3, 3) = r3[7];
return GL_TRUE;
#undef MAT
#undef SWAP_ROWS
}
/* projection du point (objx,objy,obz) sur l'ecran (winx,winy,winz) */
//GLint GLAPIENTRY;
static GLboolean gluProject(GLfloat objx, GLfloat objy, GLfloat objz,
const GLfloat model[16], const GLfloat proj[16],
const GLint viewport[4],
GLfloat * winx, GLfloat * winy, GLfloat * winz)
{
/* matrice de transformation */
GLfloat in[4], out[4];
/* initilise la matrice et le vecteur a transformer */
in[0] = objx;
in[1] = objy;
in[2] = objz;
in[3] = 1.0f;
transform_point(out, model, in);
transform_point(in, proj, out);
/* d'ou le resultat normalise entre -1 et 1 */
if (in[3] == 0.0f)
return GL_FALSE;
in[0] /= in[3];
in[1] /= in[3];
in[2] /= in[3];
/* en coordonnees ecran */
*winx = viewport[0] + (1.0f + in[0]) * viewport[2] / 2.0f;
*winy = viewport[1] + (1.0f + in[1]) * viewport[3] / 2.0f;
/* entre 0 et 1 suivant z */
*winz = (1.0f + in[2]) / 2.0f;
return GL_TRUE;
}
/* transformation du point ecran (winx,winy,winz) en point objet */
//GLint GLAPIENTRY
static GLboolean gluUnProject(GLfloat winx, GLfloat winy, GLfloat winz,
const GLfloat model[16], const GLfloat proj[16],
const GLint viewport[4],
GLfloat * objx, GLfloat * objy, GLfloat * objz)
{
/* matrice de transformation */
GLfloat m[16], A[16];
GLfloat in[4], out[4];
/* transformation coordonnees normalisees entre -1 et 1 */
in[0] = (winx - viewport[0]) * 2.0f / viewport[2] - 1.0f;
in[1] = (winy - viewport[1]) * 2.0f / viewport[3] - 1.0f;
in[2] = 2.0f * winz - 1.0f;
in[3] = 1.0f;
/* calcul transformation inverse */
matmul(A, proj, model);
invert_matrix(A, m);
/* d'ou les coordonnees objets */
transform_point(out, m, in);
if (out[3] == 0.0f)
return GL_FALSE;
*objx = out[0] / out[3];
*objy = out[1] / out[3];
*objz = out[2] / out[3];
return GL_TRUE;
}
