gluUnProject for iPhone/iOS

#ifndef __GLU_PROJECT_IOS
#define __GLU_PROJECT_IOS

#include <OpenGLES/ES1/gl.h>
#include <OpenGLES/ES1/glext.h>

void
gluPerspective(GLfloat fovy, GLfloat aspect, GLfloat zNear, GLfloat zFar);

void
gluLookAt(GLfloat eyex, GLfloat eyey, GLfloat eyez, GLfloat centerx,
    GLfloat centery, GLfloat centerz, GLfloat upx, GLfloat upy,
    GLfloat upz);

GLint
gluProject(GLfloat objx, GLfloat objy, GLfloat objz, 
     const GLfloat modelMatrix[16], 
     const GLfloat projMatrix[16],
     const GLint viewport[4],
     GLfloat *winx, GLfloat *winy, GLfloat *winz);

GLint
gluUnProject(GLfloat winx, GLfloat winy, GLfloat winz,
    const GLfloat modelMatrix[16], 
    const GLfloat projMatrix[16],
    const GLint viewport[4],
    GLfloat *objx, GLfloat *objy, GLfloat *objz);


GLint
gluUnProject4(GLfloat winx, GLfloat winy, GLfloat winz, GLfloat clipw,
     const GLfloat modelMatrix[16], 
     const GLfloat projMatrix[16],
     const GLint viewport[4],
     GLclampf nearVal, GLclampf farVal,      
     GLfloat *objx, GLfloat *objy, GLfloat *objz,
     GLfloat *objw);

void
gluPickMatrix(GLfloat x, GLfloat y, GLfloat deltax, GLfloat deltay,
     GLint viewport[4]);

#endif
And the source code:
#include "project.h"
#include <math.h>


/*
** Make m an identity matrix
*/
static void __gluMakeIdentityf(GLfloat m[16])
{
    m[0+4*0] = 1; m[0+4*1] = 0; m[0+4*2] = 0; m[0+4*3] = 0;
    m[1+4*0] = 0; m[1+4*1] = 1; m[1+4*2] = 0; m[1+4*3] = 0;
    m[2+4*0] = 0; m[2+4*1] = 0; m[2+4*2] = 1; m[2+4*3] = 0;
    m[3+4*0] = 0; m[3+4*1] = 0; m[3+4*2] = 0; m[3+4*3] = 1;
}

#define __glPi 3.14159265358979323846

void
gluPerspective(GLfloat fovy, GLfloat aspect, GLfloat zNear, GLfloat zFar)
{
    GLfloat m[4][4];
    float sine, cotangent, deltaZ;
    float radians = fovy / 2 * __glPi / 180;

    deltaZ = zFar - zNear;
    sine = sin(radians);
    if ((deltaZ == 0) || (sine == 0) || (aspect == 0)) {
 return;
    }
    cotangent = cos(radians) / sine;

    __gluMakeIdentityf(&m[0][0]);
    m[0][0] = cotangent / aspect;
    m[1][1] = cotangent;
    m[2][2] = -(zFar + zNear) / deltaZ;
    m[2][3] = -1;
    m[3][2] = -2 * zNear * zFar / deltaZ;
    m[3][3] = 0;
    glMultMatrixf(&m[0][0]);
}

static void normalize(float v[3])
{
    float r;

    r = sqrt( v[0]*v[0] + v[1]*v[1] + v[2]*v[2] );
    if (r == 0.0) return;

    v[0] /= r;
    v[1] /= r;
    v[2] /= r;
}

static void cross(float v1[3], float v2[3], float result[3])
{
    result[0] = v1[1]*v2[2] - v1[2]*v2[1];
    result[1] = v1[2]*v2[0] - v1[0]*v2[2];
    result[2] = v1[0]*v2[1] - v1[1]*v2[0];
}

void
gluLookAt(GLfloat eyex, GLfloat eyey, GLfloat eyez, GLfloat centerx,
   GLfloat centery, GLfloat centerz, GLfloat upx, GLfloat upy,
   GLfloat upz)
{
    float forward[3], side[3], up[3];
    GLfloat m[4][4];

    forward[0] = centerx - eyex;
    forward[1] = centery - eyey;
    forward[2] = centerz - eyez;

    up[0] = upx;
    up[1] = upy;
    up[2] = upz;

    normalize(forward);

    /* Side = forward x up */
    cross(forward, up, side);
    normalize(side);

    /* Recompute up as: up = side x forward */
    cross(side, forward, up);

    __gluMakeIdentityf(&m[0][0]);
    m[0][0] = side[0];
    m[1][0] = side[1];
    m[2][0] = side[2];

    m[0][1] = up[0];
    m[1][1] = up[1];
    m[2][1] = up[2];

    m[0][2] = -forward[0];
    m[1][2] = -forward[1];
    m[2][2] = -forward[2];

    glMultMatrixf(&m[0][0]);
    glTranslatef(-eyex, -eyey, -eyez);
}

static void __gluMultMatrixVecf(const GLfloat matrix[16], const GLfloat in[4],
        GLfloat out[4])
{
    int i;

    for (i=0; i<4; i++) {
 out[i] = 
     in[0] * matrix[0*4+i] +
     in[1] * matrix[1*4+i] +
     in[2] * matrix[2*4+i] +
     in[3] * matrix[3*4+i];
    }
}

/*
** Invert 4x4 matrix.
** Contributed by David Moore (See Mesa bug #6748)
*/
static int __gluInvertMatrixf(const GLfloat m[16], GLfloat invOut[16])
{
    float inv[16], det;
    int i;

    inv[0] =   m[5]*m[10]*m[15] - m[5]*m[11]*m[14] - m[9]*m[6]*m[15]
             + m[9]*m[7]*m[14] + m[13]*m[6]*m[11] - m[13]*m[7]*m[10];
    inv[4] =  -m[4]*m[10]*m[15] + m[4]*m[11]*m[14] + m[8]*m[6]*m[15]
             - m[8]*m[7]*m[14] - m[12]*m[6]*m[11] + m[12]*m[7]*m[10];
    inv[8] =   m[4]*m[9]*m[15] - m[4]*m[11]*m[13] - m[8]*m[5]*m[15]
             + m[8]*m[7]*m[13] + m[12]*m[5]*m[11] - m[12]*m[7]*m[9];
    inv[12] = -m[4]*m[9]*m[14] + m[4]*m[10]*m[13] + m[8]*m[5]*m[14]
             - m[8]*m[6]*m[13] - m[12]*m[5]*m[10] + m[12]*m[6]*m[9];
    inv[1] =  -m[1]*m[10]*m[15] + m[1]*m[11]*m[14] + m[9]*m[2]*m[15]
             - m[9]*m[3]*m[14] - m[13]*m[2]*m[11] + m[13]*m[3]*m[10];
    inv[5] =   m[0]*m[10]*m[15] - m[0]*m[11]*m[14] - m[8]*m[2]*m[15]
             + m[8]*m[3]*m[14] + m[12]*m[2]*m[11] - m[12]*m[3]*m[10];
    inv[9] =  -m[0]*m[9]*m[15] + m[0]*m[11]*m[13] + m[8]*m[1]*m[15]
             - m[8]*m[3]*m[13] - m[12]*m[1]*m[11] + m[12]*m[3]*m[9];
    inv[13] =  m[0]*m[9]*m[14] - m[0]*m[10]*m[13] - m[8]*m[1]*m[14]
             + m[8]*m[2]*m[13] + m[12]*m[1]*m[10] - m[12]*m[2]*m[9];
    inv[2] =   m[1]*m[6]*m[15] - m[1]*m[7]*m[14] - m[5]*m[2]*m[15]
             + m[5]*m[3]*m[14] + m[13]*m[2]*m[7] - m[13]*m[3]*m[6];
    inv[6] =  -m[0]*m[6]*m[15] + m[0]*m[7]*m[14] + m[4]*m[2]*m[15]
             - m[4]*m[3]*m[14] - m[12]*m[2]*m[7] + m[12]*m[3]*m[6];
    inv[10] =  m[0]*m[5]*m[15] - m[0]*m[7]*m[13] - m[4]*m[1]*m[15]
             + m[4]*m[3]*m[13] + m[12]*m[1]*m[7] - m[12]*m[3]*m[5];
    inv[14] = -m[0]*m[5]*m[14] + m[0]*m[6]*m[13] + m[4]*m[1]*m[14]
             - m[4]*m[2]*m[13] - m[12]*m[1]*m[6] + m[12]*m[2]*m[5];
    inv[3] =  -m[1]*m[6]*m[11] + m[1]*m[7]*m[10] + m[5]*m[2]*m[11]
             - m[5]*m[3]*m[10] - m[9]*m[2]*m[7] + m[9]*m[3]*m[6];
    inv[7] =   m[0]*m[6]*m[11] - m[0]*m[7]*m[10] - m[4]*m[2]*m[11]
             + m[4]*m[3]*m[10] + m[8]*m[2]*m[7] - m[8]*m[3]*m[6];
    inv[11] = -m[0]*m[5]*m[11] + m[0]*m[7]*m[9] + m[4]*m[1]*m[11]
             - m[4]*m[3]*m[9] - m[8]*m[1]*m[7] + m[8]*m[3]*m[5];
    inv[15] =  m[0]*m[5]*m[10] - m[0]*m[6]*m[9] - m[4]*m[1]*m[10]
             + m[4]*m[2]*m[9] + m[8]*m[1]*m[6] - m[8]*m[2]*m[5];

    det = m[0]*inv[0] + m[1]*inv[4] + m[2]*inv[8] + m[3]*inv[12];
    if (det == 0)
        return GL_FALSE;

    det = 1.0 / det;

    for (i = 0; i < 16; i++)
        invOut[i] = inv[i] * det;

    return GL_TRUE;
}

static void __gluMultMatricesf(const GLfloat a[16], const GLfloat b[16],
    GLfloat r[16])
{
    int i, j;

    for (i = 0; i < 4; i++) {
 for (j = 0; j < 4; j++) {
     r[i*4+j] = 
  a[i*4+0]*b[0*4+j] +
  a[i*4+1]*b[1*4+j] +
  a[i*4+2]*b[2*4+j] +
  a[i*4+3]*b[3*4+j];
 }
    }
}

GLint
gluProject(GLfloat objx, GLfloat objy, GLfloat objz, 
       const GLfloat modelMatrix[16], 
       const GLfloat projMatrix[16],
              const GLint viewport[4],
       GLfloat *winx, GLfloat *winy, GLfloat *winz)
{
    float in[4];
    float out[4];

    in[0]=objx;
    in[1]=objy;
    in[2]=objz;
    in[3]=1.0;
    __gluMultMatrixVecf(modelMatrix, in, out);
    __gluMultMatrixVecf(projMatrix, out, in);
    if (in[3] == 0.0) return(GL_FALSE);
    in[0] /= in[3];
    in[1] /= in[3];
    in[2] /= in[3];
    /* Map x, y and z to range 0-1 */
    in[0] = in[0] * 0.5 + 0.5;
    in[1] = in[1] * 0.5 + 0.5;
    in[2] = in[2] * 0.5 + 0.5;

    /* Map x,y to viewport */
    in[0] = in[0] * viewport[2] + viewport[0];
    in[1] = in[1] * viewport[3] + viewport[1];

    *winx=in[0];
    *winy=in[1];
    *winz=in[2];
    return(GL_TRUE);
}

GLint
gluUnProject(GLfloat winx, GLfloat winy, GLfloat winz,
  const GLfloat modelMatrix[16], 
  const GLfloat projMatrix[16],
                const GLint viewport[4],
         GLfloat *objx, GLfloat *objy, GLfloat *objz)
{
    float finalMatrix[16];
    float in[4];
    float out[4];

    __gluMultMatricesf(modelMatrix, projMatrix, finalMatrix);
    if (!__gluInvertMatrixf(finalMatrix, finalMatrix)) return(GL_FALSE);

    in[0]=winx;
    in[1]=winy;
    in[2]=winz;
    in[3]=1.0;

    /* Map x and y from window coordinates */
    in[0] = (in[0] - viewport[0]) / viewport[2];
    in[1] = (in[1] - viewport[1]) / viewport[3];

    /* Map to range -1 to 1 */
    in[0] = in[0] * 2 - 1;
    in[1] = in[1] * 2 - 1;
    in[2] = in[2] * 2 - 1;

    __gluMultMatrixVecf(finalMatrix, in, out);
    if (out[3] == 0.0) return(GL_FALSE);
    out[0] /= out[3];
    out[1] /= out[3];
    out[2] /= out[3];
    *objx = out[0];
    *objy = out[1];
    *objz = out[2];
    return(GL_TRUE);
}

GLint
gluUnProject4(GLfloat winx, GLfloat winy, GLfloat winz, GLfloat clipw,
       const GLfloat modelMatrix[16], 
       const GLfloat projMatrix[16],
       const GLint viewport[4],
       GLclampf nearVal, GLclampf farVal,      
       GLfloat *objx, GLfloat *objy, GLfloat *objz,
       GLfloat *objw)
{
    float finalMatrix[16];
    float in[4];
    float out[4];

    __gluMultMatricesf(modelMatrix, projMatrix, finalMatrix);
    if (!__gluInvertMatrixf(finalMatrix, finalMatrix)) return(GL_FALSE);

    in[0]=winx;
    in[1]=winy;
    in[2]=winz;
    in[3]=clipw;

    /* Map x and y from window coordinates */
    in[0] = (in[0] - viewport[0]) / viewport[2];
    in[1] = (in[1] - viewport[1]) / viewport[3];
    in[2] = (in[2] - nearVal) / (farVal - nearVal);

    /* Map to range -1 to 1 */
    in[0] = in[0] * 2 - 1;
    in[1] = in[1] * 2 - 1;
    in[2] = in[2] * 2 - 1;

    __gluMultMatrixVecf(finalMatrix, in, out);
    if (out[3] == 0.0) return(GL_FALSE);
    *objx = out[0];
    *objy = out[1];
    *objz = out[2];
    *objw = out[3];
    return(GL_TRUE);
}

void
gluPickMatrix(GLfloat x, GLfloat y, GLfloat deltax, GLfloat deltay,
    GLint viewport[4])
{
    if (deltax <= 0 || deltay <= 0) { 
 return;
    }

    /* Translate and scale the picked region to the entire window */
    glTranslatef((viewport[2] - 2 * (x - viewport[0])) / deltax,
     (viewport[3] - 2 * (y - viewport[1])) / deltay, 0);
    glScalef(viewport[2] / deltax, viewport[3] / deltay, 1.0);
}