OpenGL ES (iPhone) 触摸拾取

Question

希望在 ES 中进行经典的 OpenGL 鼠标拾取。我不想使用第三方库，GLU 端口和 OpenGL 名称堆栈等都已退出。这几乎留下了逆视图变换和光线相交，对吗？

在以下人员的帮助下我已经取得了很大的进展： http://trac.bookofhook.com/bookofhook/trac.cgi/wiki/MousePicking http://eigenclass.blogspot.com/2008 /10/opengl-es-picking-using-ray-boundingbox.html

。 。 .但我还没到那儿。这也让人觉得一定有更简单的方法！

这是一些代码：

    -(void)handleTouch:(CGPoint)point {
    GLfloat width = backingWidth;
    GLfloat height = backingHeight;
    GLfloat x = point.x;
    GLfloat y = point.y;
    GLfloat z = 0.0f;

    //viewport -> normalized dev coord -> clip
    GLfloat n[] = {
        2 * x / width - 1,
        2 * y / height,
        2 * z - 1,
        1
    };

    float fov = 45.0f * (M_PI / 180.0f);
    float near = 0.01, far = 10.0f;
    float aspect = (float)backingWidth / (float)backingHeight;
    float top = tan(fov) * near;
    //float bottom = -top;
    //float left = aspect * bottom;
    float right = aspect * top;

    //I'm a viewing volume symmetric projection matrix
    GLfloat P[] = {
        near / right, 0, 0, 0,
        0, near / top, 0, 0,
        0, 0, -(far + near) / (far - near), (-2 * far * near) / (far - near),
        0, 0, -1, 0
    };

    GLfloat Pminus1[] = {
        1/P[0], 0, 0, 0,
        0, 1/P[5], 0, 0,
        0, 0, 0, 1/P[14],
        0, 0, 1/P[11], -(P[10]/ (P[11]*P[14]))
    };

    //clip -> view
    GLfloat v[] = {
        Pminus1[0] * n[0] + Pminus1[1] * n[1] + Pminus1[2] * n[2] + Pminus1[3] * n[3],
        Pminus1[4] * n[0] + Pminus1[5] * n[1] + Pminus1[6] * n[2] + Pminus1[7] * n[3],
        Pminus1[8] * n[0] + Pminus1[9] * n[1] + Pminus1[10] * n[2] + Pminus1[11] * n[3],
        Pminus1[12] * n[0] + Pminus1[13] * n[1] + Pminus1[14] * n[2] + Pminus1[15] * n[3]
    };

    //view -> world
    GLfloat Rt[] = {
        mv[0], mv[4], mv[8],
        mv[1], mv[5], mv[9],
        mv[2], mv[6], mv[10]
    };

    GLfloat tPrime[] = {
        Rt[0] * mv[3] + Rt[1] * mv[7] + Rt[2] * mv[11],
        Rt[3] * mv[3] + Rt[4] * mv[7] + Rt[5] * mv[11],
        Rt[6] * mv[3] + Rt[7] * mv[7] + Rt[8] * mv[11]
    };

    GLfloat Mminus1[] = {
        Rt[0], Rt[1], Rt[2], -(tPrime[0]),
        Rt[3], Rt[4], Rt[5], -(tPrime[1]),
        Rt[6], Rt[7], Rt[8], -(tPrime[2]),
        0, 0, 0, 1
    };

    //point in world space
    GLfloat w[] = {
        Mminus1[0] * v[0] + Mminus1[1] * v[1] + Mminus1[2] * v[2] + Mminus1[3] * v[3],
        Mminus1[4] * v[0] + Mminus1[5] * v[1] + Mminus1[6] * v[2] + Mminus1[7] * v[3],
        Mminus1[8] * v[0] + Mminus1[9] * v[1] + Mminus1[10] * v[2] + Mminus1[11] * v[3],
        Mminus1[12] * v[0] + Mminus1[13] * v[1] + Mminus1[14] * v[2] + Mminus1[15] * v[3]
    };

    //r = a + t(w - a)
    GLfloat a[] = {0.0f, -0.1f, 0.0f};
    GLfloat wminusa[] = {w[0] - a[0], w[1] - a[1], w[2] - a[2]};

    vector[0] = a[0];
    vector[1] = a[1],
    vector[2] = a[2];
    vector[3] = w[0];
    vector[4] = w[1];
    vector[5] = -10.0f;

    //3 non-colinear points on the plane 
    GLfloat p1[] = {rect.origin.x, rect.origin.y, 0};
    GLfloat p2[] = {rect.origin.x + rect.size.width, rect.origin.y, 0};
    GLfloat p3[] = {rect.origin.x + rect.size.width, rect.origin.y + rect.size.height, 0};

    //location plane normal vector, Ax + By + Cz + D = 0
    GLfloat lp[] = {
        p1[1] * (p2[2] - p3[2]) + p2[1] * (p3[2] - p1[2]) + p3[1] * (p1[2] - p2[2]),
        p1[2] * (p2[0] - p3[0]) + p2[2] * (p3[0] - p1[0]) + p3[2] * (p1[0] - p2[0]),
        p1[0] * (p2[1] - p3[1]) + p2[0] * (p3[1] - p1[1]) + p3[0] * (p1[1] - p2[1]),
        -(p1[0] * (((p2[1] * p3[2]) - (p3[1] * p2[2]))) + p2[0] * (((p3[1] * p1[2]) - (p1[1] * p3[2]))) + p3[0] * (((p1[1] * p2[2]) - (p2[1] * p1[2]))))
    };

    GLfloat PnRd = (lp[0] * wminusa[0]) + (lp[1] * wminusa[1]) + (lp[2] * wminusa[2]);
    if(PnRd != 0) {
        GLfloat PnR0D = -((lp[0] * a[0]) + (lp[1] * a[1]) + (lp[2] * a[2]) + lp[3]);
        if(PnR0D != 0) {
            GLfloat t = PnR0D / PnRd;
            if(t >= 0) {
                GLfloat p[] = {
                    a[0] + wminusa[0] * t,
                    a[1] + wminusa[1] * t,
                    a[2] + wminusa[2] * t
                };
                if(p[0] > rect.origin.x &&
                   p[0] < rect.origin.x + rect.size.width &&
                   p[1] > rect.origin.y &&
                   p[1] < rect.origin.y + rect.size.height)
                    NSLog(@"BOOM!!!");
            }
        }
    }
}

Answer 1

这篇文章很难理解。我正在尝试使用 GLKView 在 iOS 5 上推出自己的产品；我已经研究出了如何触摸检测像素 RGBA，正如我所描述的 这里，现在我正在尝试找出如何快速将场景对象的颜色更改为唯一的，以配合此方法。

Answer 2

我设法修复它：

-(void)view2WorldPoint:(CGPoint)point :(GLfloat*)worldPoint {
    // this is the inverse translation of the modelview
    GLfloat width = (GLfloat)backingWidth;
    GLfloat height = (GLfloat)backingHeight;

    float clickX = point.x;
    float clickY = point.y;
    float clickZ = 0.0f;

    NSLog(@"click point : x = %f, y = %f, z = %f", clickX, clickY, clickZ);

    //  NSLog(@"Me : x = %f, y = %f, z = %f", a[0], a[1], a[2]);
    //  NSLog(@"Dev : x = %f, y = %f, z = %f", squareX, squareY, squareZ);

    //viewport -> normalized device coord -> clip
    GLfloat n[] = {
        2 * clickX / width - 1,
        2 * (480-clickY) / height - 1,
        2 * clickZ - 1,
        1
    };
    //  NSLog(@"Obj : x = %f, y = %f, z = %f", rect.origin.x, rect.origin.y, -0.5);
    //  NSLog(@"N : x = %f, y = %f, z = %f", n[0], n[1], n[2]); 

    //I'm a viewing volume symmetric projection matrix
    //  GLfloat P[] = {
    //      near / right, 0, 0, 0,
    //      0, near / top, 0, 0,
    //      0, 0, -(far + near) / (far - near), (-2 * far * near) / (far - near),
    //      0, 0, -1, 0
    //  };
    GLfloat P[16];
    glGetFloatv(GL_PROJECTION_MATRIX, P);
    //  [self dumpMatrix:P :@"P"];

    GLfloat Pminus1[] = {
        1/P[0], 0, 0, 0,
        0, 1/P[5], 0, 0,
        0, 0, 0, 1/P[11],
        0, 0, 1/P[14], -(P[10]/ (P[11]*P[14]))
    };

    //  [self dumpMatrix:Pminus1 :@"P-1"];

    //clip -> view
    GLfloat v[] = {
        (Pminus1[0] * n[0]) + (Pminus1[1] * n[1]) + (Pminus1[2]  * n[2]) + (Pminus1[3] * n[3]),
        (Pminus1[4] * n[0]) + (Pminus1[5] * n[1]) + (Pminus1[6]  * n[2]) + (Pminus1[7] * n[3]),
        (Pminus1[8] * n[0]) + (Pminus1[9] * n[1]) + (Pminus1[10] * n[2]) + (Pminus1[11] * n[3]),
        (Pminus1[12] * n[0]) + (Pminus1[13] * n[1]) + (Pminus1[14] * n[2]) + (Pminus1[15] * n[3])
    };

    //  NSLog(@"v = [%f, %f, %f, %f]", v[0], v[1], v[2], v[3]);


    //  [self dumpMatrix:mv :@"mv"];

    //view -> world
    GLfloat Rt[] = {
        mv[0], mv[4], -mv[8],
        mv[1], mv[5], -mv[9],
        -mv[2], -mv[6], mv[10]
    };

    //  NSLog(@"Rt0 = [%f, %f, %f]", Rt[0], Rt[1], Rt[2]);
    //  NSLog(@"Rt1 = [%f, %f, %f]", Rt[3], Rt[4], Rt[5]);
    //  NSLog(@"Rt2 = [%f, %f, %f]", Rt[6], Rt[7], Rt[8]);

    GLfloat tPrime[] = {
        Rt[0] * mv[12] + Rt[1] * mv[13] + Rt[2] * mv[14],
        Rt[3] * mv[12] + Rt[4] * mv[13] + Rt[5] * mv[14],
        Rt[6] * mv[12] + Rt[7] * mv[13] + Rt[8] * mv[14]
    };

    //  NSLog(@"tPrime = [%f, %f, %f]", tPrime[0], tPrime[1], tPrime[2]);

    GLfloat Mminus1[] = {
        Rt[0], Rt[1], Rt[2], -(tPrime[0]),
        Rt[3], Rt[4], Rt[5], -(tPrime[1]),
        Rt[6], Rt[7], Rt[8], -(tPrime[2]),
        0, 0, 0, 1
    };

    //point in world space
    GLfloat w[] = {
        Mminus1[0] * v[0] + Mminus1[1] * v[1] + Mminus1[2] * v[2] + Mminus1[3] * v[3],
        Mminus1[4] * v[0] + Mminus1[5] * v[1] + Mminus1[6] * v[2] + Mminus1[7] * v[3],
        Mminus1[8] * v[0] + Mminus1[9] * v[1] + Mminus1[10] * v[2] + Mminus1[11] * v[3],
        Mminus1[12] * v[0] + Mminus1[13] * v[1] + Mminus1[14] * v[2] + Mminus1[15] * v[3]
    };
    NSLog(@"W : x = %f, y = %f, z = %f", w[0], w[1], w[2]);
    worldPoint[0] = w[0];
    worldPoint[1] = w[1];
    worldPoint[2] = w[2];
}

Answer 3

好吧，好吧，这还是有点问题。这是现在最有效的：

-(void)view2WorldPoint:(CGPoint)point :(GLfloat*)worldPoint {
    float clickX = point.x;
    float clickY = point.y;
    float clickZ = -near;

    //viewport -> normalized device coord -> clip
    GLint viewport[4];
    glGetIntegerv(GL_VIEWPORT, viewport);

    GLfloat n[] = {
        (clickX - (float)viewport[0]) / (float)viewport[2] * 2.0 - 1.0,
        -((clickY - (float)viewport[1]) / (float)viewport[3] * 2.0 - 1.0),
        2.0 * clickZ - 1.0,
        1.0
    };

    GLfloat MP[16], MPInv[16];
    MatMatMultiply(MP, projMat, modelMat);
    GenerateInverseMatrix4f(MPInv, MP); // replace this one with the whole 1/p thang?

    GLfloat w[] = {
        (MPInv[0]  * n[0]) + (MPInv[4]  * n[1]) + (MPInv[8]  * n[2]) + (MPInv[12] * n[3]),
        (MPInv[1]  * n[0]) + (MPInv[5]  * n[1]) + (MPInv[9]  * n[2]) + (MPInv[13] * n[3]),
        (MPInv[2]  * n[0]) + (MPInv[6]  * n[1]) + (MPInv[10] * n[2]) + (MPInv[14] * n[3]),
        (MPInv[3]  * n[0]) + (MPInv[7]  * n[1]) + (MPInv[11] * n[2]) + (MPInv[15] * n[3])
    };

    worldPoint[0] = w[0] / w[3];
    worldPoint[1] = w[1] / w[3];
    worldPoint[2] = w[2] / w[3];
}


float Determinant4f(const float m[16])
{
    return
    m[12]*m[9]*m[6]*m[3]-
    m[8]*m[13]*m[6]*m[3]-
    m[12]*m[5]*m[10]*m[3]+
    m[4]*m[13]*m[10]*m[3]+
    m[8]*m[5]*m[14]*m[3]-
    m[4]*m[9]*m[14]*m[3]-
    m[12]*m[9]*m[2]*m[7]+
    m[8]*m[13]*m[2]*m[7]+
    m[12]*m[1]*m[10]*m[7]-
    m[0]*m[13]*m[10]*m[7]-
    m[8]*m[1]*m[14]*m[7]+
    m[0]*m[9]*m[14]*m[7]+
    m[12]*m[5]*m[2]*m[11]-
    m[4]*m[13]*m[2]*m[11]-
    m[12]*m[1]*m[6]*m[11]+
    m[0]*m[13]*m[6]*m[11]+
    m[4]*m[1]*m[14]*m[11]-
    m[0]*m[5]*m[14]*m[11]-
    m[8]*m[5]*m[2]*m[15]+
    m[4]*m[9]*m[2]*m[15]+
    m[8]*m[1]*m[6]*m[15]-
    m[0]*m[9]*m[6]*m[15]-
    m[4]*m[1]*m[10]*m[15]+
    m[0]*m[5]*m[10]*m[15];
}

BOOL GenerateInverseMatrix4f(float i[16], const float m[16])
{
    float x=Determinant4f(m);
    if (x==0) return FALSE;

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

    return TRUE;
}

void MatMatMultiply(GLfloat *result, GLfloat *matrix1, GLfloat *matrix2)
{
    result[0]=matrix1[0]*matrix2[0]+
    matrix1[4]*matrix2[1]+
    matrix1[8]*matrix2[2]+
    matrix1[12]*matrix2[3];
    result[4]=matrix1[0]*matrix2[4]+
    matrix1[4]*matrix2[5]+
    matrix1[8]*matrix2[6]+
    matrix1[12]*matrix2[7];
    result[8]=matrix1[0]*matrix2[8]+
    matrix1[4]*matrix2[9]+
    matrix1[8]*matrix2[10]+
    matrix1[12]*matrix2[11];
    result[12]=matrix1[0]*matrix2[12]+
    matrix1[4]*matrix2[13]+
    matrix1[8]*matrix2[14]+
    matrix1[12]*matrix2[15];
    result[1]=matrix1[1]*matrix2[0]+
    matrix1[5]*matrix2[1]+
    matrix1[9]*matrix2[2]+
    matrix1[13]*matrix2[3];
    result[5]=matrix1[1]*matrix2[4]+
    matrix1[5]*matrix2[5]+
    matrix1[9]*matrix2[6]+
    matrix1[13]*matrix2[7];
    result[9]=matrix1[1]*matrix2[8]+
    matrix1[5]*matrix2[9]+
    matrix1[9]*matrix2[10]+
    matrix1[13]*matrix2[11];
    result[13]=matrix1[1]*matrix2[12]+
    matrix1[5]*matrix2[13]+
    matrix1[9]*matrix2[14]+
    matrix1[13]*matrix2[15];
    result[2]=matrix1[2]*matrix2[0]+
    matrix1[6]*matrix2[1]+
    matrix1[10]*matrix2[2]+
    matrix1[14]*matrix2[3];
    result[6]=matrix1[2]*matrix2[4]+
    matrix1[6]*matrix2[5]+
    matrix1[10]*matrix2[6]+
    matrix1[14]*matrix2[7];
    result[10]=matrix1[2]*matrix2[8]+
    matrix1[6]*matrix2[9]+
    matrix1[10]*matrix2[10]+
    matrix1[14]*matrix2[11];
    result[14]=matrix1[2]*matrix2[12]+
    matrix1[6]*matrix2[13]+
    matrix1[10]*matrix2[14]+
    matrix1[14]*matrix2[15];
    result[3]=matrix1[3]*matrix2[0]+
    matrix1[7]*matrix2[1]+
    matrix1[11]*matrix2[2]+
    matrix1[15]*matrix2[3];
    result[7]=matrix1[3]*matrix2[4]+
    matrix1[7]*matrix2[5]+
    matrix1[11]*matrix2[6]+
    matrix1[15]*matrix2[7];
    result[11]=matrix1[3]*matrix2[8]+
    matrix1[7]*matrix2[9]+
    matrix1[11]*matrix2[10]+
    matrix1[15]*matrix2[11];
    result[15]=matrix1[3]*matrix2[12]+
    matrix1[7]*matrix2[13]+
    matrix1[11]*matrix2[14]+
    matrix1[15]*matrix2[15];
}