OpenGL Transformation

 以下图片和部分内容来源：

（1、http://www.songho.ca/opengl/gl_transform.html

    2、http://www.antongerdelan.net/opengl/index.html

    3、opengl 官网论坛）

opengl顶点从模型到窗口坐标的变换过程，原来一直对NDC到屏幕有疑惑，看到国外一个讲opengl的博客，结合另外的网站和博客，先记录下，回头再添加详细的说明。

  

OpenGL vertex transformation

下图是对OpenGL Vertex Transfermation 的详细图解。

 上图的代码表述：

glViewport(0,0,1280,720);vec3 someVtx=vec3(5,6,7);mat4 mPerspective = mat4::perspective(45.0f,...);mat4 mView = mat4::lookat(...);mat4 mModel = ...; mat4 MVP = mPerspective*mView * mModel; //--------[ GPU side !!! ]-------------------[vec4 CLIPSPACE = MVP * vec4(someVtx,1.0f); // vertex shader!!// this CLIPSPACE var is known as gl_Position  //------[ stuff out of your control ]-------[vec3 NDC = vec3(CLIPSPACE.xyz/CLIPSPACE.w); // well, you can tweak some of the numbers here, // i.e with glViewport()float screenX = (NDC.x *0.5+0.5)*1280;float screenY = (NDC.y *0.5+0.5)*720;//------------------------------------------///-------------------------------------------/

//=============================================================================================//

//上述代码中mModel 、mView 和 mPerspective 的生成。

mModel：mModel Matrix主要对模型本身进行空间变化，比较直观，不多说明。 

mView：mView Matrix 的图解

View Matrix:

// minimal implementation of Vector3 structstruct Vector3{    float x;    float y;    float z;    Vector3() : x(0), y(0), z(0) {};              // constructors    Vector3(float x, float y, float z) : x(x), y(y), z(z) {};    // functions    Vector3& normalize();                         //    Vector3  operator-(const Vector3& rhs) const; // subtract rhs    Vector3  operator*(const Vector3& rhs) const; // cross product    Vector3& operator*=(const float scale);       // scale and update itself};Vector3& Vector3::normalize() {    float invLength = 1 / sqrtf(x*x + y*y + z*z);    x *= invLength;    y *= invLength;    z *= invLength;    return *this;}Vector3 Vector3::operator-(const Vector3& rhs) const {    return Vector3(x-rhs.x, y-rhs.y, z-rhs.z);}Vector3 Vector3::cross(const Vector3& rhs) const {    return Vector3(y*rhs.z - z*rhs.y, z*rhs.x - x*rhs.z, x*rhs.y - y*rhs.x);}

///////////////////////////////////////////////////////////////////////////////// compute transform axis from object position and target point///////////////////////////////////////////////////////////////////////////////void lookAtToAxes(const Vector3& position, const Vector3& target,                  Vector3& left, Vector3& up, Vector3& forward){    // compute the forward vector    forward = target - position;    forward.normalize();    // compute temporal up vector based on the forward vector    // watch out when look up/down at 90 degree    // for example, forward vector is on the Y axis    if(fabs(forward.x) < EPSILON && fabs(forward.z) < EPSILON)    {        // forward vector is pointing +Y axis        if(forward.y > 0)            up = Vector3(0, 0, -1);        // forward vector is pointing -Y axis        else            up = Vector3(0, 0, 1);    }    // in general, up vector is straight up    else    {        up = Vector3(0, 1, 0);    }    // compute the left vector    left = up.cross(forward);  // cross product    left.normalize();    // re-calculate the orthonormal up vector    up = forward.cross(left);  // cross product    up.normalize();}

///////////////////////////////////////////////////////////////////////////////// compute transform axis from object position, target and up direction///////////////////////////////////////////////////////////////////////////////void lookAtToAxes(const Vector3& pos, const Vector3& target, const Vector3& upDir,                  Vector3& left, Vector3& up, Vector3& forward){    // compute the forward vector    forward = target - pos;    forward.normalize();    // compute the left vector    left = upDir.cross(forward);  // cross product    left.normalize();    // compute the orthonormal up vector    up = forward.cross(left);     // cross product    up.normalize();}

mPerspective：mPerspective Martix 说明图