OpenGL Transformation

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 struct
struct 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