comparing rotated coordinates - c++

Question

I'm having little trouble whit trying to compare rotated 2D Quads coordinates to rotated x and y coordinates. I'm trying to determine if mouse was clicked inside the quad.
1) the rot's are this classes objects: (note : the operator << is overloaded for the use of the rotate coords func)
class Vector{
private:
std::vector <float> Vertices;
public:
Vector(float, float);
float GetVertice(unsigned int);
void SetVertice(unsigned int, float);
std::vector<float> operator <<(double);
};
Vector::Vector(float X,float Y){
Vertices.push_back(X);
Vertices.push_back(Y);
}
float Vector::GetVertice(unsigned int Index){
return Vertices.at(Index);
}
void Vector::SetVertice(unsigned int Index,float NewVertice){
Vertices.at(Index) = NewVertice;
}
//Return rotated coords:D
std::vector <float> Vector::operator <<(double Angle){
std::vector<float> Temp;
Temp.push_back(Vertices.at(0) * cos(Angle) - Vertices.at(1) * sin(Angle));
Temp.push_back(Vertices.at(0) * sin(Angle) + Vertices.at(1) * cos(Angle));
return Temp;
}
2) Comparasion and rotation of the coordinates THE NEW VERSION
Vector Rot1(x,y),Rot3(x,y);
double Angle;
std::vector <float> result1,result3;
Rot3.SetVertice(0,NewQuads.at(Index).GetXpos() + NewQuads.at(Index).GetWidth());
Rot3.SetVertice(1,NewQuads.at(Index).GetYpos() + NewQuads.at(Index).GetHeight());
Angle = NewQuads.at(Index).GetRotation();
result1 = Rot1 << Angle; // Rotate the mouse x and y
result3 = Rot3 << Angle; // Rotate the Quad x and y
//.at(0) = x and .at(1)=y
if(result1.at(0) >= result3.at(0) - NewQuads.at(Index).GetWidth() && result1.at(0) <= result3.at(0) ){
if(result1.at(1) >= result3.at(1) - NewQuads.at(Index).GetHeight() && result1.at(1) <= result3.at(1) ){
when i run this it works perfectly at 0 angle but when you rotate the quad, it fails.
and by failing I mean the activation area seem to just disappear.
am I doing the rotation of the coordinates correctly? or is it the comparison?
if it's the comparison how would you do it properly, I have tried changing the if's but whit out any luck...
edit
the drawing of the quad(Happens before the testing):
void Quad::Render()
{
if(!CheckIfOutOfScreen()){
glPushMatrix();
glLoadIdentity();
glTranslatef(Xpos ,Ypos ,0.f);
glRotatef(Rotation,0.f,0.f,1.f); // same rotation is used for the testing later...
glBegin(GL_QUADS);
glVertex2f(Zwidth,Zheight);
glVertex2f(Width,Zheight);
glVertex2f(Width,Height);
glVertex2f(Zwidth,Height);
glEnd();
if(State != NOT_ACTIVE)
RenderShapeTools();
glPopMatrix();
}
}
basicly I'm trying to test if mouse was clicked inside this quad:
Image

Answer 1

There is more than one way to achieve what you want, But from the image you posted I assume you want to draw to a surface the same size as your screen (or window) using only 2D graphics.
As you know in 3D graphics we talk about 3 coordinate references. The first is the coordinate reference of the object or model to be drawn, the second is the coordinate reference of the camera or view and the third is the coordinate reference of the screen.
In OpenGL the first two coordinate references are established through the MODELVIEW matrix and the third is achieved by the PROJECTION matrix and the viewport transformation.
In your case you want to rotate a quad and place it somewhere on the screen. Your quad has it's own model coordinates. Let's assume that for this specific 2D quad the origin is at the center of the quad and it has the dimensions of 5 by 5. Also let's assume that if we look to the center of the quad then the X axis points to the RIGHT, the Y axis points UP and the Z axis points towards the viewer.
The unrotated coordinates of the quad will be (from bottom left clockwise): (-2.5,-2.5,0), (-2.5,2.5,0), (2.5,2.5,0), (2.5,-2.5,0)
Now we want to have a camera and projection matrices and viewport so to simulate a 2D surface with known dimensions.
//Assume WinW contains the window width and WinH contains the windows height
glViewport(0,0,WinW,WinH);//Set the viewport to the whole window
glMatrixMode (GL_PROJECTION);
glLoadIdentity ();
glOrtho (0, WinW, WinH, 0, 0, 1);//Set the projection matrix to perform a 2D orthogonal projection
glMatrixMode (GL_MODELVIEW);
glLoadIdentity ();//Set the camera matrix to be the Identity matrix
You are now ready to draw your quad an this 2D surface with dimensions WinW, WinH. In this context if you just draw your quad using it's current vertices you will have the quad drawn with it's center at the bottom left of the window with each side measuring 5 pixels so you will actually see only quarter of a quad. If you want to rotate and move it you will do something like this:
//Prepare matrices as shown above
//Viewport coordinates range from bottom left (0,0) to top right (WinW,WinH)
float dX = CenterOfQuadInViewportCoordinatesX, dY = CenterOfQuadInViewportCoordinatesY;
float rotA = QuadRotationAngleAroundZAxisInDegrees;
float verticesX[4] = {-2.5,-2.5,2.5,2.5};
float verticesY[4] = {-2.5,2.5,2.5,-2.5};
//Remember that rotate is done first and translation second
glTranslatef(dX,dY,0);//Move the quad to the desired location in the viewport
glRotate(rotA, 0,0,1);//Rotate the quad around it's origin
glBegin(GL_QUADS);
glVertex2f(verticesX[0], veriticesY[0]);
glVertex2f(verticesX[1], veriticesY[1]);
glVertex2f(verticesX[2], veriticesY[2]);
glVertex2f(verticesX[3], veriticesY[3]);
glEnd();
Now you want to know whether the click of the mouse was within the rendered quad.
Whereas the viewport coordinates start from the bottom left the window coordinates start from the top left. So when you get the mouse coordinates you have to translate them to viewport coordinates in the following way:
float mouseViewportX = mouseX, mouseViewportY = WinH - mouseY - 1;
Once you have the mouse location in viewport coordinates you need to transform it to model coordinates in the following way (Please double check the calculations since I generally use my own matrix library for that and don't calculate it by hand):
//Translate the mouse location to model coordinates reference
mouseViewportX -= dX, mouseViewportY -= dY;
//Unrotate the mouse location
float invRotARad = -rotA*DEG_TO_RAD;
float sinRA = sin(invRotARad), cosRA = cos(invRotA);
float mouseInModelX = cosRA*mouseViewportX - sinRA*mouseViewportY;
float mouseInModelY = sinRA*mouseViewportX + cosRA*mouseViewportY;
And now you can finally check if the mouse falls within the quad - as you can see this is done in quad coordinates:
bool mouseInQuad = mouseInModelX > verticesX[0] && mouseInModelY < verticesX[1] &&
mouseInModelY > verticesY[0] && mouseInModelY < verticesY[1];
Hope I didn't make too many mistakes and this puts you on the right track. If you want to deal with more complex cases and 3D then you should have a look at gluUnproject (maybe you will want to implement your own) and for even more complex scenes you may need to use a stencil or depth buffers