3 replies to this topic

[marcus12]

Hi,
I am a beginner in opengl and maths.

I want to find the normal of the plane drawn :

   	glBegin(GL_QUADS);
           glVertex2f(700.0f, 500.0f);
           glVertex2f(720.0f, 500.0f);
           glVertex2f(720.0f, 300.0f);
           glVertex2f(700.0f, 300.0f);
       glEnd();

I am trying to find collision detection using ray cast.

All suggestions are welcome.

[Brother Bob]

Your quad is exclusively in the XY-plane, so the normal vector is the Z-axis; either (0,0,1) or (0,0,-1) depending on what you consider to be the front of it.

In general though, the normal can be calculated from the cross product of two non-linearly dependent vectors on your face. You can, for example, take two edges (the vector between two pairs of vertices), and calculate the normal as the cross product of the two vectors.

[mrchrismnh]

For a plane normal you need a third dimension. Then you take two edges of the plane that share the same corners, make vectors of them, take the cross product of those vectors and then normalize the cross product. So let's give your plane a z axis... and put them in a vertex (pseudo) class so the data can be manipulated by us...

vertice plane_a(700.0f, 500.0f,0.0f);
vertice plane_b(720.0f, 500.0f,0.0f);
vertice plane_c(720.0f, 300.0f,0.0f);
vertice plane_d(700.0f, 300.0f,0.0f);

vector a(a,c);
vector b(b,c);//these constructors are defined as head - tail so the vector here is going to be c.x - b.x, c.y - b.y, c.z - b.z

vector crossvec = crossprod(a,b);
//crossprod is:
// Cx = AyBz - AzBy
//Cy = AzBx - AxBz
//Cz = AxBy - AyBx

//now you want to normalize the crossproduct you do that via sqrt(x^2 + y^2 + z^2) and then divide each of its coordinates by the value obtained. Last but not least you add the resultant vector (which is going to be 0,0,1 or ideally close to it) to one of the planes four vertices. Yeah, the normal here is one along the z but the method I described works for any plane orientation.

[FlyingDutchman]

good work! like straight out of the book :-)

For a plane normal you need a third dimension. Then you take two edges of the plane that share the same corners, make vectors of them, take the cross product of those vectors and then normalize the cross product. So let's give your plane a z axis... and put them in a vertex (pseudo) class so the data can be manipulated by us...

vertice plane_a(700.0f, 500.0f,0.0f);
vertice plane_b(720.0f, 500.0f,0.0f);
vertice plane_c(720.0f, 300.0f,0.0f);
vertice plane_d(700.0f, 300.0f,0.0f);

vector a(a,c);
vector b(b,c);//these constructors are defined as head - tail so the vector here is going to be c.x - b.x, c.y - b.y, c.z - b.z

vector crossvec = crossprod(a,b);
//crossprod is:
// Cx = AyBz - AzBy
//Cy = AzBx - AxBz
//Cz = AxBy - AyBx

//now you want to normalize the crossproduct you do that via sqrt(x^2 + y^2 + z^2) and then divide each of its coordinates by the value obtained. Last but not least you add the resultant vector (which is going to be 0,0,1 or ideally close to it) to one of the planes four vertices. Yeah, the normal here is one along the z but the method I described works for any plane orientation.