# Normalized Device Co-ordinates to World Space

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I did write a wonderfully detailed post about my problem, then accidentally closed the tab. So this'll be a little more brief, but hopefully still detailed enough to get some help!

Anyway, I'm trying to convert mouse co-ordinates to world space. At the moment, I'm passing in two normalized device co-ordinates, (x,y,-1.0f) and (x,y,1.0f), then transforming them by the inverse of (proj_matrix*view_matrix). I'm expecting to get two points - one on the near clipping plane and one on the far clipping plane, but I'm not. The near plane is 30, and the far plane is 5000, but I'm getting z values of 0.7 and 7 respectively.

I'm not doing any multiplication by any w value to get to clipping space - could that be the problem? If so, how should I get the w value to multiply all the elements by?

Here's the bits of my code that are relevant:

[code]Ray newray(0.2f,-0.2f,-1.0f,0.2f,-0.2f,1.0f);
newray.SetMatrices(cam_->GetProjectionMatrix(),cam_->GetViewMatrix());
newray.Calculate();[/code]

[code]class Ray
{
cml::matrix44f_c inv_mat_;
vector3f start_, end_;

vector3f transformed_start_, transformed_end_;
public:
Ray(float sx, float sy, float sz, float dx, float dy, float dz);
void SetRayEnds(float sx, float sy, float sz, float dx, float dy, float dz);

void SetMatrices(const cml::matrix44f_c & proj, const cml::matrix44f_c & view);
void Calculate();

vector3f GetYIntersection(float y);
};[/code]

[code]Ray::Ray(float sx, float sy, float sz, float dx, float dy, float dz) :
inv_mat_(cml::identity_4x4()),
start_(sx,sy,sz),
end_(dx,dy,dz)
{

}
void Ray::SetRayEnds(float sx, float sy, float sz, float dx, float dy, float dz)
{
start_.set(sx,sy,sz);
end_.set(dx,dy,dz);
}

void Ray::SetMatrices(const cml::matrix44f_c & proj, const cml::matrix44f_c & view)
{
inv_mat_ = cml::inverse(proj*view);
}

void Ray::Calculate()
{
transformed_start_ = cml::transform_point(inv_mat_, start_);
transformed_end_ = cml::transform_point(inv_mat_, end_);
}[/code]

To all the matrix and graphics wizards, what am I doing wrong? Is this the way that you would approach the problem?

Ben

EDIT: World space, not eye space. Edited by LordSputnik

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[quote]normalized device co-ordinates, (x,y,-1.0f) and (x,y,1.0f)[/quote]You are passing x and y in the range [-1.0,1.0], right?

Also, if you want to transform to "eye space", you only want to hit it with the inverse projection matrix. The inverse view matrix would transform from eye space to world space.

The perspective divide normalizes the x,y,z coordinates by w so that the homogeneous coordinate falls on the subspace w = 1. You shouldn't have to undo this.

Essentially, what you want to do is what gluUnProject does, but without the modelview matrix. Have a look at the pseudocode on the man page [url="http://www.opengl.org/sdk/docs/man/xhtml/gluUnProject.xml"]http://www.opengl.org/sdk/docs/man/xhtml/gluUnProject.xml[/url].