# worldtoscreen / screentoworld

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Can someone please please show me how to do a world to screen and screen to world function for a 3d game. Ive spent days searching for how to do it but havent find any good tutorials..

This is the data I have to work with

World X,Y,Z pos to convert / screen X,Y to convert

Angle - Field of View = 27.7996

Angle - Roll = 0.0

Depth of Field - Amount = 0.0

Depth of Field - Depth = 8.0

Depth of Field - End = 8.0

Depth of Field - Start = 0.0003

Distance = 34.0

Distance - Far Clip = 600.0

Distance - Near Clip = 0.0999

Distance - Shadow Clip = 75.0

Target - Pitch = 56.0

Target - X

Target - Y

Target - Yaw = 180.0

Target - Z Offset = 0.0

Edited by seasick

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To transform a point in world to screen space you need to run it through the camera projections, much like you do with any graphics that you render. Let's say you start with a position in world space, you do WORLD -> VIEW -> PROJECTION. After that you have the position in clip space. If you then divide xyz by w (remember that clip space has 4 coordinates) you get NDC or normalized device coordinates. You can then map these to whatever you want, eg. pixels. This is how I do it in my engine:

bool Camera::worldToScreen(const Vec3& worldPos, int& x, int& y)
{
Vec4 posHomogeneous(worldPos, 1.0f);
Vec4 posInClipSpace = posHomogeneous * getViewMatrix() * mProjectionMatrix;
Vec3 posInNDC(posInClipSpace.x / posInClipSpace.w, posInClipSpace.y / posInClipSpace.w, posInClipSpace.z / posInClipSpace.w);

// Check if the point is in the camera's view.
if(posInClipSpace.w > 0.0f &&
posInNDC.x >= -1.0f && posInNDC.x <= 1.0f &&
posInNDC.y >= -1.0f && posInNDC.y <= 1.0f &&
posInNDC.z >= 0.0f && posInNDC.z <= 1.0f)
{
x = (int)Math::remapFloat(posInNDC.x, -1.0f, 1.0f, 0.0f, (float)mGraphicsEngine->getScreenWidth());
y = (int)Math::remapFloat(posInNDC.y, -1.0f, 1.0f, (float)mGraphicsEngine->getScreenHeight(), 0.0f);
return true;
}

return false;
}

That would give you the screen coordinates in pixels.

To go the other way, it is a little more involved. The usual thing to do is do a ray cast from the camera and see what it hits. This is how I construct the ray (again in the camera class):

Vec3 rayOrigin;
Vec3 rayDirection;

float vx = (((2.0f * screenX) / (float)mGraphicsEngine->getScreenWidth()) - 1.0f ) / mProjectionMatrix._11;
float vy = (((-2.0f * screenY) / (float)mGraphicsEngine->getScreenHeight()) + 1.0f ) / mProjectionMatrix._22;

rayOrigin.set(0.0f, 0.0f, 0.0f);
rayDirection.set(vx, vy, 1.0f);

That gives you a ray in camera space (view space). You can then transform this into world space and do ray casting against objects using that ray. How you do the ray casting is up to you (and how the scene is organized), but I first do a ray-AABB test against all objects and then a ray-triangle test once I hit an AABB, to optimize a bit. This might not be the most efficient way.

Hope it helps!

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Thx

How do I make the view and projection matrix?

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The same way you generate them when you draw stuff. For example, in XNA there's Matrix.CreateLookAt() which you can use for view matrices, and something like Matrix.CreatePerspectiveFieldOfView() to create a projection matrix. The view matrix describes your cameras positioning and the projection matrix describes your camera 'lens'. Somewhat simplified.

Edit: If you don't know these already, chances are you are trying to learn picking etc before trying to learn rendering. You should probably go the other way around, check some tutorials on 3d rendering instead and make sure you understand the concepts of vertices, matrices, transformations, pipelines etc. Working with 3D is very different from working with 2D, so you shouldn't try to solve your problems the same ways.

Edited by DvDmanDT

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Best article I have found on the topic of OpenGL matrices. I think you should get familiar with the algebra behind the geometric pipeline if you are serious about developing a 3d game! -> http://solarianprogrammer.com/2013/05/22/opengl-101-matrices-projection-view-model/

PS: The coordinate system of Direct3D is different, but if you understand the maths its not too difficult to convert from one to the other.

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