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# RWH Component

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What the hell is it. I mean everything about it. I do know about the transformation matricies and what they do. But what does RWH have to do with a verticie? I always here soemthing general like "it''s where the verticie is after its tranformed" or soemthing of the sort. My question is, if its a new position why is it only one float? Someone please shed some light. I have no clue what RWH is. "Ogun''s Laughter Is No Joke!!!" - Ogun Kills On The Right, A Nigerian Poem.

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RHW not RWH...

Reciprocal of Homogenous W

In 3D to perform projections and translations with matrices, you use what is known as homogeneous coordinates. These are matrices with 4 columns rather than 3 (or rows depending on how you view matrices).

To transform coordinates, the process D3D follows is similar to the following:

1.
// the 3D input point (this could be the x,y,z of a vertex)
// this is in "model" or "object" space
VECTOR3 myInputPoint = {-10.5, 286.652, 199.0};

2.
// since we''ll be using homogenous space, add a W coordinate
// to the vertex and make it 4D
VECTOR4 myPoint;
myPoint.x = myInputPoint.x;
myPoint.y = myInputPoint.y;
myPoint.z = myInputPoint.z;
myPoint.w = 1.0f;

3.
// multiply the point by the world matrix
// (this moves the point from model space into world space)
VECTOR4 myPointInWorldSpace = myPoint * D3DTS_WORLD;

4.
// multiply the point by the view (camera) matrix
// (this moves the point from world space into camera space)
VECTOR4 myPointInCameraSpace = myPointInWorldSpace * D3DTS_VIEW;

5.
// multiply the point by the projection matrix
// this moves the point into _almost_ screenspace
VECTOR4 myFinalPoint = myPointInCameraSpace * D3DTS_PROJECTION;

6.
// a perspective projection from 3D to 2D requires a division by the Z coordinate
// (so that things which are further away from the viewer get smaller)
// Matrices only multiply and add so the divide is done with W

float screen_x = myFinalPoint.x / myFinalPoint.w;
float screen_y = myFinalPoint.y / myFinalPoint.w;

7.
A multiply can be faster than a divide and multiplying by the reciprocal does the same thing (for these purposes):

float rhw = 1.0f / mFinalPoint.w;
float screen_x = myFinalPoint.x * rhw;
float screen_y = myFinalPoint.y * rhw;
float z = myFinalPoint.z * rhw;

8.
After this point the point has the viewport applied to convert it into device coordinates (2D pixel positions). [I''ve deliberately left out a few steps such as lighting, concatenation of transforms, clipping etc since the question is purely about RHW].

9. The screen_x, screen_y, z and RHW get passed down to the rasteriser for each vertex.

The screen_x and screen_y tell the rasteriser where that vertex appears on the screen (it''s 2D address).

The z gets interpolated across the polygon and tested against and written to the Z buffer.

Finally the RHW is interpolated across the polygon and is used for perspective correct texturing, vertex shading and fogging.

--
Simon O''''Connor
Creative Asylum Ltd
www.creative-asylum.com

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