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rajesh_nest

OpenGL Normalized Device Coordinates.

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I have few clarification about 3D Projection.

1. In opengl (or other APIs), when you multiply Projection matrix with eye coordinates, what really happens? Does the eye coordinates, in 3D World coordinates gets converted to 2D coordinates ?

If 2D (x,y) coordinates only remans (z lost), how then we are using the Z value for Hidden surface removal (Z Buffer).


2. What is the purpose of linearly mapping eye coordinates to a cube ( NDC - Normalized Device Coordinates).


I am always confused with the underlying theory. Someone please give me a detailed description.

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Some info about what is going on:
[url="http://www.songho.ca/opengl/gl_projectionmatrix.html"]http://www.songho.ca...tionmatrix.html[/url]

In a nutshell, 3D geometry in world space is [i]projected[/i] onto a 2D view plane, defined by eye coordinates. So imagine you have 3D cube. The cube is decomposed into triangles. The triangles are clipped against the view frustum*. The visible (and clipped) triangle corners are projected onto the 2D view plane.The Z component in the triangle point is retained as a measure of distance from the view origin (camera), which will be used later for hidden surface elimination purposes. The resulting points in eye coordinates are transformed into normalised device coordinates (NDC). Generally the world->eye->NDC transform can done in a single step via the projection matrix, by combining the projection and the normalisation math.

The purpose of using normalised device coordinates is to make the incoming values unit-less and proportional to one another. The graphics card can map those normalised coordinates to whatever internal metric the hardware uses, generally in pixels, as defined by the view port size. Depth (Z) values are usually normalised to the range of [0, 1], which is mapped over a particular precision range (16, 24, or 32-bit, either float or integer), as dictated by the hardware's capabilities.


* Note, the clipping is usually done after transforming the triangle into eye coordinates, because clipping in 2D is more efficient in some cases. But conceptually, we get the same result.

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[size="2"][color="#1c2837"]
[size="2"][color="#1c2837"]Thanks a lot[/color][/size]
[size="2"][color="#1c2837"]
[/color][/size]But How come the last row of the Perspective Projection matrix become (0,0,-1,0). It is not clear.[/color][/size]

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The view frustum is looking into the -Z direction in the eye coordinate system. Therefore, the aforementioned cube model in my earlier example has a negative offset relative to the view origin along the Z axis. In order to sort depth values in the range [0, 1], we must negate the incoming Z values.

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