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3D Graphics
David Fearon introduces 3D models and rendering
Rendering realistic environments for films, games and 3D scenes is a complex art. New algorithms and techniques are constantly being developed, and the whole discipline is at the cutting edge of both computer science and mathematics. But most of the complexity of modern 3D systems comes from a need to get them drawn faster in the case of games, or more realistically in the case of 3D rendering. Whatever the 3D environment, the basic methods behind representing and displaying a 3D model are the same. In this feature, we provide a grounding in the basic ideas and the ways that real, solid objects can be represented and drawn with a computer.
The most basic representation of a 3D object is via a mesh model. This is the basis of the wireframe representations we’re all used to seeing, defined by a set of discrete points – referred to as vertices – and connected together to form the “solid” faces of the model. Mesh representations vary according to application, but for ease of rendering and calculation of lighting they’re usually organised as three- or four-sided polygons.
Perspective transformations
You’ve probably noticed that your monitor is a flat, two-dimensional surface. This means rendering a 3D model requires some trickery to get it looking three-dimensional. Artists have known for hundreds of years that the way to render 3D objects on a 2D screen is by using a perspective transformation. Parts of an object that are further away appear smaller, so the object needs to be warped accordingly. This is actually easy to do and just needs some basic geometric maths.
To transform a model from the abstract, 3D world space onto 2D screen space, all that’s needed is to project imaginary lines from the viewer’s eye, through the screen and to each vertex in turn. By calculating the point at which the line intersects the plane of the screen, the point is automatically transformed in perspective-correct screen space. Do that for both the horizontal and vertical planes and your 3D co-ordinates become 2D points that you can plot directly onscreen. The apparent field of view can be changed by varying the notional distance between the viewer’s eye and the screen. Decreasing it is equivalent to shortening the focal length of a camera, giving a wide-angle view and more exaggerated perspective. Increase it and the perspective is flattened for a telephoto view.
Copyright © 2008 Dennis Publishing
This article appeared in the February 2008 issue of PC Authority.
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