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James Gregory 2013-12-30 15:11:04 +11:00
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<meta name="vspubdate" content="07/01/97" />
<meta name="vscategory" content="Web and Software Development: Game Development,Web and Software Development: Graphics and Multimedia Development" />
<title>Michael Abrash's Graphics Programming Black Book Special Edition: Adding a Dimension</title><!-- HEADER -->
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<title>Michael Abrash's Graphics Programming Black Book Special Edition: Adding a Dimension</title>
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<meta name="pages" content="948-949" />
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<p><br /></p>
<h4 align="left"><a id="Heading9"></a>Notes on the 3-D Animation Example</h4>
<h4 align="left" id="Heading9">Notes on the 3-D Animation Example</h4>
<p>The sample program transforms the polygon&rsquo;s vertices from object space to world space to view space to the screen, as described earlier. In this case, world space and view space are congruent&mdash;we&rsquo;re looking right down the negative Z axis of world space&mdash;so the transformation matrix from world to view is the identity matrix; you might want to experiment with changing this matrix to change the viewpoint. The sample program uses 4x4 homogeneous coordinate matrices to perform transformations, as described above. Floating-point arithmetic is used for all 3-D calculations. Setting the translation from object space to world space is a simple matter of changing the appropriate entry in the fourth column of the object-to-world transformation matrix. Setting the rotation around the Y axis is almost as simple, requiring only the setting of the four matrix entries that control the Y rotation to the sines and cosines of the desired rotation. However, rotations involving more than one axis require multiple rotation matrices, one for each axis rotated around; those matrices are then concatenated together to produce the object-to-world transformation. This area is trickier than it might initially appear to be; more in the near future.</p>
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<p>Finally, observe the jaggies crawling along the edges of the polygon as it rotates. This is temporal aliasing at its finest! We won&rsquo;t address antialiasing further, realtime antialiasing being decidedly nontrivial, but this should give you an idea of why antialiasing is so desirable.</p>
<h3><a id="Heading10"></a>An Ongoing Journey</h3>
<h3 id="Heading10">An Ongoing Journey</h3>
<p>In the next chapter, we&rsquo;ll assign fronts and backs to polygons, and start drawing only those that are facing the viewer. That will enable us to handle convex polyhedrons, such as tetrahedrons and cubes. We&rsquo;ll also look at interactively controllable rotation, and at more complex rotations than the simple rotation around the Y axis that we did this time. In time, we&rsquo;ll use fixed-point arithmetic to speed things up, and do some shading and texture mapping. The journey has only begun; we&rsquo;ll get to all that and more soon.</p>
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<div align="center">
Graphics Programming Black Book &copy; 2001 Michael Abrash
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