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James Gregory 2013-12-30 14:33:39 +11:00
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</P>
<P>For our purposes, <I>projection</I> is the process of mapping coordinates onto a line or surface. <I>Perspective projection</I> projects 3-D coordinates onto a viewplane, scaling coordinates according to their z distance from the viewpoint in order to provide proper perspective. <I>Objectspace</I> is the coordinate space in which an object is defined, independent of other objects and the world itself. <I>Worldspace</I> is the absolute frame of reference for a 3-D world; all objects&rsquo; locations and orientations are with respect to worldspace, and this is the frame of reference around which the viewpoint and view direction move. <I>Viewspace</I> is worldspace as seen from the viewpoint, looking in the view direction. <I>Screenspace</I> is viewspace after perspective projection and scaling to the screen.</P>
<P>Finally, <I>transformation</I> is the process of converting points from one coordinate space into another; in our case, that&rsquo;ll mean rotating and translating (moving) points from objectspace or worldspace to viewspace.</P>
<P>For additional information, you might want to check out Foley &amp van Dam&rsquo;s <I>Computer Graphics</I> (ISBN 0-201-12110-7), or the chapters in this book dealing with my X-Sharp 3-D graphics library.</P>
<P>For additional information, you might want to check out Foley &amp; van Dam&rsquo;s <I>Computer Graphics</I> (ISBN 0-201-12110-7), or the chapters in this book dealing with my X-Sharp 3-D graphics library.</P>
<H3><A NAME="Heading5"></A>The Dot Product</H3>
<P>Now we&rsquo;re ready to move on to the dot product. Given two vectors <B>U</B> = [u<SUB>1</SUB> u<SUB>2</SUB> u<SUB>3</SUB>] and <B>V</B> = [v<SUB>1</SUB> v<SUB>2</SUB> v<SUB>3</SUB>], their dot product, denoted by the symbol &bull;, is calculated as:</P>
<P ALIGN="LEFT"><P ALIGN="CENTER"><IMG SRC="images/61-02d.jpg"></P>