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copied!<p>Some quick googling reveals the definition of the aspect angle.</p> <p><a href="http://www.answers.com/topic/aspect-angle" rel="nofollow">http://www.answers.com/topic/aspect-angle</a></p> <p>It's the angle between the geographic north on the northern hemisphere and the geographic south on the southern hemisphere. So basically it's a measure how much a slope faces the closest pole. </p> <p>If your world is planar as opposed to spherical it will simplify things, so yes - A 2D problem. I'll make this assumption having the following implications:</p> <ul> <li>In a spherical world the north pole is a point on the sphere. In a planar world the "pole" is a plane at infinity. Think about a plane somewhere far away in your world denoting "north". Only the normal of this plane is important in this task. The unit normal of this plane is <strong>N</strong>(nz,ny,nz).</li> <li>Up is a vector pointing up <strong>U</strong>(ux,uy,yz). This is the unit normal vector of the ground plane.</li> </ul> <p>The unit normal vector of the plane <strong>V</strong>(a,b,c) can now be projected onto a vector <strong>P</strong> on the ground plane as usual: <strong>P</strong> = <strong>V</strong> - (<strong>V</strong> dot <strong>U</strong>) <strong>U</strong></p> <p>Now it's easy to measure the aspect angle of the plane - It's the angle between the "pole"-plane <strong>N</strong> and the projected plane normal <strong>P</strong> given by <em>acos</em>(<strong>P</strong> dot <strong>N</strong>).</p> <p>Since north is positive Y-axis for you we have <strong>N</strong> = (0, 1, 0). And then I guess you have up is <strong>U</strong> = (0, 0, 1), positive Z. This will simplify things even more - To project on the ground plane we just strip the Z-part. The aspect angle is then the angle between (a,b) and (0,1). </p> <pre><code>aspectAngle = acos(b / sqrt(a*a + b*b)) </code></pre> <p>Note that planes parallell with the ground plane does not have a well-defined aspect angle since there is no slope to measure the aspect angle from.</p>

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