<div>I don't think this will work, this is, in general, a difficult problem. Look at <a href="http://www.cs.mcgill.ca/~tflook/geo/">http://www.cs.mcgill.ca/~tflook/geo/</a> also hunt up the reference at the end of the paper
<strong>Olivier Devillers, Giuseppe Liotta, Franco P. Preparata, and Roberto Tamassia, </strong>"<strong>Checking the Convexity of Polytopes and the Planarity of Subdivisions</strong>".</div>
<div><br><br> </div>
<div><span class="gmail_quote">On 1/22/07, <b class="gmail_sendername">PAUL</b> <<a href="mailto:polinzhuo@163.com">polinzhuo@163.com</a>> wrote:</span>
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<p><font face="Times New Roman" size="2"><span lang="EN-US" style="FONT-SIZE: 10.5pt">I want to judge whether a polyhedron is convex or non-convex by an algorithm. The algorithm is : if every vertex of the polyhedron is convex then the polyhedron is convex.
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<p><font face="Times New Roman" size="2"><span lang="EN-US" style="FONT-SIZE: 10.5pt">For each vertex, there is at least three vertexes is adjacent to it. These vertexes make up of a triangle which forms a plane. Because the direction of the plane can be gotten by the order of three vertexes according to right-hand-rule, the order of three vertexes must be counter-clockwise. If the vertex is above the plane, the vertex is convex. If not, the vertex is non-convex.
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<p><font face="Times New Roman" size="2"><span lang="EN-US" style="FONT-SIZE: 10.5pt">But I cannot assure the order of three vertexes is counter-clockwise.</span></font></p>
<p><font face="Times New Roman" size="2"><span lang="EN-US" style="FONT-SIZE: 10.5pt">And have you a better way to the question?</span></font></p>
<p><font face="Times New Roman" size="2"><span lang="EN-US" style="FONT-SIZE: 10.5pt">Look forward to your reply again.</span></font></p>
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