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<p><b>Up:</b> <a href="http://www.geom.umn.edu/locate/qhull">Home
page for Qhull</a> <br>
<b>Up:</b> <a href="qh-man.htm#TOC">Qhull manual: Table of
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<h1><a
href="http://www.geom.umn.edu/graphics/pix/Special_Topics/Computational_Geometry/4dcube.html"><img
src="qh--4d.gif" alt="[4-d cube]" align="middle" width="100"
height="100"></a> Imprecision in Qhull</h1>
<p>This section of the Qhull manual discusses the problems caused
by coplanar points and why Qhull uses options '<a
href="qh-optc.htm#C0">C-0</a>' or '<a href="qh-optq.htm#Qx">Qx</a>'
by default. If you ignore precision issues with option '<a
href="qh-optq.htm#Q0">Q0</a>', the output from Qhull can be
arbitrarily bad. If you joggle the input with option '<a
href="qh-optq.htm#QJn">QJ</a>', Qhull avoids precision problems. </p>
<p>Use option '<a href="qh-optt.htm#Tv">Tv</a>' to verify the
output from Qhull. It verifies that adjacent facets are clearly
convex. It verifies that all points are on or below all facets. </p>
<p>Qhull automatically tests for convexity if it detects
precision errors while constructing the hull. </p>
<p><i>Brad Barber, Cambridge MA, January 8, 1998</i></p>
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