275 lines
11 KiB
HTML
275 lines
11 KiB
HTML
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<title>Qhull Geomview options (G)</title>
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</head>
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<body>
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<!-- Navigation links -->
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<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
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<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
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<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
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• <a href="qh-quick.htm#options">Options</a>
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• <a href="qh-opto.htm#output">Output</a>
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• <a href="qh-optf.htm#format">Formats</a>
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• <a href="qh-optg.htm#geomview">Geomview</a>
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• <a href="qh-optp.htm#print">Print</a>
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• <a href="qh-optq.htm#qhull">Qhull</a>
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• <a href="qh-optc.htm#prec">Precision</a>
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• <a href="qh-optt.htm#trace">Trace</a>
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• <a href="../src/libqhull_r/index.htm">Functions</a></p>
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<hr>
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<!-- Main text of document -->
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<h1><a
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href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
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src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
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height="100"></a> Qhull Geomview options (G)</h1>
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This section lists the Geomview options for Qhull. These options are
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indicated by 'G' followed by a letter. See
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<a href="qh-opto.htm#output">Output</a>, <a href="qh-optp.htm#print">Print</a>,
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and <a href="qh-optf.htm#format">Format</a> for other output options.
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<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
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<hr>
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<p><a href="index.htm#TOC">»</a> <a href="qh-quick.htm#programs">Programs</a>
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<a name="geomview">•</a> <a href="qh-quick.htm#options">Options</a>
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• <a href="qh-opto.htm#output">Output</a>
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• <a href="qh-optf.htm#format">Formats</a>
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• <a href="qh-optg.htm#geomview">Geomview</a>
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• <a href="qh-optp.htm#print">Print</a>
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• <a href="qh-optq.htm#qhull">Qhull</a>
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• <a href="qh-optc.htm#prec">Precision</a>
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• <a href="qh-optt.htm#trace">Trace</a>
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• <a href="../src/libqhull_r/index.htm">Functions</a></p>
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<h2>Geomview output options</h2>
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<p><a href="http://www.geomview.org">Geomview</a> is the graphical
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viewer for visualizing Qhull output in 2-d, 3-d and 4-d.</p>
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<p>Geomview displays each facet of the convex hull. The color of
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a facet is determined by the coefficients of the facet's normal
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equation. For imprecise hulls, Geomview displays the inner and
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outer hull. Geomview can also display points, ridges, vertices,
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coplanar points, and facet intersections. </p>
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<p>For 2-d Delaunay triangulations, Geomview displays the
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corresponding paraboloid. Geomview displays the 2-d Voronoi
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diagram. For halfspace intersections, it displays the
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dual convex hull. </p>
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<dl compact>
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<dt> </dt>
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<dd><b>General</b></dd>
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<dt><a href="#G">G</a></dt>
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<dd>display Geomview output</dd>
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<dt><a href="#Gt">Gt</a></dt>
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<dd>display transparent 3-d Delaunay triangulation</dd>
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<dt><a href="#GDn">GDn</a></dt>
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<dd>drop dimension n in 3-d and 4-d output </dd>
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<dt> </dt>
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<dt> </dt>
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<dd><b>Specific</b></dd>
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<dt><a href="#Ga">Ga</a></dt>
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<dd>display all points as dots</dd>
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<dt><a href="#Gc">Gc</a></dt>
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<dd>display centrums (2-d, 3-d)</dd>
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<dt><a href="#Gp">Gp</a></dt>
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<dd>display coplanar points and vertices as radii</dd>
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<dt><a href="#Gh">Gh</a></dt>
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<dd>display hyperplane intersections</dd>
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<dt><a href="#Gi">Gi</a></dt>
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<dd>display inner planes only (2-d, 3-d)</dd>
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<dt><a href="#Go">Go</a></dt>
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<dd>display outer planes only (2-d, 3-d)</dd>
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<dt><a href="#Gr">Gr</a></dt>
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<dd>display ridges (3-d)</dd>
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<dt><a href="#Gv">Gv</a></dt>
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<dd>display vertices as spheres</dd>
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<dt><a href="#Gn">Gn</a></dt>
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<dd>do not display planes</dd>
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</dl>
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<hr>
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<h3><a href="#geomview">»</a><a name="G">G - produce output for
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viewing with Geomview</a></h3>
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<p>By default, option 'G' displays edges in 2-d, outer planes in
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3-d, and ridges in 4-d.</p>
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<p>A ridge can be explicit or implicit. An explicit ridge is a <i>(d-1)</i>-dimensional
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simplex between two facets. In 4-d, the explicit ridges are
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triangles. An implicit ridge is the topological intersection of
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two neighboring facets. It is the union of explicit ridges.</p>
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<p>For non-simplicial 4-d facets, the explicit ridges can be
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quite complex. When displaying a ridge in 4-d, Qhull projects the
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ridge's vertices to one of its facets' hyperplanes. Use '<a
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href="#Gh">Gh</a>' to project ridges to the intersection of both
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hyperplanes. This usually results in a cleaner display. </p>
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<p>For 2-d Delaunay triangulations, Geomview displays the
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corresponding paraboloid. Geomview displays the 2-d Voronoi
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diagram. For halfspace intersections, it displays the
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dual convex hull.
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<h3><a href="#geomview">»</a><a name="Ga">Ga - display all
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points as dots </a></h3>
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<p>Each input point is displayed as a green dot.</p>
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<h3><a href="#geomview">»</a><a name="Gc">Gc - display centrums
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(3-d) </a></h3>
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<p>The centrum is defined by a green radius sitting on a blue
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plane. The plane corresponds to the facet's hyperplane. If you
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sight along a facet's hyperplane, you will see that all
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neighboring centrums are below the facet. The radius is defined
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by '<a href="qh-optc.htm#Cn">C-n</a>' or '<a
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href="qh-optc.htm#Cn2">Cn</a>'.</p>
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<h3><a href="#geomview">»</a><a name="GDn">GDn - drop dimension
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n in 3-d and 4-d output </a></h3>
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<p>The result is a 2-d or 3-d object. In 4-d, this corresponds to
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viewing the 4-d object from the nth axis without perspective.
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It's best to view 4-d objects in pieces. Use the '<a
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href="qh-optp.htm#Pdk">Pdk</a>' '<a href="qh-optp.htm#Pg">Pg</a>'
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'<a href="qh-optp.htm#PG">PG</a>' '<a href="qh-optq.htm#QGn">QGn</a>'
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and '<a href="qh-optq.htm#QVn">QVn</a>' options to select a few
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facets. If one of the facets is perpendicular to an axis, then
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projecting along that axis will show the facet exactly as it is
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in 4-d. If you generate many facets, use Geomview's <tt>ginsu</tt>
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module to view the interior</p>
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<p>To view multiple 4-d dimensions at once, output the object
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without 'GDn' and read it with Geomview's <tt>ndview</tt>. As you
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rotate the object in one set of dimensions, you can see how it
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changes in other sets of dimensions.</p>
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<p>For additional control over 4-d objects, output the object
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without 'GDn' and read it with Geomview's <tt>4dview</tt>. You
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can slice the object along any 4-d plane. You can also flip the
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halfspace that's deleted when slicing. By combining these
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features, you can get some interesting cross sections.</p>
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<h3><a href="#geomview">»</a><a name="Gh">Gh - display
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hyperplane intersections (3-d, 4-d)</a></h3>
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<p>In 3-d, the intersection is a black line. It lies on two
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neighboring hyperplanes, c.f., the blue squares associated with
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centrums ('<a href="#Gc">Gc </a>'). In 4-d, the ridges are
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projected to the intersection of both hyperplanes. If you turn on
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edges (Geomview's 'appearances' menu), each triangle corresponds
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to one ridge. The ridges may overlap each other.</p>
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<h3><a href="#geomview">»</a><a name="Gi">Gi - display inner
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planes only (2-d, 3-d)</a></h3>
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<p>The inner plane of a facet is below all of its vertices. It is
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parallel to the facet's hyperplane. The inner plane's color is
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the opposite of the outer plane's color, i.e., <i>[1-r,1-g,1-b] </i>.
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Its edges are determined by the vertices.</p>
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<h3><a href="#geomview">»</a><a name="Gn">Gn - do not display
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planes </a></h3>
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<p>By default, Geomview displays the precise plane (no merging)
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or both inner and output planes (if merging). If merging,
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Geomview does not display the inner plane if the the difference
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between inner and outer is too small.</p>
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<h3><a href="#geomview">»</a><a name="Go">Go - display outer
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planes only (2-d, 3-d)</a></h3>
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<p>The outer plane of a facet is above all input points. It is
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parallel to the facet's hyperplane. Its color is determined by
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the facet's normal, and its edges are determined by the vertices.</p>
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<h3><a href="#geomview">»</a><a name="Gp">Gp - display coplanar
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points and vertices as radii </a></h3>
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<p>Coplanar points ('<a href="qh-optq.htm#Qc">Qc</a>'), interior
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points ('<a href="qh-optq.htm#Qi">Qi</a>'), outside points ('<a
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href="qh-optt.htm#TCn">TCn</a>' or '<a href="qh-optt.htm#TVn">TVn</a>'),
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and vertices are displayed as red and yellow radii. The radii are
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perpendicular to the corresponding facet. Vertices are aligned
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with an interior point. The radii define a ball which corresponds
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to the imprecision of the point. The imprecision is the maximum
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of the roundoff error, the centrum radius, and <i>maxcoord * (1 -
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</i><a href="qh-optc.htm#An"><i>A-n</i></a><i>)</i>. It is at
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least 1/20'th of the maximum coordinate, and ignores post merging
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if pre-merging is done.</p>
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<p>If '<a href="qh-optg.htm#Gv">Gv</a>' (print vertices as
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spheres) is also selected, option 'Gp' displays coplanar
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points as radii. Select options <a href="qh-optq.htm#Qc">Qc</a>'
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and/or '<a href="qh-optq.htm#Qi">Qi</a>'. Options 'Qc Gpv' displays
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coplanar points while 'Qci Gpv' displays coplanar and interior
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points. Option 'Qc' is automatically selected if 'Qi' is not
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selected with options 'Gpv'.
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<h3><a href="#geomview">»</a><a name="Gr">Gr - display ridges
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(3-d) </a></h3>
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<p>A ridge connects the two vertices that are shared by
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neighboring facets. It is displayed in green. A ridge is the
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topological edge between two facets while the hyperplane
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intersection is the geometric edge between two facets. Ridges are
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always displayed in 4-d.</p>
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<h3><a href="#geomview">»</a><a name="Gt">Gt - transparent 3-d
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Delaunay </a></h3>
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<p>A 3-d Delaunay triangulation looks like a convex hull with
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interior facets. Option 'Gt' removes the outside ridges to reveal
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the outermost facets. It automatically sets options '<a
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href="#Gr">Gr</a>' and '<a href="#GDn">GDn</a>'. See example <a
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href="qh-eg.htm#17f">eg.17f.delaunay.3</a>.</p>
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<h3><a href="#geomview">»</a><a name="Gv">Gv - display vertices
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as spheres (2-d, 3-d)</a></h3>
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<p>The radius of the sphere corresponds to the imprecision of the
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data. See '<a href="#Gp">Gp</a>' for determining the radius.</p>
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<!-- Navigation links -->
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<hr>
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<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
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<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
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<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
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• <a href="qh-quick.htm#options">Options</a>
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• <a href="qh-opto.htm#output">Output</a>
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• <a href="qh-optf.htm#format">Formats</a>
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• <a href="qh-optg.htm#geomview">Geomview</a>
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• <a href="qh-optp.htm#print">Print</a>
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• <a href="qh-optq.htm#qhull">Qhull</a>
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• <a href="qh-optc.htm#prec">Precision</a>
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• <a href="qh-optt.htm#trace">Trace</a>
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• <a href="../src/libqhull_r/index.htm">Functions</a></p>
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<!-- GC common information -->
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<hr>
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<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
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align="middle" width="40" height="40"></a><i>The Geometry Center
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Home Page </i></p>
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<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
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</a><br>
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Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
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</body>
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</html>
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