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diff --git a/src/qhull/html/qh-optg.htm b/src/qhull/html/qh-optg.htm new file mode 100644 index 000000000..a56e29df1 --- /dev/null +++ b/src/qhull/html/qh-optg.htm @@ -0,0 +1,274 @@ +<html> + +<head> +<title>Qhull Geomview options (G)</title> +</head> + +<body> +<!-- Navigation links --> + +<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br> +<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br> +<b>To:</b> <a href="qh-quick.htm#programs">Programs</a> +• <a href="qh-quick.htm#options">Options</a> +• <a href="qh-opto.htm#output">Output</a> +• <a href="qh-optf.htm#format">Formats</a> +• <a href="qh-optg.htm#geomview">Geomview</a> +• <a href="qh-optp.htm#print">Print</a> +• <a href="qh-optq.htm#qhull">Qhull</a> +• <a href="qh-optc.htm#prec">Precision</a> +• <a href="qh-optt.htm#trace">Trace</a> +• <a href="../src/libqhull_r/index.htm">Functions</a></p> + +<hr> +<!-- Main text of document --> + +<h1><a +href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img +src="qh--dt.gif" alt="[delaunay]" align="middle" width="100" +height="100"></a> Qhull Geomview options (G)</h1> + +This section lists the Geomview options for Qhull. These options are +indicated by 'G' followed by a letter. See +<a href="qh-opto.htm#output">Output</a>, <a href="qh-optp.htm#print">Print</a>, +and <a href="qh-optf.htm#format">Format</a> for other output options. + + +<p><b>Copyright © 1995-2015 C.B. Barber</b></p> + +<hr> + +<p><a href="index.htm#TOC">»</a> <a href="qh-quick.htm#programs">Programs</a> +<a name="geomview">•</a> <a href="qh-quick.htm#options">Options</a> +• <a href="qh-opto.htm#output">Output</a> +• <a href="qh-optf.htm#format">Formats</a> +• <a href="qh-optg.htm#geomview">Geomview</a> +• <a href="qh-optp.htm#print">Print</a> +• <a href="qh-optq.htm#qhull">Qhull</a> +• <a href="qh-optc.htm#prec">Precision</a> +• <a href="qh-optt.htm#trace">Trace</a> +• <a href="../src/libqhull_r/index.htm">Functions</a></p> + +<h2>Geomview output options</h2> + +<p><a href="http://www.geomview.org">Geomview</a> is the graphical +viewer for visualizing Qhull output in 2-d, 3-d and 4-d.</p> + +<p>Geomview displays each facet of the convex hull. The color of +a facet is determined by the coefficients of the facet's normal +equation. For imprecise hulls, Geomview displays the inner and +outer hull. Geomview can also display points, ridges, vertices, +coplanar points, and facet intersections. </p> + +<p>For 2-d Delaunay triangulations, Geomview displays the +corresponding paraboloid. Geomview displays the 2-d Voronoi +diagram. For halfspace intersections, it displays the +dual convex hull. </p> + +<dl compact> + <dt> </dt> + <dd><b>General</b></dd> + <dt><a href="#G">G</a></dt> + <dd>display Geomview output</dd> + <dt><a href="#Gt">Gt</a></dt> + <dd>display transparent 3-d Delaunay triangulation</dd> + <dt><a href="#GDn">GDn</a></dt> + <dd>drop dimension n in 3-d and 4-d output </dd> + + <dt> </dt> + <dt> </dt> + <dd><b>Specific</b></dd> + <dt><a href="#Ga">Ga</a></dt> + <dd>display all points as dots</dd> + <dt><a href="#Gc">Gc</a></dt> + <dd>display centrums (2-d, 3-d)</dd> + <dt><a href="#Gp">Gp</a></dt> + <dd>display coplanar points and vertices as radii</dd> + <dt><a href="#Gh">Gh</a></dt> + <dd>display hyperplane intersections</dd> + <dt><a href="#Gi">Gi</a></dt> + <dd>display inner planes only (2-d, 3-d)</dd> + <dt><a href="#Go">Go</a></dt> + <dd>display outer planes only (2-d, 3-d)</dd> + <dt><a href="#Gr">Gr</a></dt> + <dd>display ridges (3-d)</dd> + <dt><a href="#Gv">Gv</a></dt> + <dd>display vertices as spheres</dd> + <dt><a href="#Gn">Gn</a></dt> + <dd>do not display planes</dd> + +</dl> + +<hr> + +<h3><a href="#geomview">»</a><a name="G">G - produce output for +viewing with Geomview</a></h3> + +<p>By default, option 'G' displays edges in 2-d, outer planes in +3-d, and ridges in 4-d.</p> + +<p>A ridge can be explicit or implicit. An explicit ridge is a <i>(d-1)</i>-dimensional +simplex between two facets. In 4-d, the explicit ridges are +triangles. An implicit ridge is the topological intersection of +two neighboring facets. It is the union of explicit ridges.</p> + +<p>For non-simplicial 4-d facets, the explicit ridges can be +quite complex. When displaying a ridge in 4-d, Qhull projects the +ridge's vertices to one of its facets' hyperplanes. Use '<a +href="#Gh">Gh</a>' to project ridges to the intersection of both +hyperplanes. This usually results in a cleaner display. </p> + +<p>For 2-d Delaunay triangulations, Geomview displays the +corresponding paraboloid. Geomview displays the 2-d Voronoi +diagram. For halfspace intersections, it displays the +dual convex hull. + +<h3><a href="#geomview">»</a><a name="Ga">Ga - display all +points as dots </a></h3> + +<p>Each input point is displayed as a green dot.</p> + +<h3><a href="#geomview">»</a><a name="Gc">Gc - display centrums +(3-d) </a></h3> + +<p>The centrum is defined by a green radius sitting on a blue +plane. The plane corresponds to the facet's hyperplane. If you +sight along a facet's hyperplane, you will see that all +neighboring centrums are below the facet. The radius is defined +by '<a href="qh-optc.htm#Cn">C-n</a>' or '<a +href="qh-optc.htm#Cn2">Cn</a>'.</p> + +<h3><a href="#geomview">»</a><a name="GDn">GDn - drop dimension +n in 3-d and 4-d output </a></h3> + +<p>The result is a 2-d or 3-d object. In 4-d, this corresponds to +viewing the 4-d object from the nth axis without perspective. +It's best to view 4-d objects in pieces. Use the '<a +href="qh-optp.htm#Pdk">Pdk</a>' '<a href="qh-optp.htm#Pg">Pg</a>' +'<a href="qh-optp.htm#PG">PG</a>' '<a href="qh-optq.htm#QGn">QGn</a>' +and '<a href="qh-optq.htm#QVn">QVn</a>' options to select a few +facets. If one of the facets is perpendicular to an axis, then +projecting along that axis will show the facet exactly as it is +in 4-d. If you generate many facets, use Geomview's <tt>ginsu</tt> +module to view the interior</p> + +<p>To view multiple 4-d dimensions at once, output the object +without 'GDn' and read it with Geomview's <tt>ndview</tt>. As you +rotate the object in one set of dimensions, you can see how it +changes in other sets of dimensions.</p> + +<p>For additional control over 4-d objects, output the object +without 'GDn' and read it with Geomview's <tt>4dview</tt>. You +can slice the object along any 4-d plane. You can also flip the +halfspace that's deleted when slicing. By combining these +features, you can get some interesting cross sections.</p> + +<h3><a href="#geomview">»</a><a name="Gh">Gh - display +hyperplane intersections (3-d, 4-d)</a></h3> + +<p>In 3-d, the intersection is a black line. It lies on two +neighboring hyperplanes, c.f., the blue squares associated with +centrums ('<a href="#Gc">Gc </a>'). In 4-d, the ridges are +projected to the intersection of both hyperplanes. If you turn on +edges (Geomview's 'appearances' menu), each triangle corresponds +to one ridge. The ridges may overlap each other.</p> + +<h3><a href="#geomview">»</a><a name="Gi">Gi - display inner +planes only (2-d, 3-d)</a></h3> + +<p>The inner plane of a facet is below all of its vertices. It is +parallel to the facet's hyperplane. The inner plane's color is +the opposite of the outer plane's color, i.e., <i>[1-r,1-g,1-b] </i>. +Its edges are determined by the vertices.</p> + +<h3><a href="#geomview">»</a><a name="Gn">Gn - do not display +planes </a></h3> + +<p>By default, Geomview displays the precise plane (no merging) +or both inner and output planes (if merging). If merging, +Geomview does not display the inner plane if the the difference +between inner and outer is too small.</p> + +<h3><a href="#geomview">»</a><a name="Go">Go - display outer +planes only (2-d, 3-d)</a></h3> + +<p>The outer plane of a facet is above all input points. It is +parallel to the facet's hyperplane. Its color is determined by +the facet's normal, and its edges are determined by the vertices.</p> + +<h3><a href="#geomview">»</a><a name="Gp">Gp - display coplanar +points and vertices as radii </a></h3> + +<p>Coplanar points ('<a href="qh-optq.htm#Qc">Qc</a>'), interior +points ('<a href="qh-optq.htm#Qi">Qi</a>'), outside points ('<a +href="qh-optt.htm#TCn">TCn</a>' or '<a href="qh-optt.htm#TVn">TVn</a>'), +and vertices are displayed as red and yellow radii. The radii are +perpendicular to the corresponding facet. Vertices are aligned +with an interior point. The radii define a ball which corresponds +to the imprecision of the point. The imprecision is the maximum +of the roundoff error, the centrum radius, and <i>maxcoord * (1 - +</i><a href="qh-optc.htm#An"><i>A-n</i></a><i>)</i>. It is at +least 1/20'th of the maximum coordinate, and ignores post merging +if pre-merging is done.</p> + +<p>If '<a href="qh-optg.htm#Gv">Gv</a>' (print vertices as +spheres) is also selected, option 'Gp' displays coplanar +points as radii. Select options <a href="qh-optq.htm#Qc">Qc</a>' +and/or '<a href="qh-optq.htm#Qi">Qi</a>'. Options 'Qc Gpv' displays +coplanar points while 'Qci Gpv' displays coplanar and interior +points. Option 'Qc' is automatically selected if 'Qi' is not +selected with options 'Gpv'. + +<h3><a href="#geomview">»</a><a name="Gr">Gr - display ridges +(3-d) </a></h3> + +<p>A ridge connects the two vertices that are shared by +neighboring facets. It is displayed in green. A ridge is the +topological edge between two facets while the hyperplane +intersection is the geometric edge between two facets. Ridges are +always displayed in 4-d.</p> + +<h3><a href="#geomview">»</a><a name="Gt">Gt - transparent 3-d +Delaunay </a></h3> + +<p>A 3-d Delaunay triangulation looks like a convex hull with +interior facets. Option 'Gt' removes the outside ridges to reveal +the outermost facets. It automatically sets options '<a +href="#Gr">Gr</a>' and '<a href="#GDn">GDn</a>'. See example <a +href="qh-eg.htm#17f">eg.17f.delaunay.3</a>.</p> + +<h3><a href="#geomview">»</a><a name="Gv">Gv - display vertices +as spheres (2-d, 3-d)</a></h3> + +<p>The radius of the sphere corresponds to the imprecision of the +data. See '<a href="#Gp">Gp</a>' for determining the radius.</p> + +<!-- Navigation links --> + +<hr> + +<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br> +<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br> +<b>To:</b> <a href="qh-quick.htm#programs">Programs</a> +• <a href="qh-quick.htm#options">Options</a> +• <a href="qh-opto.htm#output">Output</a> +• <a href="qh-optf.htm#format">Formats</a> +• <a href="qh-optg.htm#geomview">Geomview</a> +• <a href="qh-optp.htm#print">Print</a> +• <a href="qh-optq.htm#qhull">Qhull</a> +• <a href="qh-optc.htm#prec">Precision</a> +• <a href="qh-optt.htm#trace">Trace</a> +• <a href="../src/libqhull_r/index.htm">Functions</a></p> +<!-- GC common information --> + +<hr> + +<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif" +align="middle" width="40" height="40"></a><i>The Geometry Center +Home Page </i></p> + +<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a> +</a><br> +Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p> +</body> +</html> |