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<html>
<head>
<title>
TETRAHEDRON_SLICE_DISPLAY - Display Tetrahedron/Plane Intersection
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TETRAHEDRON_SLICE_DISPLAY <br> Display Tetrahedron/Plane Intersection
</h1>
<hr>
<p>
<b>TETRAHEDRON_SLICE_DISPLAY</b>
is a MATLAB program which
displays the intersection of a tetrahedron with a plane.
</p>
<p>
The intersection of a plane and a tetrahedron is a convex
planar polygon which is bounded by 0 to 4 points. The possibilities are:
<ul>
<li>
0) empty (no intersection);
</li>
<li>
1) a single point;
</li>
<li>
2) a single line segment;
</li>
<li>
3) a triangle;
</li>
<li>
4) a quadrilateral.
</li>
</ul>
</p>
<p>
Given the data, the program displays a wireframe image of the
tetrahedron, the points of intersection, and the convex polygon.
</p>
<p>
The user defines the tetrahedron by giving a 3x4 vertex array <b>T</b>
containing the XYZ coordinates of the vertices.
</p>
<p>
The user defines the plane using the <i>normal form</i>. That is,
the user gives a single point <b>P</b> which lies on the plane,
and a vector <b>NORMAL</b> which defines the direction normal to the plane.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>tetrahedron_slice_display</b> ( <i>p</i>, <i>normal</i>, <i>t</i> )
</blockquote>
where
<ul>
<li>
<i>p</i> is a point on the plane;
</li>
<li>
<i>normal</i> is the normal vector to the plane;
</li>
<li>
<i>t</i> contains the coordinates of the vertices.
</li>
</ul>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TETRAHEDRON_SLICE_DISPLAY</b> is available in
<a href = "../../m_src/tetrahedron_slice_display/tetrahedron_slice_display.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/geometry/geometry.html">
GEOMETRY</a>,
a MATLAB library which
performs geometric calculations in 2, 3 and N dimensional space.
</p>
<p>
<a href = "../../m_src/tetrahedron_properties/tetrahedron_properties.html">
TETRAHEDRON_PROPERTIES</a>,
a MATLAB program which
computes properties of a tetrahedron
whose vertex coordinates are read from a file.
</p>
<p>
<a href = "../../m_src/tetrahedron_slice_animate/tetrahedron_slice_animate.html">
TETRAHEDRON_SLICE_ANIMATE</a>,
a MATLAB program which
is given a tetrahedron and a vector, and displays an evenly spaced sequence
of planes that intersect the tetrahedron and are normal to the vector.
</p>
<p>
<a href = "../../datasets/tetrahedrons/tetrahedrons.html">
TETRAHEDRONS</a>,
a dataset directory which
contains examples of tetrahedrons;
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "parallelogram_area_3d.m">
parallelogram_area_3d.m</a>,
computes the area of a parallelogram in 3D;
</li>
<li>
<a href = "plane_normal_tetrahedron_intersect.m">
plane_normal_tetrahedron_intersect.m</a>,
finds intersections of a normal plane and a tetrahedron;
</li>
<li>
<a href = "quad_area_3d.m">
quad_area_3d.m</a>,
returns the area of a quadrilateral in 3D;
</li>
<li>
<a href = "r8_sign_opposite_strict.m">r8_sign_opposite_strict.m</a>,
is TRUE if two R8's have strictly opposite signs.
</li>
<li>
<a href = "tetrahedron_slice_display.m">tetrahedron_slice_display.m</a>,
displays an image of the intersection of a tetrahedron and a plane.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>,
prints the YMDHMS date as a timestamp.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "tetrahedron_slice_display_test.m">tetrahedron_slice_display_test.m</a>
a sample calling program.
</li>
<li>
<a href = "slice.png">slice.png</a>
the image of the computed intersection.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 26 June 2010.
</i>
<!-- John Burkardt -->
</body>
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</html>