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<title>libgfx: 3-D Geometric Procedures</title>
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<h2>3-D Geometric Procedures</h2>
<p>Triangles are a very common modeling primitive in many graphics
applications. The <tt>libgfx</tt> library provides a package of routines for
computing various geometric properties of triangles.
To use this package you must include the standard header file
<pre>
#include <gfx/geom3d.h>
</pre>
Note that all of these functions assume that the corners of the triangle are
listed in <em>counter-clockwise order</em> around the outward pointing normal.
<p>You can compute the (signed) area of a triangle using the following
function. Note that the area will be negative if the vertices are listed in
clockwise order.
<pre>
double triangle_area(const Vec3&, const Vec3&, const Vec3&);
</pre>
<p>The following functions compute the plane defined by a triangle, and the
corresponding normal vector. The standard versions always use unit normal
vectors while the "raw" versions will use unscaled normals.
<pre>
Vec3 triangle_normal(const Vec3&, const Vec3&, const Vec3&);
Vec4 triangle_plane(const Vec3&, const Vec3&, const Vec3&);
Vec3 triangle_raw_normal(const Vec3&, const Vec3&, const Vec3&);
Vec4 triangle_raw_plane(const Vec3&, const Vec3&, const Vec3&);
</pre>
<p>For some meshing applications, it may on occasion be necessary to assess
the aspect ratio of a triangle.
<pre>
double triangle_compactness(const Vec3&, const Vec3&, const Vec3&);
</pre>
This function computes the "compactness" of a triangle. The returned value
will be between 0 and 1, with 0 meaning a degenerate (area=0) triangle and 1
meaning an equilateral triangle. The formula used, originally suggested by
Andre Gueziec, is 4*sqrt(3) * Area / (L1 + L2 + L3) where Li is the squared
length of side <i>i</i> of the triangle.
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