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<head>
<title>arith3(3) - Plan 9 from User Space</title>
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<tr><td width=20><td>
<tr><td width=20><td><b>ARITH3(3)</b><td align=right><b>ARITH3(3)</b>
<tr><td width=20><td colspan=2>
<br>
<p><font size=+1><b>NAME </b></font><br>
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add3, sub3, neg3, div3, mul3, eqpt3, closept3, dot3, cross3, len3,
dist3, unit3, midpt3, lerp3, reflect3, nearseg3, pldist3, vdiv3,
vrem3, pn2f3, ppp2f3, fff2p3, pdiv4, add4, sub4 – operations on
3-d points and planes<br>
</table>
<p><font size=+1><b>SYNOPSIS </b></font><br>
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<tt><font size=+1>#include <draw.h>
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</font></tt>
<tt><font size=+1>#include <geometry.h>
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<tt><font size=+1>Point3 add3(Point3 a, Point3 b)
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</font></tt>
<tt><font size=+1>Point3 sub3(Point3 a, Point3 b)
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</font></tt>
<tt><font size=+1>Point3 neg3(Point3 a)
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</font></tt>
<tt><font size=+1>Point3 div3(Point3 a, double b)
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</font></tt>
<tt><font size=+1>Point3 mul3(Point3 a, double b)
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</font></tt>
<tt><font size=+1>int eqpt3(Point3 p, Point3 q)
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</font></tt>
<tt><font size=+1>int closept3(Point3 p, Point3 q, double eps)
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</font></tt>
<tt><font size=+1>double dot3(Point3 p, Point3 q)
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</font></tt>
<tt><font size=+1>Point3 cross3(Point3 p, Point3 q)
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</font></tt>
<tt><font size=+1>double len3(Point3 p)
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</font></tt>
<tt><font size=+1>double dist3(Point3 p, Point3 q)
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</font></tt>
<tt><font size=+1>Point3 unit3(Point3 p)
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</font></tt>
<tt><font size=+1>Point3 midpt3(Point3 p, Point3 q)
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</font></tt>
<tt><font size=+1>Point3 lerp3(Point3 p, Point3 q, double alpha)
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</font></tt>
<tt><font size=+1>Point3 reflect3(Point3 p, Point3 p0, Point3 p1)
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</font></tt>
<tt><font size=+1>Point3 nearseg3(Point3 p0, Point3 p1, Point3 testp)
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</font></tt>
<tt><font size=+1>double pldist3(Point3 p, Point3 p0, Point3 p1)
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</font></tt>
<tt><font size=+1>double vdiv3(Point3 a, Point3 b)
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</font></tt>
<tt><font size=+1>Point3 vrem3(Point3 a, Point3 b)
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</font></tt>
<tt><font size=+1>Point3 pn2f3(Point3 p, Point3 n)
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</font></tt>
<tt><font size=+1>Point3 ppp2f3(Point3 p0, Point3 p1, Point3 p2)
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</font></tt>
<tt><font size=+1>Point3 fff2p3(Point3 f0, Point3 f1, Point3 f2)
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</font></tt>
<tt><font size=+1>Point3 pdiv4(Point3 a)
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<tt><font size=+1>Point3 add4(Point3 a, Point3 b)
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<tt><font size=+1>Point3 sub4(Point3 a, Point3 b)<br>
</font></tt>
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<p><font size=+1><b>DESCRIPTION </b></font><br>
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These routines do arithmetic on points and planes in affine or
projective 3-space. Type <tt><font size=+1>Point3</font></tt> is<br>
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<tt><font size=+1>typedef struct Point3 Point3;<br>
struct Point3{<br>
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double x, y, z, w;<br>
</table>
};<br>
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</font></tt>
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Routines whose names end in <tt><font size=+1>3</font></tt> operate on vectors or ordinary points
in affine 3-space, represented by their Euclidean <tt><font size=+1>(x,y,z)</font></tt> coordinates.
(They assume <tt><font size=+1>w=1</font></tt> in their arguments, and set <tt><font size=+1>w=1</font></tt> in their results.)<br>
Name Description<br>
<tt><font size=+1>add3</font></tt> Add the coordinates of two points.<br>
<tt><font size=+1>sub3</font></tt> Subtract coordinates of two points.<br>
<tt><font size=+1>neg3</font></tt> Negate the coordinates of a point.<br>
<tt><font size=+1>mul3</font></tt> Multiply coordinates by a scalar.<br>
<tt><font size=+1>div3</font></tt> Divide coordinates by a scalar.<br>
<tt><font size=+1>eqpt3</font></tt> Test two points for exact equality.<br>
<tt><font size=+1>closept3</font></tt> Is the distance between two points smaller than <i>eps</i>?<br>
<tt><font size=+1>dot3</font></tt> Dot product.<br>
<tt><font size=+1>cross3</font></tt> Cross product.<br>
<tt><font size=+1>len3</font></tt> Distance to the origin.<br>
<tt><font size=+1>dist3</font></tt> Distance between two points.<br>
<tt><font size=+1>unit3</font></tt> A unit vector parallel to <i>p</i>.<br>
<tt><font size=+1>midpt3</font></tt> The midpoint of line segment <i>pq</i>.<br>
<tt><font size=+1>lerp3</font></tt> Linear interpolation between <i>p</i> and <i>q</i>.<br>
<tt><font size=+1>reflect3</font></tt> The reflection of point <i>p</i> in the segment joining <i>p0</i> and
<i>p1</i>.<br>
<tt><font size=+1>nearseg3</font></tt> The closest point to <i>testp</i> on segment <i>p0 p1</i>.<br>
<tt><font size=+1>pldist3</font></tt> The distance from <i>p</i> to segment <i>p0 p1</i>.<br>
<tt><font size=+1>vdiv3</font></tt> Vector divide -- the length of the component of <i>a</i> parallel
to <i>b</i>, in units of the length of <i>b</i>.<br>
<tt><font size=+1>vrem3</font></tt> Vector remainder -- the component of <i>a</i> perpendicular to <i>b</i>.
Ignoring roundoff, we have <tt><font size=+1>eqpt3(add3(mul3(b, vdiv3(a, b)), vrem3(a,
b)), a)</font></tt>.
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The following routines convert amongst various representations
of points and planes. Planes are represented identically to points,
by duality; a point <tt><font size=+1>p</font></tt> is on a plane <tt><font size=+1>q</font></tt> whenever <tt><font size=+1>p.x*q.x+p.y*q.y+p.z*q.z+p.w*q.w=0</font></tt>.
Although when dealing with affine points we assume <tt><font size=+1>p.w=1</font></tt>, we can’t
make the same
assumption for planes. The names of these routines are extra-cryptic.
They contain an <tt><font size=+1>f</font></tt> (for ‘face’) to indicate a plane, <tt><font size=+1>p</font></tt> for a point
and <tt><font size=+1>n</font></tt> for a normal vector. The number <tt><font size=+1>2</font></tt> abbreviates the word ‘to.’
The number <tt><font size=+1>3</font></tt> reminds us, as before, that we’re dealing with affine
points. Thus <tt><font size=+1>pn2f3</font></tt> takes a point and a normal
vector and returns the corresponding plane.<br>
Name Description<br>
<tt><font size=+1>pn2f3</font></tt> Compute the plane passing through <i>p</i> with normal <i>n</i>.<br>
<tt><font size=+1>ppp2f3</font></tt> Compute the plane passing through three points.<br>
<tt><font size=+1>fff2p3</font></tt> Compute the intersection point of three planes.
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The names of the following routines end in <tt><font size=+1>4</font></tt> because they operate
on points in projective 4-space, represented by their homogeneous
coordinates.<br>
pdiv4Perspective division. Divide <tt><font size=+1>p.w</font></tt> into <i>p</i>’s coordinates, converting
to affine coordinates. If <tt><font size=+1>p.w</font></tt> is zero, the result is the same
as the argument.<br>
add4 Add the coordinates of two points.<br>
sub4 Subtract the coordinates of two points.<br>
</table>
<p><font size=+1><b>SOURCE </b></font><br>
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<tt><font size=+1>/usr/local/plan9/src/libgeometry<br>
</font></tt>
</table>
<p><font size=+1><b>SEE ALSO </b></font><br>
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<a href="../man3/matrix.html"><i>matrix</i>(3)</a><br>
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</table>
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