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-<head>
-<title>arith3(3) - Plan 9 from User Space</title>
-<meta content="text/html; charset=utf-8" http-equiv=Content-Type>
-</head>
-<body bgcolor=#ffffff>
-<table border=0 cellpadding=0 cellspacing=0 width=100%>
-<tr height=10><td>
-<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>
-
-<table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td>
-
- 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 &ndash; operations on
- 3-d points and planes<br>
-
-</table>
-<p><font size=+1><b>SYNOPSIS </b></font><br>
-
-<table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
-
-
-<table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td>
-
- <tt><font size=+1>#include &lt;draw.h&gt;
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>#include &lt;geometry.h&gt;
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>Point3 add3(Point3 a, Point3 b)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>Point3 sub3(Point3 a, Point3 b)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>Point3 neg3(Point3 a)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>Point3 div3(Point3 a, double b)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>Point3 mul3(Point3 a, double b)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>int eqpt3(Point3 p, Point3 q)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>int closept3(Point3 p, Point3 q, double eps)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>double dot3(Point3 p, Point3 q)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>Point3 cross3(Point3 p, Point3 q)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>double len3(Point3 p)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>double dist3(Point3 p, Point3 q)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>Point3 unit3(Point3 p)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>Point3 midpt3(Point3 p, Point3 q)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>Point3 lerp3(Point3 p, Point3 q, double alpha)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>Point3 reflect3(Point3 p, Point3 p0, Point3 p1)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>Point3 nearseg3(Point3 p0, Point3 p1, Point3 testp)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>double pldist3(Point3 p, Point3 p0, Point3 p1)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>double vdiv3(Point3 a, Point3 b)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>Point3 vrem3(Point3 a, Point3 b)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>Point3 pn2f3(Point3 p, Point3 n)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>Point3 ppp2f3(Point3 p0, Point3 p1, Point3 p2)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>Point3 fff2p3(Point3 f0, Point3 f1, Point3 f2)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>Point3 pdiv4(Point3 a)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>Point3 add4(Point3 a, Point3 b)
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
- <tt><font size=+1>Point3 sub4(Point3 a, Point3 b)<br>
- </font></tt>
-</table>
-<p><font size=+1><b>DESCRIPTION </b></font><br>
-
-<table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td>
-
- These routines do arithmetic on points and planes in affine or
- projective 3-space. Type <tt><font size=+1>Point3</font></tt> is<br>
-
- <table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td>
-
- <tt><font size=+1>typedef struct Point3 Point3;<br>
- struct Point3{<br>
-
- <table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td>
-
- double x, y, z, w;<br>
-
- </table>
- };<br>
-
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
- </font></tt>
-
- </table>
- 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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Description<br>
- <tt><font size=+1>add3</font></tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Add the coordinates of two points.<br>
- <tt><font size=+1>sub3</font></tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Subtract coordinates of two points.<br>
- <tt><font size=+1>neg3</font></tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Negate the coordinates of a point.<br>
- <tt><font size=+1>mul3</font></tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Multiply coordinates by a scalar.<br>
- <tt><font size=+1>div3</font></tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Divide coordinates by a scalar.<br>
- <tt><font size=+1>eqpt3</font></tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Test two points for exact equality.<br>
- <tt><font size=+1>closept3</font></tt>&nbsp;&nbsp;&nbsp;Is the distance between two points smaller than <i>eps</i>?<br>
- <tt><font size=+1>dot3</font></tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Dot product.<br>
- <tt><font size=+1>cross3</font></tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Cross product.<br>
- <tt><font size=+1>len3</font></tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Distance to the origin.<br>
- <tt><font size=+1>dist3</font></tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Distance between two points.<br>
- <tt><font size=+1>unit3</font></tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A unit vector parallel to <i>p</i>.<br>
- <tt><font size=+1>midpt3</font></tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The midpoint of line segment <i>pq</i>.<br>
- <tt><font size=+1>lerp3</font></tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Linear interpolation between <i>p</i> and <i>q</i>.<br>
- <tt><font size=+1>reflect3</font></tt>&nbsp;&nbsp;&nbsp;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>&nbsp;&nbsp;&nbsp;The closest point to <i>testp</i> on segment <i>p0 p1</i>.<br>
- <tt><font size=+1>pldist3</font></tt>&nbsp;&nbsp;&nbsp;&nbsp;The distance from <i>p</i> to segment <i>p0 p1</i>.<br>
- <tt><font size=+1>vdiv3</font></tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;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>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;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>.
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
-
- 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&#8217;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 &#8216;face&#8217;) 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 &#8216;to.&#8217;
- The number <tt><font size=+1>3</font></tt> reminds us, as before, that we&#8217;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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Description<br>
- <tt><font size=+1>pn2f3</font></tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute the plane passing through <i>p</i> with normal <i>n</i>.<br>
- <tt><font size=+1>ppp2f3</font></tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute the plane passing through three points.<br>
- <tt><font size=+1>fff2p3</font></tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute the intersection point of three planes.
- <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table>
-
- 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>&#8217;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&nbsp;&nbsp;&nbsp;Add the coordinates of two points.<br>
- sub4&nbsp;&nbsp;&nbsp;Subtract the coordinates of two points.<br>
-
-</table>
-<p><font size=+1><b>SOURCE </b></font><br>
-
-<table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td>
-
- <tt><font size=+1>/usr/local/plan9/src/libgeometry<br>
- </font></tt>
-</table>
-<p><font size=+1><b>SEE ALSO </b></font><br>
-
-<table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td>
-
- <a href="../man3/matrix.html"><i>matrix</i>(3)</a><br>
-
-</table>
-
-<td width=20>
-<tr height=20><td>
-</table>
-<!-- TRAILER -->
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