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| <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 – 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> |
| <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> |
| </font></tt> |
| <tt><font size=+1>#include <geometry.h> |
| <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> |
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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> |
| |
| <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> |
| </font></tt> |
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| </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 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>. |
| <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’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. |
| <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>’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> |
| |
| <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> |
| |
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| </table> |
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