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diff --git a/man/man3/quaternion.html b/man/man3/quaternion.html new file mode 100644 index 00000000..257ebe52 --- /dev/null +++ b/man/man3/quaternion.html @@ -0,0 +1,163 @@ +<head> +<title>quaternion(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>QUATERNION(3)</b><td align=right><b>QUATERNION(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> + + qtom, mtoq, qadd, qsub, qneg, qmul, qdiv, qunit, qinv, qlen, slerp, + qmid, qsqrt – Quaternion arithmetic<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 <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>Quaternion qadd(Quaternion q, Quaternion r) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>Quaternion qsub(Quaternion q, Quaternion r) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>Quaternion qneg(Quaternion q) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>Quaternion qmul(Quaternion q, Quaternion r) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>Quaternion qdiv(Quaternion q, Quaternion r) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>Quaternion qinv(Quaternion q) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>double qlen(Quaternion p) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>Quaternion qunit(Quaternion q) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>void qtom(Matrix m, Quaternion q) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>Quaternion mtoq(Matrix mat) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>Quaternion slerp(Quaternion q, Quaternion r, double a) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>Quaternion qmid(Quaternion q, Quaternion r) + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + </font></tt> + <tt><font size=+1>Quaternion qsqrt(Quaternion q)<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> + + The Quaternions are a non-commutative extension field of the Real + numbers, designed to do for rotations in 3-space what the complex + numbers do for rotations in 2-space. Quaternions have a real component + <i>r</i> and an imaginary vector component <i>v</i>=(<i>i</i>,<i>j</i>,<i>k</i>). Quaternions add + componentwise and multiply according to + the rule (<i>r</i>,<i>v</i>)(<i>s</i>,<i>w</i>)=(<i>rs</i>-<i>v</i>.<i>w</i>, <i>rw</i>+<i>vs</i>+<i>v</i>x<i>w</i>), where . and x are the ordinary + vector dot and cross products. The multiplicative inverse of a + non-zero quaternion (<i>r</i>,<i>v</i>) is (<i>r</i>,<i>-v</i>)/(<i>r</i>2-<i>v</i>.<i>v</i>). + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + The following routines do arithmetic on quaternions, represented + as<br> + + <table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td> + + <tt><font size=+1>typedef struct Quaternion Quaternion;<br> + struct Quaternion{<br> + + <table border=0 cellpadding=0 cellspacing=0><tr height=2><td><tr><td width=20><td> + + double r, i, j, k;<br> + + </table> + };<br> + </font></tt> + </table> + Name Description<br> + <tt><font size=+1>qadd</font></tt> Add two quaternions.<br> + <tt><font size=+1>qsub</font></tt> Subtract two quaternions.<br> + <tt><font size=+1>qneg</font></tt> Negate a quaternion.<br> + <tt><font size=+1>qmul</font></tt> Multiply two quaternions.<br> + <tt><font size=+1>qdiv</font></tt> Divide two quaternions.<br> + <tt><font size=+1>qinv</font></tt> Return the multiplicative inverse of a quaternion.<br> + <tt><font size=+1>qlen</font></tt> Return <tt><font size=+1>sqrt(q.r*q.r+q.i*q.i+q.j*q.j+q.k*q.k)</font></tt>, the length of + a quaternion.<br> + <tt><font size=+1>qunit</font></tt> Return a unit quaternion (<i>length=1</i>) with components proportional + to <i>q</i>’s. + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + A rotation by angle <i>θ</i> about axis <i>A</i> (where <i>A</i> is a unit vector) + can be represented by the unit quaternion <i>q</i>=(cos <i>θ</i>/2, <i>A</i>sin <i>θ</i>/2). + The same rotation is represented by -<i>q</i>; a rotation by -<i>θ</i> about -<i>A</i> + is the same as a rotation by <i>θ</i> about <i>A</i>. The quaternion <i>q</i> transforms + points by (0,<i>x’,y’,z’</i>) = <i>q</i>-1(0,<i>x,y,z</i>)<i>q</i>. Quaternion + multiplication composes rotations. The orientation of an object + in 3-space can be represented by a quaternion giving its rotation + relative to some ‘standard’ orientation. + <table border=0 cellpadding=0 cellspacing=0><tr height=5><td></table> + + The following routines operate on rotations or orientations represented + as unit quaternions:<br> + <tt><font size=+1>mtoq</font></tt> Convert a rotation matrix (see <a href="../man3/matrix.html"><i>matrix</i>(3)</a>) to a unit quaternion.<br> + <tt><font size=+1>qtom</font></tt> Convert a unit quaternion to a rotation matrix.<br> + <tt><font size=+1>slerp</font></tt> Spherical lerp. Interpolate between two orientations. The + rotation that carries <i>q</i> to <i>r</i> is <i>q</i>-1<i>r</i>, so <tt><font size=+1>slerp(q, r, t)</font></tt> is <i>q</i>(<i>q</i>-1<i>r</i>)<i>t</i>.<br> + <tt><font size=+1>qmid slerp(q, r, .5)<br> + qsqrt</font></tt> The square root of <i>q</i>. This is just a rotation about the same + axis by half the angle.<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/quaternion.c<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>, <a href="../man3/qball.html"><i>qball</i>(3)</a><br> + +</table> + +<td width=20> +<tr height=20><td> +</table> +<!-- TRAILER --> +<table border=0 cellpadding=0 cellspacing=0 width=100%> +<tr height=15><td width=10><td><td width=10> +<tr><td><td> +<center> +<a href="../../"><img src="../../dist/spaceglenda100.png" alt="Space Glenda" border=1></a> +</center> +</table> +<!-- TRAILER --> +</body></html> |