<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN"> <!--Converted with LaTeX2HTML 2008 (1.71) original version by: Nikos Drakos, CBLU, University of Leeds * revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan * with significant contributions from: Jens Lippmann, Marek Rouchal, Martin Wilck and others --> <HTML> <HEAD> <TITLE>Perpendicular</TITLE> <META NAME="description" CONTENT="Perpendicular"> <META NAME="keywords" CONTENT="gnuplot"> <META NAME="resource-type" CONTENT="document"> <META NAME="distribution" CONTENT="global"> <META NAME="Generator" CONTENT="LaTeX2HTML v2008"> <META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css"> <LINK REL="STYLESHEET" HREF="gnuplot.css"> <LINK REL="previous" HREF="node134.html"> <LINK REL="up" HREF="node127.html"> <LINK REL="next" HREF="node136.html"> </HEAD> <BODY > <!--Navigation Panel--> <A NAME="tex2html3020" HREF="node136.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> <A NAME="tex2html3014" HREF="node127.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> <A NAME="tex2html3010" HREF="node134.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> <A NAME="tex2html3016" HREF="node1.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A> <A NAME="tex2html3018" HREF="node467.html"> <IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index" SRC="index.png"></A> <BR> <B> Next:</B> <A NAME="tex2html3021" HREF="node136.html">Binary examples</A> <B> Up:</B> <A NAME="tex2html3015" HREF="node127.html">Keywords</A> <B> Previous:</B> <A NAME="tex2html3011" HREF="node134.html">Rotate</A> <B> <A NAME="tex2html3017" HREF="node1.html">Contents</A></B> <B> <A NAME="tex2html3019" HREF="node467.html">Index</A></B> <BR> <BR> <!--End of Navigation Panel--> <H5><A NAME="SECTION040142278000000000000"></A> <A NAME="binary_general_keywords_perpendicular"></A> <BR> Perpendicular </H5> For <B>splot</B>, the concept of a rotational vector is implemented by a triple representing the vector to be oriented normal to the two-dimensional x-y plane. Naturally, the default is (0,0,1). Thus specifying both rotate and perpendicular together can orient data myriad ways in three-space. <P> The two-dimensional rotation is done first, followed by the three-dimensional rotation. That is, if R' is the rotational 2 x 2 matrix described by an angle, and P is the 3 x 3 matrix projecting (0,0,1) to (xp,yp,zp), let R be constructed from R' at the upper left sub-matrix, 1 at element 3,3 and zeros elsewhere. Then the matrix formula for translating data is v' = P R v, where v is the 3 x 1 vector of data extracted from the data file. In cases where the data of the file is inherently not three-dimensional, logical rules are used to place the data in three-space. (E.g., usually setting the z-dimension value to zero and placing 2D data in the x-y plane.) <BR><HR> <ADDRESS> 2010-08-17 </ADDRESS> </BODY> </HTML>
