From octave-sources-request at bevo dot che dot wisc dot edu  Fri May 28 04:22:01 1999
Subject: circlespace function
From: Rolf Fabian <fabian at tu-cottbus dot de>
To: "'octave-sources at bevo dot che dot wisc dot edu'" 	 <octave-sources@bevo.che.wisc.edu>
Date: Fri, 28 May 1999 11:25:47 +-200

##USAGE      circlespace( [ N{,M} ] {, CP, P } )
##	   N equally spaced points on a  unit - circle
##	   centered at origin of complex plane
##
##	   [ N,M ] vector first argument ( M>2 ) results in
##	   N*(M-1)  equally spaced points on a  polygon  of
##	   unit-radius  centered at origin of complex plane 
##	   ( corner points are always included )
##
##OPTIONS    scalar
##M {=2}     points per polygon side
##	   we get N*(M-1) different  points because corners
##	   are considered only once
##CP={0}     set flag to 'close' polygon     i.e. add copy of
##	   first point at end, return N*(M-1)+1 data points
##P {=0}     phase shift  -pi .. pi           real positive P 
##	   invokes counter-clockwise rotation of all points
##
##NOTE       * start is 1+0i on real positive axis (at P=0)
##	   * 'equally spaced' complex vector z means that
##	      abs(diff(z)) == CONST holds (as 'linspace')
##SEE ALSO   linspace, logspace
##AUTHOR     fabian at tu-cottbus dot de 990528

#EXA(a)	NOTE set CP flag to close circles/polygons 
#CP=1; circle=circlespace(201,CP); polygon=circlespace([7,11],CP)
#plot(circle,'+',polygon,'-*')
#EXA(b) include phase shift
#clg; hold on; CP=1;
#for k=0:5 plot(circlespace([5,4],CP,k*pi/30),sprintf("- at %d%d",k,k)); end

function y=circlespace( N, CP, P ) 

	if (nargin<3) P =0; end
	if (nargin<2) CP=0; end
	if (nargin<1||any(N<2))
		fprintf(stderr,"circlespace input error .. quit.\n");
		y=[]; return		
	end
	[nr,nc]=size(N);
	if	(max(nr,nc)==1)
		M=  2;			#scalar N
	else	M=N(2); N=N(1);		#vector
	end

	t= linspace(0,2*pi,N+1)'; 	#real parameter
	c= exp(i*(t+P));		#N+1 elements representing N corners
					#1st+last elements are identical
	if ( M>2 )
	   y=zeros(N*(M-1),1);		#init COL,  N sides * (M-1) points!
	   j=1:(M-1);
	   for k=1:N
		tmp=linspace(c(k),c(k+1),M).'; tmp(M)=[];
		y(j+(k-1)*(M-1))=tmp;
	   end
	   if ( CP) y=[y;y(1)]; end
	else
	   y = c;
	   if (!CP) y(N+1)=[];	end	#evenually rm 'closed loop' entry
	end

endfunction