# csdms-contrib/slepian_alpha

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 function varargout=dphregion(th,N,region) % [phint,thp,php]=DPHREGION(th,N,region) % % Finds the longitude crossings at a given colatitude of the coastlines % of some region that is to be treated as occupying flat Cartesian % geometry (which is, admittedly, a bit of a limitation). % % INPUT: % % th Colatitudes where you want it evaluated [degrees] % N Smoothness of the spline version [only for region strings] % region A string: 'england', 'africa', 'namerica', 'greenland', % 'australia', 'eurasia', etc. OR % A matrix with XY/[lon,lat] coordinates [degrees] % note that this can be several closed curves separated by % a row of [NaN NaN] % % OUTPUT: % % phint Longitudinal interval(s) defining the integration domain % thp Colatitude matrix for plotting % php Longitude matrix for plotting % % EXAMPLE: % % dphregion('demo1',[],'africa') % dphregion('demo1',[],'contshelves') % dphregion('demo2',[],'eurasia') % dphregion('demo2',10) % % Last modified by fjsimons-at-alum.mit.edu, 07/11/2012 if ~isstr(th) % First, get the coordinates of region; these are sorted defval('N',10); if isstr(region) XY=eval(sprintf('%s(%i)',region,N)); else XY=region; end % Input now in colatitude XY(:,2)=90-XY(:,2); % Calculate the crossings of XY at th [phint,thp,php]=phicurve([XY(:,2) XY(:,1)],th); % Distribute output varns={phint,thp,php}; varargout=varns(1:nargout); % AFTER THIS NOTHING BUT DEMOS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% elseif strcmp(th,'demo1') defval('N',10) defval('region','africa') eval(sprintf('%s(%i)',region,N)); eval(sprintf('XY=%s(%i);',region,N)); thN=90-max(XY(:,2)); thS=90-min(XY(:,2)); XY(:,2)=90-XY(:,2); TH=thN+rand*(thS-thN); hold on XL=xlim; [phint,thp,php]=phicurve([XY(:,2) XY(:,1)],TH); pl=plot(php,90-thp,'g-','LineW',2); plot(XL,[90-TH 90-TH],'k--') p=plot(phint,90-TH,'o'); set(p,'MarkerE','k','MarkerF','y') t=title(num2str(length(phint)),'FontS',30); hold off if nargout==1 phint=dphi; end elseif strcmp(th,'demo2') % Plot this for the time being defval('region','africa') defval('N',200) ah(2)=subplot(212); ah(1)=subplot(211); Nk=100; eval(sprintf('%s(%i)',region,Nk)); eval(sprintf('XY=%s(%i);',region,Nk)); thN=90-max(XY(:,2)); thS=90-min(XY(:,2)); XY(:,2)=90-XY(:,2); thetas=linspace(thN,thS,N); hold on; p=[]; XL=xlim; for ind=1:length(thetas) TH=thetas(ind); l=plot(XL,[90-TH 90-TH],'k-'); % Add eps so it is never zero, essentially xmth=XY(:,2)-TH; dsx=diff(sign(xmth)); % Now it can be the one before, or after the crossing, how about colf=find(dsx); % This now returns the one on the negative side of the line colx=colf+(dsx(colf)==-2); colx2=colx-(dsx(colf)==-2)+(dsx(colf)==2); L(ind)=length(colx); if mod(L(ind),2) warning(sprintf('Cannot find pairs of crossings at th=%8.3f',TH)) end axes(ah(2)) plot(XY(:,1),xmth,'-+'); hold on; grid on xls=[min(XY(colx,1))-range(XY(colx,1))/3 ... max(XY(colx,1))+range(XY(colx,1))/3]; % We want the interpolated point at which it becomes exactly zero xlim(xls) plot(xls,[0 0],'k') ylim([-1 1]/100) % Then one point was exactly hit, this is the thN case if all(colx==colx2) dph=XY([colx(2) colx2(2)]); % This works else for ond=1:L(ind) dph(ond)=interp1(xmth([colx(ond) colx2(ond)]),... XY([colx(ond) colx2(ond)],1),0,'linear'); end end plot(XY(colx,1),xmth(colx),'bs'); plot(XY(colx2,1),xmth(colx2),'rv'); plot(dph,repmat(0,size(dph)),'g*'); clear dph hold off for indo=1:length(colx) axes(ah(1)) p(indo)=plot(XY(colx(indo),1),90-XY(colx(indo),2),'o'); end if ~isempty(p) set(p,'MarkerE','k','MarkerF','y') % t=text(362,58,num2str(L(ind)),'FontS',30); t=title(num2str(L(ind)),'FontS',30); pause delete([l p t]); p=[]; end end hold off disp(sprintf('Number of uneven crosses %i',sum(mod(L,2)))) else error('Speficy valid demo') end