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shapefinder3.m
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shapefinder3.m
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% Copyright 2016 Brian R. Long [email protected]
%
%
%
% If you use this software, please consider citing our related paper:
% B.R. Long and T.Q. Vu 'Spatial structure and diffusive dynamics from single-particle
% trajectories using spline analysis'
% Biophys J. 2010 Apr 21;98(8):1712-21.
%
% This file is part of splineAnalysis.
%
% splineAnalysis is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% splineAnalysis is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with splineAnalysis. If not, see <http://www.gnu.org/licenses/>.
function [comout, locout] = shapefinder3(traj, rshape, rshape2, firstpoint, splineParam)
% % inputs: traj a trajectory
% rshape the radius over which averages will be taken
% rdisp the distance between locout points
%
%
% output: comout points approximating the shape of the
% trajectory, including center-of-mass
% adjustments.
% locout same idea without the center-of-mass
% corrections
%%%%%%%%%%%%%% the first location is now an input,firstpoint, inferred from the output of the
%%%%%%%%%%%%%% preshape function.
% initializing a couple boolean values here:
endit = 0;
expando =0;
if nargin==4
locout(1,1:2)=firstpoint;
else
% point 1 is a little unusual. the first locout point is just the
% first point of the trajectory
locout(1,1:2) =[traj(1,1) traj(1,2)];
end
loc1 = locout(1,1:2);
% find the distance of each point from the first point in the trajectory:
distance1 = (traj(:,1)-loc1(1)).*(traj(:,1)-loc1(1))+(traj(:,2)-loc1(2)).*(traj(:,2)-loc1(2));
%now find the center of mass within rshape of locout(1,1:2):
comout(1,1:2) = mean(traj( distance1 < rshape^2 ,1:2),1);
comout(1,3) =1;
%%%%%%% now run through a loop stepping along the trajectory.
%%%%%%% This is arranged as a for loop, but functions a bit more like a while loop...subsequent
%%%%%%% versions could be an open-ended structure
if ~splineParam.noPlots
fig1 = figure;
end
for i = 2:(4*splineParam.nTrajShapePoints)
%%%% first, calculate the vectors between the com location (i-1) and each traj point
vectorsi(:,1) = traj(:,1)-comout(i-1,1);
vectorsi(:,2) = traj(:,2)-comout(i-1,2);
if expando
rshape2 = 2*rshape2;
endit = 1;
end
%%% now look at the particles in the annulus rshape < r < rshape2
avectorsi = vectorsi( (sum(vectorsi.^2,2)>rshape^2)&(sum(vectorsi.^2,2)<=rshape2^2),:);
apoints = traj( (sum(vectorsi.^2,2)>rshape^2)&(sum(vectorsi.^2,2)<=rshape2^2),:);
if ~splineParam.noPlots
figure(fig1)
plot(traj(:,1), traj(:,2), '.'), axis equal
hold all, plot(apoints(:,1), apoints(:,2), 'o')
hold all, plot(comout(i-1,1), comout(i-1,2),'* black')
rectangle('Position',[comout(i-1,1)-rshape, comout(i-1,2)-rshape, 2*rshape, 2*rshape], 'Curvature', 1)
rectangle('Position',[comout(i-1,1)-rshape2, comout(i-1,2)-rshape2, 2*rshape2,2*rshape2], 'Curvature', 1)
end
% now I need to identify the direction of the previous point... for the
% first time through the loop (i =2), there is no previous direction,
% only a previous point. so i'll have to use the direction with the
% highest density of particles.
%otherwise
if i ~=2
if ~expando
prevector = [comout(i-1,1)-comout(i-2,1), comout(i-1,2)-comout(i-2,2)];
else %if we're in expando mode (rshape2->2*rshape2), use previous, as long as there is one...
prevector = [comout(max(i-2,1),1)-comout(max(i-3,1),1), comout(max(i-2,1),2)-comout(max(i-3,1),2)] ;
end
else
prevector = [1,0]; % if there's no previous angle, just use the x axis.
end
if prevector(1)==0 % if there happened to be an expando mode point at the first point, this statement is needed
prevector = [1, 0];
end
%%%%%% below i'm using dot and cross products to figure out the angle.
%%%%% there still will be a reckoning needed to return to cartesian
%%%%% coordinates when the actual displacement is calculated.
% now calculating the cosine of the angle between prevector and avectorsi
% using the dot product
size(avectorsi(:,1)*prevector(1) + avectorsi(:,2)*prevector(2));
size((sqrt(sum(avectorsi.^2,2)*sum(prevector.^2))));
cosi = (avectorsi(:,1)*prevector(1) + avectorsi(:,2)*prevector(2))./(sqrt(sum(avectorsi.^2,2)*sum(prevector.^2)));
%%%%% but the cosine doesn't tell you the whole story. I'll use the sign of the cross
%%%%% product to get a sign to associate with the cosine.
signcrossi = sign(avectorsi(:,1).*prevector(2)-avectorsi(:,2).*prevector(1));
signcrossi(signcrossi(:) == 0)= 1;
% assign a nonzero value
% to the sign of the crossproduct for cases when the same location is
% found in the annuli of sequential angle searches.
angleinfoi = [cosi, signcrossi];
nangles =50;
subtend = splineParam.thetaRange;
angleincrement = (1/(2*(nangles+1)))*2*pi;
for bin = -nangles:nangles
binanglemin = max(-pi,bin*angleincrement-subtend/2);
binanglemax = min(bin*angleincrement + subtend/2, pi);
nsubtend(bin+nangles+1) = sum(acos(cosi).*signcrossi > binanglemin & acos(cosi).*signcrossi <=binanglemax);
end
angles = (-nangles:nangles)*angleincrement;
%%%% the first direction is just towards the maximum angle, but subsequent
%%%% (i>2) angles should be restricted to less than condition below
if i ==2
anglei = mean( angles(nsubtend== max(nsubtend)));
else
anglei = mean( angles((abs(angles) < splineParam.thetaMax)&(nsubtend== max(nsubtend(abs(angles) < splineParam.thetaMax)))));
end
sectoranglemin = max(-pi,anglei-subtend/2);
sectoranglemax = min(anglei + subtend/2, pi);
checktheangles(i) = anglei;
% the actual location set for the i-th point is the mean of the
% particle locations within the angle 'subtend/2' of 'anglei'.
locsubtend = apoints(acos(cosi).*signcrossi > sectoranglemin & acos(cosi).*signcrossi <=sectoranglemax,:);
if numel(locsubtend(:,1))== 0
if endit %if we've already been through this once (rshape2 is already expanded), quit the loop and get out
break
end
expando = 1;
comout(i,1:2) = comout(i-1,1:2);
comout(i,3) = 0;
continue
elseif numel(locsubtend(:,1))< 3
% if there are only 1 or 2 particles determining the location, mark
% the 3rd column of the comout array with a 0, in case these should be ignored
% in the spline fitting.
comout(i,1) = mean(locsubtend(:,1));
comout(i,2) = mean(locsubtend(:,2));
comout(i,3)=0;
if endit %if we've already been through this once, reset rshape2 and hope that
% things are back to normal.
rshape2 = rshape2/2;
endit = 0;
expando =0;
end
else
comout(i,3)=1;
comout(i,1) = mean(locsubtend(:,1));
comout(i,2) = mean(locsubtend(:,2));
if endit
rshape2 = rshape2/2;
endit = 0
expando =0;
end
end
end