Cartesian to Polar

Good Afternoon All,

I have a data file of cartesian coordinates that make a cylinder. I wish to take each "layer" or "slice" of the cylinder and transform into polar coordinates. If there is no tilt I can sort the coordinates by height (z). However what if there is a tilt on the axis how can I possible sort the coordinates so I can correctly obtain the correct polar coordinates? If I sort just by height I get an incorrect order of cylinder points for a tilt. Please see picture below.

http://www.mediafire.com/i/?trkt517betm434q

Also I have the code correct for no tilt but am unsure if the code is correct for an axis tilted. Any help is greatly appreciated.

function [profile, angles] = importbore1(layer,rm)
%IMPORTBORE Imports grid and displacement data from "grid.dat" and "3L_stopper_displaced.dat."
% [profile, angles] = importbore(layer,rm) imports deck (or layer) from above data set.
% rm = known radius of bore/ring
% profile = bore profile (radius as a function of angle)
% angles = angles for which profile is known

%load data files here (reverse ordering)
A=importdata('sorted_coordinates.dat');
A = flipud(A);
B=importdata('sorted_displacement.dat ');
B = flipud(B);
len = length(A);

%get grid locations and each component of displacement
x0 = A(1:len,2); y0 = A(1:len,3); z0 = A(1:len,4);
dx0 = B(1:len,2); dy0 = B(1:len,3); dz0= B(1:len,4);

%Bottom and Top deck centers
XCent = [0.004256, 0.004256]; YCent = [305.495, 305.495]; ZCent = [196, 74.25];
%the cylinder is sometimes titled in a V-engine, rotate s.t. parrallel with z-axis so center coordinates will vary
%[THETA,RHO] = cart2pol((x0 or y0),z0); %if axis is tilted
[TH,PHI,R] = cart2sph(dx0,dy0,dz0);
%tiltangle=atan((ZCent(2)-ZCent(1))/(XCent(or YCent)(2)-XCent (or YCent)(1))); %if tilted
%tiltangle=pi/4;
%THETA = THETA+tiltangle; %if tilted
%PHI = PHI + tiltangle; %if tilted
x=x0;y=y0;z=z0;
%[(x or y),z] = pol2cart(THETA,RHO); %if tilted
[dx,dy,dz]=sph2cart(TH,PHI,R);
%[THETA,RHO] = cart2pol((XCent or YCent),ZCent); %if tilted
%THETA = THETA+tiltangle; %if tilted
%[(XCent,YCent) ZCent] = pol2cart(THETA,RHO); %if tilted

%extract the deck: All decks have 72 nodes
SP = 73*(layer-1); num = 71;
%SP = (points + 1)*(layer-1); num = (points - 1);
if layer == 1
    SP = SP+1; num = 71;
end
if layer> 2
    SP = SP-(layer-2);
end
boreX = x(SP:SP+num); boreY = y(SP:SP+num); boreZ = z(SP:SP+num);
dispX = dx(SP:SP + num); dispY = dy(SP:SP + num); dispZ= dz(SP:SP + num);
centX = XCent(1); centY = YCent(1); centZ = mean(boreZ);

%calculate radial component, throw away the rest
for i=1:length(boreX)
    rv = [boreX(i)-centX, boreY(i)-centY];
    [angles1(i),grid(i)] = cart2pol(rv(1),rv(2));
    deltar(i)=cos(angles1(i))*dispX(i) + sin(angles1(i))*dispY(i);
end

%generate the profile (make sure angles are increasing)
prof = ([angles1;rm + deltar])';
prof = sortrows(prof);

angles = (prof(:,1))';
profile = (prof(:,2))';

[Oleg Komarov]

Please format the code: http://www.mathworks.com/matlabcentral/answers/13205-tutorial-how-to-format-your-question-with-markup#answer_18099

Answer 1

[Sean de Wolski]

FEX:AxelRot

I think this might be what you want.

[Melissa]

Thank you very much for always responding. Another way which worked nice was sorting by height then converting teh data to polar coordinates before sorting.