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Signed-off-by: 刘明宏 <liuminghong@mail.sdu.edu.cn>
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刘明宏
2023-06-22 06:27:19 +00:00
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父节点 186f84784d
当前提交 90b2d9ba09
共有 13 个文件被更改，包括 898 次插入 和 0 次删除
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33
lib/AddBlocks.m 普通文件
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function [object_blk,blk_pos_corner ]=AddBlocks(model,blk)
%Add blocks, used in model expansion and loading rectangular sources on the topographic surface
blk_pos_corner = [];
ins0 = 0;
for n = 1:size(blk.Lx,2)
%Size unit：m
lenx = blk.Lx(n);
leny = blk.Ly(n);
lenz = blk.Lz(n);
%Center position coordinate
xc = blk.CentCoord(n,1);
yc = blk.CentCoord(n,2);
zc = blk.CentCoord(n,3);
blk_position = [xc yc zc];
blk_size = [lenx leny lenz];
blkLabel = ['blk' num2str(n+ins0)];
model.geom('geom1').feature.create(blkLabel,'Block');
model.geom('geom1').feature(blkLabel).set('size',blk_size);
model.geom('geom1').feature(blkLabel).set('pos',blk_position);
model.geom("geom1").feature(blkLabel).set("rot", blk.angle);
model.component("mod1").geom("geom1").feature( blkLabel).set("base", "center");
object_blk{n} = blkLabel;
temp = [];
blk_pos_corner = cat(1, blk_pos_corner, temp);
end
model.component("mod1").geom("geom1").run();

34
lib/AddRecParametricSurface.m 普通文件
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function [object_rec,ps_pos_rec ]=AddRecParametricSurface(model,rec,lengthcurve,heightcurve)
%
%A vertical auxiliary parametric surfaces are added for constructing the
% receives on the terrain surface
% ins0 = 0;
% xrec=[2 10];
% yrec=[0 0];
% zrec=[0 0];
% lengthcurve=[5 5];
% heightcurve=5;
x = rec(:,1);
y = rec(:,2);
z = rec(:,3);
nrec = length(x);
object_rec=cell(1,nrec);%{};
ps_pos_rec=[];
ins0 = 0;
for n = 1:nrec
psLabel = ['ps' num2str(n+ins0)];
ps(n+ins0)= model.geom('geom1').feature.create( psLabel ,'ParametricSurface');
model.geom('geom1').feature( psLabel ).set('parmin1',num2str(x(n)-lengthcurve/2));
model.geom('geom1').feature( psLabel ).set('parmin2',num2str(z(n)-heightcurve));
model.geom('geom1').feature( psLabel ).set('parmax1',num2str(x(n)+lengthcurve/2));
model.geom('geom1').feature( psLabel ).set('parmax2',num2str(z(n)+heightcurve));
model.geom('geom1').feature( psLabel ).set('coord',{'s1',num2str(y(n)),'s2'});
model.geom('geom1').feature( psLabel ).set('maxknots',{'4'});
object_rec{n} = psLabel;
ps_pos_temp = [x(n)-lengthcurve/2 y(n) z(n)-heightcurve x(n)-lengthcurve/2 y(n) z(n)+heightcurve];
ps_pos_rec = cat(1, ps_pos_rec, ps_pos_temp);
end
model.component("mod1").geom("geom1").run();

13
lib/AndInterpolationCurve.m 普通文件
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function objectIPC = AndInterpolationCurve(model,filenames)
%Interpolating curves are added, which can be used to construct 3D irregular volumes
for n = 1:size(filenames,1)
IPCname =['ipc' num2str(n)];
model.geom('geom1').create(IPCname, 'InterpolationCurve');
model.geom('geom1').feature(IPCname).set('type', 'closed');
model.geom('geom1').feature(IPCname).set('source', 'file');
model.geom('geom1').feature(IPCname).set('filename', filenames{n});
model.geom('geom1').feature(IPCname).set('struct', 'sectionwise');
objectIPC{n} = IPCname;
end
model.geom('geom1').run;

13
lib/AndPoint.m 普通文件
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function objectIPC = AndPoint(model,p)
% Add points that can be used for the endpoints of 3D irregular volumes
for np = 1:size(p,1)
PTname =['pt' num2str(n)];
model.geom("geom1").create(PTname, "Point");
model.geom("geom1").feature(PTname).setIndex("p", p(np,1), 0);
model.geom("geom1").feature(PTname).setIndex("p", p(np,2), 1);
model.geom("geom1").feature(PTname).setIndex("p", p(np,3), 2);
objectPT{n} = PTname;
end
model.geom('geom1').run;
end

19
lib/Comsol_with_Matlab_Start.m 普通文件
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% Start the 'COMSOL Multiphysics with MATLAB' interfaces
% Required: '...\comsolmphserver.exe' and '...\Multiphysics\mli' file address
% You can also manually launch the executable COMSOL Multiphysics with MATLAB. exe
path = pwd;
try
mphtags -show
warning('Already connected to a server!');
catch
winopen('D:\Software\COMSOL60\Multiphysics\bin\win64\comsolmphserver.exe');
cd 'D:\Software\COMSOL60\Multiphysics\mli';
mphstart;
end
cd(path);

9
lib/Variables 1.txt 普通文件
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rho_xy ((abs((Ex2_G*mf.Hx-Ex1_G*mf2.Hx)/(mf.Hx*mf2.Hy-mf2.Hx*mf.Hy)))^2/(2*pi*freq*mu0_const)) "Apparent resistivity, xy"
rho_yx ((abs((Ey1_G*mf2.Hy-Ey2_G*mf.Hy)/(mf.Hx*mf2.Hy-mf2.Hx*mf.Hy)))^2/(2*pi*freq*mu0_const)) "Apparent resistivity, yx"
rho_xx ((abs((Ex1_G*mf2.Hy-Ex2_G*mf.Hy)/(mf.Hx*mf2.Hy-mf2.Hx*mf.Hy)))^2/(2*pi*freq*mu0_const)) "Apparent resistivity, xx"
rho_yy ((abs((Ey2_G*mf.Hx-Ey1_G*mf2.Hx)/(mf.Hx*mf2.Hy-mf2.Hx*mf.Hy)))^2/(2*pi*freq*mu0_const)) "Apparent resistivity, yy"
phi_xy arg(1[S]*(Ex2_G*mf.Hx-Ex1_G*mf2.Hx)/(mf.Hx*mf2.Hy-mf2.Hx*mf.Hy))[rad] "Apparent resistivity phase, xy"
phi_yx arg(1[S]*(Ey1_G*mf2.Hy-Ey2_G*mf.Hy)/(mf.Hx*mf2.Hy-mf2.Hx*mf.Hy))[rad] "Apparent resistivity phase, yx"
phi_xx arg(1[S]*(Ex1_G*mf2.Hy-Ex2_G*mf.Hy)/(mf.Hx*mf2.Hy-mf2.Hx*mf.Hy))[rad] "Apparent resistivity phase, xx"
phi_yy arg(1[S]*(Ey2_G*mf.Hx-Ey1_G*mf2.Hx)/(mf.Hx*mf2.Hy-mf2.Hx*mf.Hy))[rad] "Apparent resistivity phase, yy"
S abs((mf2.Ex/mf2.Hx+mf.Ey/mf.Hy)/(mf.Ex/mf.Hy-mf2.Ey/mf2.Hx)) ""

12
lib/Variables 2.txt 普通文件
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Ex1_G real(mf.Ex)+mf.omega*1[s]*imag(d(mf.psi0,x))/1[S/m]+i*(imag(mf.Ex)+mf.omega*1[s]*real(d(mf.psi0,x))/1[S/m]) ""
Ey1_G real(mf.Ey)+mf.omega*1[s]*imag(d(mf.psi0,y))/1[S/m]+i*(imag(mf.Ey)+mf.omega*1[s]*real(d(mf.psi0,y))/1[S/m]) ""
Ez1_G real(mf.Ez)+mf.omega*1[s]*imag(d(mf.psi0,z))/1[S/m]+i*(imag(mf.Ez)+mf.omega*1[s]*real(d(mf.psi0,z))/1[S/m]) ""
Ex2_G real(mf2.Ex)+mf2.omega*1[s]*imag(d(mf2.psi0,x))/1[S/m]+i*(imag(mf2.Ex)+mf2.omega*1[s]*real(d(mf2.psi0,x))/1[S/m]) ""
Ey2_G real(mf2.Ey)+mf2.omega*1[s]*imag(d(mf2.psi0,y))/1[S/m]+i*(imag(mf2.Ey)+mf2.omega*1[s]*real(d(mf2.psi0,y))/1[S/m]) ""
Ez2_G real(mf2.Ez)+mf2.omega*1[s]*imag(d(mf2.psi0,z))/1[S/m]+i*(imag(mf2.Ez)+mf2.omega*1[s]*real(d(mf2.psi0,z))/1[S/m]) ""
normE1_G sqrt(Ex1_G^2+Ey1_G^2+Ez1_G^2) ""
normE2_G sqrt(Ex2_G^2+Ey2_G^2+Ez2_G^2) ""
normE2_G2 sqrt(Ey2_G^2+Ez2_G^2) ""
Eyz_r (sqrt(real(Ey2_G)^2+real(Ez2_G)^2)) ""
Eyz_i (sqrt(imag(Ey2_G)^2+imag(Ez2_G)^2)) ""
Exy_i (sqrt(imag(Ex2_G)^2+imag(Ey2_G)^2)) ""

17
lib/get_curveTxtFile.m 普通文件
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%Gets the path of a file with a specific character in the folder
function filenames = get_curveTxtFile(data_dir,id,str)
% data_dir：folder path
% id：The position of the character
% Finding characters
% example: curve_01.txt;curve_02.txt
% CurveFiles = get_curveTxtFile(data_dir,[1:5],'curve');
D = dir(data_dir );
nf = 0;
for i=3:numel(D)
if strcmp(D(i).name(id),str)
nf = nf+1;
filenames{nf,1} = [data_dir '\' D(i).name] ;
end
end

420
lib/interpclosed.m 普通文件
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function varargout = interpclosed(x,y,varargin)
% INTERPCLOSED Arc-length interpolation, perimeter and area of 2D closed curves defined by points
%
% xyq = INTERPCLOSED(x,y,tq) Interpolates new data points xyq at given
% positions defined by an arc-length parametrization and the query points
% tq, along the closed curve defined by the points specified by x and y.
% The default method 'spline' is used. tq is a n-by-1 array with its
% elements constrained within [0,1], with 0 being the first point of the
% curve and 1 the last one.
%
% [len,area] = INTERPCLOSED(x,y) If tq is not specified and two output
% variables are requested, then only the perimeter and area of the
% interpolated curve are returned. Both outputs are obviously scalars.
%
% [len,area,c] = INTERPCLOSED(x,y) If tq is not specified and three output
% variables are requested, then the perimeter, area and centroid of the
% interpolated curve are returned. The centroid is a vector with the
% position as (x,y).
%
% [len,area,c,I] = INTERPCLOSED(x,y) If tq is not specified and four output
% variables are requested, then the perimeter, area, centroid, and second
% moments of area of the interpolated curve are returned. The second moment
% of area is a vector with three elements: (Ixx, Iyy, Ixy).
%
% pp = INTERPCLOSED(x,y,'pp') If only one output argument is defined and
% the string 'pp' is given as input, the returned variable is the piesewise
% polynomial pp, regardless of the definition of tq.
%
% [xyq,len,area] = INTERPCLOSED(x,y,tq) If tq is provided and there are
% three output variables, the perimeter and area are additionally returned.
%
% [xyq,len,area,c,I] = INTERPCLOSED(x,y,tq) If tq is provided and there are
% five output variables, the perimeter, the area, the centroid, and the
% second moments of area are additionally returned.
%
% [___] = INTERPCLOSED(___,method) By specifying the string method it
% is possible to change how the interpolated points are obtained.
% 'linear': Linear interpolation. The interpolated value at a query point
% is based on linear interpolation of the values at neighboring
% points in each respective dimension. This is the fastest
% method.
% 'spline': Spline interpolation using periodic end conditions. The
% interpolated value at a query point is based on a cubic
% interpolation of the values at neighboring points in each
% respective dimension. This is the default method.
% 'pchip': Shape-preserving piecewise cubic interpolation. The
% interpolated value at a query point is based on a shape-
% preserving piecewise cubic periodic interpolation of the
% values at neighboring points.
%
% [___] = INTERPCLOSED(___,print) By setting the boolean variable print to
% true, more details about the interpolation can be obtained.
%
% Examples:
% 1) Use the spline method to interpolate at 64 query points within the
% 8 points used to sample the original circle:
%
% t = linspace(0,2*pi,9);
% x = sin(t) + 0.2; y = cos(t) - 0.2;
% [len,area,c,I] = interpclosed(x,y);
% fprintf(['Perimeter: %4.5f, Area: %4.5f,\n',...
% 'Centroid: [%4.5f %4.5f], Iz: %4.5f\n',...
% 'To be compared to\n',...
% '2*pi: %4.5f, pi: %4.5f,\n',...
% 'Centroid: [%4.5f %4.5f], pi/2: %4.5f\n'],...
% len,area,c,(I(1)-area*c(2)^2+I(2)-area*c(1)^2),...
% 2*pi,pi,[0.2,-0.2],pi/2)
%
% 2) Get the piecewise polyonomial of a linear interpolation of a given
% set of points and use the polynomial to make a plot:
%
% x = [0 .82 .92 0 -.92 -.82]; y = [.66 .9 0 -.83 0 .9];
% pp = interpclosed(x,y,'pp','linear');
% tq = min(pp.breaks):0.001:max(pp.breaks);
% xyq = ppval(pp,tq);
% figure, plot(xyq(1,:),xyq(2,:))
%
% Find more examples in the File Exchange website.
%
% See also CSCVN, PCHIP, MKPP, PPVAL, INTERPARC, ARCLENGTH, INTERP1.
%
% Author: Santiago M. Benito
% Ruhr-Universität Bochum
% -------------------------------------------------------------------------
% Contact: santiago.benito@rub.de
% -------------------------------------------------------------------------
% Current version: 3.0
% -------------------------------------------------------------------------
% Last updated: 17.05.2021
% Changes:
% - It is now possible to compute the second moments of area of the
% fit with this function.
%% Manage input, output and catch eventual problems.
% Check for errors in the given inputs.
if nargin < 2
error('INTERPCLOSED:insufficientarguments', ...
'At least x and y must be supplied.')
end
if ~isvector(x) || ~isvector(y) || (length(x) ~= length(y))
error('INTERPCLOSED:baddimension', ...
'x and y must be vectors of the same length.')
end
% Set defaults.
method = 'spline';
print = false;
geomcalc = false; tqgiven = false;
pp = false;
% Initialize output variables.
len = 0;
area = 0;
c = zeros(1,2);
Ixx = 0; Iyy = 0; Ixy = 0;
% Check for other input arguments.
if numel(varargin) > 0
% At least one other argument was supplied.
for ii = 1:numel(varargin)
arg = varargin{ii};
if ischar(arg)
% It can be the method or the 'pp'-flag.
validstrings = {'pp','linear' 'pchip' 'spline'};
ind = strncmp(arg,validstrings,2);
if isempty(ind) || (sum(ind) == 0) || (sum(ind) > 1)
error('INTERPCLOSED:invalidmethod', ...
['Invalid method indicated. Only ''linear'',',...
'''pchip'',''spline'' allowed.'])
end
if ind(1) == 1
pp = true;
else
method = validstrings{ind>0};
end
elseif islogical(arg)
% It must be the print variable, set the print sampling distance.
if ~tqgiven, tq = 0:1/32:1; end
print = arg;
else
% It must be tq, defining the parametric arc-length query
% points
if ~isnumeric(arg)
error('INTERPCLOSED:badtq', ...
'tq must be numeric.')
else
if max(arg) > 1 || min(arg) < 0
error('INTERPCLOSED:badtq', ...
'tq elements must be bigger than 0 and smaller than 1.')
end
tqgiven = true;
tq = arg;
end
end
end
end
% If only one output variable is requested and the 'pp' flag was given, no
% need to compute the interpolations, regardless of the definition of tq.
% If three are given, geometry computations will be needed. If two or three
% are given, but tq was not provided, also compute the geometry computations.
if nargout == 1 && pp && ~print
tqgiven = false;
elseif (nargout == 2 || nargout == 3 || nargout == 4) && ~tqgiven
geomcalc = true;
elseif (nargout == 3 || nargout == 4 || nargout == 5)
geomcalc = true;
if ~tqgiven
error('INTERPCLOSED:badtq', ...
'tq was not defined and is needed for interpolation.')
end
end
% Be sure everything is formatted correclty and group it.
x = x(:)'; y = y(:)';
points = [x;y];
% Round to the 15th decimal position to avoid rounding errors. This is
% necessary for the function to recongnize start and ending points
% properly.
points = round(points,15);
% If the set of points does not describe a closed loop, close it.
if sum(points(:,1) ~= points(:,end)) > 0
points = [points,points(:,1)];
end
% If less than three distinct points are given, no closed curve can be
% formed.
d = sum((diff(points.').^2).');
if numel(x) - sum(d==0)-1 < 2
error('INTERPCLOSED:baddimension', ...
'x and y must be vectors describing at least three distinct points.')
end
%% Actual program start
% Compute the coefficients of the fit-polynomials according to the user's
% choice.
if strcmpi(method,'linear')
% Remove segments with length equal to zero, the linear interpolation
% has no continuous derivatives anyway.
points(:,d==0) = [];
% Compute the linear coefficients of the parametric versions of the
% lines. First compute the lengths of each segment, then the cumulative
% length and finally use the slope in each direction to get the coefs.
seglen = sqrt(sum(diff(points,[],2).^2,1));
cumarc = [0,cumsum(seglen)];
coefX = [diff(points(1,:))./diff(cumarc);points(1,1:(end-1))];
coefY = [diff(points(2,:))./diff(cumarc);points(2,1:(end-1))];
% Create a piecewise polynomial with the given coefficients.
coefs = zeros(size([coefX,coefY]));
coefs(:,1:2:end) = coefX;
coefs(:,2:2:end) = coefY;
curve = mkpp(cumarc,coefs',2);
% Provide the differentiation array for later use.
diffarray = [0 0 1;0 0 0];
% Since we already have the lenghts of the individual segments, just
% sum everything up and save some time.
len = sum(seglen);
elseif strcmpi(method,'spline')
% MATLAB(R) already has a very useful function that makes all the work
% for us.
curve = cscvn(points);
% Provide the differentiation array for later use.
diffarray = [3 0 0;0 2 0;0 0 1;0 0 0];
elseif strcmpi(method,'pchip')
% Like in the function CSCVN, if the user specified a point where the
% 2nd derivative is equal to zero, we have to be able to handle the
% situation.
d = sum((diff(points.').^2).');
if all(d > 0)
% The fit is periodic. To have the start and end slopes equal to
% each other, some tricks must be done. Extra points will be added
% right before the start and right after the end of the data set.
% The fit will be performed with these points, and then the extra
% pieces will be removed from the general fit.
%pointsNew = [x(end-2:end-1),x,x(2:3);y(end-2:end-1),y,y(2:3)];
pointsNew = [points(:,end-2:end-1),points,points(:,2:3)];
% We need the arc length of the modified dataset, therefore we will
% compute it here.
seglen = sqrt(sum(diff(pointsNew,[],2).^2,1));
cumarc = [0,cumsum(seglen)];
% Fit coefficients are obtained from the MATLAB(R) original pchip
% function.
temp = pchip(cumarc,pointsNew(1,:)); coefX = temp.coefs;
temp = pchip(cumarc,pointsNew(2,:)); coefY = temp.coefs;
% Here we remove the unnecesary pieces by removing the extra
% coefficients.
coefs = zeros(size([coefX;coefY])-[8,0]);
coefs(1:2:end,:) = coefX(3:end-2,:);
coefs(2:2:end,:) = coefY(3:end-2,:);
% Compute the actual arc length
seglen = sqrt(sum(diff(points,[],2).^2,1));
cumarc = [0,cumsum(seglen)];
else
% The 1st derivatives at the end points and at the specified points
% are not equal, while analysed from both sides. Firstly compute
% the arclength of the point distribution.
seglen = sqrt(sum(diff(points,[],2).^2,1));
cumarc = [0,cumsum(seglen)];
% Fit coefficients are obtained from the MATLAB(R) original pchip
% function, according to the desired derivative contiguity.
dp = find(d>0);
dpbig = find(diff(dp)>1);
dpbig = [dpbig,length(dp)];
idx = dp(1):(dp(dpbig(1))+1);
temp = pchip(cumarc(idx),points(1,idx)); coefX = temp.coefs;
temp = pchip(cumarc(idx),points(2,idx)); coefY = temp.coefs;
for j=2:length(dpbig)
idx = dp(dpbig(j-1)+1):(dp(dpbig(j))+1);
temp = pchip(cumarc(idx),points(1,idx));
coefX = [coefX;temp.coefs];
temp = pchip(cumarc(idx),points(2,idx));
coefY = [coefY;temp.coefs];
end
% Compiling the coefficients in a simple array.
coefs = zeros(size([coefX;coefY]));
coefs(1:2:end,:) = coefX(1:end,:);
coefs(2:2:end,:) = coefY(1:end,:);
% Update the cumulative arclength
cumarc(:,d==0) = [];
end
% Finally compute the piecewise polynomial.
curve = mkpp(cumarc,coefs,2);
% Provide the differentiation array for later use.
diffarray = [3 0 0;0 2 0;0 0 1;0 0 0];
end
% If tq is given (or a print is required), compute the interpolation using
% the piecewise evaluation function provided in MATLAB(R) and then convert
% the parametrization into an arc-lenght one.
if tqgiven || print
step = (max(curve.breaks)-min(curve.breaks))/numel(tq)/30;
auxtq = min(curve.breaks):step:max(curve.breaks);
xyq = ppval(curve,auxtq);
tqp = pdearcl(auxtq,xyq,tq,0,1);
xyq = ppval(curve,tqp);
end
% If the geometric parameters (perimeter and area) are required, compute
% them using some calculus.
if geomcalc
for ii = 1:curve.pieces
% Get the coefficients of the piecewise polynomial expresions of
% the parametric form.
coefX = curve.coefs(2*ii-1,:);
coefY = curve.coefs(2*ii,:);
% Obtain the derivatives of the polynomials.
difX = coefX*diffarray;
difY = coefY*diffarray;
% The length in the linear case is already computed, skip this bit.
if ~strcmpi(method,'linear')
% Define the function employed in the arc length and integrate
% it.
flen = @(t) sqrt(polyval(difX,t-curve.breaks(ii)).^2 ...
+ polyval(difY,t-curve.breaks(ii)).^2);
len = len + integral(flen,curve.breaks(ii),curve.breaks(ii+1));
end
% The area integral is computed here.
farea = @(t) polyval(conv(coefY,difX),...
t-curve.breaks(ii));
area = area + integral(farea,curve.breaks(ii),...
curve.breaks(ii+1));
% The centroid is computed here
fcx = @(t) polyval(conv(coefX,conv(coefY,difX)),...
t-curve.breaks(ii));
c(1) = c(1) + integral(fcx,curve.breaks(ii),...
curve.breaks(ii+1));
fcy = @(t) polyval(conv(coefY,conv(coefX,difY)),...
t-curve.breaks(ii));
c(2) = c(2) - integral(fcy,curve.breaks(ii),...
curve.breaks(ii+1));
% The area moments of inertia
fIxx = @(t) polyval(conv(coefY,conv(coefY,conv(coefY,difX))),...
t-curve.breaks(ii));
Ixx = Ixx + integral(fIxx,curve.breaks(ii),...
curve.breaks(ii+1));
fIyy = @(t) polyval(conv(coefX,conv(coefX,conv(coefX,difY))),...
t-curve.breaks(ii));
Iyy = Iyy - integral(fIyy,curve.breaks(ii),...
curve.breaks(ii+1));
fIxy = @(t) polyval(conv(coefY,conv(coefY,conv(coefX,difX))),...
t-curve.breaks(ii));
Ixy = Ixy + integral(fIxy,curve.breaks(ii),...
curve.breaks(ii+1));
end
c = c / area;
I = [1/3*Ixx,1/3*Iyy,1/2*Ixy]*sign(area);
area = abs(area);
end
%% If required, print some figures to show what the algorithm did.
if print
figure
subplot(1,2,1)
plot(xyq(1,:),xyq(2,:),'*')
hold on
plot(points(1,:),points(2,:),'o')
plot(c(1),c(2),'x')
xlabel('x'), ylabel('y'), hold off, axis equal
title('Cartesian representation'), legend('Interpolation','Points',...
'Centroid')
subplot(1,2,2)
plot(tq,xyq), hold on
for ii = (curve.breaks)/max(curve.breaks)
line([ii ii],ylim,'LineStyle','--','Color','k')
line([ii ii],ylim,'LineStyle','--','Color','k')
end
hold off, xlim([min(tq) max(tq)]), title('Parametric representation')
xlabel('t'), ylabel('x(t), y(t)'), legend('x(t)','y(t)')
end
%% Process adequately the variables to be returned.
if nargout == 2 && ~tqgiven
varargout{1} = len; varargout{2} = area;
elseif nargout == 3 && ~tqgiven
varargout{1} = len; varargout{2} = area; varargout{3} = c;
elseif nargout == 3
varargout{1} = xyq;
varargout{2} = len; varargout{3} = area;
elseif nargout == 4 && tqgiven
varargout{1} = xyq;
varargout{2} = len; varargout{3} = area; varargout{4} = c;
elseif nargout == 4 && ~tqgiven
varargout{1} = len; varargout{2} = area; varargout{3} = c;
varargout{4} = I;
elseif nargout == 5
varargout{1} = xyq;
varargout{2} = len; varargout{3} = area; varargout{4} = c;
varargout{5} = I;
elseif nargout == 1 && pp
varargout{1} = curve;
else
varargout{1} = xyq;
end

30
lib/lofting.m 普通文件
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function model = lofting(model,data_dir)
%Constructed Irregular 3D volumes from 2D contour curves
% example:
% Comsol_with_Matlab_Start;
% import com.comsol.model.util.*
% model = ModelUtil.create('Model1');% ModelUtil.remove('Model');
% model.modelNode.create('mod1');
% model.geom.create('geom1', 3);
% model.mesh.create('mesh1', 'geom1');
% data_dir = pwd ;
% model = lofting(model,data_dir)
CurveFiles = get_curveTxtFile(data_dir,[1:5],'curve');
objectIPC = AndInterpolationCurve(model,CurveFiles);
model.geom("geom1").create("loft1", "Loft");
model.geom("geom1").feature("loft1").selection("profile").set(objectIPC);
model.geom("geom1").feature("loft1").set("facepartitioning", "grid");
% model.geom("geom1").create("pare1", "PartitionEdges");
try
model.component("mod1").geom("geom1").run();
catch
warning('The automatic lofting failed, so the Partition Edges had to be added manually.');
end
mphlaunch(model);
end

27
lib/plotSlice.m 普通文件
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figure;
xyzID = ['X';'Y';'Z'];
scatter(Pn(:,1),Pn( :,2),3,"filled");
hold on;
plot(Pn(k,1),Pn(k,2),'g--','LineWidth',2);
hold on;
plot(PI(1,:),PI(2,:),'k','LineWidth',2);
title(['Silce' num2str(i)],'FontSize',12,'FontWeight','bold');
xlabel([xyzID(planeID(1)) '(m)']);
ylabel([xyzID(planeID(2)) '(m)']);
l=legend('Point cloud slice','Point cloud boundary','Smooth boundary');
set(l,'Box','off','FontSize',10);
set(gca,'color','none','linewidth',1,'FontSize',12,'FontWeight','bold');
set(gcf,'Position', [713.8000 224.2000 404.8000 361.6000]);
box on;
axis tight
axis equal;
% xlim([80,200]);
% ylim([-120,120]);
% set(gca,'color','none');
% set(gcf,'color','none');

241
lib/smooth1q.m 普通文件
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function [z,s] = smooth1q(y,s,varargin)
%SMOOTH1Q Quick & easy smoothing.
% Z = SMOOTH1Q(Y,S) smoothes the data Y using a DCT- or FFT-based spline
% smoothing method. Non finite data (NaN or Inf) are treated as missing
% values.
%
% S is the smoothing parameter. It must be a real positive scalar. The
% larger S is, the smoother the output will be. If S is empty (i.e. S =
% []), it is automatically determined by minimizing the generalized
% cross-validation (GCV) score.
%
% Z = SMOOTH1Q(...,'robust') carries out a robust smoothing that
% minimizes the influence of outlying data.
%
% Z = SMOOTH1Q(...,'periodic') assumes that the data to be smoothed must
% be periodic.
%
% [Z,S] = SMOOTH1Q(...) also returns the calculated value for the
% smoothness parameter S so that you can fine-tune the smoothing
% subsequently if required.
%
% SMOOTH1Q is a simplified and quick version of SMOOTHN for 1-D data. If
% you want to smooth N-D arrays use <a
% href="matlab:web('http://www.mathworks.com/matlabcentral/fileexchange/25634')">SMOOTHN</a>.
%
% Notes
% -----
% 1) SMOOTH1Q works with regularly spaced data only. Use SMOOTH1 for non
% regularly spaced data.
% 2) The smoothness parameter used in this algorithm is determined
% automatically by minimizing the generalized cross-validation score.
% See the references for more details.
%
% References
% ----------
% 1) Garcia D, Robust smoothing of gridded data in one and higher
% dimensions with missing values. Computational Statistics & Data
% Analysis, 2010.
% <a
% href="matlab:web('http://www.biomecardio.com/pageshtm/publi/csda10.pdf')">PDF download</a>
% 2) Buckley MJ, Fast computation of a discretized thin-plate smoothing
% spline for image data. Biometrika, 1994.
% <a
% href="matlab:web('http://biomet.oxfordjournals.org/content/81/2/247')">Link</a>
%
% Examples:
% --------
% % Simple curve
% x = linspace(0,100,200);
% y = cos(x/10)+(x/50).^2 + randn(size(x))/10;
% z = smooth1q(y,[]);
% plot(x,y,'r.',x,z,'k','LineWidth',2)
% axis tight square
%
% % Periodic curve with ouliers and missing data
% x = linspace(0,2*pi,300);
% y = cos(x)+ sin(2*x+1).^2 + randn(size(x))/5;
% y(150:155) = rand(1,6)*5;
% y(10:40) = NaN;
% subplot(121)
% z = smooth1q(y,1e3,'periodic');
% plot(x,y,'r.',x,z,'k','LineWidth',2)
% axis tight square
% title('Non robust')
% subplot(122)
% z = smooth1q(y,1e3,'periodic','robust');
% plot(x,y,'r.',x,z,'k','LineWidth',2)
% axis tight square
% title('Robust')
%
% % Lima<EFBFBD>on
% t = linspace(0,2*pi,300);
% x = cos(t).*(.5+cos(t)) + randn(size(t))*0.05;
% y = sin(t).*(.5+cos(t)) + randn(size(t))*0.05;
% z = smooth1q(complex(x,y),[],'periodic');
% plot(x,y,'r.',real(z),imag(z),'k','linewidth',2)
% axis equal tight
%
% See also SMOOTHN, SMOOTH1.
%
% -- Damien Garcia -- 2012/08, revised 2014/02/26
% website: <a
% href="matlab:web('http://www.biomecardio.com')">www.BiomeCardio.com</a>
%-- Check input arguments
error(nargchk(2,4,nargin));
assert(isvector(squeeze(y)),...
['Y must be a 1-D array. Use <a href="matlab:web(''',...
'http://www.mathworks.com/matlabcentral/fileexchange/25634'')">SMOOTHN</a> for non vector arrays.'])
if isempty(s)
isauto = 1;
else
assert(isnumeric(s),'S must be a numeric scalar')
assert(isscalar(s) && s>0,...
'The smoothing parameter S must be a scalar >0')
isauto = 0;
end
%-- Order (use m>=2, m = 2 is recommended)
m = 2; % Note: order of the smoothing process, can be modified
%-- Options ('robust' and/or 'periodic')
isrobust = 0; method = 'dct'; % default options
%--
if nargin>2
assert(all(cellfun(@ischar,varargin)),...
'The options must be ''robust'' and/or ''periodic''.')
varargin = lower(varargin);
if nargin==3
idx = ismember({'robust','periodic'},varargin);
assert(any(idx),...
'The options must be ''robust'' and/or ''periodic''.')
if idx(1), isrobust = 1; else method = 'fft'; end
else % nargin = 4
assert(all(ismember(varargin,{'robust','periodic'})),...
'The options must be ''robust'' and/or ''periodic''.')
isrobust = 1;
method = 'fft';
end
end
n = length(y);
siz0 = size(y);
y = y(:).';
%-- Weights
W0 = ones(siz0);
I = isfinite(y); % missing data (NaN or Inf values)
if any(~I) % replace the missing data (for faster convergence)
X = 1:n;
x = X(I); xi = X(~I);
y(~I) = interp1(x,y(I),xi,'linear','extrap');
end
W0(~I) = 0; % weights for missing data are 0
W = W0;
%-- Eigenvalues
switch method
case 'dct'
Lambda = 2-2*cos((0:n-1)*pi/n);
case 'fft'
Lambda = 2-2*cos(2*(0:n-1)*pi/n);
end
%-- Smoothing process
nr = 3; % Number of robustness iterations
for k = 0:nr*isrobust
if isrobust && k>0
tmp = sqrt(1+16*s);
h = sqrt(1+tmp)/sqrt(2)/tmp;
W = W0.*bisquare(y,z,I,h);
end
if ~all(W==1) % then use an iterative method
tol = Inf;
zz = y;
while tol>1e-3
switch method
case 'dct'
Y = dct(W.*(y-zz)+zz);
case 'fft'
Y = fft(W.*(y-zz)+zz);
end
if isauto
fminbnd(@GCVscore,-10,30,optimset('TolX',.1));
else
Gamma = 1./(1+s*Lambda.^m);
switch method
case 'dct'
z = idct(Gamma.*Y);
case 'fft'
if isreal(y)
z = ifft(Gamma.*Y,'symmetric');
else
z = ifft(Gamma.*Y);
end
end
end
tol = norm(zz-z)/norm(z);
zz = z;
end
else %---
% No missing values, non robust method => Direct fast method
%---
switch method
case 'dct'
Y = dct(y);
case 'fft'
Y = fft(y);
end
if isauto
fminbnd(@GCVscore,-10,30,optimset('TolX',.1));
else
Gamma = 1./(1+s*Lambda.^m);
end
switch method
case 'dct'
z = idct(Gamma.*Y);
case 'fft'
if isreal(y)
z = ifft(Gamma.*Y,'symmetric');
else
z = ifft(Gamma.*Y);
end
end
end
end
z = reshape(z,siz0);
function GCVs = GCVscore(p)
s = 10^p;
Gamma = 1./(1+s*Lambda.^m);
if any(W)
switch method
case 'dct'
z = idct(Gamma.*Y);
case 'fft'
if isreal(y)
z = ifft(Gamma.*Y,'symmetric');
else
z = ifft(Gamma.*Y);
end
end
RSS = norm(sqrt(W).*(y-z))^2;
else % No missing values, non robust method => Direct fast method
RSS = norm(Y.*(Gamma-1))^2;
end
TrH = sum(Gamma);
GCVs = RSS/(1-TrH/n)^2;
end
end
function W = bisquare(y,z,I,h)
r = y-z; % residuals
MAD = median(abs(r(I)-median(r(I)))); % median absolute deviation
u = abs(r/(1.4826*MAD)/sqrt(1-h)); % studentized residuals
W = (1-(u/4.685).^2).^2.*((u/4.685)<1); % bisquare weights
end

30
lib/smooth1qExample.m 普通文件
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% Simple curve
x = linspace(0,100,200);
y = cos(x/10)+(x/50).^2 + randn(size(x))/10;
z = smooth1q(y,[]);
plot(x,y,'r.',x,z,'k','LineWidth',2)
axis tight square
% Periodic curve with ouliers and missing data
x = linspace(0,2*pi,300);
y = cos(x)+ sin(2*x+1).^2 + randn(size(x))/5;
y(150:155) = rand(1,6)*5;
y(10:40) = NaN;
subplot(121)
z = smooth1q(y,1e3,'periodic');
plot(x,y,'r.',x,z,'k','LineWidth',2)
axis tight square
title('Non robust')
subplot(122)
z = smooth1q(y,1e3,'periodic','robust');
plot(x,y,'r.',x,z,'k','LineWidth',2)
axis tight square
title('Robust')
% Lima鏾n
t = linspace(0,2*pi,300);
x = cos(t).*(.5+cos(t)) + randn(size(t))*0.05;
y = sin(t).*(.5+cos(t)) + randn(size(t))*0.05;
z = smooth1q(complex(x,y),[],'periodic');
plot(x,y,'r.',real(z),imag(z),'k','linewidth',2)
% axis equal tight