What is the best and quick way to find the intersections points set of two 3d surfaces?

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Mehdi 2022-9-6

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https://ww2.mathworks.cn/matlabcentral/answers/1797015-what-is-the-best-and-quick-way-to-find-the-intersections-points-set-of-two-3d-surfaces

评论： Torsten 2022-9-17

采纳的回答： Matt J

在 MATLAB Online 中打开

Hi,

I am looking for the easiest best and quick way to find the intersections points of two surfaces in which the points for each curve be reported separately. As an example here there are two surfaces defined in specific domains which have two intersections. I am looking for the points on each one of these two intersection curves in seperated groups. e.g.

Curve 1:

[ x0 y0; x1 y1; x2 y2;...; xn yn]

Curve 2:

[ x0 y0; x1 y1; x2 y2;...; xn yn]

syms x y

f = (x-1)*exp(-y^3-x^2);

g = .5-sqrt(x*exp(-x^2-y^2));

ezsurf(f,[0,2],[-2,2]);

hold on

ezsurf(g,[0,2],[-2,2]);

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Torsten 2022-9-6

在 MATLAB Online 中打开

f = @(x,y)(x-1).*exp(-y.^3-x.^2);

g = @(x,y) 0.5-sqrt(x.*exp(-x.^2-y.^2));

h = @(x,y) f(x,y)-g(x,y);

fimplicit(h)

Mehdi 2022-9-7

编辑：Mehdi 2022-9-7

As I insisted in my question I am looking for a closed method that only reports the points of each curve separately. Your suggested method just plotted the f-g which is useless for me. In Maple there is a plots:-implicitplot command which groups the data of each curve seperately without plotting something. I am looking for similar command in Matlab, if any.

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采纳的回答

Matt J 2022-9-7

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1797015-what-is-the-best-and-quick-way-to-find-the-intersections-points-set-of-two-3d-surfaces#answer_1045290

编辑：Matt J 2022-9-8

在 MATLAB Online 中打开

You can to download this FEX submission,

https://www.mathworks.com/matlabcentral/fileexchange/74010-getcontourlinecoordinates?s_tid=srchtitle

f = @(x,y)(x-1).*exp(-y.^3-x.^2);
g = @(x,y) 0.5-sqrt(x.*exp(-x.^2-y.^2));
h = @(x,y) real(f(x,y)-g(x,y));
[X,Y]=deal(linspace(-6,6,1000));
[~,result]=getContourLineCoordinates(  contourc(X,Y,h(X,Y'),[0,0])   )
result = 1×2 cell array
    {996×2 double}    {327×2 double}

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Torsten 2022-9-8

在 MATLAB Online 中打开

Just to see what's going on.

f = @(x,y)(x-1).*exp(-y.^3-x.^2);

g = @(x,y) 0.5-sqrt(x.*exp(-x.^2-y.^2));

h = @(x,y) f(x,y)-g(x,y);

[X,Y]=deal(linspace(-6,6,1000));

Z=h(X,Y');

Z(imag(Z)~=0)=nan;

[~,result]=getContourLineCoordinates( contourc(X,Y,Z,[0,0]) )

result = 1×2 cell array

{996×2 double} {327×2 double}

hold on

plot(result{1}(:,1),result{1}(:,2))

plot(result{2}(:,1),result{2}(:,2))

hold off

function [contourTable, contourArray] = getContourLineCoordinates(cm)

if ishandle(cm)

cm = cm.ContourMatrix;

end

% Set up while loop

cmSize = size(cm,2); % number of columns in ContourMatrix

cmWindow = [0,0]; % [start,end] index of moving window

contourArray = {}; % Store the (x,y) coordinates of each contour line

% Extract coordinates of each contour line

while cmWindow(2) < cmSize

cmWindow(1) = cmWindow(2) + 1;

cmWindow(2) = cmWindow(2) + cm(2,cmWindow(1)) + 1;

contourArray(end+1) = {cm(:,cmWindow(1):cmWindow(2)).'}; %#ok<AGROW>

end

% Separate the level, count, and coordinates.

level = cellfun(@(c)c(1,1),contourArray).';

numCoord = cellfun(@(c)c(1,2),contourArray).';

contourArray = cellfun(@(c)c(2:end,:),contourArray,'UniformOutput',false);

% Sort by level (just in case Matlab doesn't)

[~,sortIdx] = sort(level);

% Create a table with combined coordinates from all levels and grouping variable

levelsRep = cell2mat(arrayfun(@(v,n)repmat(v,n,1),level(sortIdx),numCoord(sortIdx),...

'UniformOutput',false));

group = cell2mat(arrayfun(@(v,n)repmat(v,n,1),(1:numel(level)).',numCoord,...

'UniformOutput',false));

contourTable = array2table([levelsRep, group, vertcat(contourArray{sortIdx})],...

'VariableNames',{'Level','Group','X','Y'});

end

Mehdi 2022-9-17

编辑：Mehdi 2022-9-17

"Operator '+' is not supported for operands of type 'function_handle'" error occurs before the calculation of ZZ. How to get rid of this error first?

Torsten 2022-9-17

By not using function handles, as I wrote.

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