interpolation of coordinates in space using interp3

Question

Alberto Acri 2023-10-1

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2027869-interpolation-of-coordinates-in-space-using-interp3

回答： Torsten 2023-10-1

采纳的回答： Voss

C_new.mat

在 MATLAB Online 中打开

Hi! I have this coordinate set (C_new). I would like to add additional coordinates using interpolation.

load C_new
figure
plot3(P(:,1),P(:,2),P(:,3),'k*','Markersize',20);
hold on
plot3(C_new(:,1),C_new(:,2),C_new(:,3),'r.','Markersize',10);  
hold off
axis equal

I'm proceeding as follows but I don't know if it's the right procedure:

X = C_new(:,1);
Y = C_new(:,2);
Z = C_new(:,3);
[Xq,Yq,Zq] = meshgrid(X,Y,Z);
Vq = interp3(X,Y,Z,V,Xq,Yq,Zq);

but what should I put for V?

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Dyuman Joshi 2023-10-1

You need the equation/relation between the coordinates to interpolate, V contains the values of the the function corresponding to (X,Y,Z).

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Answer 1

Voss 2023-10-1

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2027869-interpolation-of-coordinates-in-space-using-interp3#answer_1323034

编辑：Voss 2023-10-1

在 MATLAB Online 中打开

C_new.mat

interp3 is for interpolating a function of 3 variables, i.e., if you had a function f(X,Y,Z) that returns a value for each (X,Y,Z) then you could use interp3 to interpolate those values to new points in 3D space. In this case there is no function, only the points in 3D space, so you can define a parameterizing variable and use interp1 to interpolate each of your X, Y, Z in terms of that

load C_new

% original number of points:

n = size(C_new,1);

% number of points you want (change this as desired):

n_new = floor(n/2);

% distance between adjacent points:

d = sqrt(sum(diff(C_new,1,1).^2,2));

% cumulative distance around the ring, starting with point #1:

t = [0; cumsum(d)];

% new distances (equally-spaced) at which to calculate the new (X,Y,Z) coordinates:

t_new = linspace(t(1),t(end),n_new);

% interp1 C_new from t to t_new:

C_interp = interp1(t,C_new,t_new);

% plot:

figure

plot3(C_interp(:,1),C_interp(:,2),C_interp(:,3),'g.','Markersize',6);

hold on

plot3(C_new(:,1),C_new(:,2),C_new(:,3),'r.','Markersize',10);

axis equal

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Answer 2

Torsten 2023-10-1

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https://ww2.mathworks.cn/matlabcentral/answers/2027869-interpolation-of-coordinates-in-space-using-interp3#answer_1323039

在 MATLAB Online 中打开

Given two points

P1 = [1 3 4];

and

P2 = [3 6 -1];

you can connect them by a line

s = @(t) (1-t)*P1 + t*P2;

and choose points between them:

t = [0:0.2:1];
Pq = reshape(cell2mat(arrayfun(@(t)s(t),t,'UniformOutput',0)),3,[]).'
Pq = 6×3
    1.0000    3.0000    4.0000
    1.4000    3.6000    3.0000
    1.8000    4.2000    2.0000
    2.2000    4.8000    1.0000
    2.6000    5.4000   -0.0000
    3.0000    6.0000   -1.0000