Divide the 3D surface into equal patches

Question

Trinh Nam 2021-5-26

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/839810-divide-the-3d-surface-into-equal-patches

移动：John D'Errico 2023-6-29

采纳的回答： darova

curve.txt

Hi, I am looking for a method or algorithm to divide a 3D surface into equal patches. The detail is explained below

Background:

the initial plate has grids as in picture (1). initial position of A1 (a1,b1,c1) …. A121 (a121, b121, c121). All of this position is known. A1 is the origin A1(0,0,0)

After deformation, the plate becomes 3D curve and grids has new position A’1(u1,v1,w1) …A’100(u100, v100,w100).

Currently, I used 3D scanner to get the point cloud data of deformed plate and successfully get the equation of 3D surface.

My question is: How to divide the 3D surface into 100 patches with equal area to find the grid A’2 …A’100 position. (A’1 is the origin A1(0,0,0) and coincide with A1) I already tried matlab built-in function and other software but the result gives me the mesh with different in area. (example: area of S1 ≠ S2 ≠ S100)

Attachment is the point cloud data after processed

Thanks for your support.

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Answer 1

darova 2021-5-29

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/839810-divide-the-3d-surface-into-equal-patches#answer_712290

在 MATLAB Online 中打开

Try arc length interpolation. Original link: LINK

function main
clc,clear
    % generate some data
[x,y] = meshgrid(-1:0.4:1);
z = x.^2+y.^2;
surf(x,y,z,'facecolor','none')
    % interpolation
[x1,y1,z1] = myinterp1(x,y,z);
[x2,y2,z2] = myinterp1(x1',y1',z1');
hold on
plot3(x2,y2,z2,'.r')
hold off
axis equal
function [x1,y1,z1] = myinterp1(x,y,z)
x1 = x*0;
y1 = y*0;
z1 = z*0;
for i = 1:size(x,1)
    dx = diff(x(i,:)).^2;
    dy = diff(y(i,:)).^2;
    dz = diff(z(i,:)).^2;
    t = [0 cumsum(sqrt(dx+dy+dz))];     % parameter
    t1 = linspace(0,t(end),size(x,2));  % new parameter
    x1(i,:) = interp1(t,x(i,:),t1);
    y1(i,:) = interp1(t,y(i,:),t1);
    z1(i,:) = interp1(t,z(i,:),t1);
end
end
end