Divide the 3D surface into equal patches

조회 수: 9 (최근 30일)
Trinh Nam
Trinh Nam 2021년 5월 26일
이동: John D'Errico 2023년 6월 29일
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.

채택된 답변

darova
darova 2021년 5월 29일
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
  댓글 수: 4
Trinh Nam
Trinh Nam 2021년 5월 29일
이동: John D'Errico 2023년 6월 29일
Hi Darova
thanks for your explain. But i think this solution is not general. We cannot apply for the saddle shape or the pillow shape.
Saddle shape General shape Pillow shape
I am looking for the general way to do this job, I am appreciate if you have any algorithm
Akhila
Akhila 2023년 6월 29일
이동: John D'Errico 2023년 6월 29일
Hi Trinh
Did you get the solution to your problem?
I also need this from my work, if you have the solution could you share it with me?

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추가 답변 (2개)

darova
darova 2021년 5월 26일
Try griddata to interpolate
  댓글 수: 1
Trinh Nam
Trinh Nam 2021년 5월 27일
I already tried, although it can generate the rectangle patch, but the area of these patch are not equal

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darova
darova 2021년 5월 27일
Try to interpolate in polar system. Find center of a circle
clc,clear
data = load('curve.txt');
x = data(:,1);
y = data(:,2);
z = data(:,3);
t = linspace(0,2*pi,20);
[x1,y1] = pol2cart(t,100);
plot3(x+15,y,z-100)
%line(x1,y1)
[t,r] = cart2pol(x+15,z-100);
t0 = linspace(max(t(:)),min(t(:)),10);
y0 = linspace(min(y(:)),max(y(:)),10);
[T,Y] = meshgrid(t0,y0);
R = griddata(t,y,r,T,Y);
[X,Z] = pol2cart(T,R);
hold on
plot3(X,Y,Z,'.r')
hold off
view(45,45)

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