Question

我需要从MATLAB中使用三角网格定义的3D表面中提取4D变量的等值线坐标。我需要将等值坐标按这样的方式排序，即如果按顺序跟踪它们，它们将跟踪路径，即3D打印机将遵循的点的顺序。

我找到了一个可以计算这些等值线坐标的函数（参见Isoline函数here），但问题是这个函数没有考虑isolines以正确的顺序连接而是一系列的由Nan值分隔的2个点。这使得此功能仅适用于可视化目的，而不适用于遵循的路径。

这是一个简化问题的MWE，我应用它的表面也要复杂得多，我无法分享它。其中x，y和z是节点，TRI提供元素连通性列表，v是我想要从中提取等值线的变量，并且不等于z。

如果有人对任何一个有任何想法.....

以3D三维网格的正确顺序提取等值线的函数。
如何对Isoline函数给出的数据进行排序，以使它们的顺序正确。

....非常感谢。

这是MWE，

% Create coordinates
[x y] = meshgrid( -10:0.5:10, -10:0.5:10 );
z = (x.^2 + y.^2)/20;    % Z height
v = x+y;            % 4th dimension value

% Reshape coordinates into list to be converted to tri mesh
x = reshape(x,[],1); y = reshape(y,[],1); z = reshape(z,[],1); v = reshape(v,[],1);
TRI = delaunay(x,y);    % Convertion to a tri mesh

% This function calculates the isoline coordinates
[xTows, yTows, zTows] = IsoLine( {TRI,[x, y, z]}, v, -18:2:18);

% Plotting
figure(1); clf(1)
subplot(1,2,1)
trisurf(TRI,x,y,z,v)
hold on
for i = 1:size(xTows,1)
    plot3( xTows{i,1}, yTows{i,1}, zTows{i,1}, '-k')
end
hold off
shading interp
xlabel('x'); ylabel('y'); zlabel('z'); title('Isolines'), axis equal

%% This section is solely to show that the isolines are not in order
for i = 1:size(xTows,1)

    % Arranging data into colums and getting rid of Nans that appear
    xb = xTows{i,1}; yb = yTows{i,1}; zb = zTows{i,1}; 
    xb = reshape(xb, 3, [])'; xb(:,3) = [];
    yb = reshape(yb, 3, [])'; yb(:,3) = [];
    zb = reshape(zb, 3, [])'; zb(:,3) = [];

    subplot(1,2,2)
    trisurf(TRI,x,y,z,v)
    shading interp
    view(2)
    xlabel('x'); ylabel('y'); zlabel('z'); title('Plotting Isolines in Order')
    axis equal; axis tight; hold on
    for i = 1:size(xb,1)
        plot3( [xb(i,1) xb(i,2)], [yb(i,1) yb(i,2)], [zb(i,1) zb(i,2)], '-k')
        drawnow
    end
end

这是Isoline的功能，我稍微有点过分了。

function [xTows, yTows, zTows] = IsoLine(Surf,F,V,Col)

if length(Surf)==3                % convert mesh to triangulation
  P = [Surf{1}(:) Surf{2}(:) Surf{3}(:)];
  Surf{1}(end,:) = 1i;
  Surf{1}(:,end) = 1i;
  i = find(~imag(Surf{1}(:)));
  n = size(Surf{1},1);
  T = [i i+1 i+n; i+1 i+n+1 i+n];
else
  T = Surf{1};
  P = Surf{2};
end
f = F(T(:));
if nargin==2
  V = linspace(min(f),max(f),22);
  V = V(2:end-1);
elseif numel(V)==1
  V = linspace(min(f),max(f),V+2);
  V = V(2:end-1);
end
if nargin<4
  Col = 'k';
end
H = NaN + V(:);
q = [1:3 1:3];
% -------------------------------------------------------------------------

% Loop over iso-values ----------------------------------------------------
xTows = [];
yTows = [];
zTows = [];
for k = 1:numel(V)
  R = {[],[]};
  G = F(T) - V(k);   
  C = 1./(1-G./G(:,[2 3 1]));
  f = unique(T(~isfinite(C))); % remove degeneracies by random perturbation
  F(f) = F(f).*(1+1e-12*rand(size(F(f)))) + 1e-12*rand(size(F(f)));
  G = F(T) - V(k);
  C = 1./(1-G./G(:,[2 3 1]));
  C(C<0|C>1) = -1;
  % process active triangles
  for i = 1:3
    f = any(C>=0,2) & C(:,i)<0;
    for j = i+1:i+2
      w = C(f,q([j j j]));
      R{j-i} = [R{j-i}; w.*P(T(f,q(j)),:)+(1-w).*P(T(f,q(j+1)),:)];
    end
  end
  % define isoline
  for i = 1:3
    X{i} = [R{1}(:,i) R{2}(:,i) nan+R{1}(:,i)]';
%     X{i} = [R{1}(:,i) R{2}(:,i)]';    % Changed by Matt
    X{i} = X{i}(:)';
  end
  % plot isoline
  if ~isempty(R{1})
%     hold on
%     H(k) = plot3(X{1},X{2},X{3},Col);

    % Added by M.Thomas
    xTows{k,1} = X{1};
    yTows{k,1} = X{2};
    zTows{k,1} = X{3};

  end
end

你会注意到isolines（xTows，yTows和zTows）不在那里＆＃34;跳转＆＃34;当顺序绘制时。我需要对排序进行排序，以便按顺序给出平滑的情节。

MATLAB中三维三角曲面的有序等值线计算

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