使用Matlab

Question

我想用Matlab显示物体表面的温度分布。

我以（x，y，z，V）向量的形式获得了3D数据。我想在Matlab中显示这个对象，颜色代表当地的总和＆＃34;值＆＃34;。

我可以将对象导出为STL文件。使用STL绘图可以很容易地显示它（参见stldemo）：

fv = stlread('file.stl');
patch(fv, 'EdgeColor', 'none', 'FaceLighting', 'gouraud', 'AmbientStrength', 0.15, 'FaceColor', [0.8 0.8 1.0]);
camlight('headlight');
material('dull');

要根据（x，y，z，V）对其进行着色，我需要将每个（x，y，z）点附加到贴片中的顶点（最近的一个可以工作）。如果有多个（x，y，z）点，单个STL顶点最近，我将为该顶点添加相应的V值。

顶点数量为数千。 （x，y，z）点的数量也很大。因此，通过（x，y，z）点进行循环，然后在顶点上进行内部循环以找到最近的点（这涉及计算点之间的距离）是不可能的。有没有聪明的方法可以快速完成？

注意：我无法控制数据点的位置，它们是由外部程序定义的。 STL点由另一个外部程序控制。所以我必须结婚两个不同的点集。

以下代码说明了我想要实现的目标，包括4个顶点和3个数据点：

% Create patch
figure;
p = patch;
colorbar

p.Vertices = [...
    0, 0, 0; ...
    1, 0, 0; ...
    1, 1, 0;
    0, 1, 0];
p.Faces = [ ...
    1, 2, 3; ...
    1, 3, 4];

% Data points
x = [0.1, 0.1, 0.25];
y = [0.01, 0.02, 0.75];
z = [0.01, 0.2, -0.01];
v = [1, 1, 1];

p.FaceVertexCData = zeros(size(p.Vertices, 1), 1);
% Point 1 (0.1, 0.01, 0.01) is closest to vertex 1 (0, 0, 0). Its value
% goes to vertex 1.
p.FaceVertexCData(1) = p.FaceVertexCData(1) + v(1);
% Point 2 (0.1, 0.02, 0.2) is also closest to vertex 1 (0, 0, 0). Its
% value also goes to vertex 1
p.FaceVertexCData(1) = p.FaceVertexCData(1) + v(2);
% Point 3 (0.25, 0.75, -0.01) is closest to vertex 4 (0, 1, 0). Its power
% goes to vertex 4.
p.FaceVertexCData(4) = p.FaceVertexCData(4) + v(3);
% Other vertices are left with 0.

p.FaceColor = 'interp';

Answer 1

Attaching a volume scalar value (of Temperature in your case) of a point to a neighbouring point is a tricky exercise, requires complex for loops and defining special case rules (in your case you wanted to attach the value of 2 different points to the same patch vertex, what if the 2 values to attach are different? Do you average? discard ?).

A safer approach is to re-interpolate your temperature field over your object surface. the function griddata can do that for you.

First I had to define a scalar field. Since I do not have your temperature data, I use the flow function from Matlab. I generated a scalar field the same ways than in this article: flow data.
This gave me a scalar field v (flow value but let's say it's your temperature) at for every coordinates x, y, z.

Then I created and introduced a 3D patch which will be your object. I chose a sphere but any 3D patch will work the same way. The code to get the sphere as a patch is borrowed from surf2patch
_{you will have to offset and inflate the sphere to get it exactly as in the figure below}

Now is the interesting bit. In the following code, v is the value of the scalar field (temperature for you) at the coordinates x, y, z.

%% // Extract patch vertices coordinates in separate variables
xp = fv.vertices(:,1) ;
yp = fv.vertices(:,2) ;
zp = fv.vertices(:,3) ;

%% // interpolate the temperature field over the patch coordinates
Tpv = griddata(x,y,z,v,xp,yp,zp) ;

%% // Set the patch color data to the new interpolated temperature
set(hp,'FaceVertexCData',Tpv) ;

And your object surface is now at the right interpolated temperature:
_{you can delete the slice plane if you want to observe the patch alone}