MATLAB: How to view scattered (non-uniform) intensity information in 3-D space in MATLAB 7.9 (R2009b)

MATLAB

I have intensity values defined at scattered (x,y,z) coordinates. The vertices lie on the surface of a 3-D object, and I would like to view the interpolated intensity values at all points on this object.

Best Answer

If the data falls on the surface of a convex 3-D object, then we can find the 3-D convex hull for these scattered data points. Using the TRISURF function, we can set the "FaceVertexCData" property to the vertex intensity values, and these intensities can be interpolated by setting the "FaceColor" property to "interp".

Here is a full example showing how you might do this given 'x', 'y', 'z', and 'v' data ('v' is the intensity at the point defined by x, y, and z). See attached file "vars.mat" to obtain this data.

load vars.mat
figure('renderer','painters')
X=[x y z];
K = convhulln(X);
trisurf(K,X(:,1),X(:,2),X(:,3),'FaceColor',...
      'interp','FaceVertexCData',v,'EdgeColor','none');
colorbar
view(-15,35)
xlabel('x')
ylabel('y')
zlabel('z')

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MATLAB: How to create a three-dimensional surface from unsorted coordinates in MATLAB 7.4 (R2007a)

The function SURF expects a neat rectilinear grid to be supplied to it before it can render the surface. It is not possible to use this function directly to render a surface with unordered coordinates.

As a workaround the function TRISURF can be used to create the surface in conjunction with the DELAUNAY function. The DELAUNAY function performs the triangulation and returns a mx3 matrix "Tri" which defines each triangle used to render the surface. Each row of "Tri" defines a single triangular face by indexing into the vectors or matrices that contain the X, Y, and Z vertices. This "Tri" matrix can then be used with TRISURF to generate the surface.

The following code illustrates the use of DELAUNAY and TRISURF to generate a surface:

load seamount;
tri = delaunay(x,y);
h = trisurf(tri, x, y, z);
axis off
l = light('Position',[-50 -15 29])
set(gca,'CameraPosition',[208 -50 7687])
lighting phong
shading interp
colorbar EastOutside
axis vis3d

MATLAB: How to plot a single valued function over a triangulated surface

You can do it with patch. You'll just want to set FaceColor to interp and set the FaceVertexCData to to value of your function.

But you might find it easier to use the trisurf function. Here's a simple example:

npts = 100;
x = 2*randn(npts,1);
y = 2*randn(npts,1);
z = peaks(x,y);
c = z;
tri = delaunay(x,y);
h = trisurf(tri,x,y,z,c,'FaceColor','interp');
colormap(parula(12))
axis tight

Best Answer

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MATLAB: How to create a three-dimensional surface from unsorted coordinates in MATLAB 7.4 (R2007a)

MATLAB: How to plot a single valued function over a triangulated surface

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