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Heat Transfer Visualization

This example illustrates the use of the Simulink® 3D Animation™ with the MATLAB® interface for manipulating complex objects.

In this example, matrix-type data is transferred between MATLAB and a virtual reality world. Using this feature, you can achieve massive color changes or morphing. This is useful for visualizing various physical processes.

We use precalculated data of time-based temperature distributions in an L-shaped metal block and send that data to the virtual world. This forms an animation with relatively large changes.

Load the Precalculated Data


Reshaping the Object for VRML

The geometry of the L-shaped block is stored in the 'lblock' structure. For visualization purposes, the block is subdivided into triangular facets. Surface facet vertex coordinates are stored in the 'lblock.mesh.p' field and triangle edges are described by indices into the vertex array.

vert = lblock.mesh.p';

A set of facets in VRML is defined as a single vector of vertex indices where facets are separated by -1, so we need to transform the vertex array appropriately. Indexes in VRML are zero-based, so 1 is deducted from all index values stored originally in the 1-based index array lblock.mesh.e.

facets = lblock.mesh.e(1:3,:)-1;
facets(4,:) = -1;
f = facets; f = f(:);
facets = facets';

Prepare the Colormap

Now we'll prepare a colormap that represents various levels of temperature. The MATLAB built-in 'jet' colormap is designed for these purposes.

cmap = jet(192);

Apply the Colormap

The 'lblock.sol.u' field contains a matrix describing the temperatures of vertices as time passes. We have 41 precalculated phases (1 is initial) for 262 vertices. We need to scale the temperature values so that they map into the colormap.

u = lblock.sol.u;
ucolor = (u-repmat(min(u),size(u,1),1)) .* (size(cmap,1)-1);
urange = max(u) - min(u);
urange(urange == 0) = 1;
ucolor = round(ucolor./repmat(urange,size(u,1),1));

We will calculate the first animation frame so we have something to begin with.

ci = colind';
ci = ci(:);

The data is ready so we can load the world.

world = vrworld('vrheat.x3d');

Let's start the viewer. A cube should appear in the viewer window.

fig = view(world, '-internal');

Now we'll prepare the L-shaped block. The VRML world that we loaded contains a basic cubic form that we can reshape into anything we want by setting its 'point' and 'coordIndex' fields, which represent the vertex coordinates and indices into the vertex array. We will also set the colors by setting the 'color' and 'colorIndex' fields.

We first set the colors, the color indices, the vertices, and then the vertex indices. The order is not mandatory but it is generally better this way because we can be sure there is no temporary state when there are more vertices than colors, or more indices than values, which would cause some vertices to have undefined color or some indices referring to nonexisting (yet) values.

world.IFS_Colormap.color = cmap;
world.IFS.colorIndex = ci;
world.IFS_Coords.point = vert;
world.IFS.coordIndex = f;

Working with VRML Text Objects

The textual comment can also be set to something sensible.

world.TEXT.string = {'Time = 0'};

Animate the Scene

Now we can start the animation. Watch it in the viewer. You can move around the object, or try to set other rendering modes. E.g., a wireframe mode which shows how the L-block is subdivided.

for i = 1:size(u,2)
    uslice = ucolor(:,i);
    colind = zeros(size(facets));
    colind(:,1:3) = uslice(facets(:,1:3)+1);
    colind(:,4) = -1;
    world.IFS.colorIndex = ci;
    world.TEXT.string = {sprintf('Time = %g', lblock.sol.tlist(i))};

Preserve the Virtual World Object in the MATLAB® Workspace

After you are done with a VRWORLD object, it is necessary to close and delete it. This is accomplished by using the CLOSE and DELETE commands.

close(world); delete(world);

However, we will not do it here. Instead, we leave the world open so that you can play with it further. We will clear only the used global variables.

clear ans ci cm cmap colind f facets i lblock nh u ucolor;
clear urange uslice v vert;