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Geometry from alphaShape

Create a 3-D geometry using the MATLAB alphaShape function. First, create an alphaShape object of a block with a cylindrical hole. Then import the geometry into a PDE model from the alphaShape boundary.

Create a 2-D mesh grid.

[xg,yg] = meshgrid(-3:0.25:3);
xg = xg(:);
yg = yg(:);

Create a unit disk. Remove all the mesh grid points that fall inside the unit disk, and include the unit disk points.

t = (pi/24:pi/24:2*pi)';
x = cos(t);
y = sin(t);
circShp = alphaShape(x,y,2);
in = inShape(circShp,xg,yg);
xg = [xg(~in); cos(t)];
yg = [yg(~in); sin(t)];

Create 3-D copies of the remaining mesh grid points, with the z-coordinates ranging from 0 through 1. Combine the points into an alphaShape object.

zg = ones(numel(xg),1);
xg = repmat(xg,5,1);
yg = repmat(yg,5,1);
zg = zg*(0:.25:1);
zg = zg(:);
shp = alphaShape(xg,yg,zg);

Obtain a surface mesh of the alphaShape object.

[elements,nodes] = boundaryFacets(shp);

Put the data in the correct shape for geometryFromMesh.

nodes = nodes';
elements = elements';

Create a PDE model and import the surface mesh.

model = createpde();
geometryFromMesh(model,nodes,elements);

View the geometry and face numbers.

pdegplot(model,'FaceLabels','on','FaceAlpha',0.5)

Figure contains an axes. The axes contains 3 objects of type quiver, patch, line.

To use the geometry in an analysis, create a volume mesh.

generateMesh(model);