Mesh from SDFs

The Sorotoki toolkit explores several routines for mesh generation, which are all contained in the class Mesh.m. Our primary focus is on using a modified version of the PolyMesher software developed by Talischi et al.¹. Their work provided a stable foundation for generating unstructured meshes of PolyN elements. The approach starts by defining a material domain implicitly using SDFs. The number of elements is chosen a priori, and then repeated random sampling of the SDF is performed until the number of samples that fall within the specified domain matches the number of elements. A bounded Voronoi diagram is generated using the samples and the centers of the Voronoi cells are updated using Lloyd's algorithm². To generate a mesh from an Sdf class, one can call msh = Mesh(Sdf) followed by msh = msh.generate().

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% distance function
f = @(x) sqrt( x(:,1).^2 + x(:,2).^2 ) - 1.0;

% assigning @f to Sdf class
sdf = Sdf(f,'BdBox',[-2 2 -2 2]);

% mesh from sdf class
msh = Mesh(sdf);
msh = msh.generate('NElem',20);

% show mesh
msh.show();

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% distance function
c   = sCircle(.25);    
r   = sRectangle(1);  
sdf = r.rotate(45)-c; 

% mesh from sdf class
msh = Mesh(sdf,'NElem',150);
msh = msh.generate();

% show mesh
msh.show();