Tessellation

Regarding tessellation in view of simulation, there are four simple best practices to consider:

  • Rule 1: Use preferably triangle meshes to quad meshes.
  • Rule 2: Avoid splinter (very thin) triangles and tetras.
  • Rule 3: Try to create as uniformly sized triangles and tetras as possible.
  • Rule 4: Create a good triangulation by ensuring enough randomness in the layout (Delaunay triangulation).

Carbon Cloth Tessellation

_images/tutorial_geometry_tessellation_grid.png

Basic grid.

Most modeled geometry is targeted at rendering that is made from a very uniform, easy to subdivide quad mesh. These are not suitable for simulation, as quads impose certain bending directions, and so does uniformity in the layout. Starting with such a quad geometry, the first step is to attach a Remesh node with 0 Iterations.

_images/tutorial_geometry_tessellation_remesh.png

Remesh node.

The result is that each quad gets split into two triangles. Increasing the Iterations for the Remesh node and adapting the Target Edge Length will produce different tessellations. It is quite easy to spot a good Delaunay triangulation with randomness in the layout (rule #4), but rather hard to judge if there are a lot of splinter triangles and if all the triangles are of uniform size (rule #2 and #3). The Carbon Cloth Guide Geometry provides tools for these situations. First, create a DOP Network, and add a Carbon Cloth attached to a Carbon Simulation. Then set up the SOP Path pointing to the geometry and switch to the Guide Geometry tab.

_images/tutorial_geometry_tessellation_cloth.png

Carbon Cloth UI and setup.

Angular Quality displays how regularly each triangle is shaped (if there are splinter triangles or very regular triangles). Surface Quality shows if all triangles have the same size of surface. Unfortunately, rule #2 and #3 stand in conflict with rule #4. It is rather easy to create uniformly sized triangles with a regular shape, especially when starting from a uniform quad mesh, but achieving a perfect Delaunay triangulation sometimes is simply not possible. The table below shows the initial results for 0 Iterations and then a good render mesh, which is achieved with 30 Iterations and a Target Edge Length of 0.083.

_images/tutorial_geometry_tessellation_guide.png

Carbon Cloth Guide Geometry.

Warning

It is of utmost importance to remove all splinter triangles as they are prone to flip during the simulation. This can easily cause a blowing up of the simulation.

Note

  • The only flaw in the tessellated cloth above is that the triangle in the left upper corner has got two of it’s edges at the border of the mesh. This is bad as the triangle will bend easily around the direction of the connected edge.
  • Carbon accepts quad meshes, but internally each quad is converted into two triangles by a simple split.

Carbon Tetra Tessellation

Everything mentioned in the section above also applies to the surface of a tetrahedral geometry. Most tetrahedral meshes start as a surface mesh and are then tetrahedralized using nodes like Tetrahedralize in Houdini. In such cases, ensure that the surface geometry is of good quality first, and only then tetrahedralize the geometry, extending the same principles all throughout the inside of the mesh.

For more information about how to create tetrahedral geometry, please refer to Tetrahedralization.

Note

Similar to triangle meshes, it is best to avoid having tetrahedrons that have more than one face as surface of a tetrahedral geometry. This can be avoided in the Tetrahedralize node by checking One Surface Face per Tetrahedron.