Relax Mesh

Functionality

This node moves vertices of the input mesh, in order to make it more “relaxed”, i.e. for mesh elements to have more even distribution in some sense. There are several algorithms supported, each of which has different definition of what “relaxed” is:

• Lloyd-based algorithm. This is created after well-known Lloyd algorithm. For each vertex, find centers of all incident faces, and then find the average of those points; this will be the new location of the vertex. Effectively, this algorithm tries to make each face as close to circle as possible. This algorithm shows it’s best for meshes that consist of Tris.

• Edge lengths. Scale each edge up or down, trying to make all edges of the same length. Target edge length can be minimum, maximum or average of all lengths of edges of the source mesh.

• Face areas. Scale each face up or down, trying to make all faces of the same area. Target face area can be minimum, maximum or average of all areas of faces of the source mes.

These algorithms can change the overall shape of the mesh a lot. In order to try to preserve original shape of the mesh at least partially, the following methods are supported:

• “Linear” method is supported for Lloyd algorithm only. When the algorithm has found the new location of the vertex, put it at the same distance from the plane where centers of incident faces lie, as the original vertex was. This method can be slow for large meshes.

• “Tangent”: move vertices along tangent planes of original vertexes only (i.e. perpendicular to vertex normal).

• “BVH”: use BVH tree to find the nearest point to the newly calculated vertex on the original mesh.

Inputs

This node has the following inputs:

• Vertices. Vertices of the original mesh. This input is mandatory.

• Edges. Edges of the original mesh.

• Faces. Faces of the original mesh. This input is mandatory.

• VertMask. Mask defining which vertices are to be moved. By default, all vertices can be moved.

• Iterations. Number of iterations of algorithm. Default value is 1.

• Factor. This input is available for Edge Length and Face Area algorithms. Coefficient to be used at each iteration of the algorithm. Possible values are between 0 and 1. The default value is 0.5.

Parameters

This node has the following parameters:

• Algorithm. Relaxation algorithm to be used. The available options are Lloyd, Edge Length and Face Area. The default option is Lloyd.

• Target. This parameter is available for Edge Length and Face Area algorithms. This defines which value of edge length or face area is to be used as the target value for the algorithm. The available options are Average, Minimum and Maximum. The default option is Average.

• Preserve shape. This defines the method to be used in order to preserve the shape of the original mesh at least partially. The available options are Do not use, Linear (for Lloyd algorithm only), Tangent and BVH. The default option is Do not use.

• Skip bounds. If checked, the node will not move boundary vertexes of the original mesh. Checked by default.

• X, Y, Z. These parameters define the coordinate axes along which it is allowed to move vertices. By default, all three parameters are checked, which means the node can move vertices in any direction.

Outputs

This node has the following output:

• Vertices. Vertices of the relaxed mesh.

The node does not modify edges or faces of the original mesh, it only moves the vertexes.

Example of Usage