Voronoi on Surface

This node can require SciPy library to work, depending on selected operation mode.

Functionality

This node generates a Voronoi diagram for given set of points on a Surface object.

This node can operate in different modes:

• In UV space (2D voronoi). Voronoi diagram is generated in the U/V space of the surface and then mapped onto the surface. Since mapping defined by the curve can be very non-uniform, this can be very different from real Voronoi diagram calculated by Euclidean metric in 3D space. But for not-too-curved surfaces, this can be used as “good enough” approximation.

• In 3D space. Voronoi diagram is calculated in 3D space for points on the surface. 3D Voronoi diagram is volumetric structure, not flat, so in this mode the node produces either regions or ridges of Voronoi diagram.

As Voronoi diagram is an infinite structure, this node can only generate it’s finite part. Only finite polygons / regions are generated, but even these can be very large. To generate a smaller object, clipping by vertical / horizontal planes can be applied.

Inputs

This node has the following parameters:

• Surface. The surface to generate Voronoi diagram on. This input is mandatory.

• UVPoints. Points (sites) in U/V space of the surface, for which Voronoi diagram is to be generated. Only X and Y coordinates of these points will be used. This input is mandatory.

• MaxSides. This input is available only when Mode parameter is set to UV Space, and Make faces parameter is checked. Maximum number of sides of Voronoi polygon, for which this node will generate edges. The default value is 10.

• Thickness. This input is available only when Mode parameter is set to 3D Ridges or 3D Regions. Thickness of Voronoi diagram objects. The default value is 1.0.

• Clipping. This defines the distance from outermost sites to the clipping planes. This input is only available when the Clip parameter is checked. The default value is 1.0.

Parameters

This node has the following parameters:

• Mode. Operation mode of the node. The available modes are:

  • UV Space. Voronoi diagram will be calculated in U/V space of the surface, and then mapped onto the surface.

  • 3D Ridges. Voronoi diagram will be calculated in 3D space. Only ridges that separate sites on the surface will be generated. This mode is only available when SciPy library is installed.

  • 3D Regions. Voronoi diagram will be calculated in 3D space. Only regions surrounding sites on the surface will be generated. This mode is only available when SciPy library is installed.

  The default mode is UV Space.

• Make faces. This parameter is only available when Mode parameter is set to UV Space. This defines whether the node should generate polygons of Voronoi diagram. If not checked, the node will generate edges only. Unchecked by default.

• Flat output. This parameter is only available when Mode parameter is set to 3D Ridges or 3D Regions. If checked, the node will generate one flat list of objects for all sets of input parameters. Otherwise, a separate list of objects will be generated for each set of input parameter values. In 3D modes, this node generates a separate object for each region of Voronoi diagram.

• Clip. This parameter is only available when Mode parameter is set to 3D Ridges or 3D Regions. This defines whether the node will cut the generated diagram by clipping planes. If not checked, then this node can potentially generate very large objects near edges of the surface. Checked by default.

• Correct normals. This parameter is available when Mode parameter is set to 3D Ridges or 3D Regions, or when Make faces parameter is checked. This defines whether the node should recalculate the normals of generated objects so that they all point outwards. Checked by default.

• Ordered faces. This parameter is available in the N palen only, when Mode parameter is set to UV Space, and only if Make Faces parameter is checked. If enabled, the node will make sure that generated faces are in the same order as input vertices. This procedure can take additional time. If not checked, the order of faces will not be the same as order of initial points.

Outputs

This node has the following outputs:

• Vertices. Vertices of generated ridges or regions.

• Edges. Edges of generated ridges or regions.

• Faces. Faces of generated ridges or regions.

• UVVertices. This output is available only when Mode parameter is set to UV Space. Vertices of Voronoi diagram in U/V space of the surface. Z coordinate of these vertices will always be zero.

Examples of Usage

“UV Space** mode:

• Generator-> Plane

• Transform-> Randomize

• Surfaces-> Build NURBS Surface

• Spatial-> Populate Surface

• Surfaces-> Evaluate Surface

• Viz-> Viewer Draw

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“3D Ridges” mode:

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“3D Regions” mode: