1.1.19 Voronoi

Voronoi object allows users to create a Voronoi diagram which generates partitions based on the distance of adjacent points inside a plane. This is generally used to define the tributary area for load distribution for columns.

Example:

<O N="VoronoiSurface" T="Voronoi" Color="#FF69B4" PointSize="0.1">

<O T="Point" Z="0" Y="5" X="5" />

<O T="Point" Z="0" Y="-5" X="5" />

<O T="Point" Z="0" Y="-5" X="-5" />

<O T="Point" Z="0" Y="5" X="-5" />

<O T="Surface">

<O T="Point" Z="0" Y="2.5" X="2.5" />

<O T="Point" Z="0" Y="-2.5" X="2.5" />

<O T="Point" Z="0" Y="-2.5" X="-2.5" />

<O T="Point" Z="0" Y="2.5" X="-2.5" />

</O>

</O>

Functions

voronoi (boundary, points, cutouts)

Given a surface representing the boundary of an area, a list of points within the boundary area and a list of surfaces representing the cutouts (holes) within the boundary, this function computes the areas of voronoi cells within the boundary. This function lists areas in the same order as the points in the boundary area.

Example:

<P N="boundary" V="[5,5],[5,-5],[-5,-5],[-5,5]" />

<P N="points" V="[2.5,2.5],[2.5,-2.5],[-2.5,-2.5],[-2.5,2.5]" />

<P N="Area" V="voronoi(boundary,points)" />

Figure 1.1.19.2: Areas of Voronoi cells.

voronoipts (boundary, points, cutouts)

Given a surface representing the boundary of an area, a list of points within the boundary area and a list of surfaces representing the cutouts (holes) within the boundary, this function lists the vertices of voronoi cells in the same order as the points in the boundary area.

Example:

<P N="boundary" V="[5,5],[5,-5],[-5,-5],[-5,5]" />

<P N="points" V="[2.5,2.5],[2.5,-2.5],[-2.5,-2.5],[-2.5,2.5]" />

<P N="Vertex" V="voronoipts(boundary,points)" />

Figure 1.1.19.3: Vertices of Voronoi cells.