Voronoi Diagram or Voronoi tessellation is abundantly found in nature. There are also some examples in architecture where Voronoi is used. It’s not only the aesthetics that makes Voronoi diagram special but it has some unique properties that makes it very useful in solving real life problems.   Image: Recreating Voronoi Pattern and its close resemblance with Giraffe Pattern (image source: https://quantdare.com/k-means-algorithm/giraffe-59009_1920/)  In this section, we will see how we can create Voronoi Diagram in GC and also how we can use its properties in solving some practical problems.   First let’s understand what is Voronoi diagram.   Now, imagine there are few points in a plane, we call it the Voronoi Sites. Thus, Voronoi diagram divides the plane in a set of regions based on the Voronoi Sites.  These regions are called Voronoi Region or Cells. Every cell is associated with its corresponding Voronoi Sites.  Any new points lying inside any Voronoi Cell will be closest to its corresponding Voronoi Site.  To create the Voronoi we will use the Generated-Node-Types(GNT) Voronoi. You can learn more about GNT from this wiki .  The node required some points as input. We can create some random points as shown in this wiki. These points will act as the Voronoi Sites.  Properties of Voronoi Diagram and Its Applications  Now, imagine the Voronoi Sites as number of

L-Systems or Lindenmayer Systems is a mathematical formalism developed by biologist Aristid Lindenmayer in 1968 to mimic plant growth. Later, its application was further extended in computer graphics for creating self-similar structures and generating plant models.  In this post, we will see how we can use L-Systems in GenerativeComponents to create different types of geometries.  An illustration of a geometry created using L-Systems in GC How do L-Systems work? In L-System, the key concept revolves around how to rewrite an initial element in each successive step based on certain rules in order to get the final structure. The most basic type is called DOL i.e., Deterministic, Context free L-System. Let’s understand with the following example To begin with, let us consider ‘B’ to be the initiator. This initiator is called axiom. Then, the rule of rewriting for the successive steps will be, B->A, A->BA     Rewriting in each generation as per the rule ‘DOL’ in GC When there is any term for which there are no rules, it will pass to the next generations. For the purpose of these DOL we have a function called ‘DOL’ in GC. The input for Axiom is string type, e.g., ‘A’ or ‘FFA’  The input for rule is table type, e.g., we will write the above rule in the following

The Point in Polygon test helps in determining if a given point lies inside a given polygon. For the sake of simplicity, we assume the polygon to be 2D planer. Final Result https://youtu.be/AoexUe4wbU4 This video demonstrates the point in polygon test results Solution There are many algorithms to achieve this. However, here, we will use Ray-Casting algorithm. We chose this algorithm due to its simplicity. For example, first, we project a ray in a fixed direction (here, positive X-direction).  Then we determine the test result based on the number of times the ray intersect with the given polygon: When number of intersection is 0 The point is outside the polygon When number of intersection is even The point is outside the polygon When number of intersection is odd The point is inside the polygon Implementation First, we create a custom global function in GCScript.  Then, for the ray, we use a line of a large length. This line is along the positive X-Direction. And finally, to test the intersection of this line and the given polygon, we use the AtCurveCurveIntersection technique of point node. Code   bool PointInPolygon(Point TestingPoint, ICurve TestingPolygon, CoordinateSystem CS) //Check if a Point is inside a