Delaunay Triangulation Algorithms

1631 WordsJan 29, 20187 Pages
At this point you might be asking yourself: what difference does the shape of triangles make in a triangulation and, as such, why do we care at all about Delaunay triangulations? Well, let us consider one of the most relevant application examples for the 21st century. We live in a digital age and use a multitude of electronic devices on a regular basis; much more often than people did back in 1934. Almost all electrical devices nowadays contain some electronic circuitry that controls their functioning. This circuitry is usually placed on printed circuit boards, which present us with the task of deciding where on those boards the individual components have to be placed and how they should be connected to each other (de Berg et al. 2008). Since many of the electronic components emit heat, we have to be able to place our components on the circuit board in a way that minimizes the overheating. It is difficult to predict if the overheating will cause an issue for a given component layout, so we have to either create a prototype of the particular board and test it before starting the mass production, or we could simply run a computer program to simulate this test much more efficiently. Needless to say, nowadays everyone usually picks the latter method. Since the heat transfer between different materials on the printed circuit board is a complicated process, we have to resort to approximation using finite element methods to perform the above simulation. Finite element methods
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