Dynamic Shadows of Symmetric Shapes in a 2D Environment A case study in the field of Computer Graphics

Abstract: With modern computer graphics it is easy to think that the computer has some inherent understanding of the 3D world around it. How else could a game let you experience a dynamic world so close to reality in real time. With waves distorting the light hitting the sand in shallow water, or a traffic light illuminating the exhaust fumes from the car in front of you in a dampened red hue. In reality the computer has no clue, all it does is to handle vast streams of binary data in a way that it has been instructed to. What is even more impressive is the ingenuity of some of these instructions that is tailored towards the strengths of the computer.   Let’s imagine a table with a candle and a box on it. For us it is obvious that the box will obstruct the light from the candle and cast a shadow on the table, we have seen this behavior with our own eyes. For the computer this is nonsense. It does not know what a candle is, or how light or shadow behaves, it doesn't even know what space is. We need to tell it all of these things in a common language, and that common language is math. We can instead think of the room as its dimensions, let’s say 3x3x3 meters. This is something the computer can understand. Furthermore we can tell it where in this newly defined space we want the table to be and how it looks. When we have given it enough information about where everything is in the scene we can start to instruct it on how these things affect each other. Candles cast light, boxes blocks light etc. This is where the ingenuity comes in to play. How do light really behaves mathematically and how can we simulate this efficiently in the computer.   This project will to define one such instruction. The behaviour it simulates is dynamic shadows of symmetrical shapes in a 2D environment. Furthermore it does this in constant time for a variety of shapes that satisfies certain constraints.   With additional such instructions for various effects, each as efficient as possible, the final render can hold quite a bit of realism. This methodology has for a long time been the most common approach in computer graphics, and is still used in a lot of applications today