Shown below is worksheet 4 (it was sent to another student and I am now waiting on comments back):
Introduction
The topic of my project is the use of mathematics/physics in games, relating specifically to the movements and collisions between differently shaped objects and curved surfaces. The aim of the project is to successfully implement mathematical techniques which will hopefully simulate realistic movements and collisions of an object over a curved surface without having to suffer a loss of speed or accuracy when it comes to collision detection and response.
Issues
A big issue that is integral to this project is that when it comes to mathematics/physics in games, it has been said that, ‘if it looks right, then it is right’ [Conger (2004)]. Why should the collisions be approximated and can it be successfully implemented realistically in real-time without much difficulty.
In general, I will implement objects bouncing of a curved terrain taking into account gravity and friction. Hopefully if there is time, I will look into things such as rough terrain (increased friction), wind, other objects (such as box, cylinder etc), multiple objects etc.
Research question
Can the movements and collisions of an object on a curved surface be realistically simulated in real-time?
Addressing the Question
First of all, I want to look at the movements of a point mass bouncing on a flat surface with no friction but remembering to take gravity into account. After this, the same point mass will then be demonstrated bouncing on a curved surface (represented by Bezier surface). After this is simulated, the next step would be to look at a solid sphere bouncing of the flat terrain which would then require the added movement of spinning/rotating to the ball. Of course, once this is done on a flat surface, it will be simulated on the curved plane. To get the correct bouncing effect of the sphere on a curved surface, I will have to take the tangent plane of the curve at the point of collision. With this information, the calculations of the bounce are the same as when it impacts the flat surface. After all of this has been implemented (using OpenGL), I will go back and recreate the collisions for both the point mass and the sphere but this time with friction.
Hopefully there will be time to look into more complicated problems as described above (Issues section).
With the implementation of everything I have discussed, I will hopefully find that collisions can be kept quite realistic without the loss of accuracy.
Progress
So far, I have mainly just researched around the area. I have been collecting more mathematical techniques that will be needed for this project and also teaching myself new techniques as well as revising old ones. I have realised that I will need to learn a few new mathematical techniques and this has increased my interest in the project. I have also tried a few experimental programs in DirectX and OpenGL to see which one would suit my capabilities and the projects requirements best. I have made a decision on OpenGL and hope to start implementing the beginning of my project as soon as possible.
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Meeting one with technical supervisor, Dr Lucas:
I had a meeting with my supervisor to go over everything that will be required next Monday at the presentations. As of yet, I have not wrote the presentation as I am still gathering information on my project and working out finer details. I spoke with Lucas about what I should include in my presentation. He told me not to go into too much detail, keep it to simple bullet points and to focus on the steps of how I will address the question. Another point of advice was to remember that I was still researching the topic and so if any questions came up that were difficult to answer then I should not panic about it and just say that it is something I have yet to look into. My focus now is to get a draft of my presentation done and show it to Dr Lucas this Friday at our next meeting.
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Now waiting on worksheet 4 to come back which will help in the writing of the presentation. I am having doubts about the level of difficulty of my chosen research question. I just seems to easy as if it can be answered by a simple yes or no as I do realise that there are limitations on physics calculations due to processing power which would significantly reduce the speed of a game or application. I am also still worried about how I will be able to draw results and ultimately draw a conclusion or even give a definitive answer to my question from the way in which I am addressing the question. I spoke to Lucas about this and was reassured that the way I am addressing the question is correct and just from the implementation of the ball bouncing on the curved surface, will show the question has been answered. However, I am still unsure. I feel like as it is a project that I should treat it the same way I would an experiment. Looking at the aim, the method, the experiment itself, the results and then the conclusion. And so, I am struggling to work out what results I can get as it will not give me numerical results, and hence from that draw a conclusion to answer the research question. I am sure with more research and thought over the next couple of days will help me to see where my project will go and hopefully , there will be not problems with it that may result in a change of topic.
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