"This task doesn't really fall within the thematic precincts of this unit, but as we will be having our first of three 'Skype a Scientist' sessions in December, it would be good for us to start watching this video. The task, besides watching, is taking some notes and summarizing the main ideas of the video, as well as making a list of things you didn't understand ad questions you would like to ask (for clarification of things not understood, or expanding on the topic)."
Mathematics in the Digital Age - The Algebraic Nature of Computer Graphics
I was more familiar with the word spline in the context of woodworking, where spline joints or splines miters are constructed using a third piece of wood to reinforce the joint.
But in mathematics splines are very different things. Splines are continuous curves made to pass through a set of 'fixed' points.
So, I started my first viewing of the video ... it was going well, she is talking about the history of the problem of drawing splines, but then, at 3:52, she introduces a slide titled FEM TO SOLVE PDE'S and my brain started to grind to a halt ... so I had to google those terms:
FEM = Finite Element Method
PDE = Partial Differential Equation
And I immediately just plain gave up! Partial Differential Equations! No! No! Hell no!
Regardless, I tried to keep on watching, but, I must confess, my brain just glazed over and I could not really digest any information.
I will try again tomorrow during the asynchronous class.
Ok, here I am trying again ...
I can 'understand' piecewise polynomial functions to draw lines, or 2D objects ... it does make sense and it fits nicely with my limited knowledge of Bezier curves (from my Photoshop experience) ...
But making the leap to 3D modelling using flat surfaces ... that I am finding hard ... what function or functions determine the position of each 'slab'? She says something at 11:26 and I just don't get it.
I guess I am a 2D person.
Today for dinner I will be having some Combinatorics. Never tried them before. Wish me luck!
Anyway, I am glad mathematicians are 'struggling' with the open questions they still have with the '3D subdivisions' and generalising volumes ... they deserve nothing less!!
Q1: In layman terms, what is algebraic geometry? why?
Q2: See Q1
Q3: Again in layman terms, how does a derivative (first, second, any) determine how smooth a piecewise curve function is at the junctions or edges?
Q4: Since it seems that the 'approximation methods' do a nice job at computer graphics ... would there be a lot of efficiency gains in being able to mathematically generalise 3D volumes?
Good questions. I wouldn't know the answer to any myself (excepto perhaps Q1)... As the rest, you already have an edge (I had no idea about Bezier curves). In fact, I must admit to a generally prejudiced mindset which leads me to innately disparage applied and 'useful' knowledge in general.
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