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70 points shivajikobardan | 1 comments | | HN request time: 0.22s | source

parametric cubic curve

boundary representation

blending function

spline

b-spline

cubic bezier curve

de casteljau algorithm

I have been diving into these topics since few days and I have not understood anything. I tried peter shirley's textbook on Computer Graphics. Foley et al, Hearn baker etc...

It is clear to me that I lack the mathematics preriquisites for understanding this. Thus, I am deeply asking for resources that I can do to brush up. Me being a computer engineering graduate I have done math classes, it is just that I became like a calculator instead of understanding the logic behind doing the formulas and steps so need a short revision.

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hodgehog11 ◴[] No.45059157[source]
It's a bit difficult to say, since some of those textbooks (e.g. Shirley) cover preliminary math topics as well. It sounds like you need to get a stronger understanding of calculus and linear algebra, and approach maths from a healthier viewpoint. Something like Axler's Linear Algebra Done Right often forces people to treat linear algebra with the slow care it requires, but this may be a bit too extreme.

Now that you have some applications in mind, write down all of the terms and concepts that are involved that you don't understand. Go back to a first-year textbook, something like Stewart's Calculus is probably ideal since it is designed to work up to e.g. Bezier curves. However, this time, I would not suggest relying on the exercises for understanding. Instead, place strong emphasis on the definitions and theorems, drawing them together into a diagram with the terms from earlier to really understand why each concept is required for another concept. Your objective should be to see how these ideas lead to the definition of those curves, and why it has to be that way. Be skeptical and try thinking of alternatives; you might find them to have issues, or coincide with what has already been found! Make sure you understand each concept first before you apply it; this will not be a fast process, and if you need to check something, be sure to do it. But thinking in the context of what you want to learn later is often helpful, I find.

There are other, more detailed guides out there, mostly geared toward higher level math, e.g. https://www.susanrigetti.com/math and you might find the early parts of these useful too. Also, I have found chatbots to be reasonable at giving tailored explanations for a given topic, so there is rarely harm in using them to supplement your learning. Just don't use them to solve problems for you.

replies(1): >>45060194 #
1. senderista ◴[] No.45060194[source]
I love Axler, but it is absolutely the wrong book for someone only interested in the applications of linear algebra. (Strang is usually recommended in this case but I haven’t read it.)