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Ask HN: What to learn for math for modeling?

70 points shivajikobardan | 1 comments | 27 Aug 25 07:57 UTC | HN request time: 0.409s | 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.

1. quag ◴[29 Aug 25 02:24 UTC] No.45059370[source]▶
It sounds like you've got something specific in mind when you say, "modeling". The term modeling is used in a lot of different situations to mean different things. For example, it could mean to make a 3d model in Blender, it could mean to pose for someone to paint you or to take a photo, with databases it's used to mean modeling the data, with statistics it's used to mean finding a way to simply represent and reason about the data (create a model of it).

The things you've listed out make me guess you want to write 2d or 3d image rendering software. Is that right?

If that's the case, there's no substitute for trying to recreate certain algorithms or curves using a language or tool that you're comfortable with. It'll help you build an intuition about how the mathematical object behaves and what problems it solves (and doesn't). All of these approaches were created to solve problems, understanding the theory of it doesn't quite get you there. If you don't have a good place to try out functions, I recommend https://thebookofshaders.com/05/ , https://www.desmos.com/calculator , or https://www.geogebra.org/calculator .

A good place to start is linear interpolation (lerp). It seems dead simple, but it's used extensively to blend two things together (say positions or colors) and the other things you listed are mostly fancier things built on top of linear interpolation.

https://en.wikipedia.org/wiki/Linear_interpolation

For bezier curves and surfaces here are some links I've collected over the years: https://ciechanow.ski/curves-and-surfaces/ https://pomax.github.io/bezierinfo/ https://blog.pkh.me/p/33-deconstructing-be%CC%81zier-curves.... http://www.joshbarczak.com/blog/?p=730 https://kynd.github.io/p5sketches/drawings.html https://raphlinus.github.io/graphics/curves/2019/12/23/flatt...

A final note: a lot of graphics math involves algebra. Algebra can be fun, but it also can be frustrating and tedious, particularly when you're working through something large and make a silly mistake and the result doesn't work. I suggest using sympy to rearrange equations or do substitutions and so on. It can seem like overkill but as soon as you save a few hours debugging it's worth it. It also does differentiation and integration for you along with simplifying equations.

https://docs.sympy.org/latest/tutorials/intro-tutorial/intro...