Don't mind me, I'm just writing out numbers on a whiteboard looking for patterns.

These are my calculations on what knot vector intervals of a closed #NURBS curve with repeated points that correspond to all the peaks of the basis functions associated with a particular point on the curve such that the repeated points will still result in a closed curve if I modify the size of said knot vector intervals.

I'm curious if this sequence has any other significance?

Currently being driven crazy by the fact that the word 'coincidence' and 'co-incidence' are so similar yet very distinct concepts.

#NURBS #DuplicatePoints

Here's an example of the #NURBS renderer I'm writing.
This one doesn't have such an impressive graph at the previous one, it's from early last month.

It's all in software.

There's a lot packed into this drawing of a closed #NURBS #curve I created as part of some visualization tools on a personal project!

Read the alt text for a full explanation. And I love questions! Feel free to ask.

While #programming my #NURBS renderer project in #Rust, I created type aliases for integers as Z, unsigned integers as N, and floating point numbers as Q. Of course the computer numbers only cover a tiny subset of these sets, but it is fun to use the more traditional mathematical notation.

I was just using the capital letters N, Z, and Q for these, but then I realized that I could use #Unicode in identifiers, so I committed a programming sin and started using the Unicode letters ℕ, ℤ, and ℚ for these! So impractical, yet so beautiful:

// Rational numbers
pub type ℚ = f64;
// Natural numbers
// (non-negative, include zero
// because unsigned numbers do...)
pub type ℕ = u32;
// Integers
pub type ℤ = i32;

While #programming my #NURBS renderer project in #Rust, I created type aliases for integers as Z, unsigned integers as N, and floating point numbers as Q. Of course the computer numbers only cover a tiny subset of these sets, but it is fun to use the more traditional mathematical notation.

I was just using the capital letters N, Z, and Q for these, but then I realized that I could use #Unicode in identifiers, so I committed a programming sin and started using the Unicode letters ℕ, ℤ, and ℚ for these! So impractical, yet so beautiful:

// Rational numbers
pub type ℚ = f64;
// Natural numbers
// (non-negative,
// include zero because unsigned // numbers do...)
pub type ℕ = u32;
// Integers
pub type ℤ = i32;

Some old retro-futuristic space toy designs. These were exercises in modeling with the MoI 3D NURBS / solids editor: https://moi3d.com

#space #toy #toys #3d #MoI3D #toygun #raygun #spacecraft #spaceship #fighter #jet #NURBS #solids #CAD #retrofuturism #retro #scifi #sciencefiction

#introduction
#seattle
#milwaukee
#splines
#NURBS
#python
#typescript

Bartosz Ciechanowski created something quite remarkable here that takes instruction on Curves & Surfaces to another level 🤯

Related to #GameDev, splines are often used to define motion paths or motion intensity. Their use in #Animation is similar.

Splines are also used in #VectorArt, #Fonts, & #ProductDesign (#NURBS) due to their mathematical precision. Most 3D modeling apps rely on subdivision surfaces to emulate this precision (#OpenSubdiv).

https://ciechanow.ski/curves-and-surfaces/

#References #Tutorials