The Geometry Behind Normal Maps
https://www.shlom.dev/articles/geometry-behind-normal-maps/
#HackerNews #Geometry #NormalMaps #3DGraphics #GameDevelopment #Shading #Techniques
Billy Smith
boosted
Best effort embedding of an octagonal tiling in 𝑅³ of a surface of genus 111. Each octagon has vertex valences [3,4,3,3,3,4,4,4].
hypebot
and 1 other
boosted
The different colors of the cells indicate pollen from different species of plants, packed away to be used as food for hungry honey bee larvae.
The different colors of the cells indicate pollen from different species of plants, packed away to be used as food for hungry honey bee larvae.
Best effort embedding of an octagonal tiling in 𝑅³ of a surface of genus 111. Each octagon has vertex valences [3,4,3,3,3,4,4,4].
[1/n] Continuing my work (see previous posts) about the geometric possibilities of the radiant number ρ (aka plastic ratio). Because it can serve as the base of a numeral system (just it and the golden ratio have this property among non-integers), every rectangle whose side ratio is a power of ρ can be decomposed into rectangles whose side ratio is a power of ρ. Particularly, if we take three consecutive powers of ρ we can make substitution tilings involving its corresponding rectangles. These properties are depicted in the first image. In the next images we see two possibilities regarding rectangles of ratios 1, ρ and ρ² (one just uses horizontal rectangles), and one for rectangles of ratios ρ, ρ² and ρ³. Of course any of these partitions, by rearranging/rotating/mirroring tiles, give many possible different tilings.
#Mathematics #geometry #tiling #mathart #radiantnumber
Substitutions for rectangles of side ratios ρ (purple colour), ρ² (green colour), and ρ³ (orange colour), .
Substitutions for rectangles of side ratios ρ⁰ = 1 (square, orange colour), ρ (purple colour) and ρ² (green colour), where rectangles are always put in horizontal position.
Substitutions for rectangles of side ratios ρ⁰ = 1 (square, orange colour), ρ (purple colour) and ρ² (green colour).
Seven colourful columns depict how each rectangle of ratio a power of the radiant number can be decomposed into rectangles of ratios in three consecutive powers of ρ.
When models manipulate manifolds: The geometry of a counting task
https://transformer-circuits.pub/2025/linebreaks/index.html
#HackerNews #models #manifolds #geometry #counting #task #AI #research
Geometry and Physics of Wrinkling [pdf]
https://softmath.seas.harvard.edu/wp-content/uploads/2019/10/2003-03.pdf
#HackerNews #Geometry #Physics #Wrinkling #Research #PDF #SoftMath
Anke
boosted
Alright since I'm apparently not able to find something myself (I searched on and off for the last couple of years and tried my best to calculate it myself) maybe someone here can help me. Suppose you have an ellipse and a circle in 2D is there a numerically stable way to find the intersection points between them? If there is such a solution for two ellipses that would be even better #geometry #math 
Alright since I'm apparently not able to find something myself (I searched on and off for the last couple of years and tried my best to calculate it myself) maybe someone here can help me. Suppose you have an ellipse and a circle in 2D is there a numerically stable way to find the intersection points between them? If there is such a solution for two ellipses that would be even better #geometry #math
OliverUv
boosted
The prompt for day 3 was 'Polyhedron'. In mathematics a 'convex polyhedron' is any subset of ℝ³ which can be obtained as the convex hull of finitely many noncoplanar points. However, when convexity is not required the definition of 'polyhedron' is in some dispute.
Certainly every convex polyhedron is a polyhedron, however there are multip-
On second thoughts, this post would be better expressed as an alignment chart meme.
The prompt for day 3 was 'Polyhedron'. In mathematics a 'convex polyhedron' is any subset of ℝ³ which can be obtained as the convex hull of finitely many noncoplanar points. However, when convexity is not required the definition of 'polyhedron' is in some dispute.
Certainly every convex polyhedron is a polyhedron, however there are multip-
On second thoughts, this post would be better expressed as an alignment chart meme.
Strypey
boosted
It's really tricky to spread the word about events these days! I don't support corporate social media and you don't get read attention there anyway, mailing lists aren't what they once were, and this event wants to reach people across many patterny disciplines..
Any help spreading the word across all the strange pattern-obsessed communities much appreciated!
--
Algorithmic Pattern is a new festival and conference for people curious about the practice and culture of algorithmic pattern-making, across algorithmic music, arts and craft. The first edition will take place both in Sheffield UK and online, during September 2025.
The call for talks/papers is now open, deadline 2nd June - please see our website for details: https://2025.algorithmicpattern.org/call/
#textiles #weaving #algorave #livecoding #algorithmicart #cfp #conference #patterns #pattern #craft #juggling #siteswap #origami #geometry #ethnomathmatics #choreography
STOP OCCUPATION 🍉 S. Costa
boosted
This had me captivated for a good five minutes. I just kept watching how the patterns matched up, trying to parse out the connections in my brain.
Who knew an animation of a Rubik’s Cube and some corresponding concentric circles could be so stimulating?
I have absolutely no idea who created it. Tried to find out to no avail. (Happy to edit with a citation if someone knows.)
This had me captivated for a good five minutes. I just kept watching how the patterns matched up, trying to parse out the connections in my brain.
Who knew an animation of a Rubik’s Cube and some corresponding concentric circles could be so stimulating?
I have absolutely no idea who created it. Tried to find out to no avail. (Happy to edit with a citation if someone knows.)
Jonathan Schofield
boosted
Monohedral triangle tiling of the gyroid, which is the dual tessellation of a partial Cayley surface complex of the group:
<br/>G = ⟨ f₁,t₁ | f₁², t₁⁶, (f₁t₁)⁴, (f₁t₁f₁t₁⁻¹f₁t₁²)² ⟩<br/>
Ball of radius 21. (1/2)
Module that can be used to create the structure. (2/2)
Monohedral triangle tiling of the gyroid, which is the dual tessellation of a partial Cayley surface complex of the group:
<br/>G = ⟨ f₁,t₁ | f₁², t₁⁶, (f₁t₁)⁴, (f₁t₁f₁t₁⁻¹f₁t₁²)² ⟩<br/>
Ball of radius 21. (1/2)