Freya Holmér
Shader and graphics programmer, creator of Shapes and Shader Forge, known for math-heavy visual YouTube explainers and Unity shader and tooling content. Independent developer and co-founder of Neat Corporation (Budget Cuts).
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- @freya.bsky.social: quaternion powers q², √q and qˣ scale a rotation
Raising a quaternion to a power scales its rotation: square doubles, square root halves, qˣ scales by x.
bsky.app · Sep 2026 - @freya.bsky.social: quaternion (x,y,z,0) is a 180° rotation about that axis
A unit vector as a pure quaternion gives a half-turn around it, with no trig or euler conversion.
bsky.app · Sep 2026 - @freya.bsky.social: random rotations equal uniform points on a 4D sphere
Uniformly distributed random rotation quaternions are exactly uniform random points on the 4D sphere surface.
bsky.app · Jul 2026 - @freya.bsky.social: analytic 2D lighting with complex numbers and conformal maps
Shader lighting via piecewise conformal maps of angular exposure yields fully analytic penumbras.
bsky.app · Mar 2026 - @freya.bsky.social: A+B is the midpoint of A and B in homogeneous coordinates
In homogeneous coordinates adding two points gives their midpoint, a trick behind w=0 or w=1 handling.
bsky.app · Mar 2026 - @freya.bsky.social: many game quantities are better as rational numbers than flo
Time, UI sliders and line intersections can be exact fractions, avoiding float rounding issues.
bsky.app · Dec 2025 - Freya's Guide to XYZ Axes and Handedness
Post showing a guide to XYZ axes and handedness across coordinate systems.
mastodon.social · Sep 2024 - Unity shader .cginc to draw numbers in the fragment shader (gist)
Repo: gist with a Unity shader include that draws numbers in the fragment shader for debugging.
gist.github.com · Aug 2024 - Debug-printing a view matrix from the GPU inside a shader
Post showing how to debug-print a view matrix from the GPU inside a shader.
mastodon.social · Aug 2024 - Clean way to get meters per pixel in shaders
Post showing a clean way to compute meters per pixel in shaders.
mastodon.social · Aug 2024 - Lerp smoothing is broken
Explains why the common lerp smoothing pattern is frame-rate dependent and how to fix it.
youtube.com · May 2024 - Framerate-independent lerp smoothing
Post working out framerate-independent lerp smoothing.
mastodon.social · Feb 2024 - Easing functions: linear, smoothstep, smootherstep and elevator-style curves
Post comparing easing functions like linear, smoothstep, smootherstep and elevator-style curves.
mastodon.social · Jan 2024 - Why can't you multiply vectors?
Explains why vectors have no single multiplication, covering dot, cross and other products.
youtube.com · Oct 2023 - Mathfs: Catenary2D (solving the catenary root)
Repo: Mathfs library class for solving a 2D catenary curve in Unity.
github.com · Dec 2022 - The Continuity of Splines
Explains continuity of splines and what C0, C1 and C2 mean.
youtube.com · Dec 2022 - Coordinate system chart (Unity, Unreal, 3D math)
Post sharing a coordinate system chart for Unity, Unreal and 3D math.
mastodon.social · Nov 2022 - Quaternion swizzling for cheap 180-degree rotations in Unity
Repo: code snippet using quaternion swizzling for cheap 180-degree rotations in Unity.
github.com · Nov 2022 - The Art of Real-Time Mathematics (guest lecture)
Guest lecture on real-time mathematics for game and graphics programming.
youtube.com · Nov 2022 - Math for Game Devs [2022, part 10] • Abstract Algebra, Procedural Animation & Splines
Math for game devs part 10 covering abstract algebra, procedural animation and splines.
youtube.com · Nov 2022 - Math for Game Devs [2022, part 9] • Solutions to the final assignments
Math for game devs part 9 reviewing solutions to the final assignments.
youtube.com · Nov 2022 - Math for Game Devs [2022, part 8] • Trajectories & Derivatives
Math for game devs part 8 on trajectories and derivatives.
youtube.com · Nov 2022 - Math for Game Devs [2022, part 7] • Interpolation & Point Physics
Math for game devs part 7 on interpolation and point physics.
youtube.com · Nov 2022 - Math for Game Devs [2022, part 6] • Solutions for Assignments 7-11
Math for game devs part 6 reviewing solutions for assignments 7-11.
youtube.com · Nov 2022 - Math for Game Devs [2022, part 5] • Trigonometry & Rotations
Math for game devs part 5 on trigonometry and rotations.
youtube.com · Oct 2022 - Math for Game Devs [2022, part 4] • solutions for assignments 4-6
Math for game devs part 4 reviewing solutions for assignments 4-6.
youtube.com · Oct 2022 - Math for Game Devs [2022, part 3] • Matrix4x4 & Cross Product
Math for game devs part 3 on Matrix4x4 and the cross product.
youtube.com · Oct 2022 - Math for Game Devs [2022, part 2] solutions for assignments 1-3
Math for game devs part 2 reviewing solutions for assignments 1-3.
youtube.com · Oct 2022 - Math for Game Devs [2022, part 1] • Numbers, Vectors & Dot Product
Math for game devs part 1 on numbers, vectors and the dot product.
youtube.com · Oct 2022 - How to rotate a vector
Explains how to rotate a vector in 2D and 3D.
youtube.com · Feb 2022 - The Beauty of Bézier Curves
Visual explanation of Bezier curves and how they are built.
youtube.com · Aug 2021 - Normal Maps, Tangent Space & IBL • Shaders for Game Devs [Part 3]
Shaders for game devs part 3 on normal maps, tangent space and image-based lighting.
youtube.com · Feb 2021 - Healthbars, SDFs & Lighting • Shaders for Game Devs [Part 2]
Shaders for game devs part 2 on healthbars, SDFs and lighting.
youtube.com · Feb 2021 - Shader Basics, Blending & Textures • Shaders for Game Devs [Part 1]
Shaders for game devs part 1 on shader basics, blending and textures.
youtube.com · Feb 2021 - Interpolation & Velocity • Math for Game Devs [Part 4]
Math for game devs part 4 on interpolation and velocity.
youtube.com · Nov 2020 - Trigonometry • Math for Game Devs [Part 3]
Math for game devs part 3 on trigonometry.
youtube.com · Nov 2020 - Spaces & Cross Product • Math for Game Devs [Part 2]
Math for game devs part 2 on spaces and the cross product.
youtube.com · Nov 2020 - Vectors & Dot Product • Math for Game Devs [Part 1]
Math for game devs part 1 on vectors and the dot product.
youtube.com · Nov 2020 - Intro to Tool Dev in Unity [part 4/4]
Part 4 of 4 of an intro to Unity editor tool development.
youtube.com · May 2020 - Intro to Tool Dev in Unity [part 3/4]
Part 3 of 4 of an intro to Unity editor tool development.
youtube.com · May 2020 - Intro to Tool Dev in Unity [part 2/4]
Part 2 of 4 of an intro to Unity editor tool development.
youtube.com · Apr 2020 - Intro to Tool Dev in Unity - An Improvised Live Course [part 1/4]
Part 1 of 4 of an improvised live course on Unity editor tool development.
youtube.com · Apr 2020 - Remote Math class for Game Devs (Stream Recording)
Stream recording of a remote math class for game developers.
youtube.com · Mar 2020 - Freya Holmér · YouTube channel
YouTube channel with Unity-related videos.
youtube.com · ~Mar 2020 - Math for Game Dev - An Improvised Live Course
Improvised live course on math for game development.
youtube.com · Sep 2019 - Procedural Geometry - An Improvised Live Course
Improvised live course on procedural geometry in Unity.
youtube.com · Aug 2019 - Sine and Cosine - A Visual Explanation
Visual explanation of sine and cosine.
youtube.com · Aug 2019 - Intro to Shader Coding in Unity - An Improvised Live Course
Improvised live course introducing shader coding in Unity.
youtube.com · Aug 2019 - Specular Lighting - A Visual Explanation
Visual explanation of specular lighting.
youtube.com · Aug 2019 - The Dot Product - A Visual Explanation
Visual explanation of the dot product.
youtube.com · Aug 2019