Implicit Surfaces & Independent Research
Why Hacker News recommends it
HN commenters use it as the go-to overview of Keeter's implicit-surface and interval-arithmetic work, pointing people to it when discussing SDFs, the Prospero Challenge, and interval-based evaluation.
Recommended by 2 people across 2 different months, 2025 to 2026.
What it is
Matt Keeter gives a colloquium talk at Harvey Mudd College on implicit surfaces, where a 3D solid is defined by a function ℝ³→ℝ being negative. He covers optimized rendering, interval arithmetic, fast evaluation via compilation, and data structures, then reflects on doing independent research as a hobbyist who published at a top venue.
What people said
Strong rec iamwil · 2025-03 · Hacker News · on “The Prospero Challenge”
For a given (x, y), you color the pixel black if you're outside of a shape, and color the pixel white if you're inside the shape. The math formula is a way to describe the contour of the shape. To tell if you're inside or outside of a shape, you plug in your (x, y) coordinate into the math formula, and if the output is > 0, then you're outside. If the output is < 0, then you're inside. I think they call it a signed distance field. You should watch his talk that explain it. It's really great. [this video]
Recommends mkeeter · 2025-03 · Hacker News · on “The Prospero Challenge”
> What are the practical implications of this kind of assembly language? Surely there’s more efficient means of describing 2D SDFs? By analogy, you wouldn't program in LLVM IR, but it's a useful intermediate representation for a bunch of higher-level languages. Higher-level tools can target this representation, and then they all get to use a standard set of optimizations and algorithms (fast evaluation, rendering, etc). (I gave a recent talk that's a broad overview of this research: [this video] ) > My next thought would be to evaluate the program at a low resolution to create a low res SDF texture for the shader to draw at a higher resolution. Glad you're enjoying the challenge! You may also be
Recommends iamwil · 2026-04 · Hacker News · on “Show HN: I made a calculator that works over disjoint sets of intervals”
This is great. You might be interested in Matt Keeter's work on Implicit surfaces, and using interval math for its optimization: [this video]
Cites jstanley · 2025-03 · Hacker News · on “The Prospero Challenge”
I'm thinking that we can parse the input into an expression tree, and then for each x coordinate, have each node in the tree tell us which intervals of y coordinates it would return a value < 0 (or <= 0 without loss of generality). Since we're basically dealing with real numbers we can pretend true 0 doesn't exist. Composing these intervals is trivial for all operations except addition/subtraction. (For example, `mul` is less than 0 if exactly one of its arguments is less than 0, `neg` is less than 0 if its argument is not less than 0, `min` less than 0 if either of its arguments is less than 0, etc.). And then we define add(a, b) as sub(a, neg(b)). So then we only need to work out which y v
Cites mncharity · 2026-09 · Hacker News · on “Halfspace experimental IDE for solid modeling with distance fields”
"What does this independent research look like?"[1] - timestamp link into Implicit Surfaces & Independent Research (2025) on that research page. [1] [this video] (I started the clip a few seconds early as teaser for rest of talk)