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Functions are vectors
Conceptualizing functions as infinite-dimensional vectors lets us apply the tools of linear algebra to a vast landscape of new problems, from image and geometry processing to curve fitting and machine learning.
Max Slater
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Software Engineering 5Math & Algorithms 4Games & Graphics 2AI & Machine Learning 2Systems & Performance 1
2
Exponentially Better Rotations (2022)
If you’ve done any 3D programming, you’ve likely encountered the zoo of techniques and representations used when working with 3D rotations. Some of them are better than others, depending on the situation.
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Optimizing Open Addressing
Your default hash table should be open-addressed, using Robin Hood linear probing with backward-shift deletion. When prioritizing deterministic performance over memory efficiency, two-way chaining is also a good choice.
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Differentiable programming from scratch
Differentiable programming has become a hot research topic, and not only due to the popularity of machine learning frameworks like TensorFlow, PyTorch, and JAX. Many fields apart from machine learning are finding differentiable programming to be a useful tool for solving optimization problems. In computer graphics…
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Monte Carlo Crash Course: Quasi-Monte Carlo
We’ve learned how to define and apply Monte Carlo integration—fundamentally, it’s the only tool we need. In the remaining chapters, we’ll explore ways to reduce variance and successfully sample difficult distributions.
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Monte Carlo Crash Course: Sampling
In the previous chapter, we assumed that we can uniformly randomly sample our domain. However, it’s not obvious how to actually do so—in fact, how can a deterministic computer even generate random numbers? 1
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Exploring Neural Graphics Primitives
Neural fields have quickly become an interesting and useful application of machine learning to computer graphics. The fundamental idea is quite straightforward: we can use neural models to represent all sorts of digital signals, including images, light fields, signed distance functions, and volumes.