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www.rorydriscoll.com | ||
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frozenfractal.com
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| | | | | I didn't have time during the holidays to implement any new features, so enjoy this filler post that I prepared earlier! In the very first post in this series, I wrote: The prototype took place on a rectangular map, with the left side wrapping around to the right to form a cylinder. [...] Many games do this and get away with it, but because I'm a perfectionist, I want my game to take place on an actual sphere. Today I'm going to write up in some detail why spheres are harder to work with. | |
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thenumb.at
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| | | | | Or, where does that \(\sin\theta\) come from? Integrating functions over spheres is a ubiquitous task in graphicsand a common source of confusion for beginners. In particular, understanding why integration in spherical coordinates requires multiplying by \(\sin\theta\) takes some thought. The Confusion So, we want to integrate a function \(f\) over the unit sphere. For simplicity, lets assume \(f = 1\). Integrating \(1\) over any surface computes the area of that surface: for a unit sphere, we should end... | |
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www.reedbeta.com
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| | | | | When you read BRDF theory papers, you'll often see mention of slope space. Sometimes, components of the BRDF such as NDFs or masking-shadowing functions are defined in slope space, or operations are done in slope space before being converted back to ordinary vectors or polar coordinates. However, the meaning and intuition of slope space is rarely explained. Since it may not be obvious exactly what slope space is, why it is useful, or how to transform things to and from it, I thought I would write down a ... | |
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fa.bianp.net
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| | | The Langevin algorithm is a simple and powerful method to sample from a probability distribution. It's a key ingredient of some machine learning methods such as diffusion models and differentially private learning. In this post, I'll derive a simple convergence analysis of this method in the special case when the ... | ||
