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| | jamie-wong.com
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| | One of the techniques used in many demo scenes is called ray marching. This algorithm, used in combination with a special kind of function called
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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...
| | vankessel.io
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| | A blog for my thoughts. Mostly philosophy, math, and programming.
| | blog.georgeshakan.com
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| Principal Component Analysis (PCA) is a popular technique in machine learning for dimension reduction. It can be derived from Singular Value Decomposition (SVD) which we will discuss in this post. We will cover the math, an example in python, and finally some intuition. The Math SVD asserts that any $latex m \times d$ matrix $latex...