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mattferraro.dev | ||
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thenumb.at
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| | | | | [AI summary] The text discusses the representation of functions as vectors and their applications in various domains such as signal processing, geometry, and physics. It explains how functions can be treated as vectors in a vector space, leading to the concept of eigenfunctions and eigenvalues, which are crucial for understanding and manipulating signals and geometries. The text also covers different types of Laplacians, including the standard Laplacian, higher-dimensional Laplacians, and the Laplace-Beltrami operator, and their applications in fields like image compression, computer graphics, and quantum mechanics. The discussion includes spherical harmonics, which are used in representing functions on spheres, and their applications in game engines and glo... | |
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terathon.com
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| | | | | [AI summary] The provided text is a detailed critique of the book 'Projective Geometric Algebra' by the authors, highlighting numerous errors and misunderstandings in their treatment of geometric algebra, particularly in areas such as norms, duality, and the Hodge dual. The author of the critique points out that the book's definitions and explanations are often incorrect, misleading, or based on flawed reasoning. Key issues include the misuse of the Hodge dual, incorrect definitions of norms, and a lack of understanding of fundamental concepts like operator duality and the relationship between different types of norms. The critique also addresses the authors' attempts to compare the efficiency of PGA operators with matrices, which are shown to be misleading.... | |
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alexkritchevsky.com
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| | | | | [AI summary] The article critiques Geometric Algebra (GA) for its reliance on the geometric product, which the author finds problematic for most purposes. The author argues that GA's focus on complexifying vector algebra to resemble complex numbers and quaternions is unnecessary and confusing. Instead, the author advocates for a simpler approach using exterior algebra and wedge products, emphasizing clarity and intuition over abstract algebraic structures. The author also mentions the philosophical and pedagogical issues with GA, such as its conflation of operators and primitives, and the cultural baggage associated with the term 'Geometric Algebra.' The article concludes by suggesting that while GA has value as an implementation detail, it should not be see... | |
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www.velanstudios.com
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| | | [AI summary] The text describes the rendering pipeline of the Viper Engine used in the game Knockout City. It covers various stages including the initial 3D scene rendering, post-processing steps like distortion, bloom, tonemapping, and anti-aliasing, followed by UI rendering and the final backbuffer pass. The article also mentions future enhancements and invites interested readers to apply for the Viper Engine team. | ||
