When it comes to software engineering, I’d like to think of myself as a generalist. Still, over my 12-year career, a major focus has been building scalable backends. I’ve worked at Amazon and Twitch to build out large-scale systems that support millions of users.
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In SM64 this covering space structure is used by giving Mario extremely high velocity \(v\) (a tangent vector at Marios position in \(P\)) through a different glitch called “backwards longjump”. The exponential map is then used to move Mario along the geodesic \(\exp_v(t)\) for \(t \in \mathbb{R}\). But due to hardware limitations, only discrete steps \(t_1, \dots, t_k\) for some \(k \in \mathbb{N}\) of this geodesic are actually calculated for collision detection. More on how this is related to the exponential map of Lie groups can be found in my previous post. Throughout this post, I will assume the Lie group of SM64 to have its unit at the position \(p\).。体育直播对此有专业解读
Where it can be applied¶