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 \(p\).
百年党史峥嵘。中央党校内，立于广场上的一块巨石两面，“实事求是”“为人民服务”的箴言格外醒目，校园两侧，焦裕禄、谷文昌塑像静立，映照始终不渝的初心、不随境迁的追求、不为时易的坚持。
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Photograph: Matthew Korfhage
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