40 lines
2.9 KiB
Plaintext
40 lines
2.9 KiB
Plaintext
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[video member=cmuratori stream_platform=twitch stream_username=handmade_hero project=code title="Inverse and Transpose Matrices" vod_platform=youtube id=9KaIB7PFWeE annotator=Miblo]
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[0:17][Recap and set the stage for the day]
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[1:29][Blackboard: Skew UV Mapping]
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[3:48][Blackboard: A conceptual explanation of transforming a texture map]
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[7:15][Blackboard: Our matrix equation]
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[8:08][Blackboard: The components of this equation]
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[9:27][Blackboard: Adding and taking the origin out of equation]
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[10:36][Blackboard: Transforming the U and V]
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[12:11][Blackboard: Multiplying these matrices out]
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[14:11][Blackboard: Backward transform, using dot products]
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[16:18][Blackboard: Why use dot products to compute the transformed U and V?]
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[18:42][Blackboard: Getting from wanting to invert the matrix, to taking the dot product shortcut]
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[19:47][Blackboard: Inverting an orthonormal matrix]
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[22:08][Blackboard: What it means to invert]
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[25:14][Blackboard: The algebraic explanation for why any orthonormal matrix multiplied by its transpose (i.e. inverted) gives you the identity matrix]
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[31:38][Blackboard: Putting it in meta algebraic terms]
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[33:22][Blackboard: The geometric explanation for this]
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[37:28][Blackboard: Columnar vs Row-based Matrices]
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[39:49][Blackboard: How non-uniform (yet still orthogonal) scaling affects our matrix]
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[41:11]["I hope everyone was interested in the matrix thing today"][quote 516]
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[42:16][Blackboard: Transposing the matrix for non-uniformly scaled vectors, and compensating for that scaling]
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[44:54][Blackboard: The beginnings of a formal algebraic explanation of this compensation]
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[46:53][Blackboard: Matrix multiplication is order dependent]
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[50:01][Blackboard: How this order dependence of the transform is captured by matrix maths]
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[52:41][Blackboard: A formal algebraic explanation for the scale and rotation compensation]
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[55:59][Blackboard: A glimpse into the future of actually inverting the matrix]
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[57:14][Q&A]
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[58:02][@stropheum][You've got some salty dogs in your chat tonight, Casey]
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[58:32][A few words on how cool linear algebra can get]
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[59:46][@stropheum][Did you know you were going to have to implement the sort of reverse mapping when you took that shortcut before? Was it a deliberate choice or just a cut corner that had to be uncut?]
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[1:00:35][@ttbjm][Is your elbow okay? Are you okay?]
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[1:02:24][@lord_marshall_][Other than transpose, do you need much more from linear?]
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[1:05:03][@lord_marshall_][We had one example from my linear algebra class in the book, that used computers. Was surprised to see it here]
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[1:06:21][@rohit_n][sssmcgrath said this once, but math papers should be published with C source code]
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[1:06:38][@jpmontielr][Have you seen Gilbert Strang's lectures on linear algebra?]
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[1:07:40][@d3licious][You suggest students not knowing how to solve linear algebra problems by hand?]
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[1:09:42][@jessem3y3r][Would you consider using C++ templates for matrices, say in 3D programming?]
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[1:10:57][We are done]
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[/video]
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