cinera_handmade.network/cmuratori/hero/code/code319.hmml

[video output=day319 member=cmuratori stream_platform=twitch stream_username=handmade_hero project=code title="Inverse and Transpose Matrices" vod_platform=youtube id=9KaIB7PFWeE annotator=Miblo]
[0:17][Recap and set the stage for the day]
[1:29][Blackboard: Skew UV Mapping]
[3:48][Blackboard: A conceptual explanation of transforming a texture map]
[7:15][Blackboard: Our matrix equation]
[8:08][Blackboard: The components of this equation]
[9:27][Blackboard: Adding and taking the origin out of equation]
[10:36][Blackboard: Transforming the U and V]
[12:11][Blackboard: Multiplying these matrices out]
[14:11][Blackboard: Backward transform, using dot products]
[16:18][Blackboard: Why use dot products to compute the transformed U and V?]
[18:42][Blackboard: Getting from wanting to invert the matrix, to taking the dot product shortcut]
[19:47][Blackboard: Inverting an orthonormal matrix]
[22:08][Blackboard: What it means to invert]
[25:14][Blackboard: The algebraic explanation for why any orthonormal matrix multiplied by its transpose (i.e. inverted) gives you the identity matrix]
[31:38][Blackboard: Putting it in meta algebraic terms]
[33:22][Blackboard: The geometric explanation for this]
[37:28][Blackboard: Columnar vs Row-based Matrices]
[39:49][Blackboard: How non-uniform (yet still orthogonal) scaling affects our matrix]
[41:11]["I hope everyone was interested in the matrix thing today"][quote 516]
[42:16][Blackboard: Transposing the matrix for non-uniformly scaled vectors, and compensating for that scaling]
[44:54][Blackboard: The beginnings of a formal algebraic explanation of this compensation]
[46:53][Blackboard: Matrix multiplication is order dependent]
[50:01][Blackboard: How this order dependence of the transform is captured by matrix maths]
[52:41][Blackboard: A formal algebraic explanation for the scale and rotation compensation]
[55:59][Blackboard: A glimpse into the future of actually inverting the matrix]
[57:14][Q&A][:speech]
[58:02][@stropheum][You've got some salty dogs in your chat tonight, Casey]
[58:32][A few words on how cool linear algebra can get]
[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?]
[1:00:35][@ttbjm][Is your elbow okay? Are you okay?]
[1:02:24][@lord_marshall_][Other than transpose, do you need much more from linear?]
[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]
[1:06:21][@rohit_n][sssmcgrath said this once, but math papers should be published with C source code]
[1:06:38][@jpmontielr][Have you seen Gilbert Strang's lectures on linear algebra?]
[1:07:40][@d3licious][You suggest students not knowing how to solve linear algebra problems by hand?]
[1:09:42][@jessem3y3r][Would you consider using C++ templates for matrices, say in 3D programming?]
[1:10:57][We are done][:speech]
[/video]
Cinera 0.7.0 Update Add output parameter to all of hero/code, hero/intro-to-c and hero/misc, preserving the current URLs while allowing different .hmml filenames, notably for hero/misc which now gets sorted chronologically. Update the cinera__*.css files 2020-05-09 20:59:36 +00:00			`[video output=day319 member=cmuratori stream_platform=twitch stream_username=handmade_hero project=code title="Inverse and Transpose Matrices" vod_platform=youtube id=9KaIB7PFWeE annotator=Miblo]`
Relocate riscy and add newly converted hero The idea here is to reduce the amount of superfluous stuff downloaded to each server running cinera 2017-12-06 22:26:13 +00:00			`[0:17][Recap and set the stage for the day]`
			`[1:29][Blackboard: Skew UV Mapping]`
			`[3:48][Blackboard: A conceptual explanation of transforming a texture map]`
			`[7:15][Blackboard: Our matrix equation]`
			`[8:08][Blackboard: The components of this equation]`
			`[9:27][Blackboard: Adding and taking the origin out of equation]`
			`[10:36][Blackboard: Transforming the U and V]`
			`[12:11][Blackboard: Multiplying these matrices out]`
			`[14:11][Blackboard: Backward transform, using dot products]`
			`[16:18][Blackboard: Why use dot products to compute the transformed U and V?]`
			`[18:42][Blackboard: Getting from wanting to invert the matrix, to taking the dot product shortcut]`
			`[19:47][Blackboard: Inverting an orthonormal matrix]`
			`[22:08][Blackboard: What it means to invert]`
			`[25:14][Blackboard: The algebraic explanation for why any orthonormal matrix multiplied by its transpose (i.e. inverted) gives you the identity matrix]`
			`[31:38][Blackboard: Putting it in meta algebraic terms]`
			`[33:22][Blackboard: The geometric explanation for this]`
			`[37:28][Blackboard: Columnar vs Row-based Matrices]`
			`[39:49][Blackboard: How non-uniform (yet still orthogonal) scaling affects our matrix]`
			`[41:11]["I hope everyone was interested in the matrix thing today"][quote 516]`
			`[42:16][Blackboard: Transposing the matrix for non-uniformly scaled vectors, and compensating for that scaling]`
			`[44:54][Blackboard: The beginnings of a formal algebraic explanation of this compensation]`
			`[46:53][Blackboard: Matrix multiplication is order dependent]`
			`[50:01][Blackboard: How this order dependence of the transform is captured by matrix maths]`
			`[52:41][Blackboard: A formal algebraic explanation for the scale and rotation compensation]`
			`[55:59][Blackboard: A glimpse into the future of actually inverting the matrix]`
Fix some incorrectly converted annotations Also apply some :speech categorisation 2018-03-07 21:48:09 +00:00			`[57:14][Q&A][:speech]`
Relocate riscy and add newly converted hero The idea here is to reduce the amount of superfluous stuff downloaded to each server running cinera 2017-12-06 22:26:13 +00:00			`[58:02][@stropheum][You've got some salty dogs in your chat tonight, Casey]`
			`[58:32][A few words on how cool linear algebra can get]`
			`[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?]`
			`[1:00:35][@ttbjm][Is your elbow okay? Are you okay?]`
			`[1:02:24][@lord_marshall_][Other than transpose, do you need much more from linear?]`
			`[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]`
			`[1:06:21][@rohit_n][sssmcgrath said this once, but math papers should be published with C source code]`
			`[1:06:38][@jpmontielr][Have you seen Gilbert Strang's lectures on linear algebra?]`
			`[1:07:40][@d3licious][You suggest students not knowing how to solve linear algebra problems by hand?]`
			`[1:09:42][@jessem3y3r][Would you consider using C++ templates for matrices, say in 3D programming?]`
Fix some incorrectly converted annotations Also apply some :speech categorisation 2018-03-07 21:48:09 +00:00			`[1:10:57][We are done][:speech]`
Relocate riscy and add newly converted hero The idea here is to reduce the amount of superfluous stuff downloaded to each server running cinera 2017-12-06 22:26:13 +00:00			`[/video]`