Bases Part II
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Previous: 'Bases Part I'

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0:54Blackboard: Clarify linear independence

0:54Blackboard: Clarify linear independence

0:54Blackboard: Clarify linear independence

2:18Blackboard: Bases

2:18Blackboard: Bases

2:18Blackboard: Bases

6:16Blackboard: What does it mean to say we have an origin?

6:16Blackboard: What does it mean to say we have an origin?

6:16Blackboard: What does it mean to say we have an origin?

7:46Blackboard: Consider describing origins and basis vectors in terms of other origins and basis vectors

7:46Blackboard: Consider describing origins and basis vectors in terms of other origins and basis vectors

11:52Blackboard: Why do I care about this at all?

11:52Blackboard: Why do I care about this at all?

11:52Blackboard: Why do I care about this at all?

12:12Blackboard: Rotation and scaling

12:12Blackboard: Rotation and scaling

12:12Blackboard: Rotation and scaling

14:14Blackboard: Example rotation

14:14Blackboard: Example rotation

14:14Blackboard: Example rotation

15:09Blackboard: Example scaling

15:09Blackboard: Example scaling

15:09Blackboard: Example scaling

16:03Blackboard: What does that look like in code?

16:03Blackboard: What does that look like in code?

16:03Blackboard: What does that look like in code?

19:48Blackboard: This is what we'd like to introduce into our renderer now

19:48Blackboard: This is what we'd like to introduce into our renderer now

19:48Blackboard: This is what we'd like to introduce into our renderer now

20:20Blackboard: How do we define the X and the Y axis? (Unit circle)

20:20Blackboard: How do we define the X and the Y axis? (Unit circle)

20:20Blackboard: How do we define the X and the Y axis? (Unit circle)

24:41Blackboard: A handy optimisation thanks to being in 2D

24:41Blackboard: A handy optimisation thanks to being in 2D

24:41Blackboard: A handy optimisation thanks to being in 2D

28:19Blackboard: You can also directly plug and chug this

28:19Blackboard: You can also directly plug and chug this

28:19Blackboard: You can also directly plug and chug this

29:01Blackboard: Perp operator

29:01Blackboard: Perp operator

29:01Blackboard: Perp operator

31:09Blackboard: All we have to do

31:09Blackboard: All we have to do

31:09Blackboard: All we have to do

32:26Go into the code and create one of these rotating doodads

32:26Go into the code and create one of these rotating doodads

32:26Go into the code and create one of these rotating doodads

36:18Run the game to discover that our code is hosed

36:18Run the game to discover that our code is hosed

36:18Run the game to discover that our code is hosed

37:21See what our InvalidDefaultCase says

37:21See what our InvalidDefaultCase says

37:21See what our InvalidDefaultCase says

37:58Let it hit the InvalidDefaultCase sooner

37:58Let it hit the InvalidDefaultCase sooner

37:58Let it hit the InvalidDefaultCase sooner

38:34Take a look at the RenderGroup buffer

38:34Take a look at the RenderGroup buffer

38:34Take a look at the RenderGroup buffer

39:52Step through the code with an eye on PushBufferBase

39:52Step through the code with an eye on PushBufferBase

39:52Step through the code with an eye on PushBufferBase

40:41Moment of realisation: render_entry_coordinate_system was missing its Header

40:41Moment of realisation: render_entry_coordinate_system was missing its Header

40:41Moment of realisation: render_entry_coordinate_system was missing its Header

41:57Put our coordinate_system back in there and run again until it hits the InvalidDefaultCase

41:57Put our coordinate_system back in there and run again until it hits the InvalidDefaultCase

41:57Put our coordinate_system back in there and run again until it hits the InvalidDefaultCase

42:22Put in a case for our coordinate_system

42:22Put in a case for our coordinate_system

42:22Put in a case for our coordinate_system

43:52Define the coordinate_system to be something that's visible

43:52Define the coordinate_system to be something that's visible

43:52Define the coordinate_system to be something that's visible

46:12View the results in-game and apply transforms

46:12View the results in-game and apply transforms

46:12View the results in-game and apply transforms

47:47Edit this coordinate system live

47:47Edit this coordinate system live

47:47Edit this coordinate system live

48:54Insert some points that are encoded in that axis

48:54Insert some points that are encoded in that axis

48:54Insert some points that are encoded in that axis

51:39Check it out in-game (...or not)

51:39Check it out in-game (...or not)

51:39Check it out in-game (...or not)

52:26Moment of realisation: It'd be nice if Casey actually used PIndex

52:26Moment of realisation: It'd be nice if Casey actually used PIndex

52:26Moment of realisation: It'd be nice if Casey actually used PIndex

52:38Try viewing again

52:38Try viewing again

52:38Try viewing again

53:04Step through the code watching the coordinates of the Points

53:04Step through the code watching the coordinates of the Points

53:04Step through the code watching the coordinates of the Points

53:27Reduce the number of Points and view it in-game

53:27Reduce the number of Points and view it in-game

53:27Reduce the number of Points and view it in-game

54:19Play with those axes

54:19Play with those axes

54:19Play with those axes

55:26Do we have pie?

^{α}55:26Do we have pie?

^{α}55:26Do we have pie?

^{α}56:08Continue playing

56:08Continue playing

56:08Continue playing

57:27Q&A

57:27Q&A

57:27Q&A

1:04:12Make the size proportional as well

1:04:12Make the size proportional as well

1:04:12Make the size proportional as well

1:05:20Go nuts with that

1:05:20Go nuts with that

1:05:20Go nuts with that

1:07:40Call it done for the day, with special mention made of that weird pulsating thing and a glimpse into the future

^{γ}1:07:40Call it done for the day, with special mention made of that weird pulsating thing and a glimpse into the future

^{γ}^{γ}

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Next: 'Filling Rotated and Scaled Rectangles'

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