- Happy Wednesday
- Attendance
- Class calendar for today
- Upcoming events

- did you get an email about Friday’s events?
- Math on the board revisited
- Assignment 2 will be posted later today, to be due October 25
- Enjoy the fall break

- continue reading Chapter 5
- Submit your response to this meeting before noon tomorrow
- Take the quiz before the start of our next meeting

Link to the UR Courses wiki page for this meeting

- Okay, so the recording is started. How's Everyone
- today? That's good to Hear. I
- Good. Thank You.
- You Okay, So I
- I just want to check whether you got an email from the Department
- both events on Friday.
- One person says, Yes, anyone? Else?
- Okay, thanks, I'll check on that. I
- Let me see that The advantage of The
- to Say Something
- Okay, so that's the multiplication. Ended up a lot.
- It's time with you.
- Change. Thank you. So I checked my math and seems to be okay for
- that 45 year old issue on the y axis I
- So because
- 45 degrees is halfway between
- the axis,
- so sine and cosine are the same, and
- anyway, so Let's take our point And we'll
- work out. You.
- Average so rotating around x by 90 degrees And
- we did our set by rotator unset by 90 degrees. I
- so in terms of efficiency, we always want to do three
- matrices. We want when we apply the transformation, do we want
- to keep these as individual matrices
- so we can put them together? It's more efficient in one
- matrix multiplication. So then we we
- we create one matrix, and then we apply that to all the points.
- So if we have one point, it doesn't make a difference, but
- if we have a million points,
- saving
- three changing from three operations to one, three
- multiplications to one multiplication is going to be a
- noticeable savings. So
- okay, so let's do This one first, 0000, I
- and then 00,
- minus One, zero And
- It's people. I'm just thinking, maybe easier to apply to have
- Clients benefits, because
- so here we have seven. We're
- minus five and
- two so we're rotating around the x axis, So we're
- flipping
- so we keep the x position.
- So seven is constant, and then we flip the other two positions
- so we're
- let's apply The minus 90 degree rotation so 00, minus two, four.
- Is zero, minus 500, so
- 702
- and then we transform by
- 90 degrees around the z axis. So so
- so we get five
- negative negative minus one times minus five, and
- then minus two and and
- then I and this is about the Z, so the Z doesn't change if this
- is about y, so y doesn't change. This is about x, so
- x doesn't Change. There. I,
- does that seem okay?
- Should we try and do The Matrix multiplication, 0000,
- and 0000, want to swallow.
- Okay So can someone see
- What the problem is? I
- so we rotate about
- the x axis by 90 degrees. So we've got the
- Then we rotate around the y axis by minus 90 degrees that became
- A
- rotate around the set by 90 degrees So minus One.
- Let's Try instead of
- an arbitrary block. Let's do something easier
- to visualize and
- Let's simplify 1110,
- so x, y and z1 so
- you rotate around x1 Is There?
- Let's look at The planes, X, Y,
- so Then The
- Does that make sense?
- Is that A better way to visualize it? I
- do I love do okay. So then we rotate by minus 90 around the
- bottom. Oh.
- Wk, so we get minus one
- turns to minus this one, this
- this one stays minus,
- and then The third One And
- so we Get one because you multiply minus one by minus one,
- and then
- We get minus One. So
- so any obvious mistakes In my matrix multiplication you
- I will work it out, and I promise to Not on the board and
- Come back And Pray For
- Okay, So let's have
- source code and
- so we're specifying an axis of rotation by A
- so if we're going to specify an arbitrary axis of rotation,
- so we can have Three Angles,
- so we can displace and
- and then this place is the right word. So we're going,
- we're going to apply rotations around each axis, and then that
- will give us a new axis of rotation. What's another way we
- can specify an axis of rotation and
- could be take two points. Is that Enough? I
- so we could say is This and
- another point is the
- so we specify an origin as well.
- So if you're rotating around The
- down the axis, 111, and
- then we're spinning
- Q
- on the X on
- from one vertex to Another, like,
- like the transformation he did
- of the color cube to turn it from RGB into HSV, tipped it on
- its amp.
- So having 111, as the rotation axis of zero at the origin. That
- means we would be spinning the cube like a top.
- So what's the process for rotating around an arbitrary
- axis? If we Start with Two points And
- so that process, how does
- it compare to Doing change the center
- rotation in two dimensions?
- I Does that Make sense comparison? So I
- these are all transformations we can
- apply and concatenate, so
- we'll see.
- So this gives us the ability to rotate around an arbitrary axis.
- This is an arbitrary center of rotation, so their
- transformations are
- So we'll see.
- As we get into viewing the chapter five more
- fully
- after the break, the transformations that will get us
- from our object space into a space couldn't coordinates that
- give us our display. These are all. They can all be witnesses
- to be concatenated.
- So it's a very powerful way to think about things I
- so
- I'll have
- an assignment posted later
- today we do on The
- 25th that will deal with Chapter Four stop. I
- just want to acknowledge that past couple days
- of rain on the board have
- not quickly or been to
- enthrall at night and apologize for that, and I'm
- looking forward to a better day
- to stop the break I
- any questions or concerns before I say, enjoy
- the fall break. If you have me, you can
- send me an email or come to
- see me by ourselves.
- Thank you for today, and I hope
- to see you on a Friday. Take care. Everyone.
- I
- I

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