Mtg 10/23: Wed-09-Oct-2024

Outline for Today

Math on the Board

Administration

Today

  • 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

For Next Meeting

Wiki

Link to the UR Courses wiki page for this meeting

Media

Transcript

Audio Transcript

  • 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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