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- Attendance
- Class calendar for today
- Upcoming events

Summary

- Start 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

- Hello, Monday, October, 7, You.
- So continue with chapter four. I want to bring to your attention
- a couple of events on Friday. So there's the lunch
- in Rick, 219,
- the lunch theater. And
- then there's also the seminar at the reception to follow.
- So that was an education auditorium, but it's been moved
- to Rick, 219,
- so that makes easier for for the hospitality folks to arrange
- things and coordinate amongst different activities going on
- the day that day. So the reception is in the lab calf,
- who calls it the lab calf, besides me or lab Cafe anyway,
- that's
- very close to The record. Key, One, Nine, I,
- that's F, not A T.
- So I'd like your input
- on the Judea, Could you close the door? I
- thank you. Now we'll see Whether it helps or not you
- so inspired by a 16 by 16 favicon. Anyone familiar with
- favicons, that's the little picture that comes up
- beside the website Like
- the F for Facebook there and so on. So.
- So I'm not
- going to beat this or play with this point, but I
- so I'm thinking, we're thinking about doing u
- r, CS, I
- so then we have to decide which cupcakes to ice with the
- foreground color and which ones to ice With the background color
- to bring To make this A display so
- so 16 and 16 being with more characters and
- more characters,
- eight by eight.
- Screen, so you can see that I have an app here to do the IBM
- BIOS font to
- is this related to class at All closely enough that I could
- bring it up? I
- more food.
- Okay, so?
- Let's look At last Day I
- so
- We use matrices. I
- so matrices can be used
- to specify transformations on points and
- vectors.
- If we want to do a three dimensional transformation, is
- it sufficient To have a three dimensional Matrix, three value
- matrix, if
- So we have a three by three matrix to represent the
- rotation, scaling and sharing that we want to apply to our
- model, but we don't have a way to express the translation, So
- you
- need to have a translation Vector and
- so we have point P, we transform it, and we need to do the
- addition as well. So what can we make that simpler? The idea of
- transforming
- our geometric primitives And
- you? Yeah, so
- changing His coordinates and
- bless you. I
- scale and shear. I,
- so
- your arms and lights and
- like This
- vector, a column vector and
- a one by four array or one by four matrix and a
- vector is
- so we have the extra component, w, x, y, z and w. So w is one
- for points and zero
- or vectors. So
- how do we make that distinction? Because we think of a vector as
- the difference between two points.
- So if
- we're subtracting 2.1 minus one is Zero And
- so let's talk a bit about how to identify the axis On which
- something is spinning. I
- So to begin with our spinning on the x axis and
- so let's talk about how this could be made more clear,
- because What we're doing, if we choose to rotate
- on y
- we're left with the value that was set for the rotation on the
- x axis, and now we're incrementing the y axis,
- and then We can spin on the Z axis as well. And
- so how do we get back to
- our Starting position and
- Okay, so what? What can we do to improve this display
- so it's clear Where the
- axis is?
- Okay, Let's Do
- So Any ideas I
- see it on the what If we do Something like I
- so Do from the origin i
- And then We'll Say, I
- Comments, questions. Could
- you do an example of some of the teachers algorithms for like
- tables? Let's say just like a Q over, like the y axis on just
- really some of the math so we can get Like that Central
- Understanding. Okay,
- let's finish This. Okay,
- so here we can see in the vertex shader the code for the
- different rotations.
- So remember, they're column major. So we Bring the matrix.
- So
- RX Is I
- it's going to rotate it with the origin. So
- let's see what's an angle we could rotate by
- about 90 degrees if
- cosine and
- so cosine of 90 degrees zero. Sine of 90 degrees is one
- column,
- zero and
- minus one and five cosine of 90 is 00001,
- okay, let the fiber routine.
- Pick a number between one and 10,
- seven,
- Next two
- and one more, five, one So.
- So we get seven and
- then it's minus five and
- rotate around the z the x axis by 90 degrees.
- So We have plane
- set. 252,
- and we rotate by 90 degrees. We have a
- we have two in the z direction,
- then minus
- 5y direction and
- seven. So we're staying put at seven.
- We rotate between
- the let's look at it from the x axis here. Let's put x here,
- y and z.
- So we're at x to the seven and
- two and five, and Then
- we go to
- The I needed over explaining? It
- does that make sense? So we're switching rotating around the x
- axis.
- So we start with five two here, and what's minus Five? Two.
- So we're switching places. In that case, we're
- okay, So let's write a sheets for y and sand, and then we'll
- multiply them together. So
- so CO, sign,
- minus sign, first column, I,
- okay, so what do we notice
- about the columns or the axis about which we're rotating? So
- we rotate around x, the first column
- is x,
- that's part of the identity matrix. And for
- y, we have the same thing. And then from S, Y and spy, you
- any questions back there? Okay. I
- so what is the z column going to look like for let's write
- it as rooting around z you can
- tell me what the said column will be for The Z rotation
- matrix.
- Start at zero, next zero. Yeah.
- Zero. Next,
- one, zero.
- Do that, right? I pronounced.
- Okay, so how about for me? Let me see you.
- So I believe that is square root of two over two,
- which happens to be point squares, point 7271, So One, you
- rotating around the Y axis which point is going to remain
- constant under rotation.
- Okay, so, right, seven to a seven times Seven
- plus
- nine, minus 7271, seven
- times, Five So.
- So let's say, instance,
- eight line four and four. This
- One is minus four by nine plus three. Five, so
- that's minus 1.4 so That's 8.4
- so two axis look at x In the
- net, we have seven And five,
- and rotate by 45 degrees. Approximately
- 8.4 minus 1.4
- I should have just done a 90 degree angle again. I
- so let's do 90 here again so you
- can check my math here.
- Cosine 90 is zero. Sine of 90 is 1000,
- minus one And
- so we have minus two And then
- five and one and
- Okay, Let's make this minus 90 here. I'm
- okay, so let's Do your Patience And
- rotate by x first and rotate by y, rotate by Z.
- That's what we're doing in the shade right here. So
- this is really good anyway.
- So so rotate my x Is unserved and
- and Zero.
- I throughout the time where we
- i Well, double check the work here and see what we get for the
- answer To transform
- so describing what I'm asking
- for, I prescribing project.
- Anyway, thank you, everyone.
- Bye. Shop everywhere. Oh,
- Bye. Shop everywhere. Oh,

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