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Let $S$ be the triangle with vertices $(4.2,1.2,4),(6,4,2),$ $(2,2,6) .$ Find the image of $S$ under the perspective projection with center of projection at $(0,0,10) .$

The triangle with vertices $(7,2,0),(7.5,5,0),(5,5,0)$

Algebra

Chapter 2

Matrix Algebra

Section 7

Applications to Computer Graphics

Introduction to Matrices

Missouri State University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

07:09

Let $S$ be the triangle wi…

02:06

A triangle has vertices $(…

02:21

00:07

In the figure below, $\tri…

03:45

Use matrix multiplication …

01:04

The vertices of $\Delta \m…

00:47

04:09

The vertices of a right tr…

01:18

now looking nuts. The rights off on prospects of projection prospects. Eve projection, which is just just before example. It's in this section just before example it's You can go back and look at seeds. We see that the metrics peen that's performs a prospect. Seve Projection with Sensor zero comma zero comma D is given by P equal to 1000 0100 000 minus one over D andi 001 You can go back and confirm That's not in our example. Allah Sensa is given a zero comma zero comma 10. So when compared? This and these. This implies that r D he calls to say so. That implies that our p that sees the metrics that performs in perspective projection will be given by 10000100 000 minus one over 10 which is minor. Zero points. 10001 No, um, the marginal squadron eight. It's what he needs Off the triangle off the triangle recorder were given the point. The boxes has four point. Sorry. 93 minus five. But if want to writing homogeneous coordinates all rights, it as so maybe written as All right, sit as 93 minus five. There we are, the one at the end rights on. Then the other one becomes 12. It's Sue. One on the last one is one point AIDS to point several one, and they are being one. So this isn't about Gina's coordinates, so this implies that's did its army trees. Your deeds are many trees for is, is given by. So you just turned this into images. You have nine three minus 51 Suave. It's Sue 11 point. It's super in several 11 on Also did. That's our metrics. Guts on many trees for the chance from tango for the Transformed Triangle would then be given us. You just multiply these Petey Mitch is that before? Which is 1000 0100 000 My nose. Oh, want Juan 0001 more supplied by the determined Jizz for S, which is nine three minus 51 Suave. It's 211 points. It's super 2110.711 way multiplied things off. 9301.5 suave. It's 00 point means one points. AIDS soup want 70 on, then zero points? Nine? No. Lastly, the last thing we do is that's we convert its from the homogeneous coordinates. So the columns Oh, this matrix, come on, be converted from well with Gino's coordinates by dividing by the final coordinates by the final Cordant record. That's how we change from more Gino's coordinates. So that implies that the first column, which is 9301.5, then becomes would divide everything by one points. Fine. That's a nine over 1.5 three over 1.5 and then zero over 1.5, which is a goal to 6 to 0. Similarly swore it's 00 Prinz Deeds becomes soften. Lazar points speeds. It's over zero point. AIDS zero over zero point AIDS. This is 15 cents on zero and lastly, one points. Foods soup 1700.9 becomes one points. It's over zero points. Nine super in seven over 0.9 under zero over 0.9. This is so comma zero. So this implies dots. This implies that the co ordinates off the vortices off the transforms, trying go off the transform Trying go! He's given by sees comments. Ooh, comma zero. 15 Comets in common. Zero and then Sue. Come on 30 And that's our answer.

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