Computer graphics question

Factual Questions
1

I have a small set of 2d coordinates that I want to rotate 90 degrees and I can’t remember how to do that. IIRC, it is something like (x, y) cross ((cos(theta), 0),(0, sin(theta))), but I can’t remember if that is correct. The stuff I find online is much too complicated for my purposes.

Thanks for your help,
Rob

2

[QUOTE=sweeteviljesus]
I have a small set of 2d coordinates that I want to rotate 90 degrees and I can’t remember how to do that. IIRC, it is something like (x, y) cross ((cos(theta), 0),(0, sin(theta))), but I can’t remember if that is correct. The stuff I find online is much too complicated for my purposes.

Thanks for your help,
Rob
[/QUOTE]

For starting coordinates x1,y1, and a rotation of 90° CCW,
Isn’t this just x1->y2, y1->-x2?

3

If you mean x1->y1, y1->-x1, then no, not generally.

Thanks,
Rob

4

[QUOTE=sweeteviljesus]
If you mean x1->y1, y1->-x1, then no, not generally.

Thanks,
Rob
[/QUOTE]

That’s not what I wrote.

For initial coordinates, X1,y1, a rotation without translation of 90°CCW, results in coordinates of x2,y2, such that y2 = x1, and x2 = -y1, unless I am missing something.

5

In general, to rotate (x,y) to (x’,y’) you could do something like


x' = x*cos(θ) - y*sin(θ)
y' = x*sin(θ) + y*cos(θ)

Is that what you wanted? That’s around the origin, but you could create rotation around some arbitrary point by translating the coordinates appropriately before/after.

6

[QUOTE=recessiveMeme]
In general, to rotate (x,y) to (x’,y’) you could do something like


x' = x*cos(θ) - y*sin(θ)
y' = x*sin(θ) + y*cos(θ)

Is that what you wanted? That’s around the origin, but you could create rotation around some arbitrary point by translating the coordinates appropriately before/after.
[/QUOTE]

Which for 90°, is what I wrote above…

7

My bad. I miscalculated. Thanks for your help.

Rob

8

Wikipedia is your friend (and confirms what recessiveMeme said).

On preview, given the 90 degree stipulation, it also confirms what beowulff said.

9

[QUOTE=beowulff]
Which for 90°, is what I wrote above…
[/quote]
My failure to credit your reply was an oversight on my part. Of course, you were correct. I just wanted to provide the more generalized solution in the hope that sweeteviljesus would recognize it as his forgotten transformation.

10

[QUOTE=recessiveMeme]
My failure to credit your reply was an oversight on my part. Of course, you were correct. I just wanted to provide the more generalized solution in the hope that sweeteviljesus would recognize it as his forgotten transformation.
[/QUOTE]

No problem.
I just hoped I didn’t miss something important…

As an aside, I once wrote code to rotate bitmaps by 90° - there are some interesting tradeoffs between algorithmic complexity, execution speed, and memory usage. Of course, these days you just use an API to do it…