# Computer graphics question **URL:** \ **Category:** Factual Questions\ **Created:** [August 2, 2007, 2:54pm UTC](https://boards.straightdope.com/t/computer-graphics-question/414129 "2007-08-02T14:54:37Z")\ **Posts on this page:** 10\ **Page:** 1
**Author:** ![sweeteviljesus](https://avatars.discourse-cdn.com/v4/letter/s/898d66/32.png) [@sweeteviljesus](https://boards.straightdope.com/u/sweeteviljesus)\ **Post date:** [August 2, 2007, 2:54pm UTC](https://boards.straightdope.com/t/computer-graphics-question/414129/1 "2007-08-02T14:54:37Z")
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 ---
**Author:** ![beowulff](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/beowulff/32/542_2.png) [@beowulff](https://boards.straightdope.com/u/beowulff)\ **Post date:** [August 2, 2007, 3:00pm UTC](https://boards.straightdope.com/t/computer-graphics-question/414129/2 "2007-08-02T15:00:12Z")
[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? ---
**Author:** ![sweeteviljesus](https://avatars.discourse-cdn.com/v4/letter/s/898d66/32.png) [@sweeteviljesus](https://boards.straightdope.com/u/sweeteviljesus)\ **Post date:** [August 2, 2007, 3:35pm UTC](https://boards.straightdope.com/t/computer-graphics-question/414129/3 "2007-08-02T15:35:50Z")
If you mean x1-\>y1, y1-\>-x1, then no, not generally. Thanks, Rob ---
**Author:** ![beowulff](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/beowulff/32/542_2.png) [@beowulff](https://boards.straightdope.com/u/beowulff)\ **Post date:** [August 2, 2007, 3:42pm UTC](https://boards.straightdope.com/t/computer-graphics-question/414129/4 "2007-08-02T15:42:29Z")
[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. ---
**Author:** ![recessiveMeme](https://avatars.discourse-cdn.com/v4/letter/r/46a35a/32.png) [@recessiveMeme](https://boards.straightdope.com/u/recessiveMeme)\ **Post date:** [August 2, 2007, 3:51pm UTC](https://boards.straightdope.com/t/computer-graphics-question/414129/5 "2007-08-02T15:51:07Z")
In general, to rotate (x,y) to (x’,y’) you could do something like ```auto 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. ---
**Author:** ![beowulff](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/beowulff/32/542_2.png) [@beowulff](https://boards.straightdope.com/u/beowulff)\ **Post date:** [August 2, 2007, 4:11pm UTC](https://boards.straightdope.com/t/computer-graphics-question/414129/6 "2007-08-02T16:11:31Z")
[QUOTE=recessiveMeme] In general, to rotate (x,y) to (x’,y’) you could do something like ```auto 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… ---
**Author:** ![sweeteviljesus](https://avatars.discourse-cdn.com/v4/letter/s/898d66/32.png) [@sweeteviljesus](https://boards.straightdope.com/u/sweeteviljesus)\ **Post date:** [August 2, 2007, 4:26pm UTC](https://boards.straightdope.com/t/computer-graphics-question/414129/7 "2007-08-02T16:26:22Z")
My bad. I miscalculated. Thanks for your help. Rob ---
**Author:** ![Digital\_Stimulus](https://avatars.discourse-cdn.com/v4/letter/d/aeb1de/32.png) [@Digital\_Stimulus](https://boards.straightdope.com/u/Digital_Stimulus)\ **Post date:** [August 2, 2007, 4:26pm UTC](https://boards.straightdope.com/t/computer-graphics-question/414129/8 "2007-08-02T16:26:34Z")
[Wikipedia](http://en.wikipedia.org/wiki/Coordinate_rotation) is your friend (and confirms what **recessiveMeme** said). On preview, given the 90 degree stipulation, it also confirms what **beowulff** said. ---
**Author:** ![recessiveMeme](https://avatars.discourse-cdn.com/v4/letter/r/46a35a/32.png) [@recessiveMeme](https://boards.straightdope.com/u/recessiveMeme)\ **Post date:** [August 2, 2007, 5:05pm UTC](https://boards.straightdope.com/t/computer-graphics-question/414129/9 "2007-08-02T17:05:46Z")
[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. ---
**Author:** ![beowulff](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/beowulff/32/542_2.png) [@beowulff](https://boards.straightdope.com/u/beowulff)\ **Post date:** [August 2, 2007, 5:14pm UTC](https://boards.straightdope.com/t/computer-graphics-question/414129/10 "2007-08-02T17:14:52Z")
[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…