a circle algorithm that doesn't use pi

circlemaker · 2011-10-26 13:34:55

r (radius) = any number
y (cosine) = any number between 0 and radius
tangent = √((r/y)²-1) or Math.sqrt(Math.pow(1/cos,2)-1) - I prefer computer speak
x (sine) = tangent x cosine

Say you want to make a circle with a radius of 100 on a computer. What you'd do is get every pixel on the y axis and find it's x value using the aforementioned algorithm, then draw a line to each point.

I made a function for html5 canvas that does this in quarter circles. It's optimized to not draw outside the screen boundary, though despite my efforts the built-in arc function is still more efficient. I suspect it takes some kind of shortcuts, though my method is certainly 'cleaner' as you can see with this comparison: http://www.perspectiveinfinity.com/images/arc-circle_root-circle_comparison.jpg

If your still interested here's the link where I talk about it in more detail: http://www.perspectiveinfinity.com/root_circle.html
And here's the actual function in case you wanted to use or analyze it: http://www.perspectiveinfinity.com/Scripts/rcf.js

benice · 2011-10-27 04:05:12

Hi circlemaker;

Awesome! Thank you so much for doing this work and sharing it.

ARBGenius · 2012-02-06 23:49:14

Now Try to Calculate a Sphere inside another Sphere!?

And Show the Image with the Outside Sphere Transparent So that it's Possible to See the Inner Sphere!?

ARBGenius.

bobbym · 2012-02-06 23:50:44

Hi GiB;

The software he is using may not do 3D yet.

ARBGenius · 2012-02-07 03:25:07

Who Said anything about 3D ?

You can Post an Image...That Looks like 3D But is in fact a Flat 2D Image!

ARBGenius.

Last edited by ARBGenius (2012-02-07 03:28:59)

bobbym · 2012-02-07 06:03:52

Hi GiB;

I think you did, when you said sphere. Take Geogebra for instance, just works in 2 dimensions.

ARBGenius · 2012-02-07 11:34:16

You can Post a Sphere Image...That Looks like 3D But is in fact a Flat 2D Image!

ARBGenius.

anonimnystefy · 2012-02-07 11:36:42

then that's not a sphere,but it's orthogonal projection on a 2D plane

ARBGenius · 2012-02-07 11:40:34

And the Image Looks like a Sphere!

ARBGenius.

bobbym · 2012-02-07 11:41:29

Not unless you have software that can work with x,y,z coordinates.

ARBGenius · 2012-02-07 21:58:09

Stuff the Software!...Use the Tools & Methods you have a Hand!

ARBGenius.

bobbym · 2012-02-07 22:06:29

Hi GeniusIsBack;

Okay, why don't you do it by hand and then post it.

ARBGenius · 2012-02-07 23:20:18

I Gave the Challenge! Any Takers!?...

ARBGenius.

bobbym · 2012-02-07 23:22:54

Yes you! Only you would have the courage and the genius for such a task.

ARBGenius · 2012-02-07 23:28:14

Thank you! Time Teaches... The Stubbornest!

ARBGenius.

ARBGenius · 2012-02-07 23:31:17

Respect Takes Time! The Sheep Find Their Way!...

ARBGenius.

Last edited by ARBGenius (2012-02-07 23:32:15)

bobbym · 2012-02-07 23:31:57

Hmmmm? So we are all sheep to the mighty GeniusIs Back?

ARBGenius · 2012-02-07 23:33:49

For You to Join the Other Sheep takes Extra Time!

ARBGenius.

bobbym · 2012-02-07 23:37:42

No, I was thinking about that picture you posted, you know the filthy one after you lost that argument about Houdini...

ARBGenius · 2012-02-07 23:38:36

Never Ever! Lost an Argument to You!!

ARBGenius.

bobbym · 2012-02-07 23:39:27

Then why did you post that picture and run away? It was just getting good...

ARBGenius · 2012-02-07 23:41:12

You Remember Unimportant Things! SAD!!

ARBGenius.

bobbym · 2012-02-07 23:42:59

I remember that you have been barred at least13 times under different names and for posting a lewd picture at me. For anti semitic and gay comments. For rudeness to many members. For calling people idiots and bad language. For defacing the forum. For picking offensive usernames.

circlemaker · 2012-02-27 06:41:20

Aww too bad the thread went off-topic. Anyway I just stopped by to add that while people intuitively go from a circle to a sphere when thinking of 2D to 3D projections, this geometry is easier to project as a helix when going from 2D to 3D.

A sphere is a surface while a helix is still just a curve, so all that's required is to add a dimension and stretch the circle in the direction of the new dimension (in this case, z). This geometry matches that of a sine wave when viewed from a certain perspective: http://www.perspectiveinfinity.com/sinewave3d.html

bobbym · 2012-02-27 07:16:36

Hi circlemaker;

My apology for what transpired in your thread. Normally I would clean it up but it had to be left for further review.

Math Is Fun Forum

#1 2011-10-26 13:34:55

a circle algorithm that doesn't use pi

#2 2011-10-27 04:05:12

Re: a circle algorithm that doesn't use pi

#3 2012-02-06 23:49:14

Re: a circle algorithm that doesn't use pi

#4 2012-02-06 23:50:44

Re: a circle algorithm that doesn't use pi

#5 2012-02-07 03:25:07

Re: a circle algorithm that doesn't use pi

#6 2012-02-07 06:03:52

Re: a circle algorithm that doesn't use pi

#7 2012-02-07 11:34:16

Re: a circle algorithm that doesn't use pi

#8 2012-02-07 11:36:42

Re: a circle algorithm that doesn't use pi

#9 2012-02-07 11:40:34

Re: a circle algorithm that doesn't use pi

#10 2012-02-07 11:41:29

Re: a circle algorithm that doesn't use pi

#11 2012-02-07 21:58:09

Re: a circle algorithm that doesn't use pi

#12 2012-02-07 22:06:29

Re: a circle algorithm that doesn't use pi

#13 2012-02-07 23:20:18

Re: a circle algorithm that doesn't use pi

#14 2012-02-07 23:22:54

Re: a circle algorithm that doesn't use pi

#15 2012-02-07 23:28:14

Re: a circle algorithm that doesn't use pi

#16 2012-02-07 23:31:17

Re: a circle algorithm that doesn't use pi

#17 2012-02-07 23:31:57

Re: a circle algorithm that doesn't use pi

#18 2012-02-07 23:33:49

Re: a circle algorithm that doesn't use pi

#19 2012-02-07 23:37:42

Re: a circle algorithm that doesn't use pi

#20 2012-02-07 23:38:36

Re: a circle algorithm that doesn't use pi

#21 2012-02-07 23:39:27

Re: a circle algorithm that doesn't use pi

#22 2012-02-07 23:41:12

Re: a circle algorithm that doesn't use pi

#23 2012-02-07 23:42:59

Re: a circle algorithm that doesn't use pi

#24 2012-02-27 06:41:20

Re: a circle algorithm that doesn't use pi

#25 2012-02-27 07:16:36

Re: a circle algorithm that doesn't use pi

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