Second Life Forums Archive - Equilateral Triangels

Rukos Lange

Registered User

Join date: 15 Aug 2006

Posts: 36

12-05-2006 04:29

Hello,

I'm looking for a way to build an equilateral triangle. I have been attempting to path cut a cube, and have come close through trial and error, but was hoping someone could explain an easier way to relate percentage of cut to the geometry involved, or if there is a better approach entirely. Thanks!

Zi Ree

Mrrrew!

Join date: 25 Feb 2006

Posts: 723

12-05-2006 05:08

Take a box, taper it on one side and then use "Shear" to put it in shape.

_____________________

Zi!

(SuSE Linux 10.2, Kernel 2.6.13-15, AMD64 3200+, 2GB RAM, NVidia GeForce 7800GS 512MB (AGP), KDE 3.5.5, Second Life 1.13.1 (6) alpha soon beta thingie)

Blog: http://ziree.wordpress.com/ - QAvimator: http://qavimator.org

Second Life Linux Users Group IRC Channel: irc.freenode.org #secondlifelug

Chosen Few

Alpha Channel Slave

Join date: 16 Jan 2004

Posts: 7,496

Fast Equilateral Triangle In 3 Easy Steps

12-05-2006 07:19

Well, basic geometric principle tells us the square of the height of an equilateral triangle is equal to the square of one side minus the square of half another side, right? So, it's simple math to figure out the dimensions.

If you're going for a side length of 10M, then it's H^2 = 10^2 - 5^2, or H^2=75. The square root of 75 is 8.66025404, so that's your triangle's height.

You can't get a decimal that precise in the editor, so if you want it to be perfectly exact, you'd need to use a script. I'd be inclined just to round it to 8.66 so the editor can handle it, and call it a day, but if you really want to script it you can.

In any case, the steps from here are really, really simple. Here's what to do:

Rez a cube, and set its height (Z axis) to 8.66M (or drop a script in it to set it precisely to 8.66025404, if you're an uber perfectionist).
Set the width to 10M. You can use either the X or Y for width, whichever you prefer.
Taper the cube to 100% on whichever axis you used for the width. The taper will cause the top of the cube to shrink all the way to a single point, the apex of your triangle. Now you're done.

That's all there is to it. If my math is right, and you followed the steps exactly, you should now have an equilateral triangle, 10M on each side.

_____________________

.

Land now available for rent in Indigo. Low rates. Quiet, low-lag mainland sim with good neighbors. IM me in-world if you're interested.

Rukos Lange

Registered User

Join date: 15 Aug 2006

Posts: 36

12-05-2006 07:31

Thanks so much for the help! I was good with the math, but still have lots to learn about efficient use of the various building tools and approaches. Your answers are much appreciated!

Seifert Surface

Mathematician

Join date: 14 Jun 2005

Posts: 912

12-05-2006 11:55

Alternatively, use the prism prim. I prefer Chosen's method for most uses, but if you want to get a "hollow" equilateral triangle from one prim the prism will do it.

_____________________

-Seifert Surface
2G!tGLf 2nLt9cG

Martin McConnell

Registered User

Join date: 8 Sep 2006

Posts: 116

12-05-2006 14:52

Bah, math. What's it good for?

(you hear Martin's latest creation crashing in the background)

_____________________

Martin McConnell
Still an SL Virgin
Quote: "I'm saving myself"

Equilateral Triangels
Rukos Lange Registered User Join date: 15 Aug 2006 Posts: 36	12-05-2006 04:29 Hello, I'm looking for a way to build an equilateral triangle. I have been attempting to path cut a cube, and have come close through trial and error, but was hoping someone could explain an easier way to relate percentage of cut to the geometry involved, or if there is a better approach entirely. Thanks!
Zi Ree Mrrrew! Join date: 25 Feb 2006 Posts: 723	12-05-2006 05:08 Take a box, taper it on one side and then use "Shear" to put it in shape. _____________________ Zi! (SuSE Linux 10.2, Kernel 2.6.13-15, AMD64 3200+, 2GB RAM, NVidia GeForce 7800GS 512MB (AGP), KDE 3.5.5, Second Life 1.13.1 (6) alpha soon beta thingie) Blog: http://ziree.wordpress.com/ - QAvimator: http://qavimator.org Second Life Linux Users Group IRC Channel: irc.freenode.org #secondlifelug
Chosen Few Alpha Channel Slave Join date: 16 Jan 2004 Posts: 7,496	Fast Equilateral Triangle In 3 Easy Steps 12-05-2006 07:19 Well, basic geometric principle tells us the square of the height of an equilateral triangle is equal to the square of one side minus the square of half another side, right? So, it's simple math to figure out the dimensions. If you're going for a side length of 10M, then it's H^2 = 10^2 - 5^2, or H^2=75. The square root of 75 is 8.66025404, so that's your triangle's height. You can't get a decimal that precise in the editor, so if you want it to be perfectly exact, you'd need to use a script. I'd be inclined just to round it to 8.66 so the editor can handle it, and call it a day, but if you really want to script it you can. In any case, the steps from here are really, really simple. Here's what to do: Rez a cube, and set its height (Z axis) to 8.66M (or drop a script in it to set it precisely to 8.66025404, if you're an uber perfectionist). Set the width to 10M. You can use either the X or Y for width, whichever you prefer. Taper the cube to 100% on whichever axis you used for the width. The taper will cause the top of the cube to shrink all the way to a single point, the apex of your triangle. Now you're done. That's all there is to it. If my math is right, and you followed the steps exactly, you should now have an equilateral triangle, 10M on each side. _____________________ . Land now available for rent in Indigo. Low rates. Quiet, low-lag mainland sim with good neighbors. IM me in-world if you're interested.
Rukos Lange Registered User Join date: 15 Aug 2006 Posts: 36	12-05-2006 07:31 Thanks so much for the help! I was good with the math, but still have lots to learn about efficient use of the various building tools and approaches. Your answers are much appreciated!
Seifert Surface Mathematician Join date: 14 Jun 2005 Posts: 912	12-05-2006 11:55 Alternatively, use the prism prim. I prefer Chosen's method for most uses, but if you want to get a "hollow" equilateral triangle from one prim the prism will do it. _____________________ -Seifert Surface 2G!tGLf 2nLt9cG
Martin McConnell Registered User Join date: 8 Sep 2006 Posts: 116	12-05-2006 14:52 Bah, math. What's it good for? (you hear Martin's latest creation crashing in the background) _____________________ Martin McConnell Still an SL Virgin Quote: "I'm saving myself"

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Equilateral Triangels