Precise Pentagrams and more, a mini geometry primer

[Albertoni]

Let's start this by being blunt; We've all seen those horribly misaligned pentagrams on the floor or ceiling of a beginner map. I'm going to teach you how to make them look good. And I'm going to give you a small geometry lesson at the end, so you can put your brain to use on making them look even better.

 

Suppose you want one that's 256 units of radius. Make a line twice that big:

 

Curve it: 4 vertices, 180° angle and fixed circular curve:

 

Make the second half, connect the lines and you got yourself a perfect star!

 

Now, what if we do a star inside a star? Remove those lines from the inside, and make the same circle thing, but smaller:

 

Connect all the lines again, then clean things up:

 

Simple, isn't it? 5 vertices instead of 4, and you get a David's Star, or a perfectly equilateral triangle. 6 vertices, and you get an heptagram in case you're making a tarot-inspired map:

 

Ok, for a final example on using this art: Say you want a triangle whose sides are exactly 512 units. Check out Scifista's post in this thread for an easier but less general method, and here's mine: Some good old math from the 15th century BCE, modernly known as the rule of three.

Do a half circle and curve it with 5 vertices, then draw and measure one of its sides:

 

You get 443.55 lenght. So, starting with 512 (a), we get 443.55. Starting with some number X, we get 512 (b). We get the following equation: 512 (a) / x = 443.55 / 512 (b). Cross multiply, get 512 * 512 = 443.55x. Do simple algebra and you have 512 * 512 / 443.55 = x <=> 591.01 = x. So let's try with a 591-units long starting line:

 

Shwing!

 

Now, for some NYAQ (Not-yet asked questions):

• But Albertooooni, I want the pentagram to be at an angle, not straight up! - See that initial line? Angle it however you want. The end result will be at that angle. Amazing, isn't it?
• Why exactly 4 vertices? And why 5 gives us a hexagram, and 6 an heptagram? Must it be one less than the number of points we want? - There might be a relation on it being always points - 1 but I can't say yes or no, and I'm too lazy to do the math. Triangles and squares are obvious exceptions as you can see a triangle requires 5, but it might stabilize later. But the general idea is, you want a star. It has 5 evenly-spaced points, so if you put it inside a circle, they're 360 / 5 = 72° degrees apart. So, when we make a circle with 10 vertices (2 originals from the line, plus 8 from the 2 curves), each is at 36° of separation. 36 + 36 = 72. Note how we always skip a vertex when the pentagram is made. Gez also gave some good further input down the thread.

Edited May 11, 2017 by Albertoni

[Nevander]

Very nice. This will come in handy for sure.

[LordShadowZ]

Well that solves that problem before it even began. Once I get to the hell levels I plan to make this will be extremely useful. Thank you!

[scifista42]

Sorry for my pictures being unnecessarily big, I already took them that way and downscaling in a graphic editor would make the numbers unreadable.

 

About triangles: Firstly, you say to make a curve with 5 vertices, but 2 would be sufficient:

 

 

 

Secondly, here is an alternative method. For the third step, you need to disable snapping to grid or (in Doom Builder 2 or GZDB) hold shift while drawing.

 

 

 

 

 

 

[Gez]

10 hours ago, Albertoni said:

Why exactly 4 vertices? And why 5 gives us a hexagram, and 6 an heptagram? Must it be one less than the number of points we want? - There might be a relation on it being always points - 1 but I can't say yes or no, and I'm too lazy to do the math. Triangles and squares are obvious exceptions as you can see a triangle requires 5, but it might stabilize later.

The key is that when you insert X vertices, you'll get X+2 vertices in total. Then when you do the other side, you end up with 2X+2, or 2(X+1) if you prefer.

 

Which means that you'll always get an even number of vertices, so if you want an odd number of points, you'll have to double it and skip half of them (as seen for the pentagram and heptagram). However, if you do want an even number of points, then you don't need to skip. For your David's Star, for example, you could draw it with 2 vertices (because 2*2+2=6) instead of 5 with skipping (5*2+2=12).

 

Also I'll point out again that SLADE has a draw shape feature.

[Negostrike]

Pentagrams are Satanist symbolism and as a Christian this bothers me very much please stop.

Edited May 11, 2017 by Negrostrike

[Albertoni]

@scifista42 Thanks, your method is definitely simpler as long as making the 90° angle is easy. I'll update my post to mention your method.

 

@Gez Yeah, you're right. I never used Slade's map editor, but that feature seems interesting.

 

@Negrostrike Go lick your grandma's cross, dude

[Bauul]

Or alternatively just use GZDB's "Draw Ellipse" mode to draw a five sided polygon, and draw in the pentagram.

 

 

Took about 10 seconds!

[⇛Marnetmar⇛]

1 hour ago, Negrostrike said:

Pentagrams are Satanist symbolism and as a Christian this bothers me very much please stop.

Satan is Christian symbolism and as a pentagram this bothers me very much please stop.

[Albertoni]

22 minutes ago, Bauul said:

Or alternatively just use GZDB's "Draw Ellipse" mode to draw a five sided polygon, and draw in the pentagram.

Yep, you can't draw it at an angle, but your method is certainly simpler than mine.

[Bauul]

Just now, Albertoni said:

Yep, you can't draw it at an angle, but your method is certainly simpler than mine.

Sure you can.  Just pick any angle from the "Angle" selector. 

 

This is a 45 degree example.

 

Or just select it, hit "E" and rotate it to your hearts content!

 

Granted this is only GZDB though, for DB2 your method is definitely necessary!

[Albertoni]

5 minutes ago, Bauul said:

Sure you can.

Ohhhh, guess I gotta check out in depth the less used features of GZDB then.

[Fletcher`]

12 hours ago, Negrostrike said:

Pentagrams are Satanist symbolism and as a Christian this bothers me very much please stop.

Boy are you playing the wrong game, bucko.

[Urthar]

Pentagrams are Pythagoreanism symbolism. As a Neopythagoreanist this delights me, and I bid you good health.

 

 

[esselfortium]

Okay, I think I understand the method. How did I do:

[40oz]

Thanks for this thread Albertoni. Even though Bauul schooled you with an easier way, mad props for initiating the discussion. Multiple methods for achieving the same thing is always helpful.

[Albertoni]

28 minutes ago, esselfortium said:

Okay, I think I understand the method. How did I do:

[Dravencour]

On 5/11/2017 at 0:11 PM, Negrostrike said:

Pentagrams are Satanist symbolism and as a Christian this bothers me very much please stop.

Demonic symbolism is pretty par for the course considering what game we're playing. Doom is all about killing demons from Hell.

[Dravencour]

Setting the Ellipse tool in the GZDoom Builder to 10 sides manually also provides a nice guide for pentagrams, and one that gave me an even nicer one than the first method. Now all I need to do is find out how to put this pentagram in a circle so that I can use the thing for a "summoning battle" in one of the maps that I'm working on.

Edited October 1, 2017 by Dravencour