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Pseudo-code algorithm to create regular polygon with X number of sides

Started by Ueneth Echil Sep 5, 2007 at 5:49 PM 0 replies 5.4k views

Original Post

Sep 5, 2007 at 5:49 PM

I'm working on a program for Computer Science II at my High School, I've gotten permission to get help from my teacher. Basically, you are given to write a program that will draw a polygon , a regular one where the sides are of equal length, given an x amount of sides. A draw method is provided, where you input two arrays, the x and y coordinates. Basically, you give the method a set of points, and it will draw, connect, and fill the closed polygon. I'm looking for pseudo-code, or just a description of how to do this. I've ran into problems and haven't been able to try it out, but thinking that depending on the relative location of x and y I can either add or take away to their values to move it to the left, right, up or down. ~~To figure out by how much, I would take the number of sides, divide it by two, and then divide the radius by it, the radius provided.~~ However, this will run into problems with odd numbered polygons.

Ravyne

Sep 5, 2007 at 6:17 PM

I'll take your word that its ok seek help with this function, but I won't go as far as to provide source/psuedo code.

This is the approach I would take:

Given the sole constraint that the sides must be an equal length for an arbitrary number of sides, the simplest approach is to inscribe an n-sided polygon within an arbitrary circle of your choosing.

So, choose a center for this circle and give it a reasonable radius. Then, using basic trigonometry, chose n points spaced equidistantly around the circumference of the circle (ie - if n is 3, chose 3 points on the circumference that are 120 degrees apart from one another).

This approach works for any n larger than 2, resulting in non-intersecting, convex polygons. Further, this approach even holds for degenerate polygons such as Digons (2-sided polygons) and, depending how you interpret the results, Henagons (1-sided polygons which are generally considered an imposibility in Euclidean geometry, but are defined in spherical geometry.)

[Edited by - ravyne2001 on September 5, 2007 6:17:21 PM]

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