How to draw a n sided regular polygon in cartesian coordinates?

Question

I have been trying to figure out how to write a simple program to compute the x,y points for creating a regular polygon of n sides. Can someone give me some code examples th

Answer 1

The "for n_sides:" answer is the easiest. For the guy who suggested that you could simplify the calculations by using complex numbers, nearly all math libraries have table-based cos() and sin() routines with efficient interpolation so there's no need to delve into relatively obscure solutions. Usually a regular n-gon can be initialized and the hardware scaling of OpenGL used to scale / transform it for any particular instance.

If you want to be hardcore about it, pre-generate all the n-gons you need and load them into vertex buffers.

As an aside, here's the above solution in Lua. It just prints out the coordinates, but you're of course free to return the coordinates in an array / table. The coordinates returned can be used to initialize an OpenGL GL_LINE_LOOP mesh primitive.

require 'math'

-- computes coordinates for n-sided, regular polygon of given radius and start angle
-- all values are in radians

function polypoints(sides, radius, start)
    local x_center = 0.0
    local y_center = 0.0
    local angle = start
    local angle_increment = 2 * math.pi / sides
    local x=0.0
    local y=0.0

    print(string.format("coordinates for a %d sided regular polygon of radius %d\nVertex",sides,radius),"X"," ","Y")
    for i=1,sides do
        x = x_center + radius * math.cos(angle)
        y = y_center + radius * math.sin(angle)
        print(string.format("%d\t%f\t%f",i,x,y))
        angle = angle + angle_increment
    end
end

-- Generate a regular hexagon inscribed in unit circle 
polypoints(6, 1.0, 0.0)