algorithm to draw filled symmetric polygon?

Question

I'm looking for the series of steps necessary to draw a filled polygon. I will create a function that renders it to a bitmap. I'm writing in a language similar to visual basic, but without most of the object oriented stuff like classes and inheritance, and the drawing capabilities are drawline() and drawrect() and that is it, but it can scale and rotate a completed bitmap object, so, when I fill the polygon, it will be one dot at a time in a for loop or a while loop, however, I can convert the bitmap to a byte array if that makes any difference (might be faster?) so if you have a method that would treat a completed polygon line as a byte array and fill it that way, might be faster than 100,000 plot(x,y) commands? I don't know, either way would be interesting to look at.

I'm not trying to draw irregular polygons, just symmetrical (radial symmetry) with an arbitrary number of sides, minimum 3, centered in the bitmap area.

Drawing method is cartesian with 0,0 being uppper left of the bitmap. I guess the inputs would look something like:

drawpolygon(bitmapobj,width,height,sides,radius) 

Perhaps radius is not necessary since the size of the bitmap will be the limit of the polygon?

Looking for steps in English instead of code, if possible, but code could be useful if it doesn't have too many language specific aspects (for instance, c++ has a bunch of declarations, type casting pointers, stuff I don't have to deal with and am not 100% sure how to convert to the language I'm using).

Answer 1

There is an equation given here (the last one).

By looping over all the x and y coordinates, and checking that the output of this equation is less than zero, you can determine which points are 'inside' and colour them appropraitely.