Filling a polygon - c

Question

I created this function that draws a simple polygon with n number of vertexes:
void polygon (int n)
{
double pI = 3.141592653589;
double area = min(width / 2, height / 2);
int X = 0, Y = area - 1;
double offset = Y;
int lastx, lasty;
double radius = sqrt(X * X + Y * Y);
double quadrant = atan2(Y, X);
int i;
for (i = 1; i <= n; i++)
{
lastx = X; lasty = Y;
quadrant = quadrant + pI * 2.0 / n;
X = round((double)radius * cos(quadrant));
Y = round((double)radius * sin(quadrant));
setpen((i * 255) / n, 0, 0, 0.0, 1); // r(interval) g b, a, size
moveto(offset + lastx, offset + lasty); // Moves line offset
lineto(offset + X, offset + Y); // Draws a line from offset
}
}
How can I fill it with a solid color?
I have no idea how can I modify my code in order to draw it filled.

Answer 1

The common approach to fill shapes is to find where the edges of the polygon cross either each x or each y coordinate. Usually, y coordinates are used, so that the filling can be done using horizontal lines. (On framebuffer devices like VGA, horizontal lines are faster than vertical lines, because they use consecutive memory/framebuffer addresses.)
In that vein,
void fill_regular_polygon(int center_x, int center_y, int vertices, int radius)
{
const double a = 2.0 * 3.14159265358979323846 / (double)vertices;
int i = 1;
int y, px, py, nx, ny;
if (vertices < 3 || radius < 1)
return;
px = 0;
py = -radius;
nx = (int)(0.5 + radius * sin(a));
ny = (int)(0.5 - radius * cos(a));
y = -radius;
while (y <= ny || ny > py) {
const int x = px + (nx - px) * (y - py) / (ny - py);
if (center_y + y >= 0 && center_y + y < height) {
if (center_x - x >= 0)
moveto(center_x - x, center_y + y);
else
moveto(0, center_y + y);
if (center_x + x < width)
lineto(center_x + x, center_y + y);
else
lineto(width - 1, center_y + y);
}
y++;
while (y > ny) {
if (nx < 0)
return;
i++;
px = nx;
py = ny;
nx = (int)(0.5 + radius * sin(a * (double)i));
ny = (int)(0.5 - radius * cos(a * (double)i));
}
}
}
Note that I only tested the above with a simple SVG generator, and compared the drawn lines to the polygon. Seems to work correctly, but use at your own risk; no guarantees.
For general shapes, use your favourite search engine to look for "polygon filling" algorithms. For example, this, this, this, and this.

Answer 2

There are 2 different ways to implement a solution:
Scan-line
Starting at the coordinate that is at the top (smallest y value), continue to scan down line by line (incrementing y) and see which edges intersect the line.
For convex polygons you find 2 points, (x1,y) and (x2,y). Simply draw a line between those on each scan-line.
For concave polygons this can also be a multiple of 2. Simply draw lines between each pair. After one pair, go to the next 2 coordinates. This will create a filled/unfilled/filled/unfilled pattern on that scan line which resolves to the correct overall solution.
In case you have self-intersecting polygons, you would also find coordinates that are equal to some of the polygon points, and you have to filter them out. After that, you should be in one of the cases above.
If you filtered out the polygon points during scan-lining, don't forget to draw them as well.
Flood-fill
The other option is to use flood-filling. It has to perform more work evaluating the border cases at every step per pixel, so this tends to turn out as a slower version. The idea is to pick a seed point within the polygon, and basically recursively extend up/down/left/right pixel by pixel until you hit a border.
The algorithm has to read and write the entire surface of the polygon, and does not cross self-intersection points. There can be considerable stack-buildup (for naive implementations at least) for large surfaces, and the reduced flexibility you have for the border condition is pixel-based (e.g. flooding into gaps when other things are drawn on top of the polygon). In this sense, this is not a mathematically correct solution, but it works well for many applications.

Answer 3

The most efficient solution is by decomposing the regular polygon in trapezoids (and one or two triangles).
By symmetry, the vertexes are vertically aligned and it is an easy matter to find the limiting abscissas (X + R cos(2πn/N) and X + R cos(2π(+1)N)).
You also have the ordinates (Y + R sin(2πn/N) and Y + R sin(2π(+1)N)) and it suffices to interpolate linearly between two vertexes by Y = Y0 + (Y1 - Y0) (X - X0) / (X1 - X0).
Filling in horizontal runs is a little more complex, as the vertices may not be aligned horizontally and there are more trapezoids.

Answer 4

Anyway, it seems that I / solved / this myself again, when not relying on assistance (or any attempt for it)
void polygon (int n)
{
double pI = 3.141592653589;
double area = min(width / 2, height / 2);
int X = 0, Y = area - 1;
double offset = Y;
int lastx, lasty;
while(Y-->0) {
double radius = sqrt(X * X + Y * Y);
double quadrant = atan2(Y, X);
int i;
for (i = 1; i <= n; i++)
{
lastx = X; lasty = Y;
quadrant = quadrant + pI * 2.0 / n;
X = round((double)radius * cos(quadrant));
Y = round((double)radius * sin(quadrant));
//setpen((i * 255) / n, 0, 0, 0.0, 1);
setpen(255, 0, 0, 0.0, 1); // just red
moveto(offset + lastx, offset + lasty);
lineto(offset + X, offset + Y);
} }
}
As you can see, it isn't very complex, which means it might not be the most efficient solution either.. but it is close enough.
It decrements radius and fills it by virtue of its smaller version with smaller radius.
On that way, precision plays an important role and the higher n is the less accuracy it will be filled with.