创建多边形时如何在顶点之间添加n点

Question

Let's say I'm using the following code to create the vertices in a hexagon polygon:

hexagonPoints = new Array<Vector2>();
for (int a = 0; a < 6; a++)
{
  float x = r * (float)Math.cos(a * 60 * Math.PI / 180f);
  float y = r * (float)Math.sin(a * 60 * Math.PI / 180f);
  hexagonPoints.add(new Vector2(x, y));
}

How can I add additional points along each side of the polygon, so that there are n additional points between each connecting set of vertices? All vertices must be equal distance (including the vertices that formed the initial shape). Eg before:

.   .

.   .

After (where n = 1):

. . .
.   .
. . .

edit: here's my current code based on Volker's suggestion:

float r = 3.0f;
int n = 1 + 2; // number of additional vertices between the main shape vertices
for (int a = 0; a < 6; a++)
{
    float xe = r * (float)Math.cos(a * 60 * Math.PI / 180f);
    float ye = r * (float)Math.sin(a * 60 * Math.PI / 180f);

    if (a > 0)
    {
        for (int i = 1; i < n; ++i)
        {
            float xs = ((n - i) * hexagonPoints.get(a - 1).x + i * xe) / n;
            float ys = ((n - i) * hexagonPoints.get(a - 1).y + i * ye) / n;
            hexagonPoints.add(new Vector2(xs, ys));
        }
    }

    hexagonPoints.add(new Vector2(xe, ye));
}

This plots the additional vertices, but they are not in the correct positions.

edit: seems this wasn't working because I wasn't taking into account the first vertex position.

Answer 1

Calculate the endpoints of each side as you are doing it already. Then introduce with an inner loop the additional splitting points.

for (int i=1; i<n: ++i)
{
   float xs = ((n-i)*xb + i*xe)/n;
   float ys = ((n-i)*yb + i*ye)/n;
   hexagonPoints.add(new Vector(xs, ys));
}
hexagonPoints.add(new Vector(xe, ye));

where xb, yb is the beginning of a hexagon side and xe, ye the end.

Answer 2

Here's a working solution, based on Volker's suggestion:

int size = 6;
int npoints = 2;
int nsegs = npoints + 1;

float xb = r;
float yb = 0;
hexagonPoints.add(new Vector2(xb, yb));

for (int a = 1; a <= size; a++)
{
    float xe = r * (float) Math.cos(a * 60 * Math.PI / 180f);
    float ye = r * (float) Math.sin(a * 60 * Math.PI / 180f);

    for (int i = 1; i < nsegs; ++i)
    {
        float xs = ((nsegs - i) * xb + i * xe) / nsegs;
        float ys = ((nsegs - i) * yb + i * ye) / nsegs;
        hexagonPoints.add(new Vector2(xs, ys));
    }

    if (a < size) hexagonPoints.add(new Vector2(xe, ye));
    xb = xe;
    yb = ye;
}