/// <summary>
/// Offset a Linestring the given amount perpendicular to the line
/// For example if a line should be drawn 10px to the right of its original position
///
/// Positive offset offsets right
/// Negative offset offsets left
/// </summary>
/// <param name="lineCoordinates">LineString</param>
/// <param name="offset">offset amount</param>
/// <returns>Array of coordinates for the offseted line</returns>
public static PointF[] OffsetPolyline(PointF[] lineCoordinates, float offset)
{
List<PointF> retPoints = new List<PointF>();
PointF old_pt, old_diffdir = PointF.Empty, old_offdir = PointF.Empty;
int idx = 0;
bool first = true;
/* saved metrics of the last processed point */
if (lineCoordinates.Length > 0)
{
old_pt = lineCoordinates[0];
for (int j = 1; j < lineCoordinates.Length; j++)
{
PointF pt = lineCoordinates[j]; /* place of the point */
PointF diffdir = point_norm(point_diff(pt, old_pt)); /* direction of the line */
PointF offdir = point_rotz90(diffdir);/* direction where the distance between the line and the offset is measured */
PointF offPt;
if (first)
{
first = false;
offPt = point_sum(old_pt, point_mul(offdir, offset));
}
else /* middle points */
{
/* curve is the angle of the last and the current line's direction (supplementary angle of the shape's inner angle) */
double sin_curve = point_cross(diffdir, old_diffdir);
double cos_curve = point_cross(old_offdir, diffdir);
if ((-1.0) * CURVE_SIN_LIMIT < sin_curve && sin_curve < CURVE_SIN_LIMIT)
{
offPt = point_sum(old_pt, point_mul(point_sum(offdir, old_offdir), 0.5 * offset));
}
else
{
double base_shift = -1.0 * (1.0 + cos_curve) / sin_curve;
offPt = point_sum(old_pt, point_mul(point_sum(point_mul(diffdir, base_shift), offdir), offset));
}
}
retPoints.Add(offPt);
old_pt = pt;
old_diffdir = diffdir;
old_offdir = offdir;
}
/* last point */
if (!first)
{
PointF offpt = point_sum(old_pt, point_mul(old_offdir, offset));
retPoints.Add(offpt);
idx++;
}
}
return retPoints.ToArray();
}
static PointF point_norm(PointF a)
{
double lenmul;
PointF retv = new PointF();
if (a.X == 0 && a.Y == 0)
return a;
lenmul = 1.0 / Math.Sqrt(point_abs2(a)); /* this seems to be the costly operation */
retv.X = (float)(a.X * lenmul);
retv.Y = (float)(a.Y * lenmul);
return retv;
}
static double point_cross(PointF a, PointF b)
{
return a.X * b.Y - a.Y * b.X;
}
static PointF point_diff(PointF a, PointF b)
{
PointF retv = new PointF(a.X - b.X, a.Y - b.Y);
return retv;
}
static PointF point_sum(PointF a, PointF b)
{
PointF retv = new PointF(a.X + b.X, a.Y + b.Y);
return retv;
}
/* vector multiply */
static PointF point_mul(PointF a, double b)
{
PointF retv = new PointF((float)(a.X * b), (float)(a.Y * b));
return retv;
}
/* rotate a vector 90 degrees */
static PointF point_rotz90(PointF a)
{
double nx = -1.0 * a.Y, ny = a.X;
PointF retv = new PointF();
retv.X = (float)nx; retv.Y = (float)ny;
return retv;
}
static double point_abs2(PointF a)
{
return a.X * a.X + a.Y * a.Y;
}
