PolyLine

C# WinfForms solution to calculating offset polylines based on point and line homogeneous coordinates.

Screenshot

Code

Using homogeneous coordinates for points and lines which make finding the inersections easier.

The magic happens in a function Offset() part of the SegmentList class

public SegmentList Offset(float distance)
{
    List<Line2> new_lines=new List<Line2>();
    int N=lines.Count;
    // Take each line and offset by distance, and store in
    // new list
    for (int i=0; i<N; i++)
    {
        Line2 offset_line=lines[i].Line.Offset(distance);
        new_lines.Add(offset_line);
    }
    List<LineSeg> result=new List<LineSeg>();
    for (int i=0; i<N; i++)
    {
        // i-th line
        Line2 this_line=new_lines[i];
        // Find index of previous line. If i-th is fist line,
        // the j points to last line
        int j=i>0?i-1:N-1;
        // Find index to next line. If i-th is the last line,
        // then k points to fist line
        int k=i<N-1?i+1:0;
        Line2 prev_line=new_lines[j];
        Line2 next_line=new_lines[k];
        // Trim infinate line based on intersection with
        // previous and next line.
        LineSeg offset_seg=this_line.TrimBetween(prev_line, next_line);
        result.Add(offset_seg);
    }
    // Create new polyline from array of line segments
    return new SegmentList(result.ToArray());
}

For each line segment it calls Line.Offset() first and then it finds the previous and next lines. It uses that to call .TrimBetween() that trims the ends on the line according to the infinite line of these sourounding segments.

The .Offset(d) method modifies the (a,b,c) parameters of an infinite line into (a,b,c + d*√(a^2+b^2)) this modifies the distance parameter c by moving it the amount specified by d.

The .TrimBetween(p,q) method computes the coordinates of the intersection between the offset line and the previous offset line p and also the offset line and the next offset line q and defines the line segment between those two intersections.