public static double Distance(PointR p1, PointR p2)
{
var dx = p2.X - p1.X;
var dy = p2.Y - p1.Y;
return(Math.Sqrt(dx * dx + dy * dy));
}
// determines the angle, in radians, between two points. the angle is defined
// by the circle centered on the start point with a radius to the end point,
// where 0 radians is straight right from start (+x-axis) and PI/2 radians is
// straight down (+y-axis).
public static double AngleInRadians(PointR start, PointR end, bool positiveOnly)
{
double radians = 0.0;
if (start.X != end.X)
{
radians = Math.Atan2(end.Y - start.Y, end.X - start.X);
}
else // pure vertical movement
{
if (end.Y < start.Y)
{
radians = -Math.PI / 2.0; // -90 degrees is straight up
}
else if (end.Y > start.Y)
{
radians = Math.PI / 2.0; // 90 degrees is straight down
}
}
if (positiveOnly && radians < 0.0)
{
radians += Math.PI * 2.0;
}
return(radians);
}
// Rotate a point 'p' around a point 'c' by the given radians.
// Rotation (around the origin) amounts to a 2x2 matrix of the form:
//
// [ cos A -sin A ] [ p.x ]
// [ sin A cos A ] [ p.y ]
//
// Note that the C# Math coordinate system has +x-axis stright right and
// +y-axis straight down. Rotation is clockwise such that from +x-axis to
// +y-axis is +90 degrees, from +x-axis to -x-axis is +180 degrees, and
// from +x-axis to -y-axis is -90 degrees.
public static PointR RotatePoint(PointR p, PointR c, double radians)
{
var q = PointR.Empty;
q.X = (p.X - c.X) * Math.Cos(radians) - (p.Y - c.Y) * Math.Sin(radians) + c.X;
q.Y = (p.X - c.X) * Math.Sin(radians) + (p.Y - c.Y) * Math.Cos(radians) + c.Y;
return(q);
}
// translates the points so that their centroid lies at 'toPt'
//public static ArrayList TranslateCentroidTo(ArrayList points, PointR toPt)
public static List <PointR> TranslateCentroidTo(List <PointR> points, PointR toPt)
{
//ArrayList newPoints = new ArrayList(points.Count);
var newPoints = new List <PointR>(points.Count);
var centroid = Centroid(points);
for (var i = 0; i < points.Count; i++)
{
var p = points[i];
p.X += (toPt.X - centroid.X);
p.Y += (toPt.Y - centroid.Y);
newPoints.Add(p);
}
return(newPoints);
}
// translates the points so that the upper-left corner of their bounding box lies at 'toPt'
//public static ArrayList TranslateBBoxTo(ArrayList points, PointR toPt)
public static List <PointR> TranslateBBoxTo(List <PointR> points, PointR toPt)
{
//ArrayList newPoints = new ArrayList(points.Count);
var newPoints = new List <PointR>(points.Count);
var r = FindBox(points);
for (var i = 0; i < points.Count; i++)
{
var p = points[i];
p.X += (toPt.X - r.X);
p.Y += (toPt.Y - r.Y);
newPoints.Add(p);
}
return(newPoints);
}
//public static ArrayList Resample(ArrayList points, int n)
public static List <PointR> Resample(List <PointR> points, int n)
{
var I = PathLength(points) / (n - 1); // interval length
var D = 0.0;
//ArrayList srcPts = new ArrayList(points);
var srcPts = new List <PointR>(points);
//ArrayList dstPts = new ArrayList(n);
var dstPts = new List <PointR>(n)
{
srcPts[0]
};
for (var i = 1; i < srcPts.Count; i++)
{
var pt1 = srcPts[i - 1];
var pt2 = srcPts[i];
var d = Distance(pt1, pt2);
if ((D + d) >= I)
{
var qx = pt1.X + ((I - D) / d) * (pt2.X - pt1.X);
var qy = pt1.Y + ((I - D) / d) * (pt2.Y - pt1.Y);
var q = new PointR(qx, qy);
dstPts.Add(q); // append new point 'q'
srcPts.Insert(i, q); // insert 'q' at position i in points s.t. 'q' will be the next i
D = 0.0;
}
else
{
D += d;
}
}
// somtimes we fall a rounding-error short of adding the last point, so add it if so
if (dstPts.Count == n - 1)
{
dstPts.Add(srcPts[srcPts.Count - 1]);
}
return(dstPts);
}
// copy constructor
public PointR(PointR p)
{
X = p.X;
Y = p.Y;
T = p.T;
}
// determines the angle, in degrees, between two points. the angle is defined
// by the circle centered on the start point with a radius to the end point,
// where 0 degrees is straight right from start (+x-axis) and 90 degrees is
// straight down (+y-axis).
public static double AngleInDegrees(PointR start, PointR end, bool positiveOnly)
{
double radians = AngleInRadians(start, end, positiveOnly);
return(Rad2Deg(radians));
}