// rotate the points by the given radians about their centroid
public static List <PointR> RotateByRadians(List <PointR> points, double radians)
{
List <PointR> newPoints = new List <PointR>(points.Count);
PointR c = Centroid(points);
double cos = Math.Cos(radians);
double sin = Math.Sin(radians);
double cx = c.X;
double cy = c.Y;
for (int i = 0; i < points.Count; i++)
{
PointR p = (PointR)points[i];
double dx = p.X - cx;
double dy = p.Y - cy;
PointR q = PointR.Empty;
q.X = dx * cos - dy * sin + cx;
q.Y = dx * sin + dy * cos + cy;
newPoints.Add(q);
}
return(newPoints);
}
// scales the points so that they form the size given. does not restore the
// origin of the box.
// adapted from ScaleTo() to smartly handle 1D scaling -- ie, if a gesture is 1D,
// scale to the longer dimension only, or we warp our gestures too much
// Lisa 12/28/2007
public static List <PointR> ScaleTo1D(List <PointR> points, SizeR sz)
{
List <PointR> newPoints = new List <PointR>(points.Count);
RectangleR r = FindBox(points);
// scale both by same factor
double scaleFactor = 0.0;
if (r.Width > r.Height)
{
scaleFactor = r.Width;
}
else
{
scaleFactor = r.Height;
}
for (int i = 0; i < points.Count; i++)
{
PointR p = (PointR)points[i];
if (r.Width != 0d)
{
p.X *= (sz.Width / scaleFactor);
}
if (r.Height != 0d)
{
p.Y *= (sz.Height / scaleFactor);
}
newPoints.Add(p);
}
return(newPoints);
}
// 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);
}
// copy constructor
public PointR(PointR p)
{
X = p.X;
Y = p.Y;
T = p.T;
P = p.P;
}
// new scaling methods rewritten by Lisa as of 8/9/2009 from input from Jake
public static List <PointR> Scale(List <PointR> pts, double oneDRatio, SizeR size) // scales the oriented bbox based on 1D or 2D
{
if (NDollarParameters.Instance.UseUniformScaling) // scale to a uniform circle
{
// do new thing
PointR centroid = Utils.Centroid(pts);
double radiusSquared = 1.0d;
foreach (PointR point in pts)
{
double distanceSquared = Math.Pow((centroid.X - point.X), 2.0) + Math.Pow((centroid.Y - point.Y), 2.0);
if (distanceSquared > radiusSquared)
{
radiusSquared = distanceSquared;
}
}
double factor = size.Width / Math.Sqrt(radiusSquared);//Assume that size is a square and arbitrarily select width
//this could also be replaced with a constant value (250?)
List <PointR> scaledPts = new List <PointR>();
for (int i = 0; i < pts.Count; i++)
{
PointR p = new PointR((PointR)pts[i]);
p.X *= factor;
p.Y *= factor;
scaledPts.Add(p);
}
return(scaledPts);
}
else // do old thing
{
return(Utils.ScaleByDimension(pts, oneDRatio, size));
}
}
public static double Distance(PointR p1, PointR p2)
{
double dx = p2.X - p1.X;
double dy = p2.Y - p1.Y;
return(Math.Sqrt(dx * dx + dy * dy));
}
// 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)
{
PointR 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);
}
public override bool Equals(object obj)
{
if (obj is PointR)
{
PointR p = (PointR)obj;
return(X == p.X && Y == p.Y);
}
return(false);
}
// scales by the percentages contained in the 'sz' parameter. values of 1.0 would result in the
// identity scale (that is, no change).
public static List <PointR> ScaleBy(List <PointR> points, SizeR sz)
{
List <PointR> newPoints = new List <PointR>(points.Count);
for (int i = 0; i < points.Count; i++)
{
PointR p = (PointR)points[i];
p.X *= sz.Width;
p.Y *= sz.Height;
newPoints.Add(p);
}
return(newPoints);
}
// translates the points so that their centroid lies at 'toPt'
public static List <PointR> TranslateCentroidTo(List <PointR> points, PointR toPt)
{
List <PointR> newPoints = new List <PointR>(points.Count);
PointR centroid = Centroid(points);
for (int i = 0; i < points.Count; i++)
{
PointR p = (PointR)points[i];
p.X += (toPt.X - centroid.X);
p.Y += (toPt.Y - centroid.Y);
newPoints.Add(p);
}
return(newPoints);
}
// Calculate the angle from the initial point of the array of Points (points[0])
// to points[index].
//
// Returns this angle represented by a unit vector (stored in a Point).
//
// **This is used in Gesture.cs:Gesture() to compute the start angle in support
// of the optimization to not compare candidates to templates whose start angles
// are widely different. Lisa 8/8/2009
public static PointR CalcStartUnitVector(List <PointR> points, int index)
{
// v is the vector from points[0] to points[index]
PointR v = new PointR(((PointR)points[index]).X - ((PointR)points[0]).X,
((PointR)points[index]).Y - ((PointR)points[0]).Y);
// len is the length of vector v
double len = Math.Sqrt(v.X * v.X + v.Y * v.Y);
// the unit vector representing the angle between points[0] and points[index]
// is the vector v divided by its length len
// TODO: does there need to be a divide by zero check?
return(new PointR(v.X / len, v.Y / len));
}
// translates the points so that the upper-left corner of their bounding box lies at 'toPt'
public static List <PointR> TranslateBBoxTo(List <PointR> points, PointR toPt)
{
List <PointR> newPoints = new List <PointR>(points.Count);
RectangleR r = Utils.FindBox(points);
for (int i = 0; i < points.Count; i++)
{
PointR p = (PointR)points[i];
p.X += (toPt.X - r.X);
p.Y += (toPt.Y - r.Y);
newPoints.Add(p);
}
return(newPoints);
}
// scales the points so that the length of their shorter side
// matches the length of the shorter side of the given box.
// thus, both dimensions are warped proportionally, rather than
// independently, like in the function ScaleTo.
public static List <PointR> ScaleToMin(List <PointR> points, RectangleR box)
{
List <PointR> newPoints = new List <PointR>(points.Count);
RectangleR r = FindBox(points);
for (int i = 0; i < points.Count; i++)
{
PointR p = (PointR)points[i];
p.X *= (box.MinSide / r.MinSide);
p.Y *= (box.MinSide / r.MinSide);
newPoints.Add(p);
}
return(newPoints);
}
// will return result in radians
public static double AngleBetweenUnitVectors(PointR v1, PointR v2) // gives acute angle between unit vectors from (0,0) to v1, and (0,0) to v2
{
// changed this method on 9/28/2009, Lisa
double test = v1.X * v2.X + v1.Y * v2.Y; // arc cosine of the vector dot product
// sometimes these two cases can happen because of rounding error in the dot product calculation
if (test < -1.0)
{
test = -1.0; // truncate rounding errors
}
if (test > 1.0)
{
test = 1.0; // truncate rounding errors
}
return(Math.Acos(test));
}
// scales the points so that they form the size given. does not restore the
// origin of the box.
public static List <PointR> ScaleTo(List <PointR> points, SizeR sz)
{
List <PointR> newPoints = new List <PointR>(points.Count);
RectangleR r = FindBox(points);
for (int i = 0; i < points.Count; i++)
{
PointR p = (PointR)points[i];
if (r.Width != 0d)
{
p.X *= (sz.Width / r.Width);
}
if (r.Height != 0d)
{
p.Y *= (sz.Height / r.Height);
}
newPoints.Add(p);
}
return(newPoints);
}
public static List <PointR> Resample(List <PointR> points, int n)
{
double I = PathLength(points) / (n - 1); // interval length
double D = 0.0;
List <PointR> srcPts = new List <PointR>(points);
List <PointR> dstPts = new List <PointR>(n);
dstPts.Add(srcPts[0]);
for (int i = 1; i < srcPts.Count; i++)
{
PointR pt1 = (PointR)srcPts[i - 1];
PointR pt2 = (PointR)srcPts[i];
double d = Distance(pt1, pt2);
if ((D + d) >= I)
{
double qx = pt1.X + ((I - D) / d) * (pt2.X - pt1.X);
double qy = pt1.Y + ((I - D) / d) * (pt2.Y - pt1.Y);
PointR 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);
}
public Gesture(List <PointR> points)
{
this.Name = String.Empty;
this.RawPoints = new List <PointR>(points); // copy (saved for drawing)
Points = RawPoints;
// added for debugging, Lisa 1/2/2008
// reflects new order of pre-processing steps as of 8/31/2009
// old order (from 8/8/2009) was
// 1. check for 1D
// 2. scale
// 3. resample
// 4. translate
// 5. rotate (if rot-invariant)
// 6. calculate start angle
// new order (as of 8/31/2009) is
// 1. resample
// 2. rotate (all); save amount
// 3. check for 1D
// 4. scale
// 5. rotate back (if NOT rot-invariant)
// 6. translate
// 7. calculate start angle
// first, resample (influences calculation of centroid)
Points = Utils.Resample(Points, NDollarParameters.Instance.NumResamplePoints);
// then, if we are rotation-invariant, rotate to a common reference angle
// otherwise skip that step
// Lisa 8/8/2009: this is now set by a flag in the NDollarRecognizer.cs file with all the other flags
// rotate so that the centroid-to-1st-point is at zero degrees
double radians = Utils.AngleInRadians(Utils.Centroid(Points), (PointR)Points[0], false);
Points = Utils.RotateByRadians(Points, -radians);
// then, resize to a square
// check for 1D vs 2D (because we resize differently)
// Lisa 1/2/2008
// replace with boolean, Lisa 8/9/2009
this.Is1D = Utils.Is1DGesture(RawPoints);
// scale to a common (square) dimension
// moved determination of scale method to within the scale() method for less branching here
// Lisa 8/9/2009
Points = Utils.Scale(Points, GeometricRecognizer._1DThreshold, GeometricRecognizer.ResampleScale);
// next, if NOT rotation-invariant, rotate back
if (!NDollarParameters.Instance.RotationInvariant)
{
Points = Utils.RotateByRadians(Points, +radians); // undo angle
}
// next, translate to a common origin
Points = Utils.TranslateCentroidTo(Points, GeometricRecognizer.ResampleOrigin);
// finally, save the start angle
// Lisa 8/8/2009
// store the start unit vector after post-processing steps
this.StartUnitVector = Utils.CalcStartUnitVector(Points, NDollarParameters.Instance.StartAngleIndex);
// Lisa 3/7/2011
// make the simple vector-based version for Protractor testing
this.VectorVersion = Vectorize(this.Points);
}
// 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));
}
