private void PlotBezierTangentByDegree(List <GPoint> points)
{
base.Axes.Add(new OxyPlot.Axes.LinearAxis
{
Title = "Tangent of Bezier(Degree)",
Position = OxyPlot.Axes.AxisPosition.Left
});
AddZeroLineAnnotation();
OxyPlot.Series.LineSeries ls = new OxyPlot.Series.LineSeries()
{
Title = "Tangent of Bezier(Degree)",
MarkerType = ShowMarker ? MarkerType.None : MarkerType.Plus,
MarkerStroke = OxyPlot.OxyColors.Blue
};
int degree = points.Count - 1;
NURBSCurve bspline = new NURBSCurve(points, degree);
for (double u = 0; u <= 1.0; u += 0.01)
{
double tangent = bspline.TangentByDegree(u);
ls.Points.Add(new OxyPlot.DataPoint(u * 100.0, tangent));
}
base.Series.Add(ls);
}
private void PlotCurveManeuver(List <GPoint> points, double curveLength, int degree)
{
if (points.Count < 2)
{
return;
}
double scale = (CurvatureUnit == CurvatureUnit.Centimeter) ? 0.01 : 1.0; // 1/cm or 1/m
List <GPoint> curvatures = new List <GPoint>();
NURBSCurve bspline = new NURBSCurve(points, degree);
for (double u = 0.01; u < 1.0 - 0.01; u += 0.01)
{
double curvature = bspline.Curvature(u);
double distanceFromStart = curveLength * u;
curvatures.Add(new GPoint(u * 100.0, curvature * scale, weight: distanceFromStart));
}
List <GPoint> simplified = SimplifyPolyline(curvatures, CurveManeuverParameter.CurveMinDistance);
List <GPoint> curvaturManeuvers = PolylineSimplication.SimplifyHeadingChange(simplified.ToArray(), CurveManeuverParameter.YTolerance);
List <GPoint> maneuvers = new List <GPoint>();
foreach (var p in curvaturManeuvers)
{
int index = Weight2Index(p, curveLength, points.Count);
maneuvers.Add(points[index]);
}
AddScatterSeries(maneuvers, "Maneuvers");
}
private void AddBezierByNURBS(List <GPoint> points)
{
if (points.Count() < 3)
{
return;
}
int degree = points.Count - 1;
var ls = new OxyPlot.Series.LineSeries()
{
MarkerType = ShowMarker ? MarkerType.None : MarkerType.Plus,
MarkerStroke = OxyPlot.OxyColors.Blue
};
double duration = Util.Util.MeasureExecTime(() =>
{
const int INTERVAL_NUM = 100;
double step = 1.0 / INTERVAL_NUM;
NURBSCurve bspline = new NURBSCurve(points, degree);
for (double t = 0; t < 1.0; t += step)
{
GPoint p = bspline.NonRationalBSpline(t);
ls.Points.Add(new OxyPlot.DataPoint(p.X, p.Y));
}
});
ls.Title = $"NURBS(Bezier-{degree})({duration:0.###}ms)";
base.Series.Add(ls);
}
private void AddBSplineByNURBS(List <GPoint> points, double curveLength)
{
if (points.Count() < 3)
{
return;
}
var ls = new OxyPlot.Series.LineSeries()
{
MarkerType = ShowMarker ? MarkerType.None : MarkerType.Plus,
MarkerStroke = OxyPlot.OxyColors.Blue
};
int degree = SplineDegree(points);
double duration = Util.Util.MeasureExecTime(() =>
{
NURBSCurve bspline = new NURBSCurve(points, degree);
for (double u = 0; u <= 1.0; u += 0.01)
{
GPoint p = bspline.NonRationalBSpline(u);
ls.Points.Add(new OxyPlot.DataPoint(p.X, p.Y));
}
});
ls.Title = $"NURBS({degree})[len={curveLength:0.#}]({duration:0.###}ms)";
base.Series.Add(ls);
}
public void NURBSCurve()
{
double[][] pts = null;
KnotSet knotset = null;
int degree = int.MinValue;
NURBSCurve bSpline = null;
double[] weights = null;
pts = new double[][]
{
new double[] { 0, 0, 0 },
new double[] { 2, 4, 0 },
new double[] { 4, 0, 0 },
new double[] { 6, 4, 0 },
};
knotset = new KnotSet(new double[] { 0, 0, 0, 0, 1, 1, 1, 1 });
weights = new double[] { 1, 1, 1, 1 };
degree = 3;
bSpline = new NURBSCurve(pts, knotset, weights, degree);
}
private void PlotBSplineRawCurvatureByNURBS(List <GPoint> points, double curvelength)
{
// curvature
base.Axes.Add(new OxyPlot.Axes.LinearAxis
{
Title = (CurvatureUnit == CurvatureUnit.Meter) ? "Curvature(1/m)" : "Curvature(1/cm)",
Position = OxyPlot.Axes.AxisPosition.Left
});
AddZeroLineAnnotation();
int degree = SplineDegree(points);
OxyPlot.Series.LineSeries ls = new OxyPlot.Series.LineSeries()
{
MarkerType = ShowMarker ? MarkerType.None : MarkerType.Plus,
MarkerStroke = OxyPlot.OxyColors.Blue
};
List <GPoint> curvatures = new List <GPoint>();
double duration = Util.Util.MeasureExecTime(() =>
{
double scale = (CurvatureUnit == CurvatureUnit.Centimeter) ? 0.01 : 1.0; // 1/cm or 1/m
NURBSCurve bspline = new NURBSCurve(points, degree);
for (double u = 0.01; u < 1.0 - 0.01; u += 0.01)
{
double curvature = bspline.Curvature(u) * scale;
double dist = curvelength * u;
ls.Points.Add(new OxyPlot.DataPoint(dist, curvature));
curvatures.Add(new GPoint(dist, curvature, weight: dist));
}
});
ls.Title = $"NURBS({degree}) Curvature({duration:0.###}ms)";
base.Series.Add(ls);
PlotSimplifiedPolyline(curvatures);
PlotManeuverOnCurvatureCurve(curvatures);
}
public void ParameterAt()
{
double[][] pts = null;
double[] weights = null;
KnotSet knotset = null;
int degree = int.MinValue;
NURBSCurve nurbs = null;
double[] r, a;
double t, e;
pts = new double[][]
{
new double[] { 0, 0, 0 },
new double[] { 2, 4, 0 },
new double[] { 4, 0, 0 },
};
weights = new double[] { 1, 3, 1 };
knotset = new KnotSet(new double[] { 0, 0, 0, 1, 1, 1 });
degree = 2;
nurbs = new NURBSCurve(pts, knotset, weights, degree);
t = 0.5;
a = new double[] { 2, 3, 0 };
r = nurbs.ParameterAt(t);
Assert.IsTrue(a.SequenceEqual(r));
pts = new double[][]
{
new double[] { 0, 0, 0 },
new double[] { 2, 4, 0 },
new double[] { 4, 0, 0 },
};
weights = new double[] { 1, 3, 1 };
knotset = new KnotSet(new double[] { 0, 0, 0, 1, 1, 1 });
degree = 2;
nurbs = new NURBSCurve(pts, knotset, weights, degree);
t = 1;
a = new double[] { 4, 0, 0 };
r = nurbs.ParameterAt(t);
e = 0.0001;
Assert.IsTrue(a.SequenceEqual(r, e));
pts = new double[][]
{
new double[] { 0, 0, 0 },
new double[] { 2, 4, 0 },
new double[] { 6, 4, 0 },
};
weights = new double[] { 1, 1, 1 };
knotset = new KnotSet(new double[] { 0, 0, 0, 1, 1, 1 });
degree = 2;
nurbs = new NURBSCurve(pts, knotset, weights, degree);
t = 1;
a = new double[] { 6, 4, 0 };
r = nurbs.ParameterAt(t);
e = 0.0001;
Assert.IsTrue(a.SequenceEqual(r, e));
pts = new double[][]
{
new double[] { 0.0, 0.0, 0.0 },
new double[] { 4.0, 5.0, 0.0 },
new double[] { 6.0, 1.0, 0.0 },
new double[] { 9.0, 5.0, 0.0 },
new double[] { 11.0, 3.0, 0.0 },
new double[] { 16.0, 4.0, 0.0 },
};
weights = new double[] { 1, 3, 1, 3, 1, 2 };
knotset = new KnotSet(new double[] { 0, 0, 0, 0, 1d / 3d, 2d / 3d, 1, 1, 1, 1 });
degree = 3;
nurbs = new NURBSCurve(pts, knotset, weights, degree);
t = 0.3;
a = new double[] { 5.52901, 3.849042, 0.0 };
r = nurbs.ParameterAt(t);
e = 0.0001;
Assert.IsTrue(Math.Abs(a[0] - r[0]) < e);
Assert.IsTrue(Math.Abs(a[1] - r[1]) < e);
Assert.IsTrue(Math.Abs(a[2] - r[2]) < e);
pts = new double[][]
{
new double[] { 0.0, 0.0, 0.0 },
new double[] { 4.0, 5.0, 0.0 },
new double[] { 6.0, 1.0, 0.0 },
new double[] { 9.0, 5.0, 0.0 },
new double[] { 11.0, 3.0, 0.0 },
new double[] { 16.0, 4.0, 0.0 },
};
weights = new double[] { 1, 3, 1, 3, 1, 2 };
knotset = new KnotSet(new double[] { 0, 0, 0, 0, 1d / 3d, 2d / 3d, 1, 1, 1, 1 });
degree = 3;
nurbs = new NURBSCurve(pts, knotset, weights, degree);
t = 0.3948;
a = new double[] { 6.9053986159719711, 3.6972003072706183, 0.0 };
r = nurbs.ParameterAt(t);
e = 0.0001;
Assert.IsTrue(r.SequenceEqual(a, e));
pts = new double[][]
{
new double[] { 0.0, 0.0, 0.0 },
new double[] { 4.0, 5.0, 0.0 },
new double[] { 6.0, 1.0, 0.0 },
new double[] { 9.0, 5.0, 0.0 },
new double[] { 11.0, 3.0, 0.0 },
new double[] { 16.0, 4.0, 0.0 },
};
weights = new double[] { 1, 3, 1, 3, 1, 2 };
knotset = new KnotSet(new double[] { 0, 0, 0, 0, 1d / 3d, 2d / 3d, 1, 1, 1, 1 });
degree = 3;
nurbs = new NURBSCurve(pts, knotset, weights, degree);
t = 1;
a = new double[] { 16, 4, 0 };
r = nurbs.ParameterAt(t);
e = 0.0001;
Assert.IsTrue(r.SequenceEqual(a, e));
}
