public void GetLength()
{
CatmullRomSegment2F c = new CatmullRomSegment2F
{
Point1 = new Vector2F(1, 2),
Point2 = new Vector2F(10, 3),
Point3 = new Vector2F(7, 8),
Point4 = new Vector2F(10, 2),
};
HermiteSegment2F h = new HermiteSegment2F
{
Point1 = c.Point2,
Tangent1 = (c.Point3 - c.Point1) * 0.5f,
Tangent2 = (c.Point4 - c.Point2) * 0.5f,
Point2 = c.Point3,
};
float length1 = c.GetLength(0, 1, 20, Numeric.EpsilonF);
float length2 = h.GetLength(0, 1, 20, Numeric.EpsilonF);
Assert.IsTrue(Numeric.AreEqual(length1, length2));
float approxLength = 0;
const float step = 0.0001f;
for (float u = 0; u <= 1.0f; u += step)
{
approxLength += (c.GetPoint(u) - c.GetPoint(u + step)).Length;
}
Assert.IsTrue(Numeric.AreEqual(approxLength, length1, 0.01f));
Assert.IsTrue(Numeric.AreEqual(c.GetLength(0, 1, 100, Numeric.EpsilonF), c.GetLength(0, 0.5f, 100, Numeric.EpsilonF) + c.GetLength(0.5f, 1, 100, Numeric.EpsilonF)));
Assert.IsTrue(Numeric.AreEqual(c.GetLength(0, 1, 100, Numeric.EpsilonF), c.GetLength(1, 0, 100, Numeric.EpsilonF)));
}
public void GetLength()
{
CatmullRomSegment2F c = new CatmullRomSegment2F
{
Point1 = new Vector2F(1, 2),
Point2 = new Vector2F(10, 3),
Point3 = new Vector2F(7, 8),
Point4 = new Vector2F(10, 2),
};
HermiteSegment2F h = new HermiteSegment2F
{
Point1 = c.Point2,
Tangent1 = (c.Point3 - c.Point1) * 0.5f,
Tangent2 = (c.Point4 - c.Point2) * 0.5f,
Point2 = c.Point3,
};
float length1 = c.GetLength(0, 1, 20, Numeric.EpsilonF);
float length2 = h.GetLength(0, 1, 20, Numeric.EpsilonF);
Assert.IsTrue(Numeric.AreEqual(length1, length2));
float approxLength = 0;
const float step = 0.0001f;
for (float u = 0; u <= 1.0f; u += step)
approxLength += (c.GetPoint(u) - c.GetPoint(u + step)).Length;
Assert.IsTrue(Numeric.AreEqual(approxLength, length1, 0.01f));
Assert.IsTrue(Numeric.AreEqual(c.GetLength(0, 1, 100, Numeric.EpsilonF), c.GetLength(0, 0.5f, 100, Numeric.EpsilonF) + c.GetLength(0.5f, 1, 100, Numeric.EpsilonF)));
Assert.IsTrue(Numeric.AreEqual(c.GetLength(0, 1, 100, Numeric.EpsilonF), c.GetLength(1, 0, 100, Numeric.EpsilonF)));
}
public void Flatten()
{
var s = new CatmullRomSegment2F
{
Point1 = new Vector2F(1, 2),
Point2 = new Vector2F(10, 3),
Point3 = new Vector2F(7, 8),
Point4 = new Vector2F(10, 2),
};
var points = new List<Vector2F>();
var tolerance = 0.01f;
s.Flatten(points, 10, tolerance);
Assert.IsTrue(points.Contains(s.Point2));
Assert.IsTrue(points.Contains(s.Point3));
var curveLength = s.GetLength(0, 1, 10, tolerance);
Assert.IsTrue(CurveHelper.GetLength(points) >= curveLength - tolerance * points.Count / 2);
Assert.IsTrue(CurveHelper.GetLength(points) <= curveLength);
}
public void Flatten()
{
var s = new CatmullRomSegment2F
{
Point1 = new Vector2F(1, 2),
Point2 = new Vector2F(10, 3),
Point3 = new Vector2F(7, 8),
Point4 = new Vector2F(10, 2),
};
var points = new List <Vector2F>();
var tolerance = 0.01f;
s.Flatten(points, 10, tolerance);
Assert.IsTrue(points.Contains(s.Point2));
Assert.IsTrue(points.Contains(s.Point3));
var curveLength = s.GetLength(0, 1, 10, tolerance);
Assert.IsTrue(CurveHelper.GetLength(points) >= curveLength - tolerance * points.Count / 2);
Assert.IsTrue(CurveHelper.GetLength(points) <= curveLength);
}
public void GetLength()
{
Path2F empty = new Path2F();
empty.Sort();
Assert.AreEqual(0, empty.GetLength(0, 1, 100, 0.0001f));
Path2F path = CreatePath();
path.PreLoop = CurveLoopType.Constant;
path.PostLoop = CurveLoopType.Oscillate;
Assert.IsTrue(Numeric.AreEqual((new Vector2F(0, 1) - new Vector2F(1, 2)).Length, path.GetLength(-1, 12, 100, 0.0001f), 0.001f));
Assert.IsTrue(Numeric.AreEqual((new Vector2F(0, 1) - new Vector2F(1, 2)).Length, path.GetLength(-1, 20, 100, 0.0001f), 0.001f));
CatmullRomSegment2F catmullOscillate = new CatmullRomSegment2F()
{
Point1 = new Vector2F(10, 12),
Point2 = new Vector2F(10, 14),
Point3 = new Vector2F(20, 14),
Point4 = new Vector2F(30, 14),
};
float desiredLength = catmullOscillate.GetLength(0, 1, 20, 0.0001f);
float actualLength = path.GetLength(40, 50, 20, 0.0001f);
Assert.IsTrue(Numeric.AreEqual(desiredLength, actualLength, 0.001f));
desiredLength = catmullOscillate.GetLength(1, 0.8f, 20, 0.0001f);
actualLength = path.GetLength(52, 50, 20, 0.0001f);
Assert.IsTrue(Numeric.AreEqual(desiredLength, actualLength, 0.001f));
desiredLength = catmullOscillate.GetLength(1, 0.8f, 20, 0.0001f) * 2;
actualLength = path.GetLength(52, 48, 20, 0.0001f);
Assert.IsTrue(Numeric.AreEqual(desiredLength, actualLength, 0.001f));
path.PreLoop = CurveLoopType.Linear;
path.PostLoop = CurveLoopType.Cycle;
path.PreLoop = CurveLoopType.Cycle;
path.PostLoop = CurveLoopType.CycleOffset;
path.PreLoop = CurveLoopType.CycleOffset;
path.PostLoop = CurveLoopType.Linear;
path.PreLoop = CurveLoopType.Oscillate;
path.PostLoop = CurveLoopType.Constant;
}
public void GetTangent()
{
CatmullRomSegment2F c = new CatmullRomSegment2F
{
Point1 = new Vector2F(1, 2),
Point2 = new Vector2F(10, 3),
Point3 = new Vector2F(7, 8),
Point4 = new Vector2F(10, 2),
};
HermiteSegment2F h = new HermiteSegment2F
{
Point1 = c.Point2,
Tangent1 = (c.Point3 - c.Point1) * 0.5f,
Tangent2 = (c.Point4 - c.Point2) * 0.5f,
Point2 = c.Point3,
};
Assert.IsTrue(Vector2F.AreNumericallyEqual(h.Tangent1, c.GetTangent(0)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(h.Tangent2, c.GetTangent(1)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(h.GetTangent(0.7f), c.GetTangent(0.7f)));
}
public void GetPoint()
{
CatmullRomSegment2F c = new CatmullRomSegment2F
{
Point1 = new Vector2F(1, 2),
Point2 = new Vector2F(10, 3),
Point3 = new Vector2F(7, 8),
Point4 = new Vector2F(10, 2),
};
HermiteSegment2F h = new HermiteSegment2F
{
Point1 = c.Point2,
Tangent1 = (c.Point3 - c.Point1) * 0.5f,
Tangent2 = (c.Point4 - c.Point2) * 0.5f,
Point2 = c.Point3,
};
Assert.IsTrue(Vector2F.AreNumericallyEqual(c.Point2, c.GetPoint(0)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(c.Point3, c.GetPoint(1)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(h.GetPoint(0.33f), c.GetPoint(0.33f)));
}
public void GetTangent()
{
Path2F path = CreatePath();
path.PreLoop = CurveLoopType.Constant;
path.PostLoop = CurveLoopType.Oscillate;
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(0, 0), path.GetTangent(-10)));
Assert.IsTrue(Vector2F.AreNumericallyEqual((new Vector2F(1, 2) - new Vector2F(0, 1)) / 2, path.GetTangent(10)));
Assert.IsTrue(Vector2F.AreNumericallyEqual((new Vector2F(1, 2) - new Vector2F(0, 1)) / 2, path.GetTangent(11.5f)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(0, 0), path.GetTangent(16)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(0, 0), path.GetTangent(85)));
CatmullRomSegment2F catmullOscillate = new CatmullRomSegment2F()
{
Point1 = new Vector2F(10, 12),
Point2 = new Vector2F(10, 14),
Point3 = new Vector2F(20, 14),
Point4 = new Vector2F(30, 14),
};
Assert.IsTrue(Vector2F.AreNumericallyEqual(catmullOscillate.GetTangent(0.3f) / 10.0f, path.GetTangent(43)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(-catmullOscillate.GetTangent(0.7f) / 10.0f, path.GetTangent(53)));
path.PreLoop = CurveLoopType.Linear;
path.PostLoop = CurveLoopType.Cycle;
Assert.IsTrue(Vector2F.AreNumericallyEqual((new Vector2F(1, 2) - new Vector2F(0, 1)) / 2, path.GetTangent(0)));
path.PreLoop = CurveLoopType.Cycle;
path.PostLoop = CurveLoopType.CycleOffset;
Assert.IsTrue(Vector2F.AreNumericallyEqual(catmullOscillate.GetTangent(0.4f) / 10.0f, path.GetTangent(-36)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(catmullOscillate.GetTangent(0.4f) / 10.0f, path.GetTangent(4)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(catmullOscillate.GetTangent(0.3f) / 10.0f, path.GetTangent(83)));
path.PreLoop = CurveLoopType.CycleOffset;
path.PostLoop = CurveLoopType.Linear;
Assert.IsTrue(Vector2F.AreNumericallyEqual(catmullOscillate.GetTangent(1f) / 10.0f, path.GetTangent(434)));
path.PreLoop = CurveLoopType.Oscillate;
path.PostLoop = CurveLoopType.Constant;
path = new Path2F();
path.Add(new PathKey2F()
{
Parameter = 25,
Point = new Vector2F(6, 7),
Interpolation = SplineInterpolation.Bezier,
TangentIn = new Vector2F(5, 6),
TangentOut = new Vector2F(7, 8),
});
path.Add(new PathKey2F()
{
Parameter = 35,
Point = new Vector2F(10, 12),
Interpolation = SplineInterpolation.Hermite,
TangentIn = new Vector2F(1, 0),
TangentOut = new Vector2F(1, 0),
});
path.PreLoop = CurveLoopType.Linear;
path.PostLoop = CurveLoopType.Linear;
float Δu = path[1].Parameter - path[0].Parameter;
Assert.IsTrue(Vector2F.AreNumericallyEqual((new Vector2F(6, 7) - new Vector2F(5, 6)) * 3 / Δu, path.GetTangent(0)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(1, 0) / Δu, path.GetTangent(100)));
path[1].Parameter = 25;
path[0].Parameter = 35;
path.Sort();
Δu = path[1].Parameter - path[0].Parameter;
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(1, 0) / Δu, path.GetTangent(0)));
Assert.IsTrue(Vector2F.AreNumericallyEqual((new Vector2F(7, 8) - new Vector2F(6, 7)) * 3 / Δu, path.GetTangent(100)));
path.Add(new PathKey2F()
{
Parameter = 15,
Point = new Vector2F(0, 0),
Interpolation = SplineInterpolation.BSpline,
});
path.Sort();
}
public void GetPoint()
{
Path2F path = CreatePath();
path.PreLoop = CurveLoopType.Constant;
path.PostLoop = CurveLoopType.Oscillate;
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(0, 1), path.GetPoint(-10)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(4, 5), path.GetPoint(13)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(4, 5), path.GetPoint(16)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(5, 7), path.GetPoint(17)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(5, 7), path.GetPoint(19)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(5, 7) * 0.5f + new Vector2F(6, 7)*0.5f, path.GetPoint(22.5f)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(5, 7) * 0.5f + new Vector2F(6, 7) * 0.5f, path.GetPoint(22.5f)));
CatmullRomSegment2F catmullOscillate = new CatmullRomSegment2F()
{
Point1 = new Vector2F(10, 12),
Point2 = new Vector2F(10, 14),
Point3 = new Vector2F(20, 14),
Point4 = new Vector2F(30, 14),
};
Assert.IsTrue(Vector2F.AreNumericallyEqual(catmullOscillate.GetPoint(0.3f), path.GetPoint(43)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(catmullOscillate.GetPoint(0.9f), path.GetPoint(51)));
CatmullRomSegment2F catmullCircle = new CatmullRomSegment2F()
{
Point1 = new Vector2F(10, 12),
Point2 = new Vector2F(10, 14),
Point3 = new Vector2F(20, 14),
Point4 = new Vector2F(30, 14),
};
path.PreLoop = CurveLoopType.Linear;
path.PostLoop = CurveLoopType.Cycle;
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(0, 1) - (new Vector2F(1, 2) - new Vector2F(0, 1)) / 2 * 9, path.GetPoint(1)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(catmullCircle.GetPoint(0.3f), path.GetPoint(43)));
path.PreLoop = CurveLoopType.Cycle;
path.PostLoop = CurveLoopType.CycleOffset;
var cycleOffset = new Vector2F(20, 14) - new Vector2F(0, 1);
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(10, 14) + cycleOffset, path.GetPoint(80f)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(10, 14) + cycleOffset * 2, path.GetPoint(120f)));
path.PreLoop = CurveLoopType.CycleOffset;
path.PostLoop = CurveLoopType.Linear;
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(10, 14) - cycleOffset, path.GetPoint(0f)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(10, 14) - cycleOffset * 2, path.GetPoint(-40f)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(20, 14) + catmullOscillate.GetTangent(1) / 10 * 50, path.GetPoint(100f)));
path.PreLoop = CurveLoopType.Oscillate;
path.PostLoop = CurveLoopType.Constant;
}
