public void GetLength()
{
CatmullRomSegment3F c = new CatmullRomSegment3F
{
Point1 = new Vector3F(1, 2, 3),
Point2 = new Vector3F(10, 3, 6),
Point3 = new Vector3F(7, 8, 19),
Point4 = new Vector3F(10, 2, 12),
};
HermiteSegment3F h = new HermiteSegment3F
{
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()
{
CatmullRomSegment3F c = new CatmullRomSegment3F
{
Point1 = new Vector3(1, 2, 3),
Point2 = new Vector3(10, 3, 6),
Point3 = new Vector3(7, 8, 19),
Point4 = new Vector3(10, 2, 12),
};
HermiteSegment3F h = new HermiteSegment3F
{
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 CatmullRomSegment3F
{
Point1 = new Vector3F(1, 2, 3),
Point2 = new Vector3F(10, 3, 6),
Point3 = new Vector3F(7, 8, 19),
Point4 = new Vector3F(10, 2, 12),
};
var points = new List<Vector3F>();
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 CatmullRomSegment3F
{
Point1 = new Vector3(1, 2, 3),
Point2 = new Vector3(10, 3, 6),
Point3 = new Vector3(7, 8, 19),
Point4 = new Vector3(10, 2, 12),
};
var points = new List <Vector3>();
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()
{
Path3F empty = new Path3F();
empty.Sort();
Assert.AreEqual(0, empty.GetLength(0, 1, 100, 0.0001f));
Path3F path = CreatePath();
path.PreLoop = CurveLoopType.Constant;
path.PostLoop = CurveLoopType.Oscillate;
Assert.IsTrue(Numeric.AreEqual((new Vector3F(0, 0, 1) - new Vector3F(1, 2, 3)).Length, path.GetLength(-1, 12, 100, 0.0001f), 0.001f));
Assert.IsTrue(Numeric.AreEqual((new Vector3F(0, 0, 1) - new Vector3F(1, 2, 3)).Length, path.GetLength(-1, 20, 100, 0.0001f), 0.001f));
CatmullRomSegment3F catmullOscillate = new CatmullRomSegment3F()
{
Point1 = new Vector3F(10, 12, 14),
Point2 = new Vector3F(10, 14, 8),
Point3 = new Vector3F(20, 14, 8),
Point4 = new Vector3F(30, 14, 8),
};
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()
{
CatmullRomSegment3F c = new CatmullRomSegment3F
{
Point1 = new Vector3(1, 2, 3),
Point2 = new Vector3(10, 3, 6),
Point3 = new Vector3(7, 8, 19),
Point4 = new Vector3(10, 2, 12),
};
HermiteSegment3F h = new HermiteSegment3F
{
Point1 = c.Point2,
Tangent1 = (c.Point3 - c.Point1) * 0.5f,
Tangent2 = (c.Point4 - c.Point2) * 0.5f,
Point2 = c.Point3,
};
Assert.IsTrue(Vector3.AreNumericallyEqual(h.Tangent1, c.GetTangent(0)));
Assert.IsTrue(Vector3.AreNumericallyEqual(h.Tangent2, c.GetTangent(1)));
Assert.IsTrue(Vector3.AreNumericallyEqual(h.GetTangent(0.7f), c.GetTangent(0.7f)));
}
public void GetPoint()
{
CatmullRomSegment3F c = new CatmullRomSegment3F
{
Point1 = new Vector3F(1, 2, 3),
Point2 = new Vector3F(10, 3, 6),
Point3 = new Vector3F(7, 8, 19),
Point4 = new Vector3F(10, 2, 12),
};
HermiteSegment3F h = new HermiteSegment3F
{
Point1 = c.Point2,
Tangent1 = (c.Point3 - c.Point1) * 0.5f,
Tangent2 = (c.Point4 - c.Point2) * 0.5f,
Point2 = c.Point3,
};
Assert.IsTrue(Vector3F.AreNumericallyEqual(c.Point2, c.GetPoint(0)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(c.Point3, c.GetPoint(1)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(h.GetPoint(0.33f), c.GetPoint(0.33f)));
}
public void GetTangent()
{
Path3F path = CreatePath();
path.PreLoop = CurveLoopType.Constant;
path.PostLoop = CurveLoopType.Oscillate;
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(0, 0, 0), path.GetTangent(-10)));
Assert.IsTrue(Vector3F.AreNumericallyEqual((new Vector3F(1, 2, 3) - new Vector3F(0, 0, 1)) / 2, path.GetTangent(10)));
Assert.IsTrue(Vector3F.AreNumericallyEqual((new Vector3F(1, 2, 3) - new Vector3F(0, 0, 1)) / 2, path.GetTangent(11.5f)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(0, 0, 0), path.GetTangent(16)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(0, 0, 0), path.GetTangent(85)));
CatmullRomSegment3F catmullOscillate = new CatmullRomSegment3F()
{
Point1 = new Vector3F(10, 12, 14),
Point2 = new Vector3F(10, 14, 8),
Point3 = new Vector3F(20, 14, 8),
Point4 = new Vector3F(30, 14, 8),
};
Assert.IsTrue(Vector3F.AreNumericallyEqual(catmullOscillate.GetTangent(0.3f) / 10.0f, path.GetTangent(43)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(-catmullOscillate.GetTangent(0.7f) / 10.0f, path.GetTangent(53)));
path.PreLoop = CurveLoopType.Linear;
path.PostLoop = CurveLoopType.Cycle;
Assert.IsTrue(Vector3F.AreNumericallyEqual((new Vector3F(1, 2, 3) - new Vector3F(0, 0, 1)) / 2, path.GetTangent(0)));
path.PreLoop = CurveLoopType.Cycle;
path.PostLoop = CurveLoopType.CycleOffset;
Assert.IsTrue(Vector3F.AreNumericallyEqual(catmullOscillate.GetTangent(0.4f) / 10.0f, path.GetTangent(-36)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(catmullOscillate.GetTangent(0.4f) / 10.0f, path.GetTangent(4)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(catmullOscillate.GetTangent(0.3f) / 10.0f, path.GetTangent(83)));
path.PreLoop = CurveLoopType.CycleOffset;
path.PostLoop = CurveLoopType.Linear;
Assert.IsTrue(Vector3F.AreNumericallyEqual(catmullOscillate.GetTangent(1f) / 10.0f, path.GetTangent(434)));
path.PreLoop = CurveLoopType.Oscillate;
path.PostLoop = CurveLoopType.Constant;
path = new Path3F();
path.Add(new PathKey3F()
{
Parameter = 25,
Point = new Vector3F(6, 7, 14),
Interpolation = SplineInterpolation.Bezier,
TangentIn = new Vector3F(5, 6, 13),
TangentOut = new Vector3F(7, 8, 15),
});
path.Add(new PathKey3F()
{
Parameter = 35,
Point = new Vector3F(10, 12, 14),
Interpolation = SplineInterpolation.Hermite,
TangentIn = new Vector3F(1, 0, 0),
TangentOut = new Vector3F(1, 0, 0),
});
path.PreLoop = CurveLoopType.Linear;
path.PostLoop = CurveLoopType.Linear;
float Δu = path[1].Parameter - path[0].Parameter;
Assert.IsTrue(Vector3F.AreNumericallyEqual((new Vector3F(6, 7, 14) - new Vector3F(5, 6, 13)) * 3 / Δu, path.GetTangent(0)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(1, 0, 0) / Δu, path.GetTangent(100)));
path[1].Parameter = 25;
path[0].Parameter = 35;
path.Sort();
Δu = path[1].Parameter - path[0].Parameter;
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(1, 0, 0) / Δu, path.GetTangent(0)));
Assert.IsTrue(Vector3F.AreNumericallyEqual((new Vector3F(7, 8, 15) - new Vector3F(6, 7, 14)) * 3 / Δu, path.GetTangent(100)));
path.Add(new PathKey3F()
{
Parameter = 15,
Point = new Vector3F(0, 0, 0),
Interpolation = SplineInterpolation.BSpline,
});
path.Sort();
}
public void GetPoint()
{
Path3F path = CreatePath();
path.PreLoop = CurveLoopType.Constant;
path.PostLoop = CurveLoopType.Oscillate;
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(0, 0, 1), path.GetPoint(-10)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(4, 5, 7), path.GetPoint(13)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(4, 5, 7), path.GetPoint(16)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(5, 7, 10), path.GetPoint(17)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(5, 7, 10), path.GetPoint(19)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(5, 7, 13)*0.5f + new Vector3F(6, 7, 14)*0.5f, path.GetPoint(22.5f)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(5, 7, 13) * 0.5f + new Vector3F(6, 7, 14) * 0.5f, path.GetPoint(22.5f)));
CatmullRomSegment3F catmullOscillate = new CatmullRomSegment3F()
{
Point1 = new Vector3F(10, 12, 14),
Point2 = new Vector3F(10, 14, 8),
Point3 = new Vector3F(20, 14, 8),
Point4 = new Vector3F(30, 14, 8),
};
Assert.IsTrue(Vector3F.AreNumericallyEqual(catmullOscillate.GetPoint(0.3f), path.GetPoint(43)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(catmullOscillate.GetPoint(0.9f), path.GetPoint(51)));
CatmullRomSegment3F catmullCircle = new CatmullRomSegment3F()
{
Point1 = new Vector3F(10, 12, 14),
Point2 = new Vector3F(10, 14, 8),
Point3 = new Vector3F(20, 14, 8),
Point4 = new Vector3F(30, 14, 8),
};
path.PreLoop = CurveLoopType.Linear;
path.PostLoop = CurveLoopType.Cycle;
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(0, 0, 1) - (new Vector3F(1, 2, 3) - new Vector3F(0, 0, 1)) / 2 * 9, path.GetPoint(1)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(catmullCircle.GetPoint(0.3f), path.GetPoint(43)));
path.PreLoop = CurveLoopType.Cycle;
path.PostLoop = CurveLoopType.CycleOffset;
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(10, 14, 8) + new Vector3F(20, 14, 7), path.GetPoint(80f)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(10, 14, 8) + new Vector3F(20, 14, 7) * 2, path.GetPoint(120f)));
path.PreLoop = CurveLoopType.CycleOffset;
path.PostLoop = CurveLoopType.Linear;
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(10, 14, 8) - new Vector3F(20, 14, 7), path.GetPoint(0f)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(10, 14, 8) - new Vector3F(20, 14, 7) * 2, path.GetPoint(-40f)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(new Vector3F(20, 14, 8) + catmullOscillate.GetTangent(1) / 10 * 50, path.GetPoint(100f)));
path.PreLoop = CurveLoopType.Oscillate;
path.PostLoop = CurveLoopType.Constant;
}
public void GetPoint()
{
Curve2F empty = new Curve2F();
Assert.IsTrue(float.IsNaN(empty.GetPoint(1).X));
Assert.IsTrue(float.IsNaN(empty.GetPoint(0).Y));
Curve2F curve = CreateCurve();
curve.PreLoop = CurveLoopType.Constant;
curve.PostLoop = CurveLoopType.Oscillate;
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(-10, 1), curve.GetPoint(-10)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(11, 1 + 2f/5f), curve.GetPoint(11)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(19, 5), curve.GetPoint(19)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(23, 5), curve.GetPoint(23)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(24, 4), curve.GetPoint(24)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(29, 4), curve.GetPoint(29)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(30, 7), curve.GetPoint(30)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(33.9999f, 10), curve.GetPoint(33.9999f)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(40, 3), curve.GetPoint(40)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(45, 10), curve.GetPoint(45)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(48, 5), curve.GetPoint(48)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(49, curve.GetPoint(47).Y), curve.GetPoint(49)));
// Tested with internal assert in Debug Build.
curve.GetPoint(31);
curve.GetPoint(33);
curve.GetPoint(35);
curve.GetPoint(36);
curve.GetPoint(39);
curve.GetPoint(41);
curve.GetPoint(46);
curve.GetPoint(47);
//CatmullRomSegment3F catmullOscillate = new CatmullRomSegment3F()
//{
// Point1 = new Vector3F(10, 12, 14),
// Point2 = new Vector3F(10, 14, 8),
// Point3 = new Vector3F(20, 14, 8),
// Point4 = new Vector3F(20, 14, 8),
//};
//Assert.IsTrue(Vector3F.AreNumericallyEqual(catmullOscillate.GetPoint(0.3f), curve.GetPoint(43)));
//Assert.IsTrue(Vector3F.AreNumericallyEqual(catmullOscillate.GetPoint(0.9f), curve.GetPoint(51)));
//CatmullRomSegment3F catmullCircle = new CatmullRomSegment3F()
//{
// Point1 = new Vector3F(10, 12, 14),
// Point2 = new Vector3F(10, 14, 8),
// Point3 = new Vector3F(20, 14, 8),
// Point4 = new Vector3F(0, 0, 1),
//};
curve.PreLoop = CurveLoopType.Linear;
curve.PostLoop = CurveLoopType.Cycle;
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(-10, -7), curve.GetPoint(-10)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(49, 1 + 2f/5f), curve.GetPoint(49)));
curve.PreLoop = CurveLoopType.Cycle;
curve.PostLoop = CurveLoopType.CycleOffset;
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(4, curve.GetPoint(42).Y), curve.GetPoint(4)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(50, 5 + 4f/5f), curve.GetPoint(50)));
curve.PreLoop = CurveLoopType.CycleOffset;
curve.PostLoop = CurveLoopType.Linear;
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(4, curve.GetPoint(42).Y - 4), curve.GetPoint(4f)));
CatmullRomSegment3F catmull = new CatmullRomSegment3F
{
Point1 = new Vector3F(40, 3, 0),
Point2 = new Vector3F(45, 10, 0),
Point3 = new Vector3F(48, 5, 0),
Point4 = new Vector3F(48, 5, 0),
};
Vector3F endTangent = catmull.GetTangent(1);
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(55f, 5 + (55-48) * endTangent.Y / endTangent.X), curve.GetPoint(55f)));
//Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector3F(20, 14, 8) + catmullOscillate.GetTangent(1) / 10 * 50, curve.GetPoint(100f)));
// Test more linear pre- and post-behavior.
curve = new Curve2F();
curve.PreLoop = CurveLoopType.Linear;
curve.PostLoop = CurveLoopType.Linear;
curve.Add(new CurveKey2F()
{
Point = new Vector2F(0, 0),
Interpolation = SplineInterpolation.Bezier,
TangentIn = new Vector2F(-10, 10),
TangentOut = new Vector2F(5, 4),
});
curve.Add(new CurveKey2F()
{
Point = new Vector2F(10, 3),
Interpolation = SplineInterpolation.Bezier,
TangentIn = new Vector2F(8, 2),
TangentOut = new Vector2F(15, 4),
});
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(-10, 10), curve.GetPoint(-10f)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(15, 4), curve.GetPoint(15f)));
curve = new Curve2F();
curve.PreLoop = CurveLoopType.Linear;
curve.PostLoop = CurveLoopType.Linear;
curve.Add(new CurveKey2F()
{
Point = new Vector2F(0, 0),
Interpolation = SplineInterpolation.Hermite,
TangentIn = new Vector2F(1, 2),
TangentOut = new Vector2F(5, 4),
});
curve.Add(new CurveKey2F()
{
Point = new Vector2F(10, 3),
Interpolation = SplineInterpolation.Hermite,
TangentIn = new Vector2F(8, 2),
TangentOut = new Vector2F(2, -1),
});
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(-10, -20), curve.GetPoint(-10f)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F(15, 3 - 0.5f * 5), curve.GetPoint(15f)));
}
