public void GetLength()
{
BezierSegment2F b = new BezierSegment2F
{
Point1 = new Vector2F(1, 2),
ControlPoint1 = new Vector2F(4, 5),
ControlPoint2 = new Vector2F(7, 8),
Point2 = new Vector2F(10, 2),
};
float lowerBound = (b.Point2 - b.Point1).Length;
float upperBound = (b.Point2 - b.ControlPoint2).Length
+ (b.ControlPoint2 - b.ControlPoint1).Length
+ (b.ControlPoint1 - b.Point1).Length;
Assert.Less(lowerBound, b.GetLength(0, 1, 100, Numeric.EpsilonF));
Assert.Greater(upperBound, b.GetLength(0, 1, 100, Numeric.EpsilonF));
float length1 = b.GetLength(0, 1, 20, Numeric.EpsilonF);
float length2 = b.GetLengthWithDeCasteljau(20, Numeric.EpsilonF);
Assert.IsTrue(Numeric.AreEqual(length1, length2));
// Compare numerical integration method and de Casteljau method.
float approxLength = 0;
const float step = 0.0001f;
for (float u = 0; u <= 1.0f; u += step)
approxLength += (b.GetPoint(u) - b.GetPoint(u + step)).Length;
Assert.IsTrue(Numeric.AreEqual(approxLength, length1, 0.01f));
Assert.IsTrue(Numeric.AreEqual(b.GetLength(0, 1, 100, Numeric.EpsilonF), b.GetLength(0, 0.5f, 100, Numeric.EpsilonF) + b.GetLength(0.5f, 1, 100, Numeric.EpsilonF)));
Assert.IsTrue(Numeric.AreEqual(b.GetLength(0, 1, 100, Numeric.EpsilonF), b.GetLength(1, 0, 100, Numeric.EpsilonF)));
}
public void GetLength()
{
HermiteSegment2F s = new HermiteSegment2F
{
Point1 = new Vector2F(1, 2),
Tangent1 = (new Vector2F(10, 3) - new Vector2F(1, 2)) * 3,
Tangent2 = (new Vector2F(10, 2) - new Vector2F(7, 8)) * 3,
Point2 = new Vector2F(10, 2),
};
BezierSegment2F b = new BezierSegment2F
{
Point1 = new Vector2F(1, 2),
ControlPoint1 = new Vector2F(10, 3),
ControlPoint2 = new Vector2F(7, 8),
Point2 = new Vector2F(10, 2),
};
float length1 = s.GetLength(0, 1, 20, Numeric.EpsilonF);
float length2 = b.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 += (s.GetPoint(u) - s.GetPoint(u + step)).Length;
}
Assert.IsTrue(Numeric.AreEqual(approxLength, length1, 0.01f));
Assert.IsTrue(Numeric.AreEqual(s.GetLength(0, 1, 100, Numeric.EpsilonF), s.GetLength(0, 0.5f, 100, Numeric.EpsilonF) + s.GetLength(0.5f, 1, 100, Numeric.EpsilonF)));
Assert.IsTrue(Numeric.AreEqual(s.GetLength(0, 1, 100, Numeric.EpsilonF), s.GetLength(1, 0, 100, Numeric.EpsilonF)));
}
public void GetLength()
{
HermiteSegment2F s = new HermiteSegment2F
{
Point1 = new Vector2F(1, 2),
Tangent1 = (new Vector2F(10, 3) - new Vector2F(1, 2)) * 3,
Tangent2 = (new Vector2F(10, 2) - new Vector2F(7, 8)) * 3,
Point2 = new Vector2F(10, 2),
};
BezierSegment2F b = new BezierSegment2F
{
Point1 = new Vector2F(1, 2),
ControlPoint1 = new Vector2F(10, 3),
ControlPoint2 = new Vector2F(7, 8),
Point2 = new Vector2F(10, 2),
};
float length1 = s.GetLength(0, 1, 20, Numeric.EpsilonF);
float length2 = b.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 += (s.GetPoint(u) - s.GetPoint(u + step)).Length;
Assert.IsTrue(Numeric.AreEqual(approxLength, length1, 0.01f));
Assert.IsTrue(Numeric.AreEqual(s.GetLength(0, 1, 100, Numeric.EpsilonF), s.GetLength(0, 0.5f, 100, Numeric.EpsilonF) + s.GetLength(0.5f, 1, 100, Numeric.EpsilonF)));
Assert.IsTrue(Numeric.AreEqual(s.GetLength(0, 1, 100, Numeric.EpsilonF), s.GetLength(1, 0, 100, Numeric.EpsilonF)));
}
public void GetTangent()
{
BezierSegment2F b = new BezierSegment2F
{
Point1 = new Vector2F(1, 2),
ControlPoint1 = new Vector2F(10, 3),
ControlPoint2 = new Vector2F(7, 8),
Point2 = new Vector2F(10, 2),
};
Assert.IsTrue(Vector2F.AreNumericallyEqual(3 * (b.ControlPoint1 - b.Point1), b.GetTangent(0)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(3 * (b.Point2 - b.ControlPoint2), b.GetTangent(1)));
}
public void Flatten2FLengthZero()
{
var s = new BezierSegment2F
{
Point1 = new Vector2F(1, 1),
ControlPoint1 = new Vector2F(1, 1),
ControlPoint2 = new Vector2F(1, 1),
Point2 = new Vector2F(1, 1),
};
var points = new List<Vector2F>();
s.Flatten(points, 1, 1);
Assert.AreEqual(0, points.Count);
}
public void GetPoint()
{
BezierSegment2F b = new BezierSegment2F
{
Point1 = new Vector2F(1, 2),
ControlPoint1 = new Vector2F(10, 3),
ControlPoint2 = new Vector2F(7, 8),
Point2 = new Vector2F(10, 2),
};
Assert.IsTrue(Vector2F.AreNumericallyEqual(b.Point1, b.GetPoint(0)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(b.Point2, b.GetPoint(1)));
}
public void Flatten2FLengthZero()
{
var s = new BezierSegment2F
{
Point1 = new Vector2F(1, 1),
ControlPoint1 = new Vector2F(1, 1),
ControlPoint2 = new Vector2F(1, 1),
Point2 = new Vector2F(1, 1),
};
var points = new List <Vector2F>();
s.Flatten(points, 1, 1);
Assert.AreEqual(0, points.Count);
}
public void Flatten2FLargeTolerance()
{
var s = new BezierSegment2F
{
Point1 = new Vector2F(1, 1),
ControlPoint1 = new Vector2F(2, 2),
ControlPoint2 = new Vector2F(3, 3),
Point2 = new Vector2F(4, 4),
};
var points = new List<Vector2F>();
s.Flatten(points, 1, 10);
Assert.AreEqual(2, points.Count);
Assert.IsTrue(points.Contains(s.Point1));
Assert.IsTrue(points.Contains(s.Point2));
}
public void Flatten2FLargeTolerance()
{
var s = new BezierSegment2F
{
Point1 = new Vector2F(1, 1),
ControlPoint1 = new Vector2F(2, 2),
ControlPoint2 = new Vector2F(3, 3),
Point2 = new Vector2F(4, 4),
};
var points = new List <Vector2F>();
s.Flatten(points, 1, 10);
Assert.AreEqual(2, points.Count);
Assert.IsTrue(points.Contains(s.Point1));
Assert.IsTrue(points.Contains(s.Point2));
}
public void Flatten()
{
var s = new BezierSegment2F
{
Point1 = new Vector2F(1, 2),
ControlPoint1 = new Vector2F(4, 5),
ControlPoint2 = new Vector2F(7, 8),
Point2 = new Vector2F(10, 2),
};
var points = new List<Vector2F>();
var tolerance = 0.01f;
s.Flatten(points, 10, tolerance);
Assert.IsTrue(points.Contains(s.Point1));
Assert.IsTrue(points.Contains(s.Point2));
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 BezierSegment2F
{
Point1 = new Vector2F(1, 2),
ControlPoint1 = new Vector2F(4, 5),
ControlPoint2 = new Vector2F(7, 8),
Point2 = new Vector2F(10, 2),
};
var points = new List <Vector2F>();
var tolerance = 0.01f;
s.Flatten(points, 10, tolerance);
Assert.IsTrue(points.Contains(s.Point1));
Assert.IsTrue(points.Contains(s.Point2));
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 GetTangent()
{
HermiteSegment2F s = new HermiteSegment2F
{
Point1 = new Vector2F(1, 2),
Tangent1 = (new Vector2F(10, 3) - new Vector2F(1, 2)) * 3,
Tangent2 = (new Vector2F(10, 2) - new Vector2F(7, 8)) * 3,
Point2 = new Vector2F(10, 2),
};
BezierSegment2F b = new BezierSegment2F
{
Point1 = new Vector2F(1, 2),
ControlPoint1 = new Vector2F(10, 3),
ControlPoint2 = new Vector2F(7, 8),
Point2 = new Vector2F(10, 2),
};
Assert.IsTrue(Vector2F.AreNumericallyEqual(s.Tangent1, s.GetTangent(0)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(s.Tangent2, s.GetTangent(1)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(b.GetTangent(0.7f), s.GetTangent(0.7f)));
}
public void GetPoint()
{
HermiteSegment2F s = new HermiteSegment2F
{
Point1 = new Vector2F(1, 2),
Tangent1 = (new Vector2F(10, 3) - new Vector2F(1, 2)) * 3,
Tangent2 = (new Vector2F(10, 2) - new Vector2F(7, 8)) * 3,
Point2 = new Vector2F(10, 2),
};
BezierSegment2F b = new BezierSegment2F
{
Point1 = new Vector2F(1, 2),
ControlPoint1 = new Vector2F(10, 3),
ControlPoint2 = new Vector2F(7, 8),
Point2 = new Vector2F(10, 2),
};
Assert.IsTrue(Vector2F.AreNumericallyEqual(s.Point1, s.GetPoint(0)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(s.Point2, s.GetPoint(1)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(b.GetPoint(0.33f), s.GetPoint(0.33f)));
}
public void GetLength()
{
BezierSegment2F b = new BezierSegment2F
{
Point1 = new Vector2F(1, 2),
ControlPoint1 = new Vector2F(4, 5),
ControlPoint2 = new Vector2F(7, 8),
Point2 = new Vector2F(10, 2),
};
float lowerBound = (b.Point2 - b.Point1).Length;
float upperBound = (b.Point2 - b.ControlPoint2).Length
+ (b.ControlPoint2 - b.ControlPoint1).Length
+ (b.ControlPoint1 - b.Point1).Length;
Assert.Less(lowerBound, b.GetLength(0, 1, 100, Numeric.EpsilonF));
Assert.Greater(upperBound, b.GetLength(0, 1, 100, Numeric.EpsilonF));
float length1 = b.GetLength(0, 1, 20, Numeric.EpsilonF);
float length2 = b.GetLengthWithDeCasteljau(20, Numeric.EpsilonF);
Assert.IsTrue(Numeric.AreEqual(length1, length2));
// Compare numerical integration method and de Casteljau method.
float approxLength = 0;
const float step = 0.0001f;
for (float u = 0; u <= 1.0f; u += step)
{
approxLength += (b.GetPoint(u) - b.GetPoint(u + step)).Length;
}
Assert.IsTrue(Numeric.AreEqual(approxLength, length1, 0.01f));
Assert.IsTrue(Numeric.AreEqual(b.GetLength(0, 1, 100, Numeric.EpsilonF), b.GetLength(0, 0.5f, 100, Numeric.EpsilonF) + b.GetLength(0.5f, 1, 100, Numeric.EpsilonF)));
Assert.IsTrue(Numeric.AreEqual(b.GetLength(0, 1, 100, Numeric.EpsilonF), b.GetLength(1, 0, 100, Numeric.EpsilonF)));
}
