public void GetLength()
{
BezierSegment3F b = new BezierSegment3F
{
Point1 = new Vector3F(1, 2, 3),
ControlPoint1 = new Vector3F(4, 5, 6),
ControlPoint2 = new Vector3F(7, 8, 19),
Point2 = new Vector3F(10, 2, 12),
};
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 GetPoint()
{
BezierSegment3F b = new BezierSegment3F
{
Point1 = new Vector3(1, 2, 3),
ControlPoint1 = new Vector3(10, 3, 6),
ControlPoint2 = new Vector3(7, 8, 19),
Point2 = new Vector3(10, 2, 12),
};
Assert.IsTrue(Vector3.AreNumericallyEqual(b.Point1, b.GetPoint(0)));
Assert.IsTrue(Vector3.AreNumericallyEqual(b.Point2, b.GetPoint(1)));
}
public void GetPoint()
{
BezierSegment3F b = new BezierSegment3F
{
Point1 = new Vector3F(1, 2, 3),
ControlPoint1 = new Vector3F(10, 3, 6),
ControlPoint2 = new Vector3F(7, 8, 19),
Point2 = new Vector3F(10, 2, 12),
};
Assert.IsTrue(Vector3F.AreNumericallyEqual(b.Point1, b.GetPoint(0)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(b.Point2, b.GetPoint(1)));
}
public void GetLength()
{
BezierSegment3F b = new BezierSegment3F
{
Point1 = new Vector3(1, 2, 3),
ControlPoint1 = new Vector3(4, 5, 6),
ControlPoint2 = new Vector3(7, 8, 19),
Point2 = new Vector3(10, 2, 12),
};
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 GetPoint()
{
HermiteSegment3F s = new HermiteSegment3F
{
Point1 = new Vector3F(1, 2, 3),
Tangent1 = (new Vector3F(10, 3, 6) - new Vector3F(1, 2, 3)) * 3,
Tangent2 = (new Vector3F(10, 2, 12) - new Vector3F(7, 8, 19)) * 3,
Point2 = new Vector3F(10, 2, 12),
};
BezierSegment3F b = new BezierSegment3F
{
Point1 = new Vector3F(1, 2, 3),
ControlPoint1 = new Vector3F(10, 3, 6),
ControlPoint2 = new Vector3F(7, 8, 19),
Point2 = new Vector3F(10, 2, 12),
};
Assert.IsTrue(Vector3F.AreNumericallyEqual(s.Point1, s.GetPoint(0)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(s.Point2, s.GetPoint(1)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(b.GetPoint(0.33f), s.GetPoint(0.33f)));
}
public void GetPoint()
{
HermiteSegment3F s = new HermiteSegment3F
{
Point1 = new Vector3F(1, 2, 3),
Tangent1 = (new Vector3F(10, 3, 6) - new Vector3F(1, 2, 3)) * 3,
Tangent2 = (new Vector3F(10, 2, 12) - new Vector3F(7, 8, 19)) * 3,
Point2 = new Vector3F(10, 2, 12),
};
BezierSegment3F b = new BezierSegment3F
{
Point1 = new Vector3F(1, 2, 3),
ControlPoint1 = new Vector3F(10, 3, 6),
ControlPoint2 = new Vector3F(7, 8, 19),
Point2 = new Vector3F(10, 2, 12),
};
Assert.IsTrue(Vector3F.AreNumericallyEqual(s.Point1, s.GetPoint(0)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(s.Point2, s.GetPoint(1)));
Assert.IsTrue(Vector3F.AreNumericallyEqual(b.GetPoint(0.33f), s.GetPoint(0.33f)));
}