public void Priority_OfACircleEvent_ShouldMatchThePriorityCalculatedByTrigonometry
(CircleEvent circle)
{
// Fixture setup
var a = circle.LeftArc.Site.Position;
var b = circle.MiddleArc.Site.Position;
var c = circle.RightArc.Site.Position;
var center = (a - b).CrossMultiply(c - b).Normalize();
var colatitudeOfCenter = Trig.InverseCosine(center[2]);
var radius = Trig.InverseCosine(a.ScalarMultiply(center));
var isOnOutsideOfSphere = colatitudeOfCenter + radius <= Constants.Pi;
var sign = isOnOutsideOfSphere ? 1 : -1;
var expectedPriority = sign * (1 + Trig.Cosine(colatitudeOfCenter + radius));
// Exercise system
var priority = circle.Priority;
// Verify outcome
var failureString =
String.Format(
"Expected priority was {0}\nActual priority was {1}",
expectedPriority,
priority);
Assert.True(Number.AlmostEqual(expectedPriority, priority, Tolerance), failureString);
// Teardown
}
public void Priority_OfACircleThrough0N45EAnd45N0EAnd0N45W_ShouldBeCorrect()
{
// Fixture setup
var arcA = new Arc {
Site = Utilities.SiteAt(90, 45)
};
var arcB = new Arc {
Site = Utilities.SiteAt(45, 0)
};
var arcC = new Arc {
Site = Utilities.SiteAt(90, -45)
};
var circle = new CircleEvent(arcA, arcB, arcC);
// Exercise system
var result = circle.Priority;
// Verify outcome
var expectedResult = -Trig.Cosine(Trig.DegreeToRadian(135)) - 1;
Debug.WriteLine(expectedResult);
var failureString = String.Format("Priority was {0}", result);
Assert.True(Number.AlmostEqual(result, expectedResult, Tolerance), failureString);
// Teardown
}
public static Vector3 CartesianCoordinates(double colatitude, double azimuth)
{
var x = Trig.Sine(colatitude) * Trig.Cosine(azimuth);
var y = Trig.Sine(colatitude) * Trig.Sine(azimuth);
var z = Trig.Cosine(colatitude);
return(new Vector3(x, y, z));
}
/// <summary>
/// Create a vector at the specified colatitude and azimuth at unit distance from the origin.
/// </summary>
public static Vector NewVector(double colatitude, double azimuth)
{
var x = Trig.Sine(colatitude) * Trig.Cosine(azimuth);
var y = Trig.Sine(colatitude) * Trig.Sine(azimuth);
var z = Trig.Cosine(colatitude);
return(new Vector(new [] { x, y, z }));
}
public void CanComputeCosine(
[Values(0.0, 8388608, 1.19209289550780998537e-7, -8388608, -1.19209289550780998537e-7)] double value,
[Values(1.0, -0.90175467375875928, 0.99999999999999289, -0.90175467375875928, 0.99999999999999289)] double expected)
{
var actual = Trig.Cosine(value);
AssertHelpers.AlmostEqual(expected, actual, 14);
}
private double[] VectorAt(double colatitude, float azimuth)
{
colatitude = Mathf.Deg2Rad * colatitude;
azimuth = Mathf.Deg2Rad * azimuth;
var x = Trig.Sine(colatitude) * Trig.Cosine(azimuth);
var y = Trig.Sine(colatitude) * Trig.Sine(azimuth);
var z = Trig.Cosine(colatitude);
return(new double[] { x, y, z });
}
public Vector3 CreateVectorAboveSweepline(IFixture fixture)
{
var randomZ = (-1 + 2 * _random.NextDouble());
var randomAzimuth = Constants.Pi * _random.NextDouble();
var x = Math.Sqrt(1.0 - randomZ * randomZ) * Trig.Cosine(randomAzimuth);
var y = Math.Sqrt(1.0 - randomZ * randomZ) * Trig.Sine(randomAzimuth);
var z = randomZ;
return(new Vector3(x, y, z));
}
BuildCoefficientsForLevels(
int levels
)
{
if (_realCoefficients[levels, 0] != null)
{
return;
}
int M = 1;
double uRealFw, uImagFw, uRealBw, uImagBw, angle, wRreal, wImag, uwI;
for (int level = 1; level <= levels; level++, M <<= 1)
{
if (_realCoefficients[level, 0] != null)
{
continue;
}
uRealFw = uRealBw = 1;
uImagFw = uImagBw = 0;
angle = Constants.Pi / M;
wRreal = Trig.Cosine(angle);
wImag = Trig.Sine(angle);
double[] realForward = new double[M];
double[] imagForward = new double[M];
double[] realBackward = new double[M];
double[] imagBackward = new double[M];
for (int i = 0; i < M; i++)
{
realForward[i] = uRealFw;
imagForward[i] = uImagFw;
realBackward[i] = uRealBw;
imagBackward[i] = uImagBw;
uwI = uImagFw * wRreal - uRealFw * wImag;
uRealFw = uRealFw * wRreal + uImagFw * wImag;
uImagFw = uwI;
uwI = uImagBw * wRreal + uRealBw * wImag;
uRealBw = uRealBw * wRreal - uImagBw * wImag;
uImagBw = uwI;
}
_realCoefficients[level, 0] = realForward;
_imagCoefficients[level, 0] = imagForward;
_realCoefficients[level, 1] = realBackward;
_imagCoefficients[level, 1] = imagBackward;
}
}
BuildCoefficientsForLevels(int levels)
{
if (_realCoefficients[levels, 0] != null)
{
return;
}
int m = 1;
for (int level = 1; level <= levels; level++, m <<= 1)
{
if (_realCoefficients[level, 0] != null)
{
continue;
}
double uRealFw = 1;
double uRealBw = 1;
double uImagFw = 0;
double uImagBw = 0;
double angle = Constants.Pi / m;
double wRreal = Trig.Cosine(angle);
double wImag = Trig.Sine(angle);
double[] realForward = new double[m];
double[] imagForward = new double[m];
double[] realBackward = new double[m];
double[] imagBackward = new double[m];
for (int i = 0; i < m; i++)
{
realForward[i] = uRealFw;
imagForward[i] = uImagFw;
realBackward[i] = uRealBw;
imagBackward[i] = uImagBw;
double uwI = (uImagFw * wRreal) - (uRealFw * wImag);
uRealFw = (uRealFw * wRreal) + (uImagFw * wImag);
uImagFw = uwI;
uwI = (uImagBw * wRreal) + (uRealBw * wImag);
uRealBw = (uRealBw * wRreal) - (uImagBw * wImag);
uImagBw = uwI;
}
_realCoefficients[level, 0] = realForward;
_imagCoefficients[level, 0] = imagForward;
_realCoefficients[level, 1] = realBackward;
_imagCoefficients[level, 1] = imagBackward;
}
}
private Vector3 CreateVectorBelowLast()
{
var z = -1.0 + (1 + _maxZ) * _random.NextDouble();
_maxZ = z;
var azimuth = 2 * Constants.Pi * _random.NextDouble();
var x = Math.Sqrt(1 - z * z) * Trig.Cosine(azimuth);
var y = Math.Sqrt(1 - z * z) * Trig.Sine(azimuth);
return(new Vector3(x, y, z));
}
public Vector3 CreateVectorAboveSweepline(IFixture fixture)
{
var sweepline = fixture.Create <Sweepline>();
var sweeplineZ = Trig.Cosine(sweepline.Colatitude);
var randomZ = (sweeplineZ + (1 - sweeplineZ) * _random.NextDouble());
var randomAzimuth = Constants.Pi * _random.NextDouble();
var x = Math.Sqrt(1.0 - randomZ * randomZ) * Trig.Cosine(randomAzimuth);
var y = Math.Sqrt(1.0 - randomZ * randomZ) * Trig.Sine(randomAzimuth);
var z = randomZ;
return(new Vector3(x, y, z));
}
public void Test()
{
// Fixture setup
var arcA = new Arc {
Site = Utilities.SiteAt(45, -45)
};
var arcB = new Arc {
Site = Utilities.SiteAt(0, 0)
};
var arcC = new Arc {
Site = Utilities.SiteAt(45, 45)
};
var circle = new CircleEvent(arcA, arcB, arcC);
var a = arcA.Site.Position;
var b = arcB.Site.Position;
var c = arcC.Site.Position;
var center = (a - b).CrossMultiply(c - b).Normalize();
var colatitudeOfCenter = Trig.InverseCosine(center[2]);
var radius = Trig.InverseCosine(a.ScalarMultiply(center));
var isOnOutsideOfSphere = colatitudeOfCenter + radius <= Constants.Pi;
var sign = isOnOutsideOfSphere ? 1 : -1;
var expectedPriority = sign * (1 + Trig.Cosine(colatitudeOfCenter + radius));
// Exercise system
var priority = circle.Priority;
Debug.WriteLine(expectedPriority);
Debug.WriteLine(Trig.RadianToDegree(colatitudeOfCenter));
Debug.WriteLine(Trig.RadianToDegree(radius));
// Verify outcome
var failureString =
String.Format(
"Expected priority was {0}\nActual priority was {1}",
expectedPriority,
priority);
Assert.True(Number.AlmostEqual(expectedPriority, priority, Tolerance), failureString);
// Teardown
}
public void Vectors_ShouldAllBeAboveSweepline(List <Vector3> vectors, Sweepline anonymousSweepline)
{
// Fixture setup
// Exercise system
// Verify outcome
var expectedResult = Trig.Cosine(anonymousSweepline.Colatitude);
foreach (var vector in vectors)
{
var result = vector[2];
var failureString = String.Format("Had Z {0}, expected Z was {1}", result, expectedResult);
Assert.True(result >= expectedResult, failureString);
}
// Teardown
}
public void TestExponential()
{
// exp(0) = 1
Complex zero = Complex.Zero;
Complex expZero = zero.Exponential();
Assert.That(expZero.Real, Is.EqualTo(1d), "Re{exp(0)} = 1");
Assert.That(expZero.Imag, Is.EqualTo(0d), "Im{exp(0)} = 0");
// exp(1) = e
Complex one = Complex.One;
Complex expOne = one.Exponential();
Assert.That(expOne.Real, Is.EqualTo(Constants.E), "Re{exp(1)} = e");
Assert.That(expOne.Imag, Is.EqualTo(0d), "Im{exp(1)} = 0");
// exp(i) = cos(1) + sin(1) * i
Complex I = Complex.I;
Complex expI = I.Exponential();
Assert.That(expI.Real, Is.EqualTo(Trig.Cosine(1d)), "Re{exp(i)} = cos(1)");
Assert.That(expI.Imag, Is.EqualTo(Trig.Sine(1d)), "Im{exp(i)} = sin(1)");
// exp(-1) = 1/e
Complex mOne = -Complex.One;
Complex expMOne = mOne.Exponential();
Assert.That(expMOne.Real, Is.EqualTo(1.0 / Constants.E), "Re{exp(-1)} = 1/e");
Assert.That(expMOne.Imag, Is.EqualTo(0d), "Im{exp(-1)} = 0");
// exp(-i) = cos(1) - sin(1) * i
Complex mI = -Complex.I;
Complex expMI = mI.Exponential();
Assert.That(expMI.Real, Is.EqualTo(Trig.Cosine(1d)), "Re{exp(-i)} = cos(1)");
Assert.That(expMI.Imag, Is.EqualTo(-Trig.Sine(1d)), "Im{exp(-i)} = -sin(1)");
// exp(i+1) = e * cos(1) + e * sin(1) * i
Complex onePlusI = Complex.One + Complex.I;
Complex expOnePlusI = onePlusI.Exponential();
Assert.That(expOnePlusI.Real, Is.EqualTo(Constants.E * Trig.Cosine(1d)), "Re{exp(i+1)} = e * cos(1)");
Assert.That(expOnePlusI.Imag, Is.EqualTo(Constants.E * Trig.Sine(1d)), "Im{exp(i+1)} = e * sin(1)");
}
/// <summary>Trigonometric Cosine (Cosinus) of an angle in radians</summary>
public RealValue Cosine()
{
return(new RealValue(Trig.Cosine(_dataValue)));
}
public static Vector3 PointOnEllipse(IArc arc, float azimuth, Sweepline sweepline)
{
var direction = new Generator.Vector3(Trig.Cosine(azimuth), Trig.Sine(azimuth), 0);
return(arc.PointAt(direction, sweepline).ToUnityVector3());
}
public void CanComputeCosine(double value, double expected)
{
var actual = Trig.Cosine(value);
AssertHelpers.AlmostEqual(expected, actual, 14);
}