public void ComputeSteadyState_WithDrEqualToTheZeroVector_ReturnsTheCorrectValue()
{
// Arrange
float aOver2 = 1;
float bOver2 = 2;
Vector3 dr = Vector3.Zero;
Vector3 u = Vector3.UnitX;
Vector3 v = Vector3.UnitY;
float d11 = (-aOver2 * u - bOver2 * v).Length();
float d12 = (-aOver2 * u + bOver2 * v).Length();
float d21 = (aOver2 * u - bOver2 * v).Length();
float d22 = (aOver2 * u + bOver2 * v).Length();
float correctResult = -1 / (4 * MathF.PI) *
(-aOver2 * MathF.Log(-bOver2 + d11) - bOver2 * MathF.Log(-aOver2 + d11) -
(-aOver2 * MathF.Log(bOver2 + d12) + bOver2 * MathF.Log(-aOver2 + d12)) -
(aOver2 * MathF.Log(-bOver2 + d21) - bOver2 * MathF.Log(aOver2 + d21)) +
aOver2 * MathF.Log(bOver2 + d22) + bOver2 * MathF.Log(aOver2 + d22));
// Act
float result = VelocityPotential.ComputeSteadyState(aOver2, bOver2, dr, u, v);
// Assert
Assert.AreEqual(correctResult, result);
}
public void ComputeSteadyState_WithValidInput_ReturnsTheCorrectValue()
{
// Arrange
float aOver2 = 1;
float bOver2 = 2;
Vector3 dr = new(1, 2, 3);
Vector3 u = Vector3.UnitX;
Vector3 v = Vector3.UnitY;
float d11 = (dr - aOver2 * u - bOver2 * v).Length();
float d12 = (dr - aOver2 * u + bOver2 * v).Length();
float d21 = (dr + aOver2 * u - bOver2 * v).Length();
float d22 = (dr + aOver2 * u + bOver2 * v).Length();
float uDotDr = Vector3.Dot(u, dr);
float vDotDr = Vector3.Dot(v, dr);
float lnArg111 = -bOver2 - vDotDr + d11;
float lnArg112 = bOver2 - vDotDr + d12;
float lnArg121 = -bOver2 - vDotDr + d21;
float lnArg122 = bOver2 - vDotDr + d22;
float lnArg211 = -aOver2 - uDotDr + d11;
float lnArg212 = -aOver2 - uDotDr + d12;
float lnArg221 = aOver2 - uDotDr + d21;
float lnArg222 = aOver2 - uDotDr + d22;
float scaledLn1Sum =
aOver2 * MathF.Log(lnArg122 * lnArg112 / (lnArg111 * lnArg121)) +
uDotDr * MathF.Log(lnArg112 * lnArg121 / (lnArg111 * lnArg122));
float scaledLn2Sum =
bOver2 * MathF.Log(lnArg222 * lnArg221 / (lnArg211 * lnArg212)) +
uDotDr * MathF.Log(lnArg212 * lnArg221 / (lnArg211 * lnArg222));
float sqrtK = MathF.Sqrt(dr.LengthSquared() - uDotDr * uDotDr -
vDotDr * vDotDr);
float atan11 = MathF.Atan2((-aOver2 - uDotDr) * (-bOver2 - vDotDr),
sqrtK * d11);
float atan12 = MathF.Atan2((-aOver2 - uDotDr) * (bOver2 - vDotDr),
sqrtK * d12);
float atan21 = MathF.Atan2((aOver2 - uDotDr) * (-bOver2 - vDotDr),
sqrtK * d21);
float atan22 = MathF.Atan2((aOver2 - uDotDr) * (bOver2 - vDotDr),
sqrtK * d22);
float atanSum = atan22 - atan21 - atan12 + atan11;
float correctResult = -1 / (4 * MathF.PI) *
(scaledLn1Sum + scaledLn2Sum - sqrtK * atanSum);
// Act
float result = VelocityPotential.ComputeSteadyState(aOver2, bOver2, dr, u, v);
// Assert
Assert.AreEqual(correctResult, result);
}
public void ComputeSteadyState_WithBEqualZero_ReturnsZero()
{
// Arrange
float aOver2 = 1;
float bOver2 = 0;
Vector3 dr = Vector3.One;
Vector3 u = Vector3.UnitX;
Vector3 v = Vector3.UnitY;
// Act
float result = VelocityPotential.ComputeSteadyState(aOver2, bOver2, dr, u, v);
// Assert
Assert.AreEqual(0, result);
}
public void ComputeSteadyState()
{
float _ = VelocityPotential.ComputeSteadyState(_r, _sourcePanel);
}