public static void Initialization()
{
CurveLimit curveLimitInitialize = new CurveLimit(curve);
Assert.AreEqual(CartesianCoordinate.Origin().X, curveLimitInitialize.Limit.X);
Assert.AreEqual(CartesianCoordinate.Origin().Y, curveLimitInitialize.Limit.Y);
}
public static void Initialization_at_Local_Origin_with_Radii()
{
// Expected Complex Results
CartesianCoordinate center = CartesianCoordinate.Origin();
Angle rotation = Angle.Origin();
double a = 5;
double b = 3;
double c = (a.Squared() - b.Squared()).Sqrt();
double e = c / a;
double p = a * (1 - e.Squared());
double xe = a.Squared() / c;
CartesianCoordinate vertexMajor1 = new CartesianCoordinate(a, 0);
CartesianCoordinate vertexMajor2 = new CartesianCoordinate(-a, 0);
CartesianCoordinate vertexMinor1 = new CartesianCoordinate(0, b);
CartesianCoordinate vertexMinor2 = new CartesianCoordinate(0, -b);
CartesianCoordinate focus1 = new CartesianCoordinate(c, 0);
CartesianCoordinate focus2 = new CartesianCoordinate(-c, 0);
CartesianCoordinate directrix1I = new CartesianCoordinate(xe, 0);
CartesianCoordinate directrix1J = new CartesianCoordinate(xe, 1);
CartesianCoordinate directrix2I = new CartesianCoordinate(-xe, 0);
CartesianCoordinate directrix2J = new CartesianCoordinate(-xe, 1);
// Initialization
EllipticalCurve curve = new EllipticalCurve(a, b, center, rotation, Tolerance);
// Simple properties
Assert.AreEqual(a, curve.DistanceFromVertexMajorToLocalOrigin, Tolerance);
Assert.AreEqual(b, curve.DistanceFromVertexMinorToMajorAxis, Tolerance);
Assert.AreEqual(c, curve.DistanceFromFocusToLocalOrigin, Tolerance);
Assert.AreEqual(e, curve.Eccentricity, Tolerance);
Assert.AreEqual(p, curve.SemilatusRectumDistance, Tolerance);
Assert.AreEqual(xe, curve.DistanceFromDirectrixToLocalOrigin, Tolerance);
Assert.AreEqual(xe - c, curve.DistanceFromFocusToDirectrix, Tolerance);
// Position properties
Assert.AreEqual(Angle.Origin(), curve.Rotation);
Assert.AreEqual(focus1, curve.Focus);
Assert.AreEqual(center, curve.LocalOrigin);
// Coordinate properties
Assert.AreEqual(vertexMajor1, curve.VerticesMajor.Item1);
Assert.AreEqual(vertexMajor2, curve.VerticesMajor.Item2);
Assert.AreEqual(vertexMinor1, curve.VerticesMinor.Item1);
Assert.AreEqual(vertexMinor2, curve.VerticesMinor.Item2);
Assert.AreEqual(vertexMajor1, curve.Range.Start.Limit);
Assert.AreEqual(vertexMajor1, curve.Range.End.Limit);
Assert.AreEqual(directrix1I, curve.Directrix.ControlPointI);
Assert.AreEqual(directrix1J, curve.Directrix.ControlPointJ);
// Complex Properties unique to Ellipse
Assert.AreEqual(focus2, curve.Focus2);
Assert.AreEqual(directrix2I, curve.Directrix2.ControlPointI);
Assert.AreEqual(directrix2J, curve.Directrix2.ControlPointJ);
}
public static void Initialization()
{
Curve curve = new LinearCurve(new CartesianCoordinate(-1, -2, Tolerance), new CartesianCoordinate(4, 3, Tolerance));
curve.Tolerance = Tolerance;
CurveRange range = new CurveRange(curve);
Assert.AreEqual(CartesianCoordinate.Origin(), range.Start.Limit);
Assert.AreEqual(CartesianCoordinate.Origin(), range.End.Limit);
}
/// <summary>
/// Initializes a new instance of the <see cref="BezierCurve"/> class.
/// </summary>
/// <param name="length">The length.</param>
/// <param name="numberOfControlPoints">The number of control points.</param>
/// <param name="tolerance">Tolerance to apply to the curve.</param>
public BezierCurve(
double length,
int numberOfControlPoints = _maxNumberOfControlPoints,
double tolerance = DEFAULT_TOLERANCE) : base(tolerance)
{
NumberOfControlPoints = getNumberOfControlPoints(numberOfControlPoints);
CartesianCoordinate pointI = CartesianCoordinate.Origin();
CartesianCoordinate pointJ = new CartesianCoordinate(length, 0);
double handleLength = getHandleLength(pointI, pointJ);
HandleI = new CurveHandle(pointI, handleLength);
HandleJ = getCurveHandleJ(pointJ, handleLength);
}
public static void Initialization_with_Coordinates_Results_in_Object_with_Immutable_Coordinates_Properties_List()
{
CartesianCoordinate localOriginInGlobal = new CartesianCoordinate(3, 2);
CartesianCoordinate localAxisXPtInGlobal = new CartesianCoordinate(5, 4);
Transformations transformations = new Transformations(localOriginInGlobal, localAxisXPtInGlobal);
AngularOffset angularOffset = new AngularOffset(Numbers.Pi / 4);
CartesianOffset offset = localOriginInGlobal.OffsetFrom(CartesianCoordinate.Origin());
Assert.AreEqual(localOriginInGlobal, transformations.LocalOrigin);
Assert.AreEqual(localAxisXPtInGlobal, transformations.LocalAxisX);
Assert.AreEqual(offset, transformations.Displacement);
Assert.AreEqual(angularOffset.ToAngle().Degrees, transformations.Rotation.ToAngle().Degrees, Tolerance);
}
public static void IsClosedCurve_Returns_False_When_Curve_Does_Not_Close_to_Form_a_Shape()
{
EllipticalCurve curve = new EllipticalCurve(a, b, CartesianCoordinate.Origin(), Angle.Origin(), Tolerance);
Assert.IsTrue(curve.Range.Start.Limit == curve.Range.End.Limit);
Assert.IsTrue(curve.IsClosedCurve());
// Change limits
CartesianCoordinate newRangeLimit = new CartesianCoordinate(-2, 2);
curve.Range.End.SetLimitByCoordinate(newRangeLimit);
Assert.IsFalse(curve.Range.Start.Limit == curve.Range.End.Limit);
Assert.IsFalse(curve.IsClosedCurve());
}
public static void Initialization_at_Local_Origin_with_Distances()
{
// Expected Complex Results
CartesianCoordinate center = CartesianCoordinate.Origin();
Angle rotation = Angle.Origin();
double a = 5;
double b = 2 * a;
double c = a;
double e = 1;
double p = 2 * a;
double xe = a;
CartesianCoordinate vertexMajor1 = center;
CartesianCoordinate vertexMinor1 = new CartesianCoordinate(a, b, Tolerance);
CartesianCoordinate vertexMinor2 = new CartesianCoordinate(a, -b, Tolerance);
CartesianCoordinate focus1 = new CartesianCoordinate(c, 0, Tolerance);
CartesianCoordinate directrix1I = new CartesianCoordinate(-xe, 0, Tolerance);
CartesianCoordinate directrix1J = new CartesianCoordinate(-xe, 1, Tolerance);
// Initialization
ParabolicCurve curve = new ParabolicCurve(a, center, rotation, Tolerance);
// Simple properties
Assert.AreEqual(0, curve.DistanceFromVertexMajorToLocalOrigin, Tolerance);
Assert.AreEqual(b, curve.DistanceFromVertexMinorToMajorAxis, Tolerance);
Assert.AreEqual(a, curve.DistanceFromFocusToLocalOrigin, Tolerance);
Assert.AreEqual(e, curve.Eccentricity, Tolerance);
Assert.AreEqual(p, curve.SemilatusRectumDistance, Tolerance);
Assert.AreEqual(xe, curve.DistanceFromDirectrixToLocalOrigin, Tolerance);
Assert.AreEqual(c + xe, curve.DistanceFromFocusToDirectrix, Tolerance);
// Position properties
Assert.AreEqual(Angle.Origin(), curve.Rotation);
Assert.AreEqual(focus1, curve.Focus);
Assert.AreEqual(center, curve.LocalOrigin);
// Coordinate properties
Assert.AreEqual(vertexMajor1, curve.VerticesMajor.Item1);
Assert.AreEqual(vertexMajor1, curve.VerticesMajor.Item2);
Assert.AreEqual(vertexMinor1, curve.VerticesMinor.Item1);
Assert.AreEqual(vertexMinor2, curve.VerticesMinor.Item2);
Assert.AreEqual(directrix1I, curve.Directrix.ControlPointI);
Assert.AreEqual(directrix1J, curve.Directrix.ControlPointJ);
Assert.AreEqual(vertexMajor1, curve.Range.Start.Limit);
Assert.AreEqual(vertexMajor1, curve.Range.End.Limit);
}
/// <summary>
/// Initializes a new instance of the <see cref="Transformations"/> class.
/// </summary>
/// <param name="localOriginInGlobal">The local origin in global coordinates.</param>
/// <param name="localAxisXPtInGlobal">Any point along the local x-axis in global coordinates.</param>
public Transformations(CartesianCoordinate localOriginInGlobal, CartesianCoordinate localAxisXPtInGlobal)
{
LocalOrigin = localOriginInGlobal;
LocalAxisX = localAxisXPtInGlobal;
Displacement = localOriginInGlobal.OffsetFrom(CartesianCoordinate.Origin());
if (localAxisXPtInGlobal.Y == localOriginInGlobal.Y)
{
Rotation = new AngularOffset();
}
else
{
Rotation = AngularOffset.CreateFromPoints(
localAxisXPtInGlobal,
localOriginInGlobal,
new CartesianCoordinate(localOriginInGlobal.X - 1, localOriginInGlobal.Y)
);
}
}
/// <summary>
/// The component second differentical as a function of the supplied parameter.
/// </summary>
/// <param name="parameter">The parameter, such as relative position between 0 & 1, or the angle in radians.</param>
/// <returns>System.Double.</returns>
public override CartesianCoordinate PrimeDoubleByParameter(double parameter)
{
return(CartesianCoordinate.Origin());
}
public static void Initialization_at_Offset_From_Origin_with_Distances(double x, double y)
{
// Expected Complex Results
CartesianCoordinate center = new CartesianCoordinate(x, y);
Angle rotation = Angle.Origin();
double a = 5;
double b = 3;
double c = (a.Squared() + b.Squared()).Sqrt();
double e = c / a;
double p = a * (e.Squared() - 1);
double xe = a.Squared() / c;
CartesianCoordinate vertexMajor1 = new CartesianCoordinate(a, 0);
CartesianCoordinate vertexMajor2 = new CartesianCoordinate(-a, 0);
CartesianCoordinate vertexMinor1 = new CartesianCoordinate(a, b);
CartesianCoordinate vertexMinor2 = new CartesianCoordinate(a, -b);
CartesianCoordinate vertexMinor1_2 = new CartesianCoordinate(-a, b);
CartesianCoordinate vertexMinor2_2 = new CartesianCoordinate(-a, -b);
CartesianCoordinate focus1 = new CartesianCoordinate(c, 0);
CartesianCoordinate focus2 = new CartesianCoordinate(-c, 0);
CartesianCoordinate directrix1I = new CartesianCoordinate(xe, 0);
CartesianCoordinate directrix1J = new CartesianCoordinate(xe, 1);
CartesianCoordinate directrix2I = new CartesianCoordinate(-xe, 0);
CartesianCoordinate directrix2J = new CartesianCoordinate(-xe, 1);
CartesianCoordinate Asymptote1I = CartesianCoordinate.Origin();
CartesianCoordinate Asymptote1J = vertexMinor1;
CartesianCoordinate Asymptote2I = CartesianCoordinate.Origin();
CartesianCoordinate Asymptote2J = vertexMinor2;
// Initialization
HyperbolicCurve curve = new HyperbolicCurve(a, b, center, rotation, Tolerance);
// Simple properties
Assert.AreEqual(a, curve.DistanceFromVertexMajorToLocalOrigin, Tolerance);
Assert.AreEqual(b, curve.DistanceFromVertexMinorToMajorAxis, Tolerance);
Assert.AreEqual(c, curve.DistanceFromFocusToLocalOrigin, Tolerance);
Assert.AreEqual(e, curve.Eccentricity, Tolerance);
Assert.AreEqual(p, curve.SemilatusRectumDistance, Tolerance);
Assert.AreEqual(xe, curve.DistanceFromDirectrixToLocalOrigin, Tolerance);
Assert.AreEqual(c - xe, curve.DistanceFromFocusToDirectrix, Tolerance);
// Position properties
Assert.AreEqual(rotation, curve.Rotation);
Assert.AreEqual(focus1, curve.Focus);
Assert.AreEqual(center, curve.LocalOrigin);
// Coordinate properties
Assert.AreEqual(vertexMajor1, curve.VerticesMajor.Item1);
Assert.AreEqual(vertexMajor2, curve.VerticesMajor.Item2);
Assert.AreEqual(vertexMinor1, curve.VerticesMinor.Item1);
Assert.AreEqual(vertexMinor2, curve.VerticesMinor.Item2);
Assert.AreEqual(vertexMajor1, curve.Range.Start.Limit);
Assert.AreEqual(vertexMajor1, curve.Range.End.Limit);
Assert.AreEqual(directrix1I, curve.Directrix.ControlPointI);
Assert.AreEqual(directrix1J, curve.Directrix.ControlPointJ);
// Complex Properties unique to Hyperbola
Assert.AreEqual(focus2, curve.Focus2);
Assert.AreEqual(directrix2I, curve.Directrix2.ControlPointI);
Assert.AreEqual(directrix2J, curve.Directrix2.ControlPointJ);
Assert.AreEqual(vertexMinor1_2, curve.VerticesMinor2.Item1);
Assert.AreEqual(vertexMinor2_2, curve.VerticesMinor2.Item2);
Assert.AreEqual(Asymptote1I, curve.Asymptotes.Item1.ControlPointI);
Assert.AreEqual(Asymptote1J, curve.Asymptotes.Item1.ControlPointJ);
Assert.AreEqual(Asymptote2I, curve.Asymptotes.Item2.ControlPointI);
Assert.AreEqual(Asymptote2J, curve.Asymptotes.Item2.ControlPointJ);
}