public void It_Returns_A_Vector_Rotated_By_An_Angle()
{
// Arrange
Vector3 vector = new Vector3(-7, 10, -5);
double rotationAngle1 = GSharkMath.ToRadians(-0.0000125);
Vector3 expectedResult1 = new Vector3(-7.0, 10.0, -5.0);
double rotationAngle2 = GSharkMath.ToRadians(0.0);
Vector3 expectedResult2 = new Vector3(-7.0, 10.0, -5.0);
double rotationAngle3 = GSharkMath.ToRadians(12.5);
Vector3 expectedResult3 = new Vector3(-7.454672, 10.649531, -2.239498);
double rotationAngle4 = GSharkMath.ToRadians(450);
Vector3 expectedResult4 = new Vector3(-2.867312, 4.09616, 12.206556);
Vector3 axis = new Vector3(10, 7, 0);
// Act
Vector3 result1 = vector.Rotate(axis, rotationAngle1);
Vector3 result2 = vector.Rotate(axis, rotationAngle2);
Vector3 result3 = vector.Rotate(axis, rotationAngle3);
Vector3 result4 = vector.Rotate(axis, rotationAngle4);
// Assert
result1.EpsilonEquals(expectedResult1, 1e-6).Should().Be(true);
result2.EpsilonEquals(expectedResult2, 1e-6).Should().Be(true);
result3.EpsilonEquals(expectedResult3, 1e-6).Should().Be(true);
result4.EpsilonEquals(expectedResult4, 1e-6).Should().Be(true);
}
public void It_Returns_A_Binomial_Coefficient(int n, int k, double resultValue)
{
// Act
double valToCheck = GSharkMath.GetBinomial(n, k);
// Assert
(System.Math.Abs(valToCheck - resultValue) < GSharkMath.Epsilon).Should().BeTrue();
}
public void Initializes_An_Arc_By_Three_Points()
{
// Arrange
Arc arc = _exampleArc3D;
// Assert
arc.Length.Should().BeApproximately(71.333203, GSharkMath.MaxTolerance);
arc.Radius.Should().BeApproximately(16.47719, GSharkMath.MaxTolerance);
GSharkMath.ToDegrees(arc.Angle).Should().BeApproximately(248.045414, GSharkMath.MaxTolerance);
}
public void It_Returns_A_Rotated_Plane()
{
// Arrange
Plane plane = BasePlaneByPoints;
// Act
Plane rotatedPlane = plane.Rotate(GSharkMath.ToRadians(30));
// Assert
rotatedPlane.XAxis.EpsilonEquals(new Vector3(-0.965926, -0.258819, 0), GSharkMath.MaxTolerance).Should().BeTrue();
rotatedPlane.YAxis.EpsilonEquals(new Vector3(-0.258819, 0.965926, 0), GSharkMath.MaxTolerance).Should().BeTrue();
rotatedPlane.ZAxis.EpsilonEquals(new Vector3(0, 0, -1), GSharkMath.MaxTolerance).Should().BeTrue();
}
public void It_Returns_The_Point_On_The_Circle_At_The_Give_Length(double length, double[] pts)
{
// Arrange
Point3 expectedPt = new Point3(pts[0], pts[1], pts[2]);
// Act
double normalizeLength = GSharkMath.RemapValue(length, new Interval(0.0, _circle2D.Length), new Interval(0.0, 1.0));
Point3 pt = _circle2D.PointAtLength(length);
Point3 ptNormalizedLength = _circle2D.PointAtNormalizedLength(normalizeLength);
// Assert
pt.EpsilonEquals(expectedPt, GSharkMath.MaxTolerance).Should().BeTrue();
pt.EpsilonEquals(ptNormalizedLength, GSharkMath.MaxTolerance).Should().BeTrue();
}
public ArcTests(ITestOutputHelper testOutput)
{
_testOutput = testOutput;
#region example
// Initializes an arc by plane, radius and angle.
double angle = GSharkMath.ToRadians(40);
_exampleArc2D = new Arc(Plane.PlaneXY, 15, angle);
// Initializes an arc by 3 points.
Point3 pt1 = new Point3(74.264416, 36.39316, -1.884313);
Point3 pt2 = new Point3(97.679126, 13.940616, 3.812853);
Point3 pt3 = new Point3(100.92443, 30.599893, -0.585116);
_exampleArc3D = new Arc(pt1, pt2, pt3);
#endregion
}
public void It_Creates_An_Aligned_BoundingBox()
{
// Arrange
Plane orientedPlane = Plane.PlaneXY.Rotate(GSharkMath.ToRadians(30));
var expectedMin = new Point3(45.662928, 59.230957, -4.22451);
var expectedMax = new Point3(77.622297, 78.520011, 3.812853);
// Act
var bBox = new BoundingBox(BoundingBoxCollection.BoundingBox3D(), orientedPlane);
// Assert
_testOutput.WriteLine(bBox.ToString());
bBox.Should().NotBeNull();
bBox.Min.DistanceTo(expectedMin).Should().BeLessThan(GSharkMath.MaxTolerance);
bBox.Max.DistanceTo(expectedMax).Should().BeLessThan(GSharkMath.MaxTolerance);
}
public void It_Returns_The_BoundingBox_Of_The_Arc()
{
// Arrange
double angle = GSharkMath.ToRadians(40);
Arc arc2D = new Arc(Plane.PlaneXY, 15, angle);
Arc arc3D = _exampleArc3D;
// Act
BoundingBox bBox2D = arc2D.BoundingBox();
BoundingBox bBox3D = arc3D.BoundingBox();
// Assert
bBox2D.Min.EpsilonEquals(new Vector3(11.490667, 0, 0), 6).Should().BeTrue();
bBox2D.Max.EpsilonEquals(new Vector3(15, 9.641814, 0), 6).Should().BeTrue();
bBox3D.Min.EpsilonEquals(new Vector3(69.115079, 8.858347, -1.884313), 6).Should().BeTrue();
bBox3D.Max.EpsilonEquals(new Vector3(102.068402, 36.39316, 5.246477), 6).Should().BeTrue();
}
public void It_Returns_A_Arc_Based_On_A_Start_And_An_End_Point_And_A_Direction()
{
// Arrange
Point3 startPt = new Point3(5, 5, 5);
Point3 endPt = new Point3(10, 15, 10);
Vector3 dir = new Vector3(3, 3, 0);
double radiusExpected = 12.247449;
double angleExpected = GSharkMath.ToRadians(60);
Point3 centerExpected = new Point3(0, 10, 15);
// Act
Arc arc = Arc.ByStartEndDirection(startPt, endPt, dir);
// Assert
arc.Angle.Should().BeApproximately(angleExpected, 1e-6);
arc.Radius.Should().BeApproximately(radiusExpected, 1e-6);
arc.Plane.Origin.EpsilonEquals(centerExpected, 1e-6).Should().BeTrue();
}
public void It_Returns_A_Rotated_Transformed_Matrix()
{
// Arrange
var center = new Point3(5, 5, 0);
double angleInRadians = GSharkMath.ToRadians(30);
// Act
Transform transform = Transform.Rotation(angleInRadians, center);
// Getting the angles.
Dictionary <string, double> angles = Transform.GetYawPitchRoll(transform);
// Getting the direction.
var axis = Transform.GetRotationAxis(transform);
// Assert
GSharkMath.ToDegrees(angles["Yaw"]).Should().BeApproximately(30, GSharkMath.Epsilon);
axis.Should().BeEquivalentTo(Vector3.ZAxis);
}
/// <summary>
/// Computes the derivatives at the given U and V parameters on a NURBS surface.<br/>
/// <para>Returns a two dimensional array containing the derivative vectors.<br/>
/// Increasing U partial derivatives are increasing row-wise.Increasing V partial derivatives are increasing column-wise.<br/>
/// Therefore, the[0,0] position is a point on the surface, [n,0] is the nth V partial derivative, the[n,n] position is twist vector or mixed partial derivative UV.</para>
/// <em>Corresponds to algorithm 4.4 from The NURBS Book by Piegl and Tiller.</em>
/// </summary>
/// <param name="surface">The surface.</param>
/// <param name="u">The u parameter at which to evaluate the derivatives.</param>
/// <param name="v">The v parameter at which to evaluate the derivatives.</param>
/// <param name="numDerivs">Number of derivatives to evaluate, set as default to 1.</param>
/// <returns>The derivatives.</returns>
internal static Vector3[,] RationalDerivatives(NurbsSurface surface, double u, double v, int numDerivs = 1)
{
if (u < 0.0 || u > 1.0)
{
throw new ArgumentException("The U parameter is not into the domain 0.0 to 1.0.");
}
if (v < 0.0 || v > 1.0)
{
throw new ArgumentException("The V parameter is not into the domain 0.0 to 1.0.");
}
var derivatives = Derivatives(surface, u, v, numDerivs);
Vector3[,] SKL = new Vector3[numDerivs + 1, numDerivs + 1];
for (int k = 0; k < numDerivs + 1; k++)
{
for (int l = 0; l < numDerivs - k + 1; l++)
{
Vector3 t = derivatives.Item1[k, l];
for (int j = 1; j < l + 1; j++)
{
t -= SKL[k, l - j] * (GSharkMath.GetBinomial(l, j) * derivatives.Item2[0, j]);
}
for (int i = 1; i < k + 1; i++)
{
t -= SKL[k - i, l] * (GSharkMath.GetBinomial(k, i) * derivatives.Item2[i, 0]);
Vector3 t2 = Vector3.Zero;
for (int j = 1; j < l + 1; j++)
{
t2 += SKL[k - i, l - j] * (GSharkMath.GetBinomial(l, j) * derivatives.Item2[i, j]);
}
t -= t2 * GSharkMath.GetBinomial(k, i);
}
SKL[k, l] = t / derivatives.Item2[0, 0];
}
}
return(SKL);
}
/// <summary>
/// Evaluates a point at the specif length.
/// </summary>
/// <param name="length">The length where to evaluate the point.</param>
/// <returns>The point at the length.</returns>
public override Point3 PointAtLength(double length)
{
if (length <= 0.0)
{
return(StartPoint);
}
if (length >= Length)
{
return(EndPoint);
}
double theta = GSharkMath.ToRadians((length * 360) / (Math.PI * 2 * Radius));
Vector3 xDir = Plane.XAxis * Math.Cos(theta) * Radius;
Vector3 yDir = Plane.YAxis * Math.Sin(theta) * Radius;
return(Plane.Origin + xDir + yDir);
}
public void It_Returns_A_Transformed_Plane()
{
// Arrange
var pt1 = new Point3(20, 20, 0);
var pt2 = new Point3(5, 5, 0);
var pt3 = new Point3(-5, 10, 0);
Plane plane = new Plane(pt1, pt2, pt3);
Transform translation = Transform.Translation(new Point3(10, 15, 0));
Transform rotation = Transform.Rotation(GSharkMath.ToRadians(30), new Point3(0, 0, 0));
var expectedOrigin = new Point3(17.320508, 42.320508, 0);
var expectedZAxis = new Vector3(0, 0, -1);
// Act
Transform combinedTransformations = translation.Combine(rotation);
Plane transformedPlane = plane.Transform(combinedTransformations);
// Assert
transformedPlane.Origin.EpsilonEquals(expectedOrigin, GSharkMath.MaxTolerance).Should().BeTrue();
transformedPlane.ZAxis.EpsilonEquals(expectedZAxis, GSharkMath.MaxTolerance).Should().BeTrue();
}
/// <summary>
/// Determines the derivatives of a curve at a given parameter.<br/>
/// <em>Corresponds to algorithm 4.2 from The NURBS Book by Piegl and Tiller.</em>
/// </summary>
/// <param name="curve">The curve object.</param>
/// <param name="parameter">Parameter on the curve at which the point is to be evaluated</param>
/// <param name="numberOfDerivatives">The number of derivatives required.</param>
/// <returns>The derivatives.</returns>
public static List <Vector3> RationalDerivatives(NurbsBase curve, double parameter, int numberOfDerivatives = 1)
{
List <Point4> derivatives = CurveDerivatives(curve, parameter, numberOfDerivatives);
// Array of derivative of A(t).
// Where A(t) is the vector - valued function whose coordinates are the first three coordinates
// of an homogenized pts.
// Correspond in the book to Aders.
List <Point3> rationalDerivativePoints = Point4.RationalPoints(derivatives);
// Correspond in the book to wDers.
List <double> weightDers = Point4.GetWeights(derivatives);
List <Vector3> CK = new List <Vector3>();
for (int k = 0; k < numberOfDerivatives + 1; k++)
{
Point3 rationalDerivativePoint = rationalDerivativePoints[k];
for (int i = 1; i < k + 1; i++)
{
double valToMultiply = GSharkMath.GetBinomial(k, i) * weightDers[i];
var pt = CK[k - i];
for (int j = 0; j < rationalDerivativePoint.Size; j++)
{
rationalDerivativePoint[j] = rationalDerivativePoint[j] - valToMultiply * pt[j];
}
}
for (int j = 0; j < rationalDerivativePoint.Size; j++)
{
rationalDerivativePoint[j] = rationalDerivativePoint[j] * (1 / weightDers[0]);
}
CK.Add(rationalDerivativePoint);
}
// Return C(t) derivatives.
return(CK);
}
/// <summary>
/// Constructs the string representation of the vector.
/// </summary>
/// <returns>The vector in string format.</returns>
public override string ToString()
{
return(string.Join(",", this.Select(e => GSharkMath.Truncate(e))));
}
public void It_Checks_If_A_Double_Is_Valid(double val, bool expectedResult)
{
GSharkMath.IsValidDouble(val).Should().Be(expectedResult);
}
public void It_Returns_The_Degree_From_Radians(double radians, double degreeExpected)
{
System.Math.Round(GSharkMath.ToDegrees(radians), 0).Should().Be(degreeExpected);
}
/// <summary>
/// Evaluates a point at the normalized length.
/// </summary>
/// <param name="normalizedLength">The length factor is normalized between 0.0 and 1.0.</param>
/// <returns>The point at the length.</returns>
public override Point3 PointAtNormalizedLength(double normalizedLength)
{
double length = GSharkMath.RemapValue(normalizedLength, new Interval(0.0, 1.0), new Interval(0.0, Length));
return(PointAtLength(length));
}
/// <summary>
/// Elevates the degree of a curve.
/// <em>Implementation of Algorithm A5.9 of The NURBS Book by Piegl and Tiller.</em>
/// </summary>
/// <param name="curve">The object curve to elevate.</param>
/// <param name="finalDegree">The expected final degree. If the supplied degree is less or equal the curve is returned unmodified.</param>
/// <returns>The curve after degree elevation.</returns>
internal static NurbsBase ElevateDegree(NurbsBase curve, int finalDegree)
{
if (finalDegree <= curve.Degree)
{
return(curve);
}
int n = curve.Knots.Count - curve.Degree - 2;
int p = curve.Degree;
KnotVector U = curve.Knots;
List <Point4> Pw = curve.ControlPoints;
int t = finalDegree - curve.Degree; // Degree elevate a curve t times.
// local arrays.
double[,] bezalfs = new double[p + t + 1, p + 1];
Point4[] bpts = new Point4[p + 1];
Point4[] ebpts = new Point4[p + t + 1];
Point4[] nextbpts = new Point4[p - 1];
double[] alphas = new double[p - 1];
int m = n + p + 1;
int ph = finalDegree;
int ph2 = (int)Math.Floor((double)(ph / 2));
// Output values;
List <Point4> Qw = new List <Point4>();
KnotVector Uh = new KnotVector();
// Compute Bezier degree elevation coefficients.
bezalfs[0, 0] = bezalfs[ph, p] = 1.0;
for (int i = 1; i <= ph2; i++)
{
double inv = 1.0 / GSharkMath.GetBinomial(ph, i);
int mpi = Math.Min(p, i);
for (int j = Math.Max(0, i - t); j <= mpi; j++)
{
bezalfs[i, j] = inv * GSharkMath.GetBinomial(p, j) * GSharkMath.GetBinomial(t, i - j);
}
}
for (int i = ph2 + 1; i <= ph - 1; i++)
{
int mpi = Math.Min(p, i);
for (int j = Math.Max(0, i - t); j <= mpi; j++)
{
bezalfs[i, j] = bezalfs[ph - i, p - j];
}
}
int mh = ph;
int kind = ph + 1;
int r = -1;
int a = p;
int b = p + 1;
int cind = 1;
double ua = U[0];
Qw.Add(Pw[0]);
for (int i = 0; i <= ph; i++)
{
Uh.Add(ua);
}
// Initialize first Bezier segment.
for (int i = 0; i <= p; i++)
{
bpts[i] = Pw[i];
}
// Big loop thru knot vector.
while (b < m)
{
int i = b;
while (b < m && Math.Abs(U[b] - U[b + 1]) < GSharkMath.Epsilon)
{
b += 1;
}
int mul = b - i + 1;
mh = mh + mul + t;
double ub = U[b];
int oldr = r;
r = p - mul;
// Insert knot U[b] r times.
// Checks for integer arithmetic.
int lbz = (oldr > 0) ? (int)Math.Floor((double)((2 + oldr) / 2)) : 1;
int rbz = (r > 0) ? (int)Math.Floor((double)(ph - (r + 1) / 2)) : ph;
if (r > 0)
{
// Inserts knot to get Bezier segment.
double numer = ub - ua;
for (int k = p; k > mul; k--)
{
alphas[k - mul - 1] = (numer / (U[a + k] - ua));
}
for (int j = 1; j <= r; j++)
{
int save = r - j;
int s = mul + j;
for (int k = p; k >= s; k--)
{
bpts[k] = Point4.Interpolate(bpts[k], bpts[k - 1], alphas[k - s]);
}
nextbpts[save] = bpts[p];
}
}
// End of insert knot.
// Degree elevate Bezier.
for (int j = lbz; j <= ph; j++)
{
ebpts[j] = Point4.Zero;
int mpi = Math.Min(p, j);
for (int k = Math.Max(0, j - t); k <= mpi; k++)
{
ebpts[j] += bpts[k] * bezalfs[j, k];
}
}
if (oldr > 1)
{
// Must remove knot u=U[a] oldr times.
int first = kind - 2;
int last = kind;
double den = ub - ua;
double bet = (ub - Uh[kind - 1]) / den;
for (int tr = 1; tr < oldr; tr++)
{
// Knot removal loop.
int ii = first;
int jj = last;
int kj = jj - kind + 1;
while (jj - ii > tr)
{
// Loop and compute the new control points for one removal step.
if (ii < cind)
{
double alf = (ub - Uh[ii]) / (ua - Uh[ii]);
Qw.Add(Point4.Interpolate(Qw[ii], Qw[ii - 1], alf));
}
if (jj >= lbz)
{
if (jj - tr <= kind - ph + oldr)
{
double gam = (ub - Uh[jj - tr]) / den;
ebpts[kj] = Point4.Interpolate(ebpts[kj], ebpts[kj + 1], gam);
}
else
{
ebpts[kj] = Point4.Interpolate(ebpts[kj], ebpts[kj + 1], bet);
}
}
ii += 1;
jj -= 1;
kj -= 1;
}
first -= 1;
last += 1;
}
}
// End of removing knot, n = U[a].
if (a != p)
{
// Load the knot ua.
for (int j = 0; j < ph - oldr; j++)
{
Uh.Add(ua);
}
}
for (int j = lbz; j <= rbz; j++)
{
// Load control points into Qw.
Qw.Add(ebpts[j]);
}
if (b < m)
{
// Set up for the next pass thru loop.
for (int j = 0; j < r; j++)
{
bpts[j] = nextbpts[j];
}
for (int j = r; j <= p; j++)
{
bpts[j] = Pw[b - p + j];
}
a = b;
b += 1;
ua = ub;
}
else
{
// End knot.
for (int j = 0; j <= ph; j++)
{
Uh.Add(ub);
}
}
}
return(new NurbsCurve(finalDegree, Uh, Qw));
}
/// <summary>
/// Gets the text representation of an arc.
/// </summary>
/// <returns>Text value.</returns>
public override string ToString()
{
return($"Arc(R:{Radius} - A:{GSharkMath.ToDegrees(Angle)})");
}
public void It_Returns_The_Radians_From_Degree(double degree, double radiansExpected)
{
System.Math.Round(GSharkMath.ToRadians(degree), 6).Should().Be(radiansExpected);
}