public virtual Point3 ClosestPoint(Point3 point)
{
double t = Analyze.Curve.ClosestParameter(this, point);
Point3 pointAt = Evaluate.Curve.PointAt(this, t);
return(Point4.PointDehomogenizer(pointAt));
}
protected NurbsBase(int degree, KnotVector knots, List <Point4> controlPoints)
{
if (controlPoints is null)
{
throw new ArgumentNullException(nameof(controlPoints));
}
if (knots is null)
{
throw new ArgumentNullException(nameof(knots));
}
if (degree < 1)
{
throw new ArgumentException("Degree must be greater than 1!");
}
if (knots.Count != controlPoints.Count + degree + 1)
{
throw new ArgumentException("Number of controlPoints + degree + 1 must equal knots length!");
}
if (!knots.IsValid(degree, controlPoints.Count))
{
throw new ArgumentException("Invalid knot format! Should begin with degree + 1 repeats and end with degree + 1 repeats!");
}
Weights = Point4.GetWeights(controlPoints);
Degree = degree;
Knots = knots;
ControlPointLocations = Point4.PointDehomogenizer1d(controlPoints);
ControlPoints = controlPoints;
}
/// <summary>
/// Initializes a new point by copying coordinates from a four-dimensional point.
/// The first three coordinates are divided by the last one.
/// If the W (fourth) dimension of the input point is zero, then it will be discarded.
/// </summary>
/// <param name="point">A point.</param>
public Point3(Point4 point)
{
double w = (Math.Abs(point.W - 1.0) > GSharkMath.Epsilon && point.W != 0.0) ? 1.0 / point.W : 1.0;
X = point.X * w;
Y = point.Y * w;
Z = point.Z * w;
}
/// <summary>
/// Internal constructor used to validate the NURBS surface.
/// </summary>
/// <param name="degreeU">The degree in the U direction.</param>
/// <param name="degreeV">The degree in the V direction.</param>
/// <param name="knotsU">The knotVector in the U direction.</param>
/// <param name="knotsV">The knotVector in the V direction.</param>
/// <param name="controlPts">Two dimensional array of points.</param>
internal NurbsSurface(int degreeU, int degreeV, KnotVector knotsU, KnotVector knotsV, List <List <Point4> > controlPts)
{
if (controlPts == null)
{
throw new ArgumentNullException("Control points array connot be null!");
}
if (degreeU < 1)
{
throw new ArgumentException("DegreeU must be greater than 1!");
}
if (degreeV < 1)
{
throw new ArgumentException("DegreeV must be greater than 1!");
}
if (knotsU == null)
{
throw new ArgumentNullException("KnotU cannot be null!");
}
if (knotsV == null)
{
throw new ArgumentNullException("KnotV cannot be null!");
}
if (knotsU.Count != controlPts.Count() + degreeU + 1)
{
throw new ArgumentException("Points count + degreeU + 1 must equal knotsU count!");
}
if (knotsV.Count != controlPts.First().Count() + degreeV + 1)
{
throw new ArgumentException("Points count + degreeV + 1 must equal knotsV count!");
}
if (!knotsU.IsValid(degreeU, controlPts.Count()))
{
throw new ArgumentException("Invalid knotsU!");
}
if (!knotsV.IsValid(degreeV, controlPts.First().Count()))
{
throw new ArgumentException("Invalid knotsV!");
}
DegreeU = degreeU;
DegreeV = degreeV;
KnotsU = (Math.Abs(knotsU.GetDomain(degreeU).Length - 1.0) > GSharkMath.Epsilon) ? knotsU.Normalize() : knotsU;
KnotsV = (Math.Abs(knotsV.GetDomain(degreeV).Length - 1.0) > GSharkMath.Epsilon) ? knotsV.Normalize() : knotsV;
Weights = Point4.GetWeights2d(controlPts);
ControlPointLocations = Point4.PointDehomogenizer2d(controlPts);
ControlPoints = controlPts;
DomainU = new Interval(KnotsU.First(), KnotsU.Last());
DomainV = new Interval(KnotsV.First(), KnotsV.Last());
}
/// <summary>
/// Defines the NURBS form of the polyline.
/// </summary>
private void ToNurbsForm()
{
if (_segments.Count == 1)
{
Weights = Point4.GetWeights(_segments[0].ControlPoints);
Degree = _segments[0].Degree;
Knots = _segments[0].Knots;
ControlPointLocations = Point4.PointDehomogenizer1d(_segments[0].ControlPoints);
ControlPoints = _segments[0].ControlPoints;
return;
}
// Extract the biggest degree between the curves.
int finalDegree = _segments.Max(c => c.Degree);
// Homogenized degree curves.
IEnumerable <NurbsBase> homogenizedCurves = _segments.Select(curve => curve.Degree != finalDegree ? Modify.Curve.ElevateDegree(curve, finalDegree) : curve);
// Join curves.
List <double> joinedKnots = new List <double>();
List <Point4> joinedControlPts = new List <Point4>();
joinedKnots.AddRange(homogenizedCurves.First().Knots.Take(homogenizedCurves.First().Knots.Count - 1));
joinedControlPts.AddRange(homogenizedCurves.First().ControlPoints);
foreach (NurbsBase curve in homogenizedCurves.Skip(1))
{
joinedKnots.AddRange(curve.Knots.Take(curve.Knots.Count - 1).Skip(finalDegree + 1).Select(k => k + joinedKnots.Last()).ToList());
joinedControlPts.AddRange(curve.ControlPoints.Skip(1));
}
// Appending the last knot to the end.
joinedKnots.Add(joinedKnots.Last());
Weights = Point4.GetWeights(joinedControlPts);
Degree = finalDegree;
Knots = joinedKnots.ToKnot().Normalize();
ControlPointLocations = Point4.PointDehomogenizer1d(joinedControlPts);
ControlPoints = joinedControlPts;
}
/// <summary>
/// Creates a surface of revolution through an arbitrary angle, and axis.
/// <em>Corresponds the algorithm A8.1 of The NURBS Book by Piegl and Tiller.</em>
/// </summary>
/// <param name="curveProfile">Profile curve.</param>
/// <param name="axis">Revolution axis.</param>
/// <param name="rotationAngle">Angle in radiance.</param>
/// <returns>The revolution surface.</returns>
public static NurbsSurface Revolved(NurbsBase curveProfile, Ray axis, double rotationAngle)
{
// if angle is less than 90.
int arcCount = 1;
KnotVector knotsU = Vector.Zero1d(6).ToKnot();
if (rotationAngle <= Math.PI && rotationAngle > (Math.PI / 2))
{
arcCount = 2;
knotsU[3] = knotsU[4] = 0.5;
}
if (rotationAngle <= (3 * Math.PI / 2) && rotationAngle > Math.PI)
{
arcCount = 3;
knotsU = Vector.Zero1d(6 + 2 * (arcCount - 1)).ToKnot();
knotsU[3] = knotsU[4] = (double)1 / 3;
knotsU[5] = knotsU[6] = (double)2 / 3;
}
if (rotationAngle <= (4 * Math.PI) && rotationAngle > (3 * Math.PI / 2))
{
arcCount = 4;
knotsU = Vector.Zero1d(6 + 2 * (arcCount - 1)).ToKnot();
knotsU[3] = knotsU[4] = (double)1 / 4;
knotsU[5] = knotsU[6] = (double)1 / 2;
knotsU[7] = knotsU[8] = (double)3 / 4;
}
// load start and end knots.
int t = 3 + 2 * (arcCount - 1);
for (int i = 0; i < 3; i++, t++)
{
knotsU[i] = 0.0;
knotsU[t] = 1.0;
}
// some initialization.
double divideAngle = rotationAngle / arcCount;
int n = 2 * arcCount;
double wm = divideAngle / 2; // is the base angle.
// initialize the sines and cosines only once.
double angle = 0.0;
double[] sines = new double[arcCount + 1];
double[] cosines = new double[arcCount + 1];
for (int i = 1; i <= arcCount; i++)
{
angle += divideAngle;
sines[i] = Math.Sin(angle);
cosines[i] = Math.Cos(angle);
}
// loop and compute each u row of control points and weights.
List <List <Point4> > controlPts = new List <List <Point4> >();
for (int r = 0; r < 2 * arcCount + 1; r++)
{
List <Point4> temp = CollectionHelpers.RepeatData(Point4.Zero, curveProfile.ControlPoints.Count);
controlPts.Add(temp);
}
for (int j = 0; j < curveProfile.ControlPointLocations.Count; j++)
{
Point3 ptO = axis.ClosestPoint(curveProfile.ControlPointLocations[j]);
Vector3 vectorX = curveProfile.ControlPointLocations[j] - ptO;
double radius = vectorX.Length; // the radius at that length.
Vector3 vectorY = Vector3.CrossProduct(axis.Direction, vectorX);
if (radius > GSharkMath.Epsilon)
{
vectorX *= (1 / radius);
vectorY *= (1 / radius);
}
// initialize the first control points and weights.
Point3 pt0 = curveProfile.ControlPointLocations[j];
controlPts[0][j] = new Point4(pt0, curveProfile.Weights[j]);
Vector3 tangent0 = vectorY;
int index = 0;
for (int i = 1; i <= arcCount; i++)
{
// rotated generatrix point.
Point3 pt2 = (Math.Abs(radius) < GSharkMath.Epsilon)
? ptO
: ptO + (vectorX * (cosines[i] * radius) + vectorY * (sines[i] * radius));
controlPts[index + 2][j] = new Point4(pt2, curveProfile.Weights[j]);
// construct the vector tangent to the rotation.
Vector3 rotationTangent = vectorX * (-1 * sines[i]) + vectorY * cosines[i];
// construct the next control point.
if (Math.Abs(radius) < GSharkMath.Epsilon)
{
controlPts[index + 1][j] = ptO;
}
else
{
Line ln0 = new Line(pt0, tangent0, tangent0.Length);
Line ln1 = new Line(pt2, rotationTangent, rotationTangent.Length);
Intersection.Intersect.LineLine(ln0, ln1, out Point3 intersectionPt, out _, out _, out _);
controlPts[index + 1][j] = new Point4(intersectionPt, wm * curveProfile.Weights[j]);
}
index += 2;
if (i >= arcCount)
{
continue;
}
pt0 = pt2;
tangent0 = rotationTangent;
}
}
return(new NurbsSurface(2, curveProfile.Degree, knotsU, curveProfile.Knots, controlPts.Select(pts => pts.ToList()).ToList()));
}
/// <summary>
/// Constructs a nurbs curve representation of this arc.<br/>
/// <em>Implementation of Algorithm A7.1 from The NURBS Book by Piegl and Tiller.</em>
/// </summary>
/// <returns>A nurbs curve shaped like this arc.</returns>
internal void ToNurbs()
{
Vector3 axisX = Plane.XAxis;
Vector3 axisY = Plane.YAxis;
double curveAngle = _domain.Length;
int numberOfArc;
Point3[] pts;
Point4[] ctrPts;
double[] weights;
// Number of arcs.
double piNum = 0.5 * Math.PI;
if ((curveAngle - piNum) <= GSharkMath.Epsilon)
{
numberOfArc = 1;
pts = new Point3[3];
ctrPts = new Point4[3];
weights = new double[3];
}
else if ((curveAngle - piNum * 2) <= GSharkMath.Epsilon)
{
numberOfArc = 2;
pts = new Point3[5];
ctrPts = new Point4[5];
weights = new double[5];
}
else if ((curveAngle - piNum * 3) <= GSharkMath.Epsilon)
{
numberOfArc = 3;
pts = new Point3[7];
ctrPts = new Point4[7];
weights = new double[7];
}
else
{
numberOfArc = 4;
pts = new Point3[9];
ctrPts = new Point4[9];
weights = new double[9];
}
double detTheta = curveAngle / numberOfArc;
double weight = Math.Cos(detTheta / 2);
Point3 p0 = Center + (axisX * (Radius * Math.Cos(_domain.T0)) + axisY * (Radius * Math.Sin(_domain.T0)));
Vector3 t0 = axisY * Math.Cos(_domain.T0) - axisX * Math.Sin(_domain.T0);
KnotVector knots = new KnotVector(CollectionHelpers.RepeatData(0.0, ctrPts.Length + 3));
int index = 0;
double angle = _domain.T0;
pts[0] = p0;
ctrPts[0] = new Point4(p0);
weights[0] = weight;
for (int i = 1; i < numberOfArc + 1; i++)
{
angle += detTheta;
Point3 p2 = Center + (axisX * (Radius * Math.Cos(angle)) + axisY * (Radius * Math.Sin(angle)));
ctrPts[index + 2] = new Point4(p2);
pts[index + 2] = p2;
weights[index + 2] = 1.0;
Vector3 t2 = (axisY * Math.Cos(angle)) - (axisX * Math.Sin(angle));
Line ln0 = new Line(p0, t0.Unitize() + p0);
Line ln1 = new Line(p2, t2.Unitize() + p2);
Intersect.LineLine(ln0, ln1, out _, out _, out double u0, out _);
Point3 p1 = p0 + (t0 * u0);
ctrPts[index + 1] = new Point4(p1, weight);
pts[index + 1] = p1;
weights[index + 1] = weight;
index += 2;
if (i >= numberOfArc)
{
continue;
}
p0 = p2;
t0 = t2;
}
int j = 2 * numberOfArc + 1;
for (int i = 0; i < 3; i++)
{
knots[i] = 0.0;
knots[i + j] = 1.0;
}
switch (numberOfArc)
{
case 2:
knots[3] = knots[4] = 0.5;
break;
case 3:
knots[3] = knots[4] = (double)1 / 3;
knots[5] = knots[6] = (double)2 / 3;
break;
case 4:
knots[3] = knots[4] = 0.25;
knots[5] = knots[6] = 0.5;
knots[7] = knots[8] = 0.75;
break;
}
Weights = weights.ToList();
Degree = 2;
Knots = knots;
ControlPoints = ctrPts.ToList();
ControlPointLocations = pts.ToList();
}