/// <summary>
/// Find Curve Segment At a given Length.
/// When there is no curve segments in the PolyCurve, return null;
/// If the provided length is greater than the PolyCurve Length, then it return the last segment in PolyCurve;
/// </summary>
/// <param name="length">Segment Length</param>
public NurbsBase SegmentAtLength(double length)
{
NurbsBase segment = null;
if (length > Length)
{
return(_segments.Last());
}
if (_segments.Count == 1)
{
return(_segments.First());
}
double temp = 0;
foreach (NurbsBase curve in _segments)
{
double cumulativeLength = curve.Length + temp;
if (length >= temp && length < cumulativeLength)
{
segment = curve;
break;
}
temp = cumulativeLength;
}
return(segment);
}
/// <summary>
/// Constructs a ruled surface between two curves.
/// <em>Follows the algorithm at page 337 of The NURBS Book by Piegl and Tiller.</em>
/// </summary>
/// <param name="curveA">The first curve.</param>
/// <param name="curveB">The second curve.</param>
/// <returns>A ruled surface.</returns>
public static NurbsSurface Ruled(NurbsBase curveA, NurbsBase curveB)
{
IList <NurbsBase> curves = new[] { curveA, curveB };
curves = CurveHelpers.NormalizedDegree(curves);
curves = CurveHelpers.NormalizedKnots(curves);
return(new NurbsSurface(1, curves[0].Degree, new KnotVector(1, 2), curves[0].Knots,
new List <List <Point4> > {
curves[0].ControlPoints, curves[1].ControlPoints
}));
}
/// <summary>
/// Constructs a surface extruding a curve profile long a direction.
/// </summary>
/// <param name="direction">The extrusion direction.</param>
/// <param name="profile">The profile curve to extrude.</param>
/// <returns>The extruded surface.</returns>
public static NurbsSurface FromExtrusion(Vector3 direction, NurbsBase profile)
{
Transform xForm = Core.Transform.Translation(direction);
List <Point4> translatedControlPts =
profile.ControlPoints.Select(controlPoint => controlPoint.Transform(xForm)).ToList();
return(new NurbsSurface(1, profile.Degree, new KnotVector {
0, 0, 1, 1
}, profile.Knots,
new List <List <Point4> > {
profile.ControlPoints, translatedControlPts
}));
}
/// <summary>
/// Constructs a sweep surface with one rail curve.
/// <em>Follows the algorithm A10.2 at page 477 of The NURBS Book by Piegl and Tiller.</em>
/// </summary>
/// <param name="rail">The rail curve.</param>
/// <param name="profile">The section curve.</param>
/// <returns>The sweep surface.</returns>
public static NurbsSurface FromSweep(NurbsBase rail, NurbsBase profile)
{
var(tValues, _) = Sampling.Curve.AdaptiveSample(rail, GSharkMath.MaxTolerance);
List <Plane> frames = rail.PerpendicularFrames(tValues);
List <NurbsBase> curves = new List <NurbsBase> {
profile
};
for (int i = 1; i <= frames.Count; i++)
{
Transform xForm = Core.Transform.PlaneToPlane(frames[0], frames[i]);
curves.Add(((NurbsCurve)curves[0]).Transform(xForm));
}
return(FromLoft(curves));
}
/// <summary>
/// Checks to define if the curve can be appended.
/// </summary>
private void HealthChecks(NurbsBase curve, NurbsBase curveToAppend)
{
if (_segments.Count <= 0)
{
return;
}
if (curve.IsClosed)
{
throw new InvalidOperationException($"The polyCurve is closed can not be possible to connect the {curveToAppend.GetType()}.");
}
if (curve.EndPoint.DistanceTo(curveToAppend.StartPoint) > GSharkMath.Epsilon)
{
throw new InvalidOperationException("The two curves can not be connected.");
}
}
/// <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 surface from a set of NURBS curves.<br/>
/// </summary>
/// <param name="curves">Set of a minimum of two curves to create the surface.</param>
/// <param name="loftType">Enum to choose the type of loft generation.</param>
/// <returns>A NURBS surface.</returns>
public static NurbsSurface FromLoft(IList <NurbsBase> curves, LoftType loftType = LoftType.Normal)
{
if (curves == null)
{
throw new ArgumentException("An invalid number of curves to perform the loft.");
}
if (curves.Count < 2)
{
throw new ArgumentException("An invalid number of curves to perform the loft.");
}
if (curves.Any(x => x == null))
{
throw new ArgumentException("The input set contains null curves.");
}
bool isClosed = curves[0].IsClosed;
foreach (NurbsBase c in curves.Skip(1))
{
if (isClosed != c.IsClosed)
{
throw new ArgumentException("Loft only works if all curves are open, or all curves are closed.");
}
}
// Copy curves for possible operation of homogenization.
IList <NurbsBase> copyCurves = new List <NurbsBase>(curves);
// Clamp curves if periodic.
if (copyCurves[0].IsPeriodic)
{
for (int i = 0; i < copyCurves.Count; i++)
{
copyCurves[i] = copyCurves[i].ClampEnds();
}
}
// If necessary, the curves can be brought to a common degree and knots, as we do for the ruled surface.
// In fact, the ruled surface is a special case of a skinned surface.
if (copyCurves.Any(c => c.Degree != copyCurves[0].Degree))
{
copyCurves = CurveHelpers.NormalizedDegree(copyCurves);
copyCurves = CurveHelpers.NormalizedKnots(copyCurves);
}
int degreeV = copyCurves[0].Degree;
int degreeU = 3;
KnotVector knotVectorU = new KnotVector();
KnotVector knotVectorV = copyCurves[0].Knots;
List <List <Point4> > surfaceControlPoints = new List <List <Point4> >();
switch (loftType)
{
case LoftType.Normal:
List <List <Point4> > tempPts = new List <List <Point4> >();
for (int n = 0; n < copyCurves[0].ControlPointLocations.Count; n++)
{
List <Point3> pts = copyCurves.Select(c => c.ControlPointLocations[n]).ToList();
NurbsBase crv = Fitting.Curve.Interpolated(pts, degreeU);
tempPts.Add(crv.ControlPoints);
knotVectorU = crv.Knots;
}
surfaceControlPoints = CollectionHelpers.Transpose2DArray(tempPts);
break;
case LoftType.Loose:
surfaceControlPoints = copyCurves.Select(c => c.ControlPoints).ToList();
knotVectorU = new KnotVector(degreeU, copyCurves.Count);
break;
}
return(new NurbsSurface(degreeU, degreeV, knotVectorU, knotVectorV, surfaceControlPoints));
}