public void It_Returns_The_Closest_Point()
{
// Arrange
Ray ray = new Ray(new Point3(0, 0, 0), new Vector3(30, 45, 0));
var pt = new Point3(10, 20, 0);
var expectedPt = new Point3(12.30769230769231, 18.461538461538463, 0);
// Act
var closestPt = ray.ClosestPoint(pt);
// Assert
closestPt.Should().BeEquivalentTo(expectedPt);
}
/// <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()));
}