public void It_Returns_False_If_Three_Points_Are_Not_Collinear()
{
// Arrange
Point3 pt1 = new Point3(25.923, 27.057, 0.0);
Point3 pt2 = new Point3(35.964, 20.451, 0.0);
Point3 pt3 = new Point3(51.299, 37.950, 0.0);
// Assert
Trigonometry.ArePointsCollinear(pt1, pt2, pt3).Should().BeFalse();
}
/// <summary>
/// Constructs a plane from three non-collinear points.
/// </summary>
/// <param name="pt1">Firs point representing the origin.</param>
/// <param name="pt2">Second point representing the x direction.</param>
/// <param name="pt3">Third point representing the y direction.</param>
public Plane(Point3 pt1, Point3 pt2, Point3 pt3)
{
if (Trigonometry.ArePointsCollinear(pt1, pt2, pt3))
{
throw new Exception("Plane cannot be created, the tree points must not be collinear");
}
Vector3 dir1 = pt2 - pt1;
Vector3 dir2 = pt3 - pt1;
Vector3 normal = Vector3.CrossProduct(dir1, dir2);
Origin = pt1;
XAxis = dir1.Unitize();
YAxis = Vector3.CrossProduct(normal, dir1).Unitize();
}
/// <summary>
/// Find four points in the point cloud that are not coplanar for the
/// seed hull
/// </summary>
private void FindInitialHullIndices(List <Point3> points, out int b0, out int b1, out int b2, out int b3)
{
int count = points.Count;
for (int i0 = 0; i0 < count - 3; i0++)
{
for (int i1 = i0 + 1; i1 < count - 2; i1++)
{
Vector3 p0 = points[i0];
Vector3 p1 = points[i1];
if (p0.EpsilonEquals(p1, GSharkMath.MinTolerance))
{
continue;
}
for (int i2 = i1 + 1; i2 < count - 1; i2++)
{
Vector3 p2 = points[i2];
if (Trigonometry.ArePointsCollinear(p0, p1, p2))
{
continue;
}
for (int i3 = i2 + 1; i3 < count - 0; i3++)
{
Vector3 p3 = points[i3];
if (Trigonometry.ArePointsCoplanar(new List <Point3> {
p0, p1, p2, p3
}))
{
continue;
}
b0 = i0;
b1 = i1;
b2 = i2;
b3 = i3;
return;
}
}
}
}
throw new System.ArgumentException("Can't generate hull, points are coplanar");
}
/// <summary>
/// Samples a curve in an adaptive way. <br/>
/// <em>Corresponds to this algorithm http://ariel.chronotext.org/dd/defigueiredo93adaptive.pdf <br/>
/// https://www.modelical.com/en/grasshopper-scripting-107/ </em>
/// </summary>
/// <param name="curve">The curve to sampling.</param>
/// <param name="start">The start parameter for sampling.</param>
/// <param name="end">The end parameter for sampling.</param>
/// <param name="tolerance">Tolerance for the adaptive scheme. The default tolerance is set as (1e-6).</param>
/// <returns>A tuple with the set of points and the t parameter where the point was evaluated.</returns>
public static (List <double> tValues, List <Point3> pts) AdaptiveSampleRange(NurbsBase curve, double start, double end, double tolerance = GSharkMath.MinTolerance)
{
// Sample curve at three pts.
Random random = new Random();
double t = 0.5 + 0.2 * random.NextDouble();
double mid = start + (end - start) * t;
Point3 pt1 = Point4.PointDehomogenizer(Evaluate.Curve.PointAt(curve, start));
Point3 pt2 = Point4.PointDehomogenizer(Evaluate.Curve.PointAt(curve, mid));
Point3 pt3 = Point4.PointDehomogenizer(Evaluate.Curve.PointAt(curve, end));
Vector3 diff = pt1 - pt3;
Vector3 diff2 = pt1 - pt2;
if ((Vector3.DotProduct(diff, diff) < tolerance && Vector3.DotProduct(diff2, diff2) > tolerance) ||
!Trigonometry.ArePointsCollinear(pt1, pt2, pt3, tolerance))
{
// Get the exact middle value or a random value start + (end - start) * (0.45 + 0.1 * random.NextDouble());
double tMiddle = start + (end - start) * 0.5;
// Recurse the two halves.
(List <double> tValues, List <Point3> pts)leftHalves = AdaptiveSampleRange(curve, start, tMiddle, tolerance);
(List <double> tValues, List <Point3> pts)rightHalves = AdaptiveSampleRange(curve, tMiddle, end, tolerance);
leftHalves.tValues.RemoveAt(leftHalves.tValues.Count - 1);
List <double> tMerged = leftHalves.tValues.Concat(rightHalves.tValues).ToList();
leftHalves.pts.RemoveAt(leftHalves.pts.Count - 1);
List <Point3> ptsMerged = leftHalves.pts.Concat(rightHalves.pts).ToList();
return(tMerged, ptsMerged);
}
return(new List <double> {
start, end
}, new List <Point3> {
pt1, pt3
});
}