public bool IsOnShortLine(clsPoint3d pt1, double aTol = 0, bool excludeEnds = false)
{
clsLine3d l1 = default(clsLine3d);
clsLine3d l2 = default(clsLine3d);
double d = 0;
if (aTol == 0)
{
aTol = mdlGeometry.myTol;
}
if (Abs(DistanceToPoint(pt1)) > aTol)
{
return(false);
}
l1 = new clsLine3d(P1, pt1);
l2 = Copy();
l2.Normalise();
d = l1.Dot(l2);
if (d < -aTol)
{
return(false);
}
if (d > Length + aTol)
{
return(false);
}
if (excludeEnds && (P1 == pt1 | P2 == pt1))
{
return(false);
}
return(true);
}
public clsPoint3d ClosestPointToLine(clsLine3d l2)
{
clsPoint3d v1;
clsPoint3d v2;
clsPoint3d M;
double m2;
clsPoint3d R;
clsPoint3d P21;
double t1;
clsPoint3d Q1;
//Find the actual point on this line where the perpendicular distance hits.
v1 = new clsPoint3d(DX(), DY(), DZ());
v1.Normalise();
v2 = new clsPoint3d(l2.DX(), l2.DY(), l2.DZ());
v2.Normalise();
M = v2.Cross(v1);
m2 = M.Dot(M);
if (m2 < mdlGeometry.myTol)
{
return(l2.P1);
}
//Parallel
P21 = new clsPoint3d(l2.X1 - X1, l2.Y1 - Y1, l2.Z1 - Z1);
R = P21.Cross(M);
R.Scale(1 / m2);
t1 = R.Dot(v2);
Q1 = P1 + t1 * v1;
return(Q1);
}
public clsPoint3d DistanceAlongLine(double d)
{
clsLine3d l1 = default(clsLine3d);
l1 = Copy();
l1.Normalise();
return(new clsPoint3d(X1 + d * l1.DX(), Y1 + d * l1.DY(), Z1 + d * l1.DZ()));
}
public clsPoint3d PointFromLambda(double l)
{
clsLine3d l1 = default(clsLine3d);
l1 = Copy();
l1.Scale(l);
return(l1.P2);
}
public double DistanceToLine(clsLine3d l2)
{
//Perpendicular distance between 3d lines. Limited to the line segments.
double myNormalDist;
clsPoint3d v1;
clsPoint3d v2;
clsPoint3d M;
double m2;
clsPoint3d R;
clsPoint3d P21;
double t1;
double t2;
clsPoint3d Q1;
clsPoint3d Q2;
//Find the actual point on this line where the perpendicular distance hits. If it is off the line, then find the minimum distance between the end points
v1 = new clsPoint3d(DX(), DY(), DZ());
v1.Normalise();
v2 = new clsPoint3d(l2.DX(), l2.DY(), l2.DZ());
v2.Normalise();
P21 = new clsPoint3d(l2.X1 - X1, l2.X1 - X1, l2.X1 - X1);
M = v2.Cross(v1);
m2 = M.Dot(M);
if (m2 < mdlGeometry.myTol)
{
return(DistanceToPoint(l2.P1));
}
//Parallel
myNormalDist = Abs(P21.Dot(M)) / Sqrt(m2);
//Perpendicular distance
R = P21.Cross(M);
R.Scale(1 / m2);
t1 = R.Dot(v2);
Q1 = P1 + t1 * v1;
if (t1 < 0)
{
Q1 = P1;
}
if (t1 > Length)
{
Q1 = P2;
}
t2 = R.Dot(v1);
Q2 = l2.P1 + t2 * v2;
if (t2 < 0)
{
Q2 = l2.P1;
}
if (t2 > l2.Length)
{
Q2 = l2.P2;
}
return(Q1.Dist(Q2));
}
public double Lambda(clsPoint3d pt1)
{
clsLine3d l1 = default(clsLine3d);
clsLine3d l2 = default(clsLine3d);
l1 = new clsLine3d(P1, pt1);
l2 = Copy();
l2.Normalise();
return(l1.Dot(l2) / Length);
}
public clsLine3d Cross(clsLine3d l1)
{
double x = 0;
double y = 0;
double z = 0;
x = DY() * l1.DZ() - DZ() * l1.DY();
y = -(DX() * l1.DZ() - DZ() * l1.DX());
z = DX() * l1.DY() - DY() * l1.DX();
return(new clsLine3d(0, 0, 0, x, y, z));
}
public bool IsOnLine(clsPoint3d aPt)
{
clsLine3d l1 = default(clsLine3d);
l1 = new clsLine3d(P2, aPt);
if (mdlGeometry.IsSameDbl(Cross(l1).Length, 0))
{
return(true);
}
return(false);
}
public static clsPoint3d ProjectPoint(clsPoint3d p1, clsLine3d l1)
{
double d1 = 0;
clsLine3d l2 = new clsLine3d();
clsLine3d l3 = new clsLine3d();
l2 = l1.Copy();
l2.Normalise();
l3 = new clsLine3d(l1.P1, p1);
d1 = l2.Dot(l3);
l2.Length = d1;
return(l2.P2);
}
public clsPoint3d IntersectQuick(clsLine3d l1)
{
//Both infinite
double lambda = 0;
if (Abs((X2 - X1) * (l1.Y1 - l1.Y2) + (Y2 - Y1) * (l1.X2 - l1.X1)) < mdlGeometry.myTol / 10)
{
return(null);
}
//No intersection
lambda = ((l1.X2 - X1) * (l1.Y1 - l1.Y2) + (l1.Y2 - Y1) * (l1.X2 - l1.X1)) / ((X2 - X1) * (l1.Y1 - l1.Y2) + (Y2 - Y1) * (l1.X2 - l1.X1));
return(new clsPoint3d(X1 + lambda * (X2 - X1), Y1 + lambda * (Y2 - Y1), 0));
}
public double DistanceToPoint(clsPoint3d aPt)
{
double d1 = 0;
double d2 = 0;
clsLine3d l2 = default(clsLine3d);
clsLine3d l3 = default(clsLine3d);
l2 = Copy();
l2.Normalise();
l3 = new clsLine3d(P1, aPt);
d1 = l2.Dot(l3);
d2 = l3.Length;
return(Sqrt(Pow(d2, 2) - Pow(d1, 2)));
}
public static double Dist3d(clsPoint3d p1, clsLine3d l1)
{
double d1 = 0;
double d2 = 0;
clsLine3d l2 = new clsLine3d();
clsLine3d l3 = new clsLine3d();
l2 = l1.Copy();
l2.Normalise();
l3 = new clsLine3d(l1.P1, p1);
d1 = l2.Dot(l3);
d2 = l3.Length;
return(Sqrt(Pow(d2, 2) - Pow(d1, 2)));
}
public static double DistancePointLine3D(clsPoint3d p1, clsLine3d l1)
{
//Distance between 3D point and truncated 3D line
clsPoint3d p3d = new clsPoint3d();
double l = 0;
p3d = ProjectPoint(p1, l1);
l = l1.Lambda(p3d);
if (l < 0)
{
return(p1.Dist(l1.P1));
}
if (l > 1)
{
return(p1.Dist(l1.P2));
}
return(p1.Dist(p3d));
}
public static clsPoint3d ProjectPointOntoPlaneAlongZ(clsPoint p, clsLine3d l1)
{
clsLine3d v1 = new clsLine3d();
double u = 0;
double r = 0;
double z = 0;
clsPoint3d p1 = new clsPoint3d();
v1 = new clsLine3d(new clsPoint3d(0, 0, 0), new clsPoint3d(0, 0, 1));
u = v1.Dot(l1);
//This is the length of the normal vector, measured in the vertical direction
p1 = new clsPoint3d(p.X - l1.X1, p.Y - l1.Y1, 0 - l1.Z1);
r = p1.Dot(l1.DP());
//r is the distance of our point to the nearest point on the plane
//r = v1.Dot(myV)
z = r / u;
//z is the vertical distance of our point to the plane. It is sign sensitive - positive is above the plane.
return(new clsPoint3d(p.X, p.Y, -z));
}
public bool Overlaps(clsLine3d aLine, double aTol = 0)
{
clsLine3d l1 = default(clsLine3d);
clsPoint3d p3 = default(clsPoint3d);
clsPoint3d p4 = default(clsPoint3d);
if (aTol == 0)
{
aTol = mdlGeometry.myTol;
}
l1 = aLine.Copy();
if ((!IsOnLine(l1.P1)) | (!IsOnLine(l1.P2)))
{
return(false);
}
if (Dot(l1) < 0)
{
l1.Reverse();
}
p3 = l1.P1;
p4 = l1.P2;
if (P1 == p3)
{
return(true);
}
if (P1 == p4 | P2 == p3)
{
return(false);
}
if (IsOnShortLine(p4))
{
return(true);
}
if (l1.IsOnShortLine(P1, aTol) | l1.IsOnShortLine(P2, aTol))
{
return(true);
}
return(false);
}
public void RotateAboutLine(clsLine3d l1, double theta)
{
clsPoint3d p1 = default(clsPoint3d);
clsPoint3d p2 = default(clsPoint3d);
clsPoint3d p2a = default(clsPoint3d);
clsPoint3d p2b = default(clsPoint3d);
clsPoint3d p3 = default(clsPoint3d);
clsLine3d l2 = default(clsLine3d);
if (l1.IsOnLine(this))
{
return;
}
//Setup a coordinate system with X running along l1 and the origin at l1.p2
l2 = new clsLine3d(l1.P2.Copy(), Copy());
p1 = new clsPoint3d(l1.DX(), l1.DY(), l1.DZ());
p1.Length = 1;
p2 = new clsPoint3d(l2.DX(), l2.DY(), l2.DZ());
p2a = new clsPoint3d(l2.DX(), l2.DY(), l2.DZ());
p2.Length = 1;
p3 = p1.Cross(p2);
p3.Length = 1;
p2 = p1.Cross(p3);
p2.Length = 1;
if (p2.Dot(p2a) < 0)
{
p2.Scale(-1);
}
p2b = new clsPoint3d(p1.Dot(p2a), p2.Dot(p2a), p3.Dot(p2a));
p2b.RotateAboutX(theta);
myX = l1.X2 + p2b.x * p1.x + p2b.y * p2.x + p2b.z * p3.x;
myY = l1.Y2 + p2b.x * p1.y + p2b.y * p2.y + p2b.z * p3.y;
myZ = l1.Z2 + p2b.x * p1.z + p2b.y * p2.z + p2b.z * p3.z;
}
public clsPoint3d Intersect(clsLine3d l1)
{
//Both infinite. More accurate that IntersectQuick
double l = 0;
clsLine3d l2 = default(clsLine3d);
clsLine3d l3 = default(clsLine3d);
if (Length < mdlGeometry.myTol | l1.Length < mdlGeometry.myTol)
{
return(null);
}
l2 = Copy();
l3 = l1.Copy();
l2.Length = 1000;
l3.Length = 1000;
if (Abs(((l2.X2 - l2.X1) * (l3.Y1 - l3.Y2) + (l2.Y2 - l2.Y1) * (l3.X2 - l3.X1))) < mdlGeometry.myTol / 10)
{
return(null);
}
//No intersection
l = ((l3.X2 - l2.X1) * (l3.Y1 - l3.Y2) + (l3.Y2 - l2.Y1) * (l3.X2 - l3.X1)) / ((l2.X2 - l2.X1) * (l3.Y1 - l3.Y2) + (l2.Y2 - l2.Y1) * (l3.X2 - l3.X1));
return(new clsPoint3d(l2.X1 + l * (l2.X2 - l2.X1), l2.Y1 + l * (l2.Y2 - l2.Y1), 0));
}
public double Dot(clsLine3d l1)
{
return((P2.X - P1.X) * (l1.P2.X - l1.P1.X) + (P2.Y - P1.Y) * (l1.P2.Y - l1.P1.Y) + (P2.Z - P1.Z) * (l1.P2.Z - l1.P1.Z));
}
public void RotateAboutLine(clsLine3d l1, double a)
{
P1.RotateAboutLine(l1, a);
P2.RotateAboutLine(l1, a);
}
/// <summary>
/// Processes the point list pair.
/// </summary>
/// <param name="estimatedLocationPoints">The estimated location points (from AR Toolkit).</param>
/// <param name="axisStartPoints">The axis start point (from the camera).</param>
/// <param name="axisEndPoints">The axis end point (from the camera).</param>
/// <param name="myNumPtsCalculated">Nnumber of points calculated.</param>
/// <returns>The average point of all processed points if successful, otherwise a zero length vector.</returns>
/// <remarks>estimatedLocationPoints and seenFromCameraPoints must be matched lists.</remarks>
/// <exception cref="ArgumentNullException"></exception>
/// <exception cref="ArgumentException">estimatedLocationPoints and seenFromCameraPoints should be matched lists.</exception>
private clsPoint3d ProcessPointListPair(List <clsPoint3d> estimatedLocationPoints, List <clsPoint3d> seenFromCameraPoints, ref int myNumPtsCalculated)
{
if (estimatedLocationPoints == null || seenFromCameraPoints == null)
{
throw new ArgumentNullException();
}
if (estimatedLocationPoints.Count != seenFromCameraPoints.Count)
{
throw new ArgumentException("estimatedLocationPoints and seenFromCameraPoints should be matched lists.");
}
myNumPtsCalculated = 0;
// Take copies of the list, such as not to affect the passed list
estimatedLocationPoints = estimatedLocationPoints.ToList();
seenFromCameraPoints = seenFromCameraPoints.ToList();
// Get the points within 12.5mm of the average
var points = GetPointsWithinDistanceOfAveragePoint(estimatedLocationPoints, 12.5);
// Align the matched lists by removing the axis points matched to the estimated location points that have been removed
var removedPoints = estimatedLocationPoints.Where(p => !points.Contains(p)).ToList();
removedPoints.ForEach(p => {
var index = estimatedLocationPoints.IndexOf(p);
estimatedLocationPoints.RemoveAt(index);
seenFromCameraPoints.RemoveAt(index);
});
// Don't process anything if we have less than 3 usable points
if (points.Count <= 3)
{
return(new clsPoint3d(0, 0, 0));
}
var intersectionPoints = new List <clsPoint3d>();
// Get the first line - don't loop through all as we compare to the next line
for (var i = 0; i <= estimatedLocationPoints.Count - 2; i++)
{
var line1 = new clsLine3d(estimatedLocationPoints[i], seenFromCameraPoints[i]);
// Compare to the next line
for (var j = i + 1; j <= estimatedLocationPoints.Count - 1; j++)
{
var line2 = new clsLine3d(estimatedLocationPoints[j].Copy(), seenFromCameraPoints[j].Copy());
// Get midpoint of each line
var p1 = line1.Point;
p1.Normalise();
var p2 = line2.Point;
p2.Normalise();
// Determine angle between lines
var a = Acos(p1.Dot(p2)) * 180 / PI;
if (a > myPGAngleTol)
{
// Angle is above minimum threshold, so determine the point on each line which is closest to the other line
var p3 = line1.ClosestPointToLine(line2);
var p4 = line2.ClosestPointToLine(line1);
// Determine the distance between the closest points
var d = p3.Dist(p4);
if (d < myPGPointTol)
{
// Distance is below threshold so add the intersection point as the midpoint between them
intersectionPoints.Add(new clsPoint3d((p3.X + p4.X) / 2, (p3.Y + p4.Y) / 2, (p3.Z + p4.Z) / 2));
}
}
}
}
var intersectionPointsToFind = 10;
if (intersectionPoints.Count >= intersectionPointsToFind)
{
myNumPtsCalculated = intersectionPoints.Count;
return(GetAveragePoint(intersectionPoints));
}
else
{
DebugStringList.Add($"{intersectionPoints.Count} / {intersectionPointsToFind}");
}
return(new clsPoint3d(0, 0, 0));
}