/// <summary>
/// The volume of the bounding box.
/// Note that antipodal points would result in an infinite number of great circles, but can
/// be ignored since we are assuming the thickness of this solid is greater than 0.
/// </summary>
/// <param name="gaussianSphere">The gaussian sphere.</param>
/// <param name="vector1">The vector1.</param>
/// <param name="vector2">The vector2.</param>
/// <param name="referenceArc">The reference arc.</param>
internal GreatCircleOrthogonalToArc(GaussianSphere gaussianSphere, double[] vector1, double[] vector2,
Arc referenceArc)
{
ArcList = new List <Arc>();
Intersections = new List <Intersection>();
var tempIntersections = new List <Intersection>();
ReferenceVertices = new List <Vertex>();
Normal = vector1.crossProduct(vector2);
foreach (var arc in gaussianSphere.Arcs)
{
var segmentBool = false;
//Create two planes given arc and the great circle
var norm2 = arc.Nodes[0].Vector.crossProduct(arc.Nodes[1].Vector);
//Check whether the planes are the same.
if (Math.Abs(Normal[0] - norm2[0]) < 0.0001 && Math.Abs(Normal[1] - norm2[1]) < 0.0001 &&
Math.Abs(Normal[2] - norm2[2]) < 0.0001)
{
segmentBool = true; //All points intersect
}
if (Math.Abs(Normal[0] + norm2[0]) < 0.0001 && Math.Abs(Normal[1] + norm2[1]) < 0.0001 &&
Math.Abs(Normal[2] + norm2[2]) < 0.0001)
{
segmentBool = true; //All points intersect
}
//if (Normal[0].IsPracticallySame(norm2[0]) && Normal[1].IsPracticallySame(norm2[1]) &&
// Normal[2].IsPracticallySame(norm2[2])) segmentBool = true; //All points intersect
//Check whether the planes are the same, but built with opposite normals.
//if (Normal[0].IsPracticallySame(-norm2[0]) && Normal[1].IsPracticallySame(-norm2[1]) &&
// Normal[2].IsPracticallySame(-norm2[2])) segmentBool = true; //All points intersect
if (segmentBool)
{
//The arc should be on the arc list.
ArcList.Add(arc);
}
//Find points of intersection between two planes
var position1 = Normal.crossProduct(norm2).normalize(3);
var position2 = new[] { -position1[0], -position1[1], -position1[2] };
var vertices = new[] { position1, position2 };
//Check to see if the intersection is on the arc. We already know it is on the great circle.
for (var i = 0; i < 2; i++)
{
var l1 = arc.ArcLength;
var l2 = ArcLength(arc.Nodes[0].Vector, vertices[i]);
var l3 = ArcLength(arc.Nodes[1].Vector, vertices[i]);
var total = l1 - l2 - l3;
if (Math.Abs(total) > 0.00001)
{
continue;
}
var node = arc.NextNodeAlongRotation(referenceArc.Direction);
//todo: NEED spherical distance along rotation. Below is an attempt
//Subtract the reference arc direction vector from the node and determine where it intersects the great circle
var theta = referenceArc.Direction[0] - node.Theta;
var phi = referenceArc.Direction[1] - node.Phi;
var x = Math.Cos(theta) * Math.Sin(phi);
var y = Math.Sin(theta) * Math.Sin(phi);
var z = Math.Cos(phi);
var point = new[] { x, y, z };
//Create two planes given the great circle and this new temporary arc
var tempNorm = point.crossProduct(node.Vector);
//Find points of intersection between two planes
var position3 = Normal.crossProduct(tempNorm).normalize(3);
var position4 = new[] { -position3[0], -position3[1], -position3[2] };
var vertices2 = new[] { position3, position4 };
for (var j = 0; j < 2; j++)
{
var tempL1 = ArcLength(node.Vector, point);
var tempL2 = ArcLength(node.Vector, vertices2[j]);
var tempL3 = ArcLength(point, vertices2[j]);
var tempTotal = tempL1 - tempL2 - tempL3;
if (Math.Abs(tempTotal) > 0.00001)
{
continue;
}
var intersection = new Intersection(node, tempL3, arc);
tempIntersections.Add(intersection);
ArcList.Add(arc);
break;
}
break;
}
}
//Sort intersections
var tempIntersections2 = tempIntersections.OrderBy(intersection => intersection.SphericalDistance).ToList();
//Remove duplicates
for (var i = 0; i < tempIntersections2.Count - 1; i++)
{
var intersection1 = tempIntersections2[i];
var intersection2 = tempIntersections2[i + 1];
if (intersection1.Node != intersection2.Node)
{
Intersections.Add(intersection1);
//Add the last intersection to the list if it was no the same as the current
if (i == tempIntersections2.Count - 2)
{
Intersections.Add(intersection2);
}
}
}
//Add the reference vertices to a list
foreach (var arc in ArcList)
{
foreach (var referenceVertex in arc.ReferenceVertices)
{
if (!ReferenceVertices.Contains(referenceVertex))
{
ReferenceVertices.Add(referenceVertex);
}
}
}
}
/// <summary>
/// The volume of the bounding box.
/// Note that antipodal points would result in an infinite number of great circles, but can
/// be ignored since we are assuming the thickness of this solid is greater than 0.
/// </summary>
/// <param name="gaussianSphere">The gaussian sphere.</param>
/// <param name="vector1">The vector1.</param>
/// <param name="vector2">The vector2.</param>
/// <param name="referenceArc">The reference arc.</param>
internal GreatCircleAlongArc(GaussianSphere gaussianSphere, double[] vector1, double[] vector2, Arc referenceArc)
{
var antiPoint1 = new[] { -referenceArc.Nodes[0].X, -referenceArc.Nodes[0].Y, -referenceArc.Nodes[0].Z };
//var antiPoint2 = new[] { -referenceArc.Nodes[1].X, -referenceArc.Nodes[1].Y, -referenceArc.Nodes[1].Z };
ArcList = new List <Arc>();
Intersections = new List <Intersection>();
var tempIntersections = new List <Intersection>();
ReferenceVertices = new List <Vertex>();
Normal = vector1.crossProduct(vector2);
foreach (var arc in gaussianSphere.Arcs)
{
if (arc == referenceArc)
{
continue;
}
var segmentBool = false;
//Create two planes given arc and the great circle
var norm2 = arc.Nodes[0].Vector.crossProduct(arc.Nodes[1].Vector).normalize(3);
//Check whether the planes are the same.
if (Math.Abs(Normal[0] - norm2[0]) < 0.0001 && Math.Abs(Normal[1] - norm2[1]) < 0.0001 &&
Math.Abs(Normal[2] - norm2[2]) < 0.0001)
{
segmentBool = true; //All points intersect
}
if (Math.Abs(Normal[0] + norm2[0]) < 0.0001 && Math.Abs(Normal[1] + norm2[1]) < 0.0001 &&
Math.Abs(Normal[2] + norm2[2]) < 0.0001)
{
segmentBool = true; //All points intersect
}
//if (Normal[0].IsPracticallySame(norm2[0]) && Normal[1].IsPracticallySame(norm2[1]) &&
// Normal[2].IsPracticallySame(norm2[2])) segmentBool = true; //All points intersect
//Check whether the planes are the same, but built with opposite normals.
//if (Normal[0].IsPracticallySame(-norm2[0]) && Normal[1].IsPracticallySame(-norm2[1]) &&
// Normal[2].IsPracticallySame(-norm2[2])) segmentBool = true; //All points intersect
//Set the intersection vertices
double[][] vertices;
if (segmentBool)
{
vertices = new[] { arc.Nodes[0].Vector, arc.Nodes[1].Vector };
}
else
{
//Find points of intersection between two planes
var position1 = Normal.crossProduct(norm2).normalize(3);
var position2 = new[] { -position1[0], -position1[1], -position1[2] };
vertices = new[] { position1, position2 };
}
for (var i = 0; i < 2; i++)
{
double l1;
double l2;
double l3;
//If not on the same plane, check to see if intersection is on arc.
if (!segmentBool)
{
l1 = arc.ArcLength;
l2 = ArcLength(arc.Nodes[0].Vector, vertices[i]);
l3 = ArcLength(arc.Nodes[1].Vector, vertices[i]);
//Check to see if the intersection is on the arc. We already know it is on the great circle.
//It is ok if the vertex == the node.Vector.
var total = l1 - l2 - l3;
if ((l2.IsNegligible() && l3.IsNegligible()) || Math.Abs(total) > 0.00001)
{
continue; //Go to next.
}
}
var intersectionVertex = new Vertex(vertices[i]);
//Find distance from the reference arc's antipodal point 1 in direction of the reference arc.
l1 = referenceArc.ArcLength;
l2 = Math.PI - referenceArc.ArcLength;
l3 = ArcLength(referenceArc.Nodes[0].Vector, vertices[i]);
var l4 = ArcLength(referenceArc.Nodes[1].Vector, vertices[i]);
var l5 = ArcLength(antiPoint1, vertices[i]);
Intersection intersection;
//Case 1: Inbetween point1 and point2
var total1 = l1 - l3 - l4;
//Case 2: Inbetween point2 and antiPoint1
var total2 = l2 - l4 - l5;
if (Math.Abs(total1) < 0.00001 || Math.Abs(total2) < 0.00001)
{
intersection = new Intersection(intersectionVertex, l3, arc);
tempIntersections.Add(intersection);
continue;
}
//Case 3: Inbetween antiPoint1 and antiPoint2
//Case 4: Inbetween antiPoint2 and Point1
intersection = new Intersection(intersectionVertex, Constants.TwoPi - l3, arc);
tempIntersections.Add(intersection);
//Only one intersection is possible per arc, since the case of multiple intersections is captured above.
break;
}
}
var tempIntersections2 = tempIntersections.OrderBy(intersection => intersection.SphericalDistance).ToList();
//Remove duplicates
for (var i = 0; i < tempIntersections2.Count - 1; i++)
{
var intersection1 = tempIntersections2[i];
var intersection2 = tempIntersections2[i + 1];
if (Math.Abs(intersection1.SphericalDistance - intersection2.SphericalDistance) > 0.00001)
{
Intersections.Add(intersection1);
}
//Add the last intersection to the list if it was no the same as the current
if (i == tempIntersections2.Count - 2)
{
Intersections.Add(intersection2);
}
}
}
