public bool IsValidConnection(GameObject thisSystem, GameObject targetSystem) //Returns true if no intersection
{
Vector3 lineA = MathsFunctions.ABCLineEquation(thisSystem.transform.position, targetSystem.transform.position); //Line equation from current system to target system
Vector3 roughCentre = (thisSystem.transform.position + targetSystem.transform.position) / 2f;
if (roughCentre.x < 65f && roughCentre.x > 55f) //If the intersection exists in the galactic core, ignore it
{
if (roughCentre.y < 65f && roughCentre.y > 55f)
{
return(false);
}
}
for (int i = 0; i < coordinateList.Count; ++i) //For all existing connections
{
if (coordinateList[i].systemOne == thisSystem && coordinateList[i].systemTwo == targetSystem) //If a connection already exists between the current system and the target system, continue to the next connection
{
continue;
}
if (coordinateList[i].systemTwo == thisSystem && coordinateList[i].systemOne == targetSystem) //Continuation of above
{
continue;
}
if (coordinateList[i].systemOne == thisSystem || coordinateList[i].systemTwo == thisSystem) //If the connection contains this system it will not make intersections with the temporary connection
{
continue;
}
if (coordinateList[i].systemOne == targetSystem || coordinateList[i].systemTwo == targetSystem) //If the connection contains the target system it will not make intersections with the temporary connection
{
continue;
}
//if(CheckIfIntersectionCouldOccur(thisSystem, targetSystem, coordinateList[i].systemOne, coordinateList[i].systemTwo) == false)
//{
// continue;
//
Vector3 lineB = MathsFunctions.ABCLineEquation(coordinateList[i].systemOne.transform.position, coordinateList[i].systemTwo.transform.position); //Get the line equation between of the connection
Vector2 intersection = MathsFunctions.IntersectionOfTwoLines(lineA, lineB); //Find the intersection of the two lines
if (intersection == Vector2.zero) //If the lines are parallel the method returns a zero vector continue to the next connection
{
continue;
}
if (MathsFunctions.PointLiesOnLine(thisSystem.transform.position, targetSystem.transform.position, intersection)) //If the intersection lies on the temporary connection
{
if (MathsFunctions.PointLiesOnLine(coordinateList[i].systemOne.transform.position, coordinateList[i].systemTwo.transform.position, intersection)) //And it lies on the current permanent connection
{
return(false); //Return true, an intersection does exist
}
}
}
return(true);
}
public bool CheckIsDelaunay(Triangle triOne, Triangle triTwo)
{
List <GameObject> sharedSides = MasterScript.triangulation.CheckIfSharesSide(triOne, triTwo); //Find if triangles share a side (this actually returns the 2 shared and 2 unshared vertices)
if (sharedSides.Count == 4) //If 4 vertices are shared
{
GameObject sharedPointA = sharedSides[0]; //Assign the shared points
GameObject sharedPointB = sharedSides[1];
GameObject unsharedPointA = sharedSides[2]; //Assign the unshared points
GameObject unsharedPointB = sharedSides[3];
float angleAlpha = 0f, angleBeta = 0f; //Set some angles to 0
angleAlpha = MathsFunctions.AngleBetweenLineSegments(unsharedPointA.transform.position, sharedPointA.transform.position, sharedPointB.transform.position); //First angle is at one unshared point
angleBeta = MathsFunctions.AngleBetweenLineSegments(unsharedPointB.transform.position, sharedPointA.transform.position, sharedPointB.transform.position); //Second angle is at the other unshared point
Vector3 sharedPointLine = MathsFunctions.ABCLineEquation(sharedPointA.transform.position, sharedPointB.transform.position); //Get the line between the shared points
Vector3 unsharedPointLine = MathsFunctions.ABCLineEquation(unsharedPointA.transform.position, unsharedPointB.transform.position); //Get the line between the unshared points
Vector2 intersection = MathsFunctions.IntersectionOfTwoLines(sharedPointLine, unsharedPointLine); //Find the intersection of the two lines
if (MathsFunctions.PointLiesOnLine(sharedPointA.transform.position, sharedPointB.transform.position, intersection) == false) //If the intersection does not lie between the shared points then this is a non convex hull
{
return(true); //So it cannot be flipped, continue to the next triangle
}
if (angleAlpha + angleBeta > 180f) //If the polygon is convex, and the two angles combine to be greater than 180 degrees, the triangles are non delaunay, so we flip them
{
int triPosOne = MasterScript.triangulation.triangles.IndexOf(triOne); //Find the position of the two triangles in the triangles list
int triPosTwo = MasterScript.triangulation.triangles.IndexOf(triTwo);
triOne.points[0] = unsharedPointA; //Reassign the vertices of tri one to make the previously unshared vertices the shared vertices. One of the previously shared vertices is now the unshared vertex.
triOne.points[1] = unsharedPointB;
triOne.points[2] = sharedPointA;
triOne.lines[0] = MathsFunctions.ABCLineEquation(triOne.points[0].transform.position, triOne.points[1].transform.position); //Get the line equations for all the sides
triOne.lines[1] = MathsFunctions.ABCLineEquation(triOne.points[1].transform.position, triOne.points[2].transform.position);
triOne.lines[2] = MathsFunctions.ABCLineEquation(triOne.points[2].transform.position, triOne.points[0].transform.position);
MasterScript.triangulation.triangles[triPosOne] = triOne; //Replace the original triangle with this new, flipped triangle
triTwo.points[0] = unsharedPointA; //Do the same for tri two
triTwo.points[1] = unsharedPointB;
triTwo.points[2] = sharedPointB;
triTwo.lines[0] = MathsFunctions.ABCLineEquation(triTwo.points[0].transform.position, triTwo.points[1].transform.position);
triTwo.lines[1] = MathsFunctions.ABCLineEquation(triTwo.points[1].transform.position, triTwo.points[2].transform.position);
triTwo.lines[2] = MathsFunctions.ABCLineEquation(triTwo.points[2].transform.position, triTwo.points[0].transform.position);
MasterScript.triangulation.triangles[triPosTwo] = triTwo;
++flips; //Increase the number of flips that have been made this pass.
return(false); //Return false (a flip has been made)
}
}
return(true); //Otherwise continue to the next triangle
}
private bool IsIllegalIntersection(int externalPoint, int unvisitedPoint, Vector3 curToExtLine)
{
for (int j = 0; j < triangles.Count; ++j) //For every triangle
{
if (triangles[j].isInternal == true) //If the triangle is internal we don't need to worry about it, so move onto the next triangle
{
continue;
}
for (int k = 0; k < 3; ++k) //For each line in that triangle
{
GameObject pointA = null; //Get the points at each end of the line
GameObject pointB = null;
if (k == 0)
{
pointA = triangles[j].points[0];
pointB = triangles[j].points[1];
}
if (k == 1)
{
pointA = triangles[j].points[1];
pointB = triangles[j].points[2];
}
if (k == 2)
{
pointA = triangles[j].points[2];
pointB = triangles[j].points[0];
}
if (pointA.name == externalPoints[externalPoint].name || pointB.name == externalPoints[externalPoint].name) //If the line contains the external point we can ignore it
{
continue;
}
Vector2 intersection = MathsFunctions.IntersectionOfTwoLines(curToExtLine, triangles[j].lines[k]); //Get the intersection of the line with the current star to external point line
if (MathsFunctions.PointLiesOnLine(externalPoints[externalPoint].transform.position, unvisitedStars[unvisitedPoint].transform.position, intersection)) //If the point lies elsewhere on the line
{
if (MathsFunctions.PointLiesOnLine(pointA.transform.position, pointB.transform.position, intersection))
{
return(true); //This IS an illegal intersection so return that, otherwise keep checking
}
}
}
}
return(false);
}
private void CheckForNonDelaunayTriangles()
{
List <Triangle> numberofnondelaunay = new List <Triangle>();
for (int i = 0; i < triangles.Count; ++i)
{
for (int j = 0; j < triangles.Count; ++j)
{
if (i == j)
{
continue;
}
List <GameObject> sharedSides = CheckIfSharesSide(triangles[i], triangles[j]);
if (sharedSides.Count == 4)
{
GameObject sharedPointA = sharedSides[0];
GameObject sharedPointB = sharedSides[1];
GameObject unsharedPointA = sharedSides[2];
GameObject unsharedPointB = sharedSides[3];
float angleAlpha = 0f, angleBeta = 0f;
angleAlpha = MathsFunctions.AngleBetweenLineSegments(unsharedPointA.transform.position, sharedPointA.transform.position, sharedPointB.transform.position);
angleBeta = MathsFunctions.AngleBetweenLineSegments(unsharedPointB.transform.position, sharedPointA.transform.position, sharedPointB.transform.position);
Vector3 sharedPointLine = MathsFunctions.ABCLineEquation(sharedPointA.transform.position, sharedPointB.transform.position);
Vector3 unsharedPointLine = MathsFunctions.ABCLineEquation(unsharedPointA.transform.position, unsharedPointB.transform.position);
Vector2 intersection = MathsFunctions.IntersectionOfTwoLines(sharedPointLine, unsharedPointLine);
if (MathsFunctions.PointLiesOnLine(sharedPointA.transform.position, sharedPointB.transform.position, intersection) == false) //Is non-convex
{
continue;
}
if (angleBeta + angleAlpha > 180)
{
numberofnondelaunay.Add(triangles[i]);
}
}
}
}
Debug.Log(numberofnondelaunay.Count + " | " + triangles.Count);
}