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 void Update()
{
if (MasterScript.systemListConstructor.loaded == true && iterator == 0)
{
//start = true;
}
if (start == true)
{
triangles.Clear();
tempTri.Clear();
unvisitedStars.Clear();
externalPoints.Clear();
CacheNearestStars(); //First add all the star systems to a list
Triangle newTri = new Triangle(); //Create a new triangle
newTri.points.Add(unvisitedStars [0]); //Add the first 3 ordered points from the centre
newTri.points.Add(unvisitedStars [1]);
newTri.points.Add(unvisitedStars[2]);
newTri.lines.Add(MathsFunctions.ABCLineEquation(newTri.points[0].transform.position, newTri.points[1].transform.position)); //Calculate the line equations between the points
newTri.lines.Add(MathsFunctions.ABCLineEquation(newTri.points[1].transform.position, newTri.points[2].transform.position));
newTri.lines.Add(MathsFunctions.ABCLineEquation(newTri.points[2].transform.position, newTri.points[0].transform.position));
externalPoints.Add(unvisitedStars [0]); //Add the points to the external points list
externalPoints.Add(unvisitedStars [1]);
externalPoints.Add(unvisitedStars [2]);
triangles.Add(newTri); //Add the triangle to the triangle list
unvisitedStars.RemoveRange(0, 3); //Remove the points from the unvisited points list
start = false;
iterate = true;
timer = Time.time;
}
if (start == false && iterate == true)
{
if (iterator < unvisitedStars.Count)
{
LinkPointToTris(iterator);
CacheTempTris(iterator);
DrawDebugTriangles();
++iterator;
timer = Time.time;
}
if (iterator == unvisitedStars.Count)
{
DrawDebugTriangles();
iterate = false;
}
}
}
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 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);
}
public void SimpleTriangulation() //This function controls the triangulation and conversion to delaunay of the stars
{
CacheNearestStars(); //First add all the star systems to a list
Triangle newTri = new Triangle(); //Create a new triangle
newTri.points.Add(unvisitedStars [0]); //Add the first 3 ordered points from the centre
newTri.points.Add(unvisitedStars [1]);
newTri.points.Add(unvisitedStars[2]);
newTri.lines.Add(MathsFunctions.ABCLineEquation(newTri.points[0].transform.position, newTri.points[1].transform.position)); //Calculate the line equations between the points
newTri.lines.Add(MathsFunctions.ABCLineEquation(newTri.points[1].transform.position, newTri.points[2].transform.position));
newTri.lines.Add(MathsFunctions.ABCLineEquation(newTri.points[2].transform.position, newTri.points[0].transform.position));
externalPoints.Add(unvisitedStars [0]); //Add the points to the external points list
externalPoints.Add(unvisitedStars [1]);
externalPoints.Add(unvisitedStars [2]);
triangles.Add(newTri); //Add the triangle to the triangle list
unvisitedStars.RemoveRange(0, 3); //Remove the points from the unvisited points list
for (int i = 0; i < unvisitedStars.Count; ++i) //For all unchecked points
{
LinkPointToTris(i); //Link this unvisited point to all possible external points
CacheTempTris(i); //Add all the triangles formed by this linking to the triangle list
}
bool isDelaunay = false; //Say that the list isn't delaunay
while (isDelaunay == false) //While it isn't delaunay
{
isDelaunay = MasterScript.voronoiGenerator.TriangulationToDelaunay(); //Make it delaunay, if the method returns true, the triangulation is delaunay and the while loop will stop
}
CheckForNonDelaunayTriangles(); //Debugging method outputs the number of non-delaunay triangles to the log. This has not output any bad values for some time.
}
private void LinkPointToTris(int curPoint) //Send the current unvisited star as the seed point SOMETHING WRONG
{
for (int i = 0; i < externalPoints.Count; ++i) //For all the external points
{
int nextPoint = i + 1; //Assign the next point
if (nextPoint == externalPoints.Count) //If the next point is out of range
{
nextPoint = 0; //Set it to the first point in the list
}
Vector3 lineCurToExternal = MathsFunctions.ABCLineEquation(unvisitedStars[curPoint].transform.position, externalPoints[i].transform.position); //Create a line between the external point and the unvisited star
if (IsIllegalIntersection(i, curPoint, lineCurToExternal)) //If there is an illegal intersection between the external point-current point line and the external point-unvisited point line
{
continue; //Move onto the next external point
}
Vector3 lineCurToNextExternal = MathsFunctions.ABCLineEquation(unvisitedStars[curPoint].transform.position, externalPoints[nextPoint].transform.position);
if (IsIllegalIntersection(nextPoint, curPoint, lineCurToNextExternal)) //If there is an illegal intersection between the next point-current point line and the external point-unvisited point line
{
continue; //Move onto the next external point
}
bool illegal = false; //Say that the line is not illegal
for (int j = 0; j < externalPoints.Count; ++j) //Check through all other external points
{
if (j == i || j == nextPoint)
{
continue;
}
if (MathsFunctions.IsInTriangle(externalPoints[i].transform.position, externalPoints[nextPoint].transform.position, unvisitedStars[curPoint].transform.position, externalPoints[j].transform.position) == true) //If the point lies in any of the triangles
{
//if(MathsFunctions.PointsAreColinear(externalPoints[i].transform.position, externalPoints[nextPoint].transform.position, externalPoints[j].transform.position) == false)
//{
//if(MathsFunctions.PointsAreColinear(externalPoints[i].transform.position, unvisitedStars[curPoint].transform.position, externalPoints[j].transform.position) == false)
//{
//if(MathsFunctions.PointsAreColinear(externalPoints[nextPoint].transform.position, unvisitedStars[curPoint].transform.position, externalPoints[j].transform.position) == false)
//{
illegal = true; //It is an illegal triangle
break; //
//}
//}
//}
}
}
if (illegal) //If it's an illegal triangle
{
continue; //Skip to the next point
}
GameObject pointA = externalPoints[i]; //Otherwise assign the points of the triangle
GameObject pointB = externalPoints[nextPoint];
GameObject pointC = unvisitedStars[curPoint];
Triangle newTri = new Triangle(); //Create a new triangle object
newTri.points.Add(pointA); //Add the points
newTri.points.Add(pointB);
newTri.points.Add(pointC);
newTri.lines.Add(MathsFunctions.ABCLineEquation(pointA.transform.position, pointB.transform.position)); //Calculate the line equations between the points
newTri.lines.Add(MathsFunctions.ABCLineEquation(pointB.transform.position, pointC.transform.position));
newTri.lines.Add(MathsFunctions.ABCLineEquation(pointC.transform.position, pointA.transform.position));
tempTri.Add(newTri); //Add the triangle to the temptriangle list
}
}