public static Vector2D GetPointLineIntersectLine(Pair2D lineA, Pair2D lineB)
{
double dx_cx = lineB.B.x - lineB.A.x;
double dy_cy = lineB.B.y - lineB.A.y;
double bx_ax = lineA.B.x - lineA.A.x;
double by_ay = lineA.B.y - lineA.A.y;
double de = bx_ax * dy_cy - by_ay * dx_cx;
if (System.Math.Abs(de) < 0.0001d)
{
return(null);
}
if (de > -tor && de < tor)
{
return(null);
}
double ax_cx = lineA.A.x - lineB.A.x;
double ay_cy = lineA.A.y - lineB.A.y;
double r = (ay_cy * dx_cx - ax_cx * dy_cy) / de;
double s = (ay_cy * bx_ax - ax_cx * by_ay) / de;
if ((r < 0) || (r > 1) || (s < 0) || (s > 1))
{
return(null);
}
return(new Vector2D(lineA.A.x + r * bx_ax, lineA.A.y + r * by_ay));
}
public static bool GetBoolLineIntersectLine(Pair2D lineA, Pair2D lineB)
{
double dx_cx = lineB.B.x - lineB.A.x;
double dy_cy = lineB.B.y - lineB.A.y;
double bx_ax = lineA.B.x - lineA.A.x;
double by_ay = lineA.B.y - lineA.A.y;
double de = bx_ax * dy_cy - by_ay * dx_cx;
if (System.Math.Abs(de) < 0.0001d)
{
return(false);
}
if (de > -tor && de < tor)
{
return(false);
}
double ax_cx = lineA.A.x - lineB.A.x;
double ay_cy = lineA.A.y - lineB.A.y;
double r = (ay_cy * dx_cx - ax_cx * dy_cy) / de;
double s = (ay_cy * bx_ax - ax_cx * by_ay) / de;
if ((r < 0) || (r > 1) || (s < 0) || (s > 1))
{
return(false);
}
return(true);
}
public static bool SliceIntersectPoly(List <Vector2D> slice, Polygon2D poly)
{
Pair2D pairA = new Pair2D(null, null);
foreach (Vector2D pointA in slice)
{
pairA.B = pointA;
if (pairA.A != null && pairA.B != null)
{
Pair2D pairB = new Pair2D(new Vector2D(poly.pointsList.Last()), null);
foreach (Vector2D pointB in poly.pointsList)
{
pairB.B = pointB;
if (LineIntersectLine(pairA, pairB))
{
return(true);
}
pairB.A = pointB;
}
}
pairA.A = pointA;
}
return(false);
}
public static bool SliceIntersectItself(List <Vector2D> slice)
{
Pair2D pairA = new Pair2D(null, null);
Pair2D pairB = new Pair2D(null, null);
for (int i = 0; i < slice.Count - 1; i++)
{
pairA.A = slice[i];
pairA.B = slice[i + 1];
for (int x = 0; x < slice.Count - 1; x++)
{
pairB.A = slice[x];
pairB.B = slice[x + 1];
if (GetBoolLineIntersectLine(pairA, pairB))
{
if (pairA.A != pairB.A && pairA.B != pairB.B && pairA.A != pairB.B && pairA.B != pairB.A)
{
return(true);
}
}
}
}
return(false);
}
static public bool IntersectLine(Pair2D line, Vector2D circle, float radius)
{
double sx = line.B.x - line.A.x;
double sy = line.B.y - line.A.y;
double q = ((circle.x - line.A.x) * (line.B.x - line.A.x) + (circle.y - line.A.y) * (line.B.y - line.A.y)) / (sx * sx + sy * sy);
if (q < 0.0f)
{
q = 0.0f;
}
else if (q > 1.0)
{
q = 1.0f;
}
double dx = circle.x - ((1.0f - q) * line.A.x + q * line.B.x);
double dy = circle.y - ((1.0f - q) * line.A.y + q * line.B.y);
if (dx * dx + dy * dy < radius * radius)
{
return(true);
}
else
{
return(false);
}
}
static public void RemoveClosePoints(List <Vector2D> list, float closePrecision = 0.005f)
{
List <Vector2D> points = new List <Vector2D>(list);
Pair2D pair = new Pair2D(list.Last(), null);
//Vector2D lastPos = null;
for (int i = 0; i < points.Count; i++)
{
pair.B = points[i];
if (points.Count < 4)
{
break;
}
if (Vector2D.Distance(pair.A, pair.B) < closePrecision)
{
//Debug.LogWarning("Smart Utility 2D: Polygon points are too close");
list.Remove(pair.A);
}
else
{
pair.A = pair.B;
}
}
}
public static bool LineIntersectLine(Pair2D lineA, Pair2D lineB)
{
if (GetBoolLineIntersectLine(lineA, lineB))
{
return(true);
}
return(false);
}
static public bool IntersectSlice(List <Vector2D> points, Vector2D circle, float radius)
{
foreach (Pair2D id in Pair2D.GetList(points, false)) // Remove GetList()
{
if (IntersectLine(id, circle, radius) == true)
{
return(true);
}
}
return(false);
}
static public bool IntersectPolygon(Polygon2D poly, Vector2D circle, float radius)
{
foreach (Pair2D id in Pair2D.GetList(poly.pointsList)) // Remove GetList()
{
if (IntersectLine(id, circle, radius) == true)
{
return(true);
}
}
return(false);
}
/// <summary>
/// Return a list which starts with first interesction with given line
/// </summary>
public static List <Vector2D> GetListStartingIntersectLine(List <Vector2D> pointsList, Pair2D line)
{
List <Vector2D> result = new List <Vector2D> ();
bool start = false;
Pair2D id = pair2D;
Vector2D r;
id.B = pointsList.Last();
for (int x = 0; x < pointsList.Count; x++)
{
id.A = pointsList[x];
r = Math2D.GetPointLineIntersectLine(id, line);
if (start == true)
{
result.Add(id.B);
}
if (r != null)
{
result.Add(r);
start = true;
}
id.B = id.A;
}
id.B = pointsList.Last();
for (int x = 0; x < pointsList.Count; x++)
{
id.A = pointsList[x];
r = Math2D.GetPointLineIntersectLine(id, line);
if (start == true)
{
result.Add(id.B);
}
if (r != null)
{
result.Add(r);
start = false;
}
id.B = id.A;
}
return(result);
}
public List <Vector2D> GetListLineIntersectPoly(Pair2D line)
{
List <Vector2D> intersections = Math2D.GetListLineIntersectPoly(line, this);
foreach (Polygon2D poly in holesList)
{
foreach (Vector2D p in Math2D.GetListLineIntersectPoly(line, poly))
{
intersections.Add(p);
}
}
return(intersections);
}
public List <Polygon2D> LineIntersectHoles(Pair2D pair)
{
List <Polygon2D> resultList = new List <Polygon2D>();
foreach (Polygon2D poly in holesList)
{
if (Math2D.LineIntersectPoly(pair, poly) == true)
{
resultList.Add(poly);
}
}
return(resultList);
}
public static bool PointInPoly(Vector2D point, Polygon2D poly)
{
if (poly.pointsList.Count < 3)
{
return(false);
}
int total = 0;
int diff = 0;
Pair2D id = pair2D;
id.A = poly.pointsList[poly.pointsList.Count - 1];
for (int i = 0; i < poly.pointsList.Count; i++)
{
id.B = poly.pointsList[i];
diff = (GetQuad(point, id.A) - GetQuad(point, id.B));
switch (diff)
{
case -2:
case 2:
if ((id.B.x - (((id.B.y - point.y) * (id.A.x - id.B.x)) / (id.A.y - id.B.y))) < point.x)
{
diff = -diff;
}
break;
case 3:
diff = -1;
break;
case -3:
diff = 1;
break;
default:
break;
}
total += diff;
id.A = id.B;
}
return(Mathf.Abs(total) == 4);
}
public static bool LineIntersectSlice(Pair2D pairA, List <Vector2D> slice)
{
Pair2D pairB = new Pair2D(null, null);
for (int i = 0; i < slice.Count - 1; i++)
{
pairB.A = slice[i];
pairB.B = slice[i + 1];
if (LineIntersectLine(pairA, pairB))
{
return(true);
}
}
return(false);
}
public static List <Vector2D> GetListLineIntersectSlice(Pair2D pair, List <Vector2D> slice)
{
List <Vector2D> resultList = new List <Vector2D> ();
Pair2D id = new Pair2D(null, null);
Vector2D result;
for (int i = 0; i < slice.Count - 1; i++)
{
id.A = slice[i];
id.B = slice[i + 1];
result = GetPointLineIntersectLine(id, pair);
if (result != null)
{
resultList.Add(result);
}
}
return(resultList);
}
public static double PointToLine(Vector2D p, Pair2D pair)
{
double A = p.x - pair.A.x;
double B = p.y - pair.A.y;
double C = pair.B.x - pair.A.x;
double D = pair.B.y - pair.A.y;
double dot = A * C + B * D;
double len_sq = C * C + D * D;
double param = -1;
// in case of 0 length line
if (len_sq != 0)
{
param = dot / len_sq;
}
double xx, yy;
if (param < 0)
{
xx = pair.A.x;
yy = pair.A.y;
}
else if (param > 1)
{
xx = pair.B.x;
yy = pair.B.y;
}
else
{
xx = pair.A.x + param * C;
yy = pair.A.y + param * D;
}
double dx = p.x - xx;
double dy = p.y - yy;
return(System.Math.Sqrt(dx * dx + dy * dy));
}
public static bool LineIntersectPoly(Pair2D line, Polygon2D poly)
{
Pair2D pair = line_intersect_poly;
pair.A = new Vector2D(poly.pointsList.Last());
pair.B = new Vector2D(Vector2.zero);
for (int i = 0; i < poly.pointsList.Count; i++)
{
pair.B = poly.pointsList[i];
if (LineIntersectLine(line, pair))
{
return(true);
}
pair.A = pair.B;
}
return(false);
}
public static Rect GetBounds(Pair2D pair)
{
double rMinX = 1e+10f;
double rMinY = 1e+10f;
double rMaxX = -1e+10f;
double rMaxY = -1e+10f;
Vector2D id = pair.A;
rMinX = System.Math.Min(rMinX, id.x);
rMinY = System.Math.Min(rMinY, id.y);
rMaxX = System.Math.Max(rMaxX, id.x);
rMaxY = System.Math.Max(rMaxY, id.y);
id = pair.B;
rMinX = System.Math.Min(rMinX, id.x);
rMinY = System.Math.Min(rMinY, id.y);
rMaxX = System.Math.Max(rMaxX, id.x);
rMaxY = System.Math.Max(rMaxY, id.y);
return(new Rect((float)rMinX, (float)rMinY, (float)System.Math.Abs(rMinX - rMaxX), (float)System.Math.Abs(rMinY - rMaxY)));
}
// Getting List is Slower
public static List <Vector2D> GetListLineIntersectPoly(Pair2D line, Polygon2D poly)
{
List <Vector2D> result = new List <Vector2D>();
Vector2D intersection;
Pair2D pair = new Pair2D(new Vector2D(poly.pointsList.Last()), null);
for (int i = 0; i < poly.pointsList.Count; i++)
{
pair.B = poly.pointsList[i];
intersection = GetPointLineIntersectLine(line, pair);
if (intersection != null)
{
result.Add(intersection);
}
pair.A = pair.B;
}
return(result);
}
// Might Break (Only for 2 collisions)
/// <summary>
/// Return a list which starts with first interesction with given slice
/// </summary>
public static List <Vector2D> GetListStartingIntersectSlice(List <Vector2D> pointsList, List <Vector2D> slice)
{
List <Vector2D> result = new List <Vector2D> ();
bool start = false;
List <Pair2D> pointsPairList = Pair2D.GetList(pointsList);
foreach (Pair2D p in pointsPairList)
{
List <Vector2D> r = Math2D.GetListLineIntersectSlice(p, slice);
if (start == true)
{
result.Add(p.A);
}
if (r.Count > 0)
{
result.Add(r.First());
start = true;
}
}
foreach (Pair2D p in pointsPairList)
{
List <Vector2D> r = Math2D.GetListLineIntersectSlice(p, slice);
if (start == true)
{
result.Add(p.A);
}
if (r.Count > 0)
{
result.Add(r.First());
start = false;
}
}
return(result);
}
// Lighting 2D
public static List <Vector2D> GetConvexHull(List <Vector2D> points)
{
//If we have just 3 points, then they are the convex hull, so return those
if (points.Count == 3)
{
//These might not be ccw, and they may also be colinear
return(points);
}
//If fewer points, then we cant create a convex hull
if (points.Count < 3)
{
return(null);
}
//The list with points on the convex hull
List <Vector2D> convexHull = new List <Vector2D>();
//Step 1. Find the vertex with the smallest x coordinate
//If several have the same x coordinate, find the one with the smallest z
Vector2D startVertex = points[0];
Vector2 startPos = startVertex.ToVector2();
for (int i = 1; i < points.Count; i++)
{
Vector2 testPos = points[i].ToVector2();
//Because of precision issues, we use Mathf.Approximately to test if the x positions are the same
if (testPos.x < startPos.x || (Mathf.Approximately(testPos.x, startPos.x) && testPos.y < startPos.y))
{
startVertex = points[i];
startPos = startVertex.ToVector2();
}
}
//This vertex is always on the convex hull
convexHull.Add(startVertex);
points.Remove(startVertex);
//Step 2. Loop to generate the convex hull
Vector2D currentPoint = convexHull[0];
//Store colinear points here - better to create this list once than each loop
List <Vector2D> colinearPoints = new List <Vector2D>();
int counter = 0;
while (true)
{
//After 2 iterations we have to add the start position again so we can terminate the algorithm
//Cant use convexhull.count because of colinear points, so we need a counter
if (counter == 2)
{
points.Add(convexHull[0]);
}
//Pick next point randomly
Vector2D nextPoint = points[Random.Range(0, points.Count)];
//To 2d space so we can see if a point is to the left is the vector ab
Vector2 a = currentPoint.ToVector2();
Vector2 b = nextPoint.ToVector2();
//Test if there's a point to the right of ab, if so then it's the new b
for (int i = 0; i < points.Count; i++)
{
//Dont test the point we picked randomly
if (points[i].Equals(nextPoint))
{
continue;
}
Vector2 c = points[i].ToVector2();
//Where is c in relation to a-b
// < 0 -> to the right
// = 0 -> on the line
// > 0 -> to the left
float relation = IsAPointLeftOfVectorOrOnTheLine(a, b, c);
//Colinear points
//Cant use exactly 0 because of floating point precision issues
//This accuracy is smallest possible, if smaller points will be missed if we are testing with a plane
float accuracy = 0.00001f;
if (relation < accuracy && relation > -accuracy)
{
colinearPoints.Add(points[i]);
}
//To the right = better point, so pick it as next point on the convex hull
else if (relation < 0f)
{
nextPoint = points[i];
b = nextPoint.ToVector2();
//Clear colinear points
colinearPoints.Clear();
}
//To the left = worse point so do nothing
}
//If we have colinear points
if (colinearPoints.Count > 0)
{
colinearPoints.Add(nextPoint);
//Sort this list, so we can add the colinear points in correct order
colinearPoints = colinearPoints.OrderBy(n => Vector3.SqrMagnitude(n.ToVector2() - currentPoint.ToVector2())).ToList();
convexHull.AddRange(colinearPoints);
currentPoint = colinearPoints[colinearPoints.Count - 1];
//Remove the points that are now on the convex hull
for (int i = 0; i < colinearPoints.Count; i++)
{
points.Remove(colinearPoints[i]);
}
colinearPoints.Clear();
}
else
{
convexHull.Add(nextPoint);
points.Remove(nextPoint);
currentPoint = nextPoint;
}
//Have we found the first point on the hull? If so we have completed the hull
if (currentPoint.Equals(convexHull[0]))
{
//Then remove it because it is the same as the first point, and we want a convex hull with no duplicates
convexHull.RemoveAt(convexHull.Count - 1);
break;
}
counter += 1;
}
return(convexHull);
}
public static Mesh Triangulate3D(Polygon2D polygon, float z, Vector2 UVScale, Vector2 UVOffset, float UVRotation, Triangulation triangulation)
{
polygon.Normalize();
Mesh result = null;
switch (triangulation)
{
case Triangulation.Advanced:
List <Vector2> uvs = new List <Vector2>();
List <Vector3> sideVertices = new List <Vector3>();
List <int> sideTriangles = new List <int>();
Vector3 pointA = new Vector3(0, 0, 0);
Vector3 pointB = new Vector3(0, 0, 0);
Vector3 pointC = new Vector3(0, 0, z);
Vector3 pointD = new Vector3(0, 0, z);
Vector2 uv0 = new Vector2();
Vector2 uv1 = new Vector2();
float a, b;
int vCount = 0;
Pair2D pair = new Pair2D(new Vector2D(polygon.pointsList.Last()), null);
foreach (Vector2D p in polygon.pointsList)
{
pair.B = p;
pointA.x = (float)pair.A.x;
pointA.y = (float)pair.A.y;
pointB.x = (float)pair.B.x;
pointB.y = (float)pair.B.y;
pointC.x = (float)pair.B.x;
pointC.y = (float)pair.B.y;
pointD.x = (float)pair.A.x;
pointD.y = (float)pair.A.y;
sideVertices.Add(pointA);
sideVertices.Add(pointB);
sideVertices.Add(pointC);
sideVertices.Add(pointD);
a = ((float)pair.A.x + 25f) / 50 + UVOffset.x / 2;
b = ((float)pair.B.x + 25f) / 50 + UVOffset.x / 2;
uv0.x = a;
uv0.y = a;
uv1.x = b;
uv1.y = b;
uvs.Add(new Vector2(0, 0));
uvs.Add(new Vector2(0, 1));
uvs.Add(new Vector2(1, 1));
uvs.Add(new Vector2(1, 0));
sideTriangles.Add(vCount + 2);
sideTriangles.Add(vCount + 1);
sideTriangles.Add(vCount + 0);
sideTriangles.Add(vCount + 0);
sideTriangles.Add(vCount + 3);
sideTriangles.Add(vCount + 2);
vCount += 4;
pair.A = pair.B;
}
Mesh mainMesh = new Mesh();
mainMesh.subMeshCount = 2;
Mesh surfaceMesh = PerformTriangulationAdvanced(polygon, UVScale, UVOffset, UVRotation);
///// UVS /////
foreach (Vector2 p in surfaceMesh.uv)
{
uvs.Add(p);
}
foreach (Vector2 p in surfaceMesh.uv)
{
uvs.Add(p);
}
surfaceMesh.triangles = surfaceMesh.triangles.Reverse().ToArray();
///// VERTICES ////
List <Vector3> vertices = new List <Vector3>();
foreach (Vector3 v in sideVertices)
{
vertices.Add(v);
}
foreach (Vector3 v in surfaceMesh.vertices)
{
Vector3 nV = v;
nV.z = z;
vertices.Add(nV);
}
foreach (Vector3 v in surfaceMesh.vertices)
{
vertices.Add(v);
}
mainMesh.SetVertices(vertices);
///// TRIANGLES /////
List <int> triangles = new List <int>();
foreach (int p in sideTriangles)
{
triangles.Add(p);
}
mainMesh.SetTriangles(triangles, 0);
triangles.Clear();
int count = sideVertices.Count();
foreach (int p in surfaceMesh.triangles)
{
triangles.Add(p + count);
}
int trisCount = surfaceMesh.triangles.Count() / 3;
int[] tris = surfaceMesh.triangles;
for (var i = 0; i < trisCount; i++)
{
var tmp = tris[i * 3];
tris[i * 3] = tris[i * 3 + 1];
tris[i * 3 + 1] = tmp;
}
count += surfaceMesh.vertices.Count();
foreach (int p in tris)
{
triangles.Add(p + count);
}
mainMesh.SetTriangles(triangles, 1);
///// LEFTOVERS /////
mainMesh.uv = uvs.ToArray();
mainMesh.RecalculateNormals();
mainMesh.RecalculateBounds();
result = mainMesh;
break;
}
return(result);
}
