dsasadasdasd

Game/Physics2D/Abstract/ICollider2D.cs

@@ -19,7 +19,7 @@ public interface ICollider2D : IBehaviour, IAssignableTransform
     IReadOnlyList<Vector2> Vertices { get; }
 
 
-    bool CheckCollision(Vector2 point, ICollider2D otherCollider, out CollisionInformation collisionInformation);
+    bool CheckCollision(Vector2 point, ICollider2D otherCollider, out CollisionInformation? collisionInformation);
 
     void RecalculateVertices();
 }

Game/Physics2D/Collider2DBehaviour.cs

@@ -2,8 +2,11 @@ using System;
 using System.Collections.Generic;
 using System.Collections.ObjectModel;
 using System.Diagnostics.CodeAnalysis;
+
 using Microsoft.Xna.Framework;
+
 using Pong;
+
 using Syntriax.Engine.Core;
 using Syntriax.Engine.Core.Abstract;
 using Syntriax.Engine.Graphics.TwoDimensional;
@@ -11,6 +14,7 @@ using Syntriax.Engine.Physics2D.Abstract;
 
 namespace Syntriax.Engine.Physics2D;
 
+
 public class Collider2DBehaviour(IList<Vector2> vertices) : BehaviourOverride, ICollider2D
 {
     private List<Triangle> triangles = new List<Triangle>(32);
@@ -49,19 +53,19 @@ public class Collider2DBehaviour(IList<Vector2> vertices) : BehaviourOverride, I
 
         foreach (var triangle in triangles)
         {
-            if (!isInside(point, triangle))
+            if (!PhysicsMath.IsInTriangle(point, triangle))
                 continue;
 
             OnCollision?.Invoke(this, otherCollider);
 
-            Edge main = new() { A = otherCollider.Transform.Position, B = point };
+            Line main = new(otherCollider.Transform.Position, point);
 
-            foreach (var edge in GetEdges(triangle))
+            foreach (var line in PhysicsMath.GetLines([triangle.A, triangle.B, triangle.C]))
             {
-                if (!DoIntersect(main, edge))
+                if (!PhysicsMath.DoIntersect(main, line))
                     continue;
 
-                Vector2 contactPoint = ClosestPointOnEdge(point, edge);
+                Vector2 contactPoint = PhysicsMath.ClosestPointOnLine(point, line);
 
                 Vector2 normal = contactPoint - point;
                 if (normal.LengthSquared() < 0.001f)
@@ -89,11 +93,11 @@ public class Collider2DBehaviour(IList<Vector2> vertices) : BehaviourOverride, I
             _vertices.Add(scaledPosition + Transform.Position);
         }
 
-        Triangle superTriangle = GetSuperTriangle(_vertices);
+        Triangle superTriangle = PhysicsMath.GetSuperTriangle(_vertices);
         triangles.Add(superTriangle);
 
         List<Triangle> badTriangles = new(32);
-        List<Edge> polygon = new(32);
+        List<Line> polygon = new(32);
 
         foreach (var vertex in _vertices)
         {
@@ -102,30 +106,21 @@ public class Collider2DBehaviour(IList<Vector2> vertices) : BehaviourOverride, I
 
             foreach (var triangle in triangles)
             {
-                Circle circle = GetCircumCircle(triangle);
+                Circle circle = PhysicsMath.GetCircumCircle(triangle);
                 if (Vector2.DistanceSquared(circle.Center, vertex) <= circle.Radius * circle.Radius)
                     badTriangles.Add(triangle);
             }
 
             foreach (var triangle in badTriangles)
-                foreach (var edge in GetEdges(triangle))
+                foreach (var line in PhysicsMath.GetLines([triangle.A, triangle.B, triangle.C]))
-                {
+                    if (PhysicsMath.DoesLineExistInVertices(line, [triangle.A, triangle.B, triangle.C]))
-                    if (DoesEdgeExistInTriangles(edge, badTriangles))
+                        polygon.Add(line);
-                        polygon.Add(edge);
-                }
 
             foreach (var triangle in badTriangles)
                 triangles.Remove(triangle);
 
-            foreach (var edge in polygon)
+            foreach (var line in polygon)
-            {
+                triangles.Add(new(line.From, line.To, vertex));
-                triangles.Add(new()
-                {
-                    A = edge.A,
-                    B = edge.B,
-                    C = vertex
-                });
-            }
         }
 
         for (int i = triangles.Count - 1; i >= 0; i--)
@@ -150,15 +145,15 @@ public class Collider2DBehaviour(IList<Vector2> vertices) : BehaviourOverride, I
         for (int i = 0; i < triangles.Count; i++)
         {
             Triangle triangle = triangles[i];
-            foreach (var edge in GetEdges(triangle))
+            foreach (var line in PhysicsMath.GetLines([triangle.A, triangle.B, triangle.C]))
             {
                 GameObject gameObject = Game1.gameManager.InstantiateGameObject<GameObject>();
                 DisplayableSpriteBehaviour displayableSpriteBehaviour = gameObject.BehaviourController.AddBehaviour<DisplayableSpriteBehaviour>();
                 displayableSpriteBehaviour.Color = Color.Aqua;
                 displayableSpriteBehaviour.Origin = new(0.5f, 1f);
                 displayableSpriteBehaviour.Assign(Game1.spriteBox);
-                gameObject.Transform.Position = edge.A;
+                gameObject.Transform.Position = line.From;
-                Vector2 vector2 = edge.B - edge.A;
+                Vector2 vector2 = line.To - line.From;
                 gameObject.Transform.Scale = new Vector2(2f, .0f) + Vector2.UnitY * vector2.Length();
                 gameObject.Transform.Rotation = (float)Math.Atan2(vector2.X, vector2.Y);
                 gameObjects.Add(gameObject);
@@ -167,7 +162,7 @@ public class Collider2DBehaviour(IList<Vector2> vertices) : BehaviourOverride, I
                 displayableSpriteBehaviour = gameObject.BehaviourController.AddBehaviour<DisplayableSpriteBehaviour>();
                 displayableSpriteBehaviour.Color = Color.Crimson;
                 displayableSpriteBehaviour.Assign(Game1.spriteBox);
-                gameObject.Transform.Position = edge.B;
+                gameObject.Transform.Position = line.To;
                 gameObject.Transform.Scale = new Vector2(4f, 4f);
                 gameObjects.Add(gameObject);
             }
@@ -187,200 +182,4 @@ public class Collider2DBehaviour(IList<Vector2> vertices) : BehaviourOverride, I
 
     private List<IGameObject> gameObjects = new List<IGameObject>(32);
 
-    private Vector2 ClosestPointOnEdge(Vector2 point, Edge edge)
-    {
-        // Convert edge points to vectors
-        var edgeVector = new Vector2(edge.B.X - edge.A.X, edge.B.Y - edge.A.Y);
-        var pointVector = new Vector2(point.X - edge.A.X, point.Y - edge.A.Y);
-
-        // Calculate the projection of pointVector onto edgeVector
-        double t = (pointVector.X * edgeVector.X + pointVector.Y * edgeVector.Y) / (edgeVector.X * edgeVector.X + edgeVector.Y * edgeVector.Y);
-
-        // Clamp t to the range [0, 1] to ensure the closest point is on the edge
-        t = Math.Max(0, Math.Min(1, t));
-
-        // Calculate the closest point on the edge
-        double closestX = edge.A.X + t * edgeVector.X;
-        double closestY = edge.A.Y + t * edgeVector.Y;
-
-        return new Vector2((float)closestX, (float)closestY);
-    }
-
-    private bool DoesEdgeExistInTriangles(Edge edge, List<Triangle> triangles)
-    {
-        foreach (var triangle in triangles)
-            foreach (var edgeOther in GetEdges(triangle))
-                if (edge.A == edgeOther.A && edge.B == edgeOther.B)
-                    return true;
-                else if (edge.A == edgeOther.B && edge.B == edgeOther.A)
-                    return true;
-        return false;
-    }
-
-    private List<Edge> GetEdges(Triangle triangle)
-        => [
-            new() { A = triangle.A, B = triangle.B },
-            new() { A = triangle.B, B = triangle.C },
-            new() { A = triangle.C, B = triangle.A }
-        ];
-
-    private Triangle GetSuperTriangle(IReadOnlyList<Vector2> vertices)
-    {
-        double minX = double.MaxValue, minY = double.MaxValue;
-        double maxX = double.MinValue, maxY = double.MinValue;
-
-        foreach (Vector2 point in vertices)
-        {
-            minX = Math.Min(minX, point.X);
-            minY = Math.Min(minY, point.Y);
-            maxX = Math.Max(maxX, point.X);
-            maxY = Math.Max(maxY, point.Y);
-        }
-
-        double dx = maxX - minX;
-        double dy = maxY - minY;
-        double deltaMax = Math.Max(dx, dy);
-        double midX = (minX + maxX) / 2;
-        double midY = (minY + maxY) / 2;
-
-        Vector2 p1 = new Vector2((float)midX - 20f * (float)deltaMax, (float)midY - (float)deltaMax);
-        Vector2 p2 = new Vector2((float)midX, (float)midY + 20 * (float)deltaMax);
-        Vector2 p3 = new Vector2((float)midX + 20 * (float)deltaMax, (float)midY - (float)deltaMax);
-
-        return new Triangle() { A = p1, B = p2, C = p3 };
-    }
-
-    private struct Triangle { public Vector2 A, B, C; }
-
-    private double GetArea(Triangle triangle)
-    {
-        return Math.Abs((triangle.A.X * (triangle.B.Y - triangle.C.Y) +
-                         triangle.B.X * (triangle.C.Y - triangle.A.Y) +
-                         triangle.C.X * (triangle.A.Y - triangle.B.Y)) / 2.0);
-    }
-
-    /* A function to check whether point P(x, y) lies
-    inside the triangle formed by A(x1, y1),
-    B(x2, y2) and C(x3, y3) */
-    private bool isInside(Vector2 point, Triangle triangle)
-    {
-        double A = GetArea(triangle);
-        /* Calculate area of triangle ABC */
-        // double A = area(x1, y1, x2, y2, x3, y3);
-
-        double A1 = GetArea(new() { A = point, B = triangle.B, C = triangle.C });
-        /* Calculate area of triangle PBC */
-        // double A1 = area(x, y, x2, y2, x3, y3);
-
-        /* Calculate area of triangle PAC */
-        double A2 = GetArea(new() { A = triangle.A, B = point, C = triangle.C });
-        // double A2 = area(x1, y1, x, y, x3, y3);
-
-        /* Calculate area of triangle PAB */
-        double A3 = GetArea(new() { A = triangle.A, B = triangle.B, C = point });
-        // double A3 = area(x1, y1, x2, y2, x, y);
-
-        /* Check if sum of A1, A2 and A3 is same as A */
-        return A >= A1 + A2 + A3;
-    }
-
-    private struct Edge
-    {
-        public Vector2 A;
-        public Vector2 B;
-    }
-
-    private struct Circle
-    {
-        public double Radius;
-        public Vector2 Center;
-    }
-
-    private Circle GetCircumCircle(Triangle triangle)
-    {
-        Circle result = new();
-
-        Vector2 midAB = (triangle.A + triangle.B) / 2;
-        Vector2 midBC = (triangle.B + triangle.C) / 2;
-
-        double slopeAB = (triangle.B.Y - triangle.A.Y) / (triangle.B.X - triangle.A.X);
-        double slopeBC = (triangle.C.Y - triangle.B.Y) / (triangle.C.X - triangle.B.X);
-
-        // Check if the slopes are not parallel
-        if (Math.Abs(slopeAB - slopeBC) > double.Epsilon)
-        {
-            double x = (slopeAB * slopeBC * (triangle.A.Y - triangle.C.Y) + slopeBC * (triangle.A.X + triangle.B.X) - slopeAB * (triangle.B.X + triangle.C.X)) / (2 * (slopeBC - slopeAB));
-            double y = -(x - (triangle.A.X + triangle.B.X) / 2) / slopeAB + (triangle.A.Y + triangle.B.Y) / 2;
-
-            result.Center = new Vector2((float)x, (float)y);
-            result.Radius = Vector2.Distance(result.Center, triangle.A);
-        }
-        else
-        {
-            // If slopes are parallel, use the midpoints of the sides as the circumcenter
-            result.Center = (midAB + midBC) / 2;
-            result.Radius = Vector2.Distance(result.Center, triangle.A);
-        }
-
-        return result;
-    }
-
-    // Given three collinear points p, q, r, the function checks if 
-    // point q lies on line segment 'pr' 
-    private bool OnSegment(Vector2 p, Vector2 q, Vector2 r)
-    {
-        if (q.X <= Math.Max(p.X, r.X) && q.X >= Math.Min(p.X, r.X) &&
-            q.Y <= Math.Max(p.Y, r.Y) && q.Y >= Math.Min(p.Y, r.Y))
-            return true;
-
-        return false;
-    }
-
-    // To find orientation of ordered triplet (p, q, r). 
-    // The function returns following values 
-    // 0 --> p, q and r are collinear 
-    // 1 --> Clockwise 
-    // 2 --> Counterclockwise 
-    private int Orientation(Vector2 p, Vector2 q, Vector2 r)
-    {
-        // See https://www.geeksforgeeks.org/orientation-3-ordered-points/ 
-        // for details of below formula. 
-        double val = (q.Y - p.Y) * (r.X - q.X) -
-                (q.X - p.X) * (r.Y - q.Y);
-
-        if (val == 0) return 0; // collinear 
-
-        return (val > 0) ? 1 : 2; // clock or counterclock wise 
-    }
-
-    // The main function that returns true if line segment 'edge1.Aedge1.B' 
-    // and 'edge2.Aedge2.B' intersect. 
-    private bool DoIntersect(Edge edge1, Edge edge2)
-    {
-        // Find the four orientations needed for general and 
-        // special cases 
-        int o1 = Orientation(edge1.A, edge1.B, edge2.A);
-        int o2 = Orientation(edge1.A, edge1.B, edge2.B);
-        int o3 = Orientation(edge2.A, edge2.B, edge1.A);
-        int o4 = Orientation(edge2.A, edge2.B, edge1.B);
-
-        // General case 
-        if (o1 != o2 && o3 != o4)
-            return true;
-
-        // Special Cases 
-        // edge1.A, edge1.B and edge2.A are collinear and edge2.A lies on segment edge1.Aedge1.B 
-        if (o1 == 0 && OnSegment(edge1.A, edge2.A, edge1.B)) return true;
-
-        // edge1.A, edge1.B and edge2.B are collinear and edge2.B lies on segment edge1.Aedge1.B 
-        if (o2 == 0 && OnSegment(edge1.A, edge2.B, edge1.B)) return true;
-
-        // edge2.A, edge2.B and edge1.A are collinear and edge1.A lies on segment edge2.Aedge2.B 
-        if (o3 == 0 && OnSegment(edge2.A, edge1.A, edge2.B)) return true;
-
-        // edge2.A, edge2.B and edge1.B are collinear and edge1.B lies on segment edge2.Aedge2.B 
-        if (o4 == 0 && OnSegment(edge2.A, edge1.B, edge2.B)) return true;
-
-        return false; // Doesn't fall in any of the above cases 
-    }
 }

Game/Physics2D/PhysicsEngine2D.cs

@@ -51,71 +51,6 @@ public class PhysicsEngine2D : IPhysicsEngine2D
             foreach (var collider in colliders)
                 collider.RecalculateVertices();
 
-            for (int colliderIX = 0; colliderIX < colliders.Count; colliderIX++)
-            {
-                ICollider2D colliderX = colliders[colliderIX];
-                for (int colliderIY = colliderIX + 1; colliderIY < colliders.Count; colliderIY++)
-                    for (int verticesIndex = 0; verticesIndex < colliderX.Vertices.Count; verticesIndex++)
-                    {
-                        ICollider2D colliderY = colliders[colliderIY];
-                        bool v = colliderY.CheckCollision(colliderX.Vertices[verticesIndex], colliderX, out var _);
-                        if (!colliderY.CheckCollision(colliderX.Vertices[verticesIndex], colliderX, out var collisionInformation))
-                            continue;
-
-                        if (colliderX.BehaviourController.TryGetBehaviour(out IRigidBody2D? rigidX))
-                        {
-                            Vector2 xVertex = colliderX.Vertices[verticesIndex];
-                            Vector2 edgeDirection = new Vector2(collisionInformation.Normal.Y, collisionInformation.Normal.X);
-                            Vector2 p1 = xVertex - rigidX.Velocity * intervalDeltaTime;
-                            float t = IntersectionParameterT(collisionInformation.ContactPosition - edgeDirection * 100f, collisionInformation.ContactPosition + edgeDirection * 100f, xVertex, p1);
-                            Vector2 vertexNewPosition = Vector2.Lerp(xVertex, p1, t);
-                            rigidX.Velocity = Vector2.Reflect(rigidX.Velocity, collisionInformation.Normal);
-                            rigidX.Transform.Position -= xVertex - vertexNewPosition;
-
-                            // {
-                            //     GameObject gameObject = Game1.gameManager.InstantiateGameObject<GameObject>();
-                            //     DisplayableSpriteBehaviour displayableSpriteBehaviour = gameObject.BehaviourController.AddBehaviour<DisplayableSpriteBehaviour>();
-                            //     displayableSpriteBehaviour.Assign(Game1.spriteBox);
-                            //     gameObject.Transform.Position = collisionInformation.ContactPosition;
-                            //     gameObject.Transform.Scale = new Vector2(1f, .01f) * 100f;
-                            //     gameObject.Transform.Rotation = (float)Math.Atan2(collisionInformation.Normal.Y, collisionInformation.Normal.X);
-                            // }
-                            // {
-                            //     GameObject gameObject = Game1.gameManager.InstantiateGameObject<GameObject>();
-                            //     DisplayableSpriteBehaviour displayableSpriteBehaviour = gameObject.BehaviourController.AddBehaviour<DisplayableSpriteBehaviour>();
-                            //     displayableSpriteBehaviour.Color = Color.Aqua;
-                            //     displayableSpriteBehaviour.Assign(Game1.spriteBox);
-                            //     gameObject.Transform.Position = collisionInformation.ContactPosition;
-                            //     gameObject.Transform.Scale = new Vector2(1f, .01f) * 100f;
-                            //     gameObject.Transform.Rotation = (float)Math.Atan2(rigidX.Velocity.Y, rigidX.Velocity.X);
-                            // }
-                            // {
-                            //     GameObject gameObject = Game1.gameManager.InstantiateGameObject<GameObject>();
-                            //     DisplayableSpriteBehaviour displayableSpriteBehaviour = gameObject.BehaviourController.AddBehaviour<DisplayableSpriteBehaviour>();
-                            //     displayableSpriteBehaviour.Color = Color.Pink;
-                            //     displayableSpriteBehaviour.Assign(Game1.spriteBox);
-                            //     gameObject.Transform.Position = collisionInformation.ContactPosition;
-                            //     gameObject.Transform.Scale = new Vector2(1f, .01f) * 100f;
-                            //     gameObject.Transform.Rotation = (float)Math.Atan2(edgeDirection.Y, edgeDirection.X);
-                            // }
-                            // {
-                            //     GameObject gameObject = Game1.gameManager.InstantiateGameObject<GameObject>();
-                            //     DisplayableSpriteBehaviour displayableSpriteBehaviour = gameObject.BehaviourController.AddBehaviour<DisplayableSpriteBehaviour>();
-                            //     displayableSpriteBehaviour.Color = Color.DarkGoldenrod;
-                            //     displayableSpriteBehaviour.Assign(Game1.spriteBox);
-                            //     gameObject.Transform.Position = collisionInformation.ContactPosition;
-                            //     gameObject.Transform.Scale = new Vector2(1f, .01f) * 100f;
-                            //     gameObject.Transform.Rotation = (float)Math.Atan2((xVertex - p1).Y, (xVertex - p1).X);
-                            // }
-
-                            StepRigidBody(rigidX, intervalDeltaTime * (1f - t));
-                            colliders[colliderIX].RecalculateVertices();
-                            verticesIndex--;
-                        }
-                        Console.WriteLine($"/////////////////////////////////////////////");
-                        // Console.WriteLine($"Collision");
-                    }
-            }
         }
     }
 
@@ -127,15 +62,6 @@ public class PhysicsEngine2D : IPhysicsEngine2D
         rigidBody.Transform.Position = nextPosition;
     }
 
-    private float IntersectionParameterT(Vector2 p0, Vector2 p1, Vector2 q0, Vector2 q1)
-    {
-        // Solve the linear interpolation equation for 't'
-        float t = ((q0.X - p0.X) * (p1.Y - p0.Y) - (q0.Y - p0.Y) * (p1.X - p0.X)) /
-                  ((q1.Y - q0.Y) * (p1.X - p0.X) - (q1.X - q0.X) * (p1.Y - p0.Y));
-
-        return t;
-    }
-
     private void OnBehaviourAdded(IBehaviourController controller, IBehaviour behaviour)
     {
         if (behaviour is not ICollider2D collider2D)

Game/Physics2D/PhysicsMath.cs

@@ -0,0 +1,210 @@
+using System;
+using System.Collections.Generic;
+using System.Diagnostics.CodeAnalysis;
+
+using Microsoft.Xna.Framework;
+
+namespace Syntriax.Engine.Physics2D;
+
+public record Line(Vector2 From, Vector2 To);
+public record Triangle(Vector2 A, Vector2 B, Vector2 C);
+public record Circle(Vector2 Center, double Radius);
+
+public static class PhysicsMath
+{
+    public static float IntersectionParameterT(Vector2 p0, Vector2 p1, Vector2 q0, Vector2 q1)
+        => ((q0.X - p0.X) * (p1.Y - p0.Y) - (q0.Y - p0.Y) * (p1.X - p0.X)) /
+            ((q1.Y - q0.Y) * (p1.X - p0.X) - (q1.X - q0.X) * (p1.Y - p0.Y));
+
+    public static float IntersectionParameterT(Line l1, Line l2)
+        => ((l2.From.X - l1.From.X) * (l1.To.Y - l1.From.Y) - (l2.From.Y - l1.From.Y) * (l1.To.X - l1.From.X)) /
+            ((l2.To.Y - l2.From.Y) * (l1.To.X - l1.From.X) - (l2.To.X - l2.From.X) * (l1.To.Y - l1.From.Y));
+
+    public static Vector2 GetIntersectionPoint(Line l1, Line l2)
+        => Vector2.Lerp(l1.From, l1.To, IntersectionParameterT(l1, l2));
+
+    public static Vector2 ClosestPointOnLine(Vector2 point, Line line)
+    {
+        // Convert edge points to vectors
+        var edgeVector = new Vector2(line.To.X - line.From.X, line.To.Y - line.From.Y);
+        var pointVector = new Vector2(point.X - line.From.X, point.Y - line.From.Y);
+
+        // Calculate the projection of pointVector onto edgeVector
+        double t = (pointVector.X * edgeVector.X + pointVector.Y * edgeVector.Y) / (edgeVector.X * edgeVector.X + edgeVector.Y * edgeVector.Y);
+
+        // Clamp t to the range [0, 1] to ensure the closest point is on the edge
+        t = Math.Max(0, Math.Min(1, t));
+
+        // Calculate the closest point on the edge
+        double closestX = line.From.X + t * edgeVector.X;
+        double closestY = line.From.Y + t * edgeVector.Y;
+
+        return new Vector2((float)closestX, (float)closestY);
+    }
+
+    public static double GetArea(Triangle triangle)
+    {
+        return Math.Abs((triangle.A.X * (triangle.B.Y - triangle.C.Y) +
+                         triangle.B.X * (triangle.C.Y - triangle.A.Y) +
+                         triangle.C.X * (triangle.A.Y - triangle.B.Y)) * .5f);
+    }
+
+    public static bool IsInTriangle(Vector2 point, Triangle triangle)
+    {
+        double A = GetArea(triangle);
+        /* Calculate area of triangle ABC */
+        // double A = area(x1, y1, x2, y2, x3, y3);
+
+        double A1 = GetArea(new Triangle(point, triangle.B, triangle.C));
+        /* Calculate area of triangle PBC */
+        // double A1 = area(x, y, x2, y2, x3, y3);
+
+        /* Calculate area of triangle PAC */
+        double A2 = GetArea(new Triangle(triangle.A, point, triangle.C));
+        // double A2 = area(x1, y1, x, y, x3, y3);
+
+        /* Calculate area of triangle PAB */
+        double A3 = GetArea(new Triangle(triangle.A, triangle.B, point));
+        // double A3 = area(x1, y1, x2, y2, x, y);
+
+        /* Check if sum of A1, A2 and A3 is same as A */
+        return A >= A1 + A2 + A3;
+    }
+
+    // Given three collinear points p, q, r, the function checks if 
+    // point q lies on line segment 'pr' 
+    public static bool OnSegment(Vector2 p, Vector2 q, Vector2 r)
+    {
+        if (q.X <= Math.Max(p.X, r.X) && q.X >= Math.Min(p.X, r.X) &&
+            q.Y <= Math.Max(p.Y, r.Y) && q.Y >= Math.Min(p.Y, r.Y))
+            return true;
+
+        return false;
+    }
+
+    // To find orientation of ordered triplet (p, q, r). 
+    // The function returns following values 
+    // 0 --> p, q and r are collinear 
+    // 1 --> Clockwise 
+    // 2 --> Counterclockwise 
+    public static int Orientation(Vector2 p, Vector2 q, Vector2 r)
+    {
+        // See https://www.geeksforgeeks.org/orientation-3-ordered-points/ 
+        // for details of below formula. 
+        double val = (q.Y - p.Y) * (r.X - q.X) -
+                (q.X - p.X) * (r.Y - q.Y);
+
+        if (val == 0) return 0; // collinear 
+
+        return (val > 0) ? 1 : 2; // clock or counterclock wise 
+    }
+
+    public static bool DoIntersect(Line l1, Line l2)
+    {
+        int o1 = Orientation(l1.From, l1.To, l2.From);
+        int o2 = Orientation(l1.From, l1.To, l2.To);
+        int o3 = Orientation(l2.From, l2.To, l1.From);
+        int o4 = Orientation(l2.From, l2.To, l1.To);
+
+        if (o1 != o2 && o3 != o4)
+            return true;
+
+        if (o1 == 0 && OnSegment(l1.From, l2.From, l1.To)) return true;
+        if (o2 == 0 && OnSegment(l1.From, l2.To, l1.To)) return true;
+        if (o3 == 0 && OnSegment(l2.From, l1.From, l2.To)) return true;
+        if (o4 == 0 && OnSegment(l2.From, l1.To, l2.To)) return true;
+
+        return false;
+    }
+
+    public static bool DoIntersect(Line l1, Line l2, [NotNullWhen(returnValue: true)] out Vector2? point)
+    {
+        point = null;
+
+        bool result = DoIntersect(l1, l2);
+
+        if (result)
+            point = GetIntersectionPoint(l1, l2);
+
+        return result;
+    }
+
+    public static Circle GetCircumCircle(Triangle triangle)
+    {
+        Vector2 midAB = (triangle.A + triangle.B) / 2;
+        Vector2 midBC = (triangle.B + triangle.C) / 2;
+
+        double slopeAB = (triangle.B.Y - triangle.A.Y) / (triangle.B.X - triangle.A.X);
+        double slopeBC = (triangle.C.Y - triangle.B.Y) / (triangle.C.X - triangle.B.X);
+
+        Vector2 center;
+        if (Math.Abs(slopeAB - slopeBC) > double.Epsilon)
+        {
+            double x = (slopeAB * slopeBC * (triangle.A.Y - triangle.C.Y) + slopeBC * (triangle.A.X + triangle.B.X) - slopeAB * (triangle.B.X + triangle.C.X)) / (2 * (slopeBC - slopeAB));
+            double y = -(x - (triangle.A.X + triangle.B.X) / 2) / slopeAB + (triangle.A.Y + triangle.B.Y) / 2;
+            center = new Vector2((float)x, (float)y);
+        }
+        else
+            center = (midAB + midBC) * .5f;
+
+        return new(center, Vector2.Distance(center, triangle.A));
+    }
+
+    public static Triangle GetSuperTriangle(IList<Vector2> vertices)
+    {
+        double minX = double.MaxValue, minY = double.MaxValue;
+        double maxX = double.MinValue, maxY = double.MinValue;
+
+        foreach (Vector2 point in vertices)
+        {
+            minX = Math.Min(minX, point.X);
+            minY = Math.Min(minY, point.Y);
+            maxX = Math.Max(maxX, point.X);
+            maxY = Math.Max(maxY, point.Y);
+        }
+
+        double dx = maxX - minX;
+        double dy = maxY - minY;
+        double deltaMax = Math.Max(dx, dy);
+        double midX = (minX + maxX) / 2;
+        double midY = (minY + maxY) / 2;
+
+        Vector2 p1 = new Vector2((float)midX - 20f * (float)deltaMax, (float)midY - (float)deltaMax);
+        Vector2 p2 = new Vector2((float)midX, (float)midY + 20 * (float)deltaMax);
+        Vector2 p3 = new Vector2((float)midX + 20 * (float)deltaMax, (float)midY - (float)deltaMax);
+
+        return new Triangle(p1, p2, p3);
+    }
+
+    public static List<Line> GetLines(IList<Vector2> vertices)
+    {
+        List<Line> lines = new List<Line>(vertices.Count - 1);
+        GetLines(vertices, lines);
+        return lines;
+    }
+
+    public static void GetLines(IList<Vector2> vertices, IList<Line> lines)
+    {
+        lines.Clear();
+        for (int i = 0; i < vertices.Count - 1; i++)
+            lines.Add(new(vertices[i], vertices[i + 1]));
+        lines.Add(new(vertices[^1], vertices[0]));
+    }
+
+    public static bool DoesLineExistInVertices(Line lineToCheck, List<Vector2> vertices)
+    {
+        for (int i = 0; i < vertices.Count - 1; i++)
+        {
+            Vector2 vertexCurrent = vertices[i];
+            Vector2 vertexNext = vertices[i];
+            if (lineToCheck.From == vertexCurrent && lineToCheck.To == vertexNext) return true;
+            if (lineToCheck.From == vertexNext && lineToCheck.To == vertexCurrent) return true;
+        }
+
+        Vector2 vertexFirst = vertices[0];
+        Vector2 vertexLast = vertices[^1];
+        if (lineToCheck.From == vertexFirst && lineToCheck.To == vertexLast) return true;
+        if (lineToCheck.From == vertexLast && lineToCheck.To == vertexFirst) return true;
+        return false;
+    }
+}