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@ -19,7 +19,7 @@ public interface ICollider2D : IBehaviour, IAssignableTransform
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IReadOnlyList<Vector2> Vertices { get; }
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IReadOnlyList<Vector2> Vertices { get; }
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bool CheckCollision(Vector2 point, ICollider2D otherCollider, out CollisionInformation collisionInformation);
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bool CheckCollision(Vector2 point, ICollider2D otherCollider, out CollisionInformation? collisionInformation);
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void RecalculateVertices();
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void RecalculateVertices();
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}
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}
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@ -2,8 +2,11 @@ using System;
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using System.Collections.Generic;
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using System.Collections.Generic;
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using System.Collections.ObjectModel;
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using System.Collections.ObjectModel;
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using System.Diagnostics.CodeAnalysis;
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using System.Diagnostics.CodeAnalysis;
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using Microsoft.Xna.Framework;
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using Microsoft.Xna.Framework;
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using Pong;
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using Pong;
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using Syntriax.Engine.Core;
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using Syntriax.Engine.Core;
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using Syntriax.Engine.Core.Abstract;
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using Syntriax.Engine.Core.Abstract;
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using Syntriax.Engine.Graphics.TwoDimensional;
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using Syntriax.Engine.Graphics.TwoDimensional;
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@ -11,6 +14,7 @@ using Syntriax.Engine.Physics2D.Abstract;
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namespace Syntriax.Engine.Physics2D;
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namespace Syntriax.Engine.Physics2D;
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public class Collider2DBehaviour(IList<Vector2> vertices) : BehaviourOverride, ICollider2D
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public class Collider2DBehaviour(IList<Vector2> vertices) : BehaviourOverride, ICollider2D
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{
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{
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private List<Triangle> triangles = new List<Triangle>(32);
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private List<Triangle> triangles = new List<Triangle>(32);
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@ -49,19 +53,19 @@ public class Collider2DBehaviour(IList<Vector2> vertices) : BehaviourOverride, I
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foreach (var triangle in triangles)
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foreach (var triangle in triangles)
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{
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{
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if (!isInside(point, triangle))
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if (!PhysicsMath.IsInTriangle(point, triangle))
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continue;
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continue;
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OnCollision?.Invoke(this, otherCollider);
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OnCollision?.Invoke(this, otherCollider);
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Edge main = new() { A = otherCollider.Transform.Position, B = point };
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Line main = new(otherCollider.Transform.Position, point);
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foreach (var edge in GetEdges(triangle))
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foreach (var line in PhysicsMath.GetLines([triangle.A, triangle.B, triangle.C]))
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{
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{
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if (!DoIntersect(main, edge))
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if (!PhysicsMath.DoIntersect(main, line))
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continue;
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continue;
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Vector2 contactPoint = ClosestPointOnEdge(point, edge);
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Vector2 contactPoint = PhysicsMath.ClosestPointOnLine(point, line);
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Vector2 normal = contactPoint - point;
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Vector2 normal = contactPoint - point;
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if (normal.LengthSquared() < 0.001f)
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if (normal.LengthSquared() < 0.001f)
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@ -89,11 +93,11 @@ public class Collider2DBehaviour(IList<Vector2> vertices) : BehaviourOverride, I
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_vertices.Add(scaledPosition + Transform.Position);
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_vertices.Add(scaledPosition + Transform.Position);
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}
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}
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Triangle superTriangle = GetSuperTriangle(_vertices);
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Triangle superTriangle = PhysicsMath.GetSuperTriangle(_vertices);
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triangles.Add(superTriangle);
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triangles.Add(superTriangle);
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List<Triangle> badTriangles = new(32);
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List<Triangle> badTriangles = new(32);
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List<Edge> polygon = new(32);
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List<Line> polygon = new(32);
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foreach (var vertex in _vertices)
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foreach (var vertex in _vertices)
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{
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{
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@ -102,30 +106,21 @@ public class Collider2DBehaviour(IList<Vector2> vertices) : BehaviourOverride, I
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foreach (var triangle in triangles)
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foreach (var triangle in triangles)
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{
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{
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Circle circle = GetCircumCircle(triangle);
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Circle circle = PhysicsMath.GetCircumCircle(triangle);
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if (Vector2.DistanceSquared(circle.Center, vertex) <= circle.Radius * circle.Radius)
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if (Vector2.DistanceSquared(circle.Center, vertex) <= circle.Radius * circle.Radius)
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badTriangles.Add(triangle);
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badTriangles.Add(triangle);
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}
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}
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foreach (var triangle in badTriangles)
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foreach (var triangle in badTriangles)
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foreach (var edge in GetEdges(triangle))
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foreach (var line in PhysicsMath.GetLines([triangle.A, triangle.B, triangle.C]))
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{
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if (PhysicsMath.DoesLineExistInVertices(line, [triangle.A, triangle.B, triangle.C]))
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if (DoesEdgeExistInTriangles(edge, badTriangles))
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polygon.Add(line);
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polygon.Add(edge);
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}
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foreach (var triangle in badTriangles)
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foreach (var triangle in badTriangles)
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triangles.Remove(triangle);
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triangles.Remove(triangle);
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foreach (var edge in polygon)
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foreach (var line in polygon)
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{
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triangles.Add(new(line.From, line.To, vertex));
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triangles.Add(new()
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{
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A = edge.A,
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B = edge.B,
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C = vertex
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});
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}
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}
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}
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for (int i = triangles.Count - 1; i >= 0; i--)
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for (int i = triangles.Count - 1; i >= 0; i--)
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@ -150,15 +145,15 @@ public class Collider2DBehaviour(IList<Vector2> vertices) : BehaviourOverride, I
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for (int i = 0; i < triangles.Count; i++)
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for (int i = 0; i < triangles.Count; i++)
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{
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{
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Triangle triangle = triangles[i];
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Triangle triangle = triangles[i];
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foreach (var edge in GetEdges(triangle))
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foreach (var line in PhysicsMath.GetLines([triangle.A, triangle.B, triangle.C]))
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{
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{
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GameObject gameObject = Game1.gameManager.InstantiateGameObject<GameObject>();
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GameObject gameObject = Game1.gameManager.InstantiateGameObject<GameObject>();
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DisplayableSpriteBehaviour displayableSpriteBehaviour = gameObject.BehaviourController.AddBehaviour<DisplayableSpriteBehaviour>();
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DisplayableSpriteBehaviour displayableSpriteBehaviour = gameObject.BehaviourController.AddBehaviour<DisplayableSpriteBehaviour>();
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displayableSpriteBehaviour.Color = Color.Aqua;
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displayableSpriteBehaviour.Color = Color.Aqua;
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displayableSpriteBehaviour.Origin = new(0.5f, 1f);
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displayableSpriteBehaviour.Origin = new(0.5f, 1f);
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displayableSpriteBehaviour.Assign(Game1.spriteBox);
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displayableSpriteBehaviour.Assign(Game1.spriteBox);
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gameObject.Transform.Position = edge.A;
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gameObject.Transform.Position = line.From;
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Vector2 vector2 = edge.B - edge.A;
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Vector2 vector2 = line.To - line.From;
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gameObject.Transform.Scale = new Vector2(2f, .0f) + Vector2.UnitY * vector2.Length();
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gameObject.Transform.Scale = new Vector2(2f, .0f) + Vector2.UnitY * vector2.Length();
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gameObject.Transform.Rotation = (float)Math.Atan2(vector2.X, vector2.Y);
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gameObject.Transform.Rotation = (float)Math.Atan2(vector2.X, vector2.Y);
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gameObjects.Add(gameObject);
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gameObjects.Add(gameObject);
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@ -167,7 +162,7 @@ public class Collider2DBehaviour(IList<Vector2> vertices) : BehaviourOverride, I
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displayableSpriteBehaviour = gameObject.BehaviourController.AddBehaviour<DisplayableSpriteBehaviour>();
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displayableSpriteBehaviour = gameObject.BehaviourController.AddBehaviour<DisplayableSpriteBehaviour>();
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displayableSpriteBehaviour.Color = Color.Crimson;
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displayableSpriteBehaviour.Color = Color.Crimson;
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displayableSpriteBehaviour.Assign(Game1.spriteBox);
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displayableSpriteBehaviour.Assign(Game1.spriteBox);
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gameObject.Transform.Position = edge.B;
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gameObject.Transform.Position = line.To;
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gameObject.Transform.Scale = new Vector2(4f, 4f);
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gameObject.Transform.Scale = new Vector2(4f, 4f);
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gameObjects.Add(gameObject);
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gameObjects.Add(gameObject);
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}
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}
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@ -187,200 +182,4 @@ public class Collider2DBehaviour(IList<Vector2> vertices) : BehaviourOverride, I
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private List<IGameObject> gameObjects = new List<IGameObject>(32);
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private List<IGameObject> gameObjects = new List<IGameObject>(32);
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private Vector2 ClosestPointOnEdge(Vector2 point, Edge edge)
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{
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// Convert edge points to vectors
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var edgeVector = new Vector2(edge.B.X - edge.A.X, edge.B.Y - edge.A.Y);
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var pointVector = new Vector2(point.X - edge.A.X, point.Y - edge.A.Y);
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// Calculate the projection of pointVector onto edgeVector
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double t = (pointVector.X * edgeVector.X + pointVector.Y * edgeVector.Y) / (edgeVector.X * edgeVector.X + edgeVector.Y * edgeVector.Y);
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// Clamp t to the range [0, 1] to ensure the closest point is on the edge
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t = Math.Max(0, Math.Min(1, t));
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// Calculate the closest point on the edge
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double closestX = edge.A.X + t * edgeVector.X;
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double closestY = edge.A.Y + t * edgeVector.Y;
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return new Vector2((float)closestX, (float)closestY);
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}
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private bool DoesEdgeExistInTriangles(Edge edge, List<Triangle> triangles)
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{
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foreach (var triangle in triangles)
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foreach (var edgeOther in GetEdges(triangle))
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if (edge.A == edgeOther.A && edge.B == edgeOther.B)
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return true;
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else if (edge.A == edgeOther.B && edge.B == edgeOther.A)
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return true;
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return false;
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}
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private List<Edge> GetEdges(Triangle triangle)
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=> [
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new() { A = triangle.A, B = triangle.B },
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new() { A = triangle.B, B = triangle.C },
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new() { A = triangle.C, B = triangle.A }
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];
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private Triangle GetSuperTriangle(IReadOnlyList<Vector2> vertices)
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{
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double minX = double.MaxValue, minY = double.MaxValue;
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double maxX = double.MinValue, maxY = double.MinValue;
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foreach (Vector2 point in vertices)
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{
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minX = Math.Min(minX, point.X);
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minY = Math.Min(minY, point.Y);
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maxX = Math.Max(maxX, point.X);
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maxY = Math.Max(maxY, point.Y);
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}
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double dx = maxX - minX;
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double dy = maxY - minY;
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double deltaMax = Math.Max(dx, dy);
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double midX = (minX + maxX) / 2;
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double midY = (minY + maxY) / 2;
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Vector2 p1 = new Vector2((float)midX - 20f * (float)deltaMax, (float)midY - (float)deltaMax);
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Vector2 p2 = new Vector2((float)midX, (float)midY + 20 * (float)deltaMax);
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Vector2 p3 = new Vector2((float)midX + 20 * (float)deltaMax, (float)midY - (float)deltaMax);
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return new Triangle() { A = p1, B = p2, C = p3 };
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}
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private struct Triangle { public Vector2 A, B, C; }
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private double GetArea(Triangle triangle)
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{
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return Math.Abs((triangle.A.X * (triangle.B.Y - triangle.C.Y) +
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triangle.B.X * (triangle.C.Y - triangle.A.Y) +
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triangle.C.X * (triangle.A.Y - triangle.B.Y)) / 2.0);
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}
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/* A function to check whether point P(x, y) lies
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inside the triangle formed by A(x1, y1),
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B(x2, y2) and C(x3, y3) */
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private bool isInside(Vector2 point, Triangle triangle)
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{
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double A = GetArea(triangle);
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/* Calculate area of triangle ABC */
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// double A = area(x1, y1, x2, y2, x3, y3);
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double A1 = GetArea(new() { A = point, B = triangle.B, C = triangle.C });
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/* Calculate area of triangle PBC */
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// double A1 = area(x, y, x2, y2, x3, y3);
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/* Calculate area of triangle PAC */
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double A2 = GetArea(new() { A = triangle.A, B = point, C = triangle.C });
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// double A2 = area(x1, y1, x, y, x3, y3);
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/* Calculate area of triangle PAB */
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double A3 = GetArea(new() { A = triangle.A, B = triangle.B, C = point });
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// double A3 = area(x1, y1, x2, y2, x, y);
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/* Check if sum of A1, A2 and A3 is same as A */
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return A >= A1 + A2 + A3;
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}
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private struct Edge
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{
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public Vector2 A;
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public Vector2 B;
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}
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private struct Circle
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{
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public double Radius;
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public Vector2 Center;
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}
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private Circle GetCircumCircle(Triangle triangle)
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{
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Circle result = new();
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Vector2 midAB = (triangle.A + triangle.B) / 2;
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Vector2 midBC = (triangle.B + triangle.C) / 2;
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double slopeAB = (triangle.B.Y - triangle.A.Y) / (triangle.B.X - triangle.A.X);
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double slopeBC = (triangle.C.Y - triangle.B.Y) / (triangle.C.X - triangle.B.X);
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// Check if the slopes are not parallel
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if (Math.Abs(slopeAB - slopeBC) > double.Epsilon)
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{
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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));
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double y = -(x - (triangle.A.X + triangle.B.X) / 2) / slopeAB + (triangle.A.Y + triangle.B.Y) / 2;
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result.Center = new Vector2((float)x, (float)y);
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result.Radius = Vector2.Distance(result.Center, triangle.A);
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}
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else
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{
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// If slopes are parallel, use the midpoints of the sides as the circumcenter
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result.Center = (midAB + midBC) / 2;
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result.Radius = Vector2.Distance(result.Center, triangle.A);
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}
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return result;
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}
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// Given three collinear points p, q, r, the function checks if
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// point q lies on line segment 'pr'
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private bool OnSegment(Vector2 p, Vector2 q, Vector2 r)
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{
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if (q.X <= Math.Max(p.X, r.X) && q.X >= Math.Min(p.X, r.X) &&
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q.Y <= Math.Max(p.Y, r.Y) && q.Y >= Math.Min(p.Y, r.Y))
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return true;
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return false;
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}
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// To find orientation of ordered triplet (p, q, r).
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// The function returns following values
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// 0 --> p, q and r are collinear
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// 1 --> Clockwise
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// 2 --> Counterclockwise
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private int Orientation(Vector2 p, Vector2 q, Vector2 r)
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{
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// See https://www.geeksforgeeks.org/orientation-3-ordered-points/
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// for details of below formula.
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double val = (q.Y - p.Y) * (r.X - q.X) -
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(q.X - p.X) * (r.Y - q.Y);
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if (val == 0) return 0; // collinear
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return (val > 0) ? 1 : 2; // clock or counterclock wise
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}
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// The main function that returns true if line segment 'edge1.Aedge1.B'
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// and 'edge2.Aedge2.B' intersect.
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private bool DoIntersect(Edge edge1, Edge edge2)
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{
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// Find the four orientations needed for general and
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// special cases
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int o1 = Orientation(edge1.A, edge1.B, edge2.A);
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int o2 = Orientation(edge1.A, edge1.B, edge2.B);
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int o3 = Orientation(edge2.A, edge2.B, edge1.A);
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int o4 = Orientation(edge2.A, edge2.B, edge1.B);
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// General case
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if (o1 != o2 && o3 != o4)
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return true;
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// Special Cases
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// edge1.A, edge1.B and edge2.A are collinear and edge2.A lies on segment edge1.Aedge1.B
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if (o1 == 0 && OnSegment(edge1.A, edge2.A, edge1.B)) return true;
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// edge1.A, edge1.B and edge2.B are collinear and edge2.B lies on segment edge1.Aedge1.B
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if (o2 == 0 && OnSegment(edge1.A, edge2.B, edge1.B)) return true;
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|
||||||
// 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
|
|
||||||
}
|
|
||||||
}
|
}
|
||||||
|
|
|
||||||
|
|
@ -51,71 +51,6 @@ public class PhysicsEngine2D : IPhysicsEngine2D
|
||||||
foreach (var collider in colliders)
|
foreach (var collider in colliders)
|
||||||
collider.RecalculateVertices();
|
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;
|
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)
|
private void OnBehaviourAdded(IBehaviourController controller, IBehaviour behaviour)
|
||||||
{
|
{
|
||||||
if (behaviour is not ICollider2D collider2D)
|
if (behaviour is not ICollider2D collider2D)
|
||||||
|
|
|
||||||
|
|
@ -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;
|
||||||
|
}
|
||||||
|
}
|
||||||
Loading…
Reference in New Issue