एक मोबाइल PvP शूटर के लिए भौतिकी और हमने ECS के साथ कैसे दोस्ती की

public sealed class PhysicsWorld { public const int HistoryLength = 32; private readonly VoltWorld _voltWorld; private readonly Dictionary<uint, VoltBody> _cache = new Dictionary<uint, VoltBody>(); public PhysicsWorld(float deltaTime) { _voltWorld = new VoltWorld(HistoryLength) { DeltaTime = deltaTime }; } public bool HasBody(uint tag) { return _cache.ContainsKey(tag); } public VoltBody GetBody(uint tag) { VoltBody body; _cache.TryGetValue(tag, out body); return body; } public VoltRayResult RayCast(Vector2 origin, Vector2 direction, float distance, VoltBodyFilter filter, int ticksBehind) { var ray = new VoltRayCast(origin, direction.normalized, distance); var result = new VoltRayResult(); _voltWorld.RayCast(ref ray, ref result, filter, ticksBehind); return result; } public VoltRayResult CircleCast(Vector2 origin, Vector2 direction, float distance, float radius, VoltBodyFilter filter, int ticksBehind) { var ray = new VoltRayCast(origin, direction.normalized, distance); var result = new VoltRayResult(); _voltWorld.CircleCast(ref ray, radius, ref result, filter, ticksBehind); return result; } public void Update() { _voltWorld.Update(); } public void Update(uint tag) { var body = _cache[tag]; _voltWorld.Update(body, true); } public void UpdateBody(uint tag, Vector2 position, float angle) { var body = _cache[tag]; body.Set(position, angle); } public void CreateStaticCircle(Vector2 origin, float radius, uint tag) { var shape = _voltWorld.CreateCircleWorldSpace(origin, radius, 1f, 0f, 0f); var body = _voltWorld.CreateStaticBody(origin, 0, shape); body.UserData = tag; } public void CreateDynamicCircle(Vector2 origin, float radius, uint tag) { var shape = _voltWorld.CreateCircleWorldSpace(origin, radius, 1f, 0f, 0f); var body = _voltWorld.CreateDynamicBody(origin, 0, shape); body.UserData = tag; body.CollisionFilter = StaticCollisionFilter; _cache.Add(tag, body); } public void CreateStaticSquare(Vector2 origin, float rotationAngle, Vector2 extents, uint tag) { var shape = _voltWorld.CreatePolygonBodySpace(extents.GetRectFromExtents(), 1, 0, 0); var body = _voltWorld.CreateStaticBody(origin, rotationAngle, shape); body.UserData = tag; } public void CreateDynamicSquare(Vector2 origin, float rotationAngle, Vector2 extents, uint tag) { var shape = _voltWorld.CreatePolygonBodySpace(extents.GetRectFromExtents(), 1, 0, 0); var body = _voltWorld.CreateDynamicBody(origin, rotationAngle, shape); body.UserData = tag; body.CollisionFilter = StaticCollisionFilter; _cache.Add(tag, body); } public IEnumerable<VoltBody> GetBodies() { return _voltWorld.Bodies; } private static bool StaticCollisionFilter(VoltBody a, VoltBody b) { return b.IsStatic; } } 

 using System; ... using Volatile; public sealed class MovePhysicsSystem : ExecutableSystem { private readonly PhysicsWorld _physicsWorld; private readonly CollisionFilter _moveFilter; private readonly VoltBodyFilter _collisionFilterDelegate; public MovePhysicsSystem(PhysicsWorld physicsWorld) { _physicsWorld = physicsWorld; _moveFilter = new CollisionFilter(true, CollisionLayer.ExplosiveBarrel); _collisionFilterDelegate = _moveFilter.Filter; } public override void Execute(GameState gs) { _moveFilter.State = gs; foreach (var pair in gs.WorldState.Movement) { ExecuteMovement(gs, pair.Key, pair.Value); } _physicsWorld.Update(); foreach (var pair in gs.WorldState.PhysicsDynamicBody) { if(pair.Value.IsAlive) { ExecutePhysicsDynamicBody(gs, pair.Key); } } } public override void Execute(GameState gs, uint avatarId) { _moveFilter.State = gs; var movement = gs.WorldState.Movement[avatarId]; if (movement != null) { ExecuteMovement(gs, avatarId, movement); _physicsWorld.Update(avatarId); var physicsDynamicBody = gs.WorldState.PhysicsDynamicBody[avatarId]; if (physicsDynamicBody != null && physicsDynamicBody.IsAlive) ExecutePhysicsDynamicBody(gs, avatarId); } } private void ExecutePhysicsDynamicBody(GameState gs, uint entityId) { var body = _physicsWorld.GetBody(entityId); if (body != null) { var transform = gs.WorldState.Transform[entityId]; transform.Position = body.Position; } } private void ExecuteMovement(GameState gs, uint entityId, Movement movement) { var body = _physicsWorld.GetBody(entityId); if (body != null) { float raycastRadius; if (CalculateRadius(gs, entityId, out raycastRadius)) { return; } body.AngularVelocity = 0; body.LinearVelocity = movement.Velocity; var movPhysicInfo = gs.WorldState.MovementPhysicInfo[entityId]; var collisionDirection = CircleRayCastSpeedCorrection(body, GameState.TickDurationSec, raycastRadius); CheckMoveInWall(movement, movPhysicInfo, collisionDirection, gs.WorldState.Transform[entityId]); } } private static bool CalculateRadius(GameState gs, uint id, out float raycastRadius) { raycastRadius = 0; var circleShape = gs.WorldState.DynamicCircleCollider[id]; if (circleShape != null) { raycastRadius = circleShape.Radius; } else { var boxShape = gs.WorldState.DynamicBoxCollider[id]; if (boxShape != null) { raycastRadius = boxShape.RaycastRadius; } else { gs.Log.Error(string.Format("Physics body {0} doesn't contains shape!", id)); return true; } } return false; } private static void CheckMoveInWall(Movement movement, MovementPhysicInfo movPhysicInfo, Vector2 collisionDirection, Transform transform) { // 60 is the max angle when player move in wall and can shoot through the wall from weapon without target. const float maxAngleToWall = 60; if (movement.Velocity.IsEqual(Vector2.zero)) { if (movPhysicInfo.LastCollisionDirection.IsEqual(Vector2.zero)) { var angleToCollision = transform.Angle.GetDirection().CalculateAbsoluteAngleInDegrees(movPhysicInfo.LastCollisionDirection); movPhysicInfo.TurnOnWall = angleToCollision <= maxAngleToWall; } return; } movPhysicInfo.LastCollisionDirection = collisionDirection * -1f; if (movPhysicInfo.LastCollisionDirection.IsEqual(Vector2.zero)) { movPhysicInfo.TurnOnWall = false; movPhysicInfo.LastCollisionDirection = collisionDirection; } else { var angleToCollision = transform.Angle.GetDirection().CalculateAbsoluteAngleInDegrees(movPhysicInfo.LastCollisionDirection); movPhysicInfo.TurnOnWall = angleToCollision <= maxAngleToWall; } } // I can't believe we are using a physics engine and have to write such kludges private Vector2 CircleRayCastSpeedCorrection(VoltBody targetBody, float deltaSeconds, float rayCastRadius) { if (rayCastRadius <= 0) { return Vector2.zero; } var speed = targetBody.LinearVelocity; var position = targetBody.Position; var direction = speed * deltaSeconds; var rayCastResult = _physicsWorld.CircleCast(position + direction.normalized * 0.1f, direction, direction.magnitude, rayCastRadius, _collisionFilterDelegate, 0); if (rayCastResult.Body == null) { return Vector2.zero; } var magSpeed = speed.magnitude; if (rayCastResult.Distance > 0) { var penetratingDistance = magSpeed * deltaSeconds - rayCastResult.Distance; var sinVelocityEdge = Vector2.Dot(-speed.normalized, rayCastResult.Normal); var biasSpeed = penetratingDistance * sinVelocityEdge / deltaSeconds; var biasVector = rayCastResult.Normal * biasSpeed * 1.1f; var resultVelocity = speed + biasVector; if (magSpeed <= 0) { resultVelocity = Vector2.zero; } targetBody.LinearVelocity = resultVelocity; return rayCastResult.Normal; } var destination = rayCastResult.Body.Position; direction = destination - position; var rayCastResultToBody = _physicsWorld.RayCast(position, direction, direction.magnitude, _collisionFilterDelegate, 0); if (rayCastResultToBody.IsValid) targetBody.LinearVelocity = rayCastResultToBody.Normal * magSpeed * deltaSeconds; return rayCastResultToBody.Normal; } } 

 using PS.Logs.Unity; /// <summary> /// Compares the same avatar in two states. Compares the values potentially /// affected by prediction. /// </summary> public sealed class GameStateComparer : IGameStateComparer { public bool IsSame(GameState s1, GameState s2, uint avatarId) { if (s1 == null && s2 != null || s1 != null && s2 == null) { return false; } if (s1 == null && s2 == null) return false; var entity1 = s1.WorldState[avatarId]; var entity2 = s2.WorldState[avatarId]; if (entity1 == null && entity2 == null) { return false; } if (entity1 == null || entity2 == null) { LogManager.Debug("entity is different"); return false; } if (s1.Time != s2.Time) { LogManager.Warning(string.Format("Trying to compare states with different time! Predicted time: {0} Server time: {1}", s1.Time, s2.Time)); return false; } if (s1.WorldState.Transform[avatarId] != s2.WorldState.Transform[avatarId]) { LogManager.Debug("Transform is different"); return false; } // ... some code ... return true; } } 

 public static bool operator ==(Transform a, Transform b) { if ((object)a == null && (object)b == null) { return true; } if ((object)a == null && (object)b != null) { return false; } if ((object)a != null && (object)b == null) { return false; } if (Math.Abs(a.Angle - b.Angle) > 0.01f) { return false; } if (Math.Abs(a.Position.x - b.Position.x) > 0.01f || Math.Abs(a.Position.y - b.Position.y) > 0.01f) { return false; } return true; } 

 using System; // ... some code ... using Volatile; namespace Common.WorldState { public sealed class GrenadeMovementSystem : ExecutableSystem { private struct Projection { public float Min; public float Max; } private float _r; private readonly Vector2[] _vertices = new Vector2[4]; private readonly Vector2[] _verticesV = new Vector2[4]; private Vector2 _Vunit; private Vector2 _VTunit; private Projection _wallProj1; private Projection _wallProj2; private Projection _wallProj1V; private Projection _wallProj2V; private const float CollisionPrecision = 1e-3f; private static readonly float HalfSlope = Mathf.Cos(Mathf.PI / 4.0f); private readonly ContactPointList _contactPoints = new ContactPointList(3); public override void Execute(GameState gs) { var settings = gs.RuleBook.GrenadeConfig[1]; _r = settings.R; var floorDampeningPerTick = (float)Math.Pow(settings.FloorDampening, 1.0 / GameState.Hz); foreach (var grenade in gs.WorldState.GrenadeMovement) { // Gravity must take effect before collision // because contact with walls may and will adjust vertical velocity // and penetration will even move the ball up. grenade.Value.VerticalVelocity -= settings.Gravity * GameState.TickDurationSec; grenade.Value.Height += grenade.Value.VerticalVelocity * GameState.TickDurationSec; // prevent falling through floor if (grenade.Value.Height <= _r) { // slow down horizontal movement by floor friction // actually, friciton is simplified to just dampening coefficient var spdH = grenade.Value.Velocity.sqrMagnitude; var spdV = grenade.Value.VerticalVelocity; var cos = spdH / Mathf.Sqrt(spdH * spdH + spdV * spdV); grenade.Value.Velocity *= floorDampeningPerTick * cos; // slow down vertical movement grenade.Value.VerticalVelocity = settings.FloorRestitution * Math.Abs(grenade.Value.VerticalVelocity); // move up to the floor level grenade.Value.Height = _r; } // A collision will stop the ball and change its velocity. // Otherwise it will be moved by velocity PerformCollisionAndMovement(gs, grenade.Key, grenade.Value); } } private void PerformCollisionAndMovement(GameState gs, uint id, GrenadeMovement grenade) { var settings = gs.RuleBook.GrenadeConfig[1]; var velocity = grenade.Velocity * GameState.TickDurationSec; var trans = gs.WorldState.Transform[id]; var position = trans.Position; _Vunit = velocity.normalized; _VTunit = new Vector2(-_Vunit.y, _Vunit.x); _vertices[0] = position + _VTunit * _r; _vertices[1] = position - _VTunit * _r; _vertices[2] = _vertices[1] + velocity; _vertices[3] = _vertices[0] + velocity; _contactPoints.Reset(); int collisions = 0; var grenProj1V = ProjectCapsule(_Vunit, _vertices, position, velocity); var grenProj2V = ProjectCapsule(_VTunit, _vertices, position, velocity); collisions += CollideWithStaticBoxes(gs, id, position, velocity, grenade, grenProj1V, grenProj2V); collisions += CollideWithCircles(gs, gs.RuleBook.StaticCircleCollider, gs.RuleBook.Transform, id, position, velocity, grenade, grenProj1V, grenProj2V, (CollisionLayer)~0); collisions += CollideWithCircles(gs, gs.WorldState.DynamicCircleCollider, gs.WorldState.Transform, id, position, velocity, grenade, grenProj1V, grenProj2V, ~CollisionLayer.Character); if (collisions == 0) { trans.Position += velocity; } else { var contactSuperposition = CalculateContactSuperposition(); trans.Position += velocity * contactSuperposition.TravelDistance; var reflectedVelocity = grenade.Velocity - 2.0f * Vector2.Dot(grenade.Velocity, contactSuperposition.Normal) * contactSuperposition.Normal; reflectedVelocity *= settings.WallRestitution; #if DEBUG_GRENADES gs.Log.Debug("contact" + "\n\ttravel " + contactSuperposition.TravelDistance + "\n\tcontactNormal " + contactSuperposition.Normal.x + ":" + contactSuperposition.Normal.y + "\n\treflected V " + reflectedVelocity.x + ":" + reflectedVelocity.y); #endif grenade.Velocity = reflectedVelocity; } } private int CollideWithStaticBoxes( GameState gs, uint id, Vector2 position, Vector2 velocity, GrenadeMovement grenade, Projection grenProj1V, Projection grenProj2V) { var settings = gs.RuleBook.GrenadeConfig[1]; var collisions = 0; // TODO spatial query foreach (var collider in gs.RuleBook.StaticBoxCollider) { var wall = collider.Value; var transform = gs.RuleBook.Transform[collider.Key]; var colliderData = gs.RuleBook.PrecomputedColliderData[collider.Key]; // test projection to V _wallProj1V = ProjectPolygon(_Vunit, colliderData.Vertices); if (!Overlap(_wallProj1V, grenProj1V)) continue; // test projection to VT _wallProj2V = ProjectPolygon(_VTunit, colliderData.Vertices); if (!Overlap(_wallProj2V, grenProj2V)) continue; // test projection to wall axis 1 _wallProj1 = ProjectPolygon(colliderData.Axis1, colliderData.Vertices); var grenProj1 = ProjectCapsule(colliderData.Axis1, _vertices, position, velocity); if (!Overlap(_wallProj1, grenProj1)) continue; // test projection to wall axis 2 _wallProj2 = ProjectPolygon(colliderData.Axis2, colliderData.Vertices); var grenProj2 = ProjectCapsule(colliderData.Axis2, _vertices, position, velocity); if (!Overlap(_wallProj2, grenProj2)) continue; var lowWall = wall.Height < settings.TallWallHeight; if (lowWall) { // the wall is too far below, ignore it completely if (grenade.Height > wall.Height + _r) continue; // if grenade if falling down, it can bounce off the top of the wall if (grenade.VerticalVelocity < 0f) { if (grenade.Height > wall.Height - _r) { var localPV = WorldToBoxLocal(transform.Position, colliderData, position + velocity); #if DEBUG_GRENADES gs.Log.Debug("fall on wall" + "\n\tP+V " + (Px + Vx) + ":" + (Py + Vy) + "\n\tlocal " + localPV.x + ":" + localPV.y + "\n\tH w " + wall.Height + " g " + grenade.Height ); #endif if (Math.Abs(localPV.x) < wall.Size.x * 0.5f || Math.Abs(localPV.y) < wall.Size.y * 0.5f) { grenade.Height = wall.Height + _r; grenade.VerticalVelocity = settings.WallRestitution * Math.Abs(grenade.VerticalVelocity); continue; } } } } // collision detected // try to find minimal V before collision var scaleV = CalcTranslationScaleBeforeCollision(CheckBoxCollision, colliderData, 0, position, velocity); var contactPoint = CalcBoxContactPoint(transform.Position, wall, colliderData, position); #if DEBUG_GRENADES gs.Log.Debug("collision grenade #" + id + " with static box #" + collider.Key + "\n\tP=" + Px + ":" + Py + "\n\tV=" + Vx + ":" + Vy + " scale=" + scaleV + "\n\tP+Vs=" + (Px + Vx * scaleV) + ":" + (Py + Vy * scaleV) + "\n\twall pos " + transform.Position.x + ":" + transform.Position.y + " sz " + wall.Size.x + ":" + wall.Size.y + " angle " + transform.Angle + "\n\tproj V w " + _wallProj1V.Min + ":" + _wallProj1V.Max + " g " + grenProj1V.Min + ":" + grenProj1V.Max + " overlap=" + Overlap(_wallProj1V, grenProj1V) + "\n\tproj VT w " + _wallProj2V.Min + ":" + _wallProj2V.Max + " g " + grenProj2V.Min + ":" + grenProj2V.Max + " overlap=" + Overlap(_wallProj2V, grenProj2V) + "\n\taxis1 " + colliderData.Axis1.x + ":" + colliderData.Axis1.y + "\n\tproj 1 w " + _wallProj1.Min + ":" + _wallProj1.Max + " g " + grenProj1.Min + ":" + grenProj1.Max + " overlap=" + Overlap(_wallProj1, grenProj1) + "\n\taxis2 " + colliderData.Axis2.x + ":" + colliderData.Axis2.y + "\n\tproj 2 w " + _wallProj2.Min + ":" + _wallProj2.Max + " g " + grenProj2.Min + ":" + grenProj2.Max + " overlap=" + Overlap(_wallProj2, grenProj2) + "\n\tpoint " + contactPoint.Point.x + ":" + contactPoint.Point.y + " dotV " + Vector2.Dot(P - contactPoint.Point, V) ); #endif // ignore colliders that are behind if (Vector2.Dot(position - contactPoint.Point, velocity) >= 0.0f) continue; contactPoint.TravelDistance = velocity.magnitude * scaleV; _contactPoints.Add(ref contactPoint); collisions++; } return collisions; } private bool CheckBoxCollision(PrecomputedColliderData colliderData, int x, Vector2 position, Vector2 velocity) { _verticesV[0] = _vertices[0]; _verticesV[1] = _vertices[1]; _verticesV[2] = _vertices[1] + velocity; _verticesV[3] = _vertices[0] + velocity; // test projection to V var grenProj1V = ProjectCapsule(_Vunit, _verticesV, position, velocity); if (!Overlap(_wallProj1V, grenProj1V)) return false; // testing projection to VT would be redundant // test projection to wall axis 1 var grenProj1 = ProjectCapsule(colliderData.Axis1, _verticesV, position, velocity); if (!Overlap(_wallProj1, grenProj1)) return false; // test projection to wall axis 2 var grenProj2 = ProjectCapsule(colliderData.Axis2, _verticesV, position, velocity); if (!Overlap(_wallProj2, grenProj2)) return false; return true; } private int CollideWithCircles( GameState gs, Table<CircleCollider> colliderTable, Table<Transform> transformTable, uint id, Vector2 position, Vector2 velocity, GrenadeMovement grenade, Projection grenProj1V, Projection grenProj2V, CollisionLayer collisionLayers) { var settings = gs.RuleBook.GrenadeConfig[1]; var collisions = 0; foreach (var collider in colliderTable) { if ((int)collisionLayers != ~0) { var body = gs.WorldState.PhysicsDynamicBody[collider.Key]; if (body != null && (body.CollisionLayer & collisionLayers) == 0) continue; } var wall = collider.Value; var transform = transformTable[collider.Key]; // test projection to V _wallProj1V = ProjectCircle(_Vunit, transform.Position, wall.Radius); if (!Overlap(_wallProj1V, grenProj1V)) continue; // test projection to VT _wallProj2V = ProjectCircle(_VTunit, transform.Position, wall.Radius); if (!Overlap(_wallProj2V, grenProj2V)) continue; // test distance from the circle wall to semicircles on capsule ends var collisionDistance = (_r + wall.Radius) * (_r + wall.Radius); if ((position - transform.Position).sqrMagnitude > collisionDistance) continue; var distSqr = (position + velocity - transform.Position).sqrMagnitude; if (distSqr > collisionDistance) continue; var lowWall = wall.Height < settings.TallWallHeight; if (lowWall) { // the wall is too far below, ignore it completely if (grenade.Height > wall.Height + _r) continue; // if grenade if falling down, it can bounce off the top of the wall if (grenade.VerticalVelocity < 0f) { if (grenade.Height > wall.Height - _r) { #if DEBUG_GRENADES gs.Log.Debug("grenade #" + id + " falls on wall" + "\n\tP+V " + (Px + Vx) + ":" + (Py + Vy) + "\n\tdist " + Mathf.Sqrt(distSqr) + "\n\tH w " + wall.Height + " g " + grenade.Height ); #endif if (distSqr < wall.Radius * wall.Radius) { grenade.Height = wall.Height + _r; grenade.VerticalVelocity = settings.WallRestitution * Math.Abs(grenade.VerticalVelocity); continue; } } } } // collision detected // try to find minimal V before collision var scaleV = CalcTranslationScaleBeforeCollision(CheckCircleCollision, transform.Position, wall, position, velocity); var contactPoint = CalcCircleContactPoint(transform.Position, wall, position); #if DEBUG_GRENADES gs.Log.Debug("collision grenade #" + id + " with circle #" + collider.Key + "\n\tP=" + Px + ":" + Py + "\n\tV=" + Vx + ":" + Vy + " scale=" + scaleV + "\n\tP+Vs=" + (Px + Vx * scaleV) + ":" + (Py + Vy * scaleV) + "\n\tcircle pos " + transform.Position.x + ":" + transform.Position.y + " r " + wall.Radius + "\n\tdist " + (transform.Position - (P + V * scaleV)).magnitude + "\n\tproj V w " + _wallProj1V.Min + ":" + _wallProj1V.Max + " g " + grenProj1V.Min + ":" + grenProj1V.Max + " overlap=" + Overlap(_wallProj1V, grenProj1V) + "\n\tproj VT w " + _wallProj2V.Min + ":" + _wallProj2V.Max + " g " + grenProj2V.Min + ":" + grenProj2V.Max + " overlap=" + Overlap(_wallProj2V, grenProj2V) + "\n\tpoint " + contactPoint.Point.x + ":" + contactPoint.Point.y + " dotV " + Vector2.Dot(P - contactPoint.Point, V) ); #endif // ignore colliders that are behind if (Vector2.Dot(position - contactPoint.Point, velocity) >= 0.0f) continue; contactPoint.TravelDistance = velocity.magnitude * scaleV; _contactPoints.Add(ref contactPoint); collisions++; } return collisions; } private bool CheckCircleCollision(Vector2 wallCentre, CircleCollider wall, Vector2 position, Vector2 velocity) { _verticesV[0] = _vertices[0]; _verticesV[1] = _vertices[1]; _verticesV[2] = _vertices[1] + velocity; _verticesV[3] = _vertices[0] + velocity; // test projection to V var grenProj1V = ProjectCapsule(_Vunit, _verticesV, position, velocity); if (!Overlap(_wallProj1V, grenProj1V)) return false; // testing projection to VT would be redundant // test distance from the circle wall to the semicircle on the second capsule end var dSqr = (_r + wall.Radius) * (_r + wall.Radius); return (position + velocity - wallCentre).sqrMagnitude < dSqr; } private static float CalcTranslationScaleBeforeCollision<TData1, TData2>( Func<TData1, TData2, Vector2, Vector2, bool> collision, TData1 colliderData1, TData2 colliderData2, Vector2 position, Vector2 vector) { var min = 0.0f; var max = 1.0f; while (true) { var d = (max - min) * 0.5f; if (d < CollisionPrecision) break; var scale = min + d; if (collision(colliderData1, colliderData2, position, vector * scale)) { max = scale; } else { min = scale; } } return min; } private ContactPoint CalculateContactSuperposition() { ContactPoint contactSuperposition; _contactPoints.TryPopClosest(1000f, out contactSuperposition); ContactPoint contact; while (_contactPoints.TryPopClosest(contactSuperposition.TravelDistance, out contact)) { contactSuperposition.Normal += contact.Normal; } contactSuperposition.Normal = contactSuperposition.Normal.normalized; return contactSuperposition; } private static Projection ProjectPolygon(Vector2 axisNormalised, Vector2[] vertices) { Projection proj; var d = Vector2.Dot(axisNormalised, vertices[0]); proj.Min = d; proj.Max = d; for (var i = 1; i < vertices.Length; i++) { d = Vector2.Dot(axisNormalised, vertices[i]); proj.Min = Mathf.Min(proj.Min, d); proj.Max = Mathf.Max(proj.Max, d); } return proj; } private Projection ProjectCapsule(Vector2 axisNormalised, Vector2[] vertices, Vector2 p, Vector2 v) { var proj = ProjectPolygon(axisNormalised, vertices); proj = AddCircleProjection(proj, axisNormalised, p, _r); proj = AddCircleProjection(proj, axisNormalised, p + v, _r); return proj; } private static Projection AddCircleProjection(Projection proj, Vector2 axisNormalised, Vector2 centre, float r) { var c = Vector2.Dot(axisNormalised, centre); proj.Min = Mathf.Min(proj.Min, c - r); proj.Max = Mathf.Max(proj.Max, c + r); return proj; } private static Projection ProjectCircle(Vector2 axisNormalised, Vector2 centre, float r) { Projection proj; var c = Vector2.Dot(axisNormalised, centre); proj.Min = c - r; proj.Max = c + r; return proj; } private static bool Overlap(Projection p1, Projection p2) { return p1.Min < p2.Min ? p1.Max > p2.Min : p2.Max > p1.Min; } private static Vector2 WorldToBoxLocal(Vector2 wallCentre, PrecomputedColliderData colliderData, Vector2 position) { return new Vector2( Vector2.Dot(colliderData.Axis1, position) - Vector2.Dot(colliderData.Axis1, wallCentre), Vector2.Dot(colliderData.Axis2, position) - Vector2.Dot(colliderData.Axis2, wallCentre) ); } private static ContactPoint CalcBoxContactPoint(Vector2 wallCentre, BoxCollider wall, PrecomputedColliderData colliderData, Vector2 position) { var contactPoint = CaclBoxLocalContactPoint(wall.Size * 0.5f, WorldToBoxLocal(wallCentre, colliderData, position)); var worldAxisX = new Vector2(colliderData.Axis1.x, -colliderData.Axis1.y); var worldAxisY = new Vector2(colliderData.Axis1.y, colliderData.Axis1.x); contactPoint.Point = wallCentre + new Vector2(Vector2.Dot(worldAxisX, contactPoint.Point), Vector2.Dot(worldAxisY, contactPoint.Point)); contactPoint.Normal = new Vector2(Vector2.Dot(worldAxisX, contactPoint.Normal), Vector2.Dot(worldAxisY, contactPoint.Normal)); return contactPoint; } private static ContactPoint CaclBoxLocalContactPoint(Vector2 boxHalfSize, Vector2 localPosition) { ContactPoint localContactPoint = default(ContactPoint); // cases are numbered like numpad keys // 1, 2, 3 if (localPosition.y < -boxHalfSize.y) { // 1 if (localPosition.x < -boxHalfSize.x) { localContactPoint.Point = new Vector2(-boxHalfSize.x, -boxHalfSize.y); localContactPoint.Normal = new Vector2(-HalfSlope, -HalfSlope); } // 2, 3 else { // 3 if (localPosition.x > boxHalfSize.x) { localContactPoint.Point = new Vector2(boxHalfSize.x, -boxHalfSize.y); localContactPoint.Normal = new Vector2(HalfSlope, -HalfSlope); } // 2 else { localContactPoint.Point = new Vector2(localPosition.x, -boxHalfSize.y); localContactPoint.Normal = new Vector2(0.0f, -1.0f); } } } // 4, 6, 7, 8, 9 else { // 7, 8, 9 if (localPosition.y > boxHalfSize.y) { // 7 if (localPosition.x < -boxHalfSize.x) { localContactPoint.Point = new Vector2(-boxHalfSize.x, boxHalfSize.y); localContactPoint.Normal = new Vector2(-HalfSlope, HalfSlope); } // 8, 9 else { // 9 if (localPosition.x > boxHalfSize.x) { localContactPoint.Point = new Vector2(boxHalfSize.x, boxHalfSize.y); localContactPoint.Normal = new Vector2(HalfSlope, HalfSlope); } // 8 else { localContactPoint.Point = new Vector2(localPosition.x, boxHalfSize.y); localContactPoint.Normal = new Vector2(0.0f, 1.0f); } } } // 4, 6 else { // 4 if (localPosition.x < -boxHalfSize.x) { localContactPoint.Point = new Vector2(-boxHalfSize.x, localPosition.y); localContactPoint.Normal = new Vector2(-1.0f, 0.0f); } // 6 else { localContactPoint.Point = new Vector2(boxHalfSize.x, localPosition.y); localContactPoint.Normal = new Vector2(1.0f, 0.0f); } } } return localContactPoint; } private static ContactPoint CalcCircleContactPoint(Vector2 wallCentre, CircleCollider wall, Vector2 position) { ContactPoint contactPoint = default(ContactPoint); contactPoint.Normal = (position - wallCentre).normalized; contactPoint.Point = wallCentre + wall.Radius * contactPoint.Normal; return contactPoint; } } }