+ astar project

1 files changed, 208 insertions, 0 deletions

diff --git a/Other/AstarPathfindingDemo/Packages/com.arongranberg.astar/Core/Control/MovementUtilities.cs b/Other/AstarPathfindingDemo/Packages/com.arongranberg.astar/Core/Control/MovementUtilities.cs
new file mode 100644
index 0000000..cf08a20
--- /dev/null
+++ b/Other/AstarPathfindingDemo/Packages/com.arongranberg.astar/Core/Control/MovementUtilities.cs
@@ -0,0 +1,208 @@
+using UnityEngine;
+
+namespace Pathfinding.Util {
+	public static class MovementUtilities {
+		public static float FilterRotationDirection (ref Vector2 state, ref Vector2 state2, Vector2 deltaPosition, float threshold, float deltaTime, bool avoidingOtherAgents) {
+			const float Decay = 0.5f;
+
+			var lastState = state;
+
+			if (!avoidingOtherAgents) {
+				// When not avoiding other agents, we can be a bit more aggressive with rotating towards the target.
+				// This is because in that case, the velocity is much less noisy.
+				state += deltaPosition * 10;
+			} else {
+				state += deltaPosition;
+			}
+
+			// Decay the state slowly (has the most effect if the agent is standing still)
+			state *= Mathf.Clamp01(1.0f - deltaTime*Decay);
+			float stateLength = state.magnitude;
+
+			if (stateLength > threshold*2f) {
+				state = state * (threshold*2f/stateLength);
+				stateLength = threshold*2f;
+			}
+
+			// TODO: Figure out what to do with
+			state2 += (state - lastState) * Decay;
+			state2 *= Mathf.Clamp01(1.0f - deltaTime*Decay);
+
+			// Prevent rotation if the agent doesn't move much
+			float speed = stateLength > threshold ? 1.0f : 0.0f;
+			return speed;
+		}
+
+		/// <summary>
+		/// Clamps the velocity to the max speed and optionally the forwards direction.
+		///
+		/// Note that all vectors are 2D vectors, not 3D vectors.
+		///
+		/// Returns: The clamped velocity in world units per second.
+		/// </summary>
+		/// <param name="velocity">Desired velocity of the character. In world units per second.</param>
+		/// <param name="maxSpeed">Max speed of the character. In world units per second.</param>
+		/// <param name="speedLimitFactor">Value between 0 and 1 which determines how much slower the character should move than normal.
+		///      Normally 1 but should go to 0 when the character approaches the end of the path.</param>
+		/// <param name="slowWhenNotFacingTarget">Slow the character down if the desired velocity is not in the same direction as the forward vector.</param>
+		/// <param name="preventMovingBackwards">Prevent the velocity from being too far away from the forward direction of the character.</param>
+		/// <param name="forward">Forward direction of the character. Used together with the slowWhenNotFacingTarget parameter.</param>
+		public static Vector2 ClampVelocity (Vector2 velocity, float maxSpeed, float speedLimitFactor, bool slowWhenNotFacingTarget, bool preventMovingBackwards, Vector2 forward) {
+			// Max speed to use for this frame
+			var currentMaxSpeed = maxSpeed * speedLimitFactor;
+
+			// Check if the agent should slow down in case it is not facing the direction it wants to move in
+			if (slowWhenNotFacingTarget && (forward.x != 0 || forward.y != 0)) {
+				float currentSpeed;
+				var normalizedVelocity = VectorMath.Normalize(velocity, out currentSpeed);
+				float dot = Vector2.Dot(normalizedVelocity, forward);
+
+				// Lower the speed when the character's forward direction is not pointing towards the desired velocity
+				// 1 when velocity is in the same direction as forward
+				// 0.2 when they point in the opposite directions
+				float directionSpeedFactor = Mathf.Clamp(dot+0.707f, 0.2f, 1.0f);
+				currentMaxSpeed *= directionSpeedFactor;
+				currentSpeed = Mathf.Min(currentSpeed, currentMaxSpeed);
+
+				if (preventMovingBackwards) {
+					// Angle between the forwards direction of the character and our desired velocity
+					float angle = Mathf.Acos(Mathf.Clamp(dot, -1, 1));
+
+					// Clamp the angle to 20 degrees
+					// We cannot keep the velocity exactly in the forwards direction of the character
+					// because we use the rotation to determine in which direction to rotate and if
+					// the velocity would always be in the forwards direction of the character then
+					// the character would never rotate.
+					// Allow larger angles when near the end of the path to prevent oscillations.
+					angle = Mathf.Min(angle, (20f + 180f*(1 - speedLimitFactor*speedLimitFactor))*Mathf.Deg2Rad);
+
+					float sin = Mathf.Sin(angle);
+					float cos = Mathf.Cos(angle);
+
+					// Determine if we should rotate clockwise or counter-clockwise to move towards the current velocity
+					sin *= Mathf.Sign(normalizedVelocity.x*forward.y - normalizedVelocity.y*forward.x);
+					// Rotate the #forward vector by #angle radians
+					// The rotation is done using an inlined rotation matrix.
+					// See https://en.wikipedia.org/wiki/Rotation_matrix
+					return new Vector2(forward.x*cos + forward.y*sin, forward.y*cos - forward.x*sin) * currentSpeed;
+				} else {
+					return normalizedVelocity * currentSpeed;
+				}
+			} else {
+				return Vector2.ClampMagnitude(velocity, currentMaxSpeed);
+			}
+		}
+
+		/// <summary>Calculate an acceleration to move deltaPosition units and get there with approximately a velocity of targetVelocity</summary>
+		public static Vector2 CalculateAccelerationToReachPoint (Vector2 deltaPosition, Vector2 targetVelocity, Vector2 currentVelocity, float forwardsAcceleration, float rotationSpeed, float maxSpeed, Vector2 forwardsVector) {
+			// Guard against div by zero
+			if (forwardsAcceleration <= 0) return Vector2.zero;
+
+			float currentSpeed = currentVelocity.magnitude;
+
+			// Convert rotation speed to an acceleration
+			// See https://en.wikipedia.org/wiki/Centripetal_force
+			var sidewaysAcceleration = currentSpeed * rotationSpeed * Mathf.Deg2Rad;
+
+			// To avoid weird behaviour when the rotation speed is very low we allow the agent to accelerate sideways without rotating much
+			// if the rotation speed is very small. Also guards against division by zero.
+			sidewaysAcceleration = Mathf.Max(sidewaysAcceleration, forwardsAcceleration);
+
+			// Transform coordinates to local space where +X is the forwards direction
+			// This is essentially equivalent to Transform.InverseTransformDirection.
+			deltaPosition = VectorMath.ComplexMultiplyConjugate(deltaPosition, forwardsVector);
+			targetVelocity = VectorMath.ComplexMultiplyConjugate(targetVelocity, forwardsVector);
+			currentVelocity = VectorMath.ComplexMultiplyConjugate(currentVelocity, forwardsVector);
+			float ellipseSqrFactorX = 1 / (forwardsAcceleration*forwardsAcceleration);
+			float ellipseSqrFactorY = 1 / (sidewaysAcceleration*sidewaysAcceleration);
+
+			// If the target velocity is zero we can use a more fancy approach
+			// and calculate a nicer path.
+			// In particular, this is the case at the end of the path.
+			if (targetVelocity == Vector2.zero) {
+				// Run a binary search over the time to get to the target point.
+				float mn = 0.01f;
+				float mx = 10;
+				while (mx - mn > 0.01f) {
+					var time = (mx + mn) * 0.5f;
+
+					// Given that we want to move deltaPosition units from out current position, that our current velocity is given
+					// and that when we reach the target we want our velocity to be zero. Also assume that our acceleration will
+					// vary linearly during the slowdown. Then we can calculate what our acceleration should be during this frame.
+
+					//{ t = time
+					//{ deltaPosition = vt + at^2/2 + qt^3/6
+					//{ 0 = v + at + qt^2/2
+					//{ solve for a
+					// a = acceleration vector
+					// q = derivative of the acceleration vector
+					var a = (6*deltaPosition - 4*time*currentVelocity)/(time*time);
+					var q = 6*(time*currentVelocity - 2*deltaPosition)/(time*time*time);
+
+					// Make sure the acceleration is not greater than our maximum allowed acceleration.
+					// If it is we increase the time we want to use to get to the target
+					// and if it is not, we decrease the time to get there faster.
+					// Since the acceleration is described by acceleration = a + q*t
+					// we only need to check at t=0 and t=time.
+					// Note that the acceleration limit is described by an ellipse, not a circle.
+					var nextA = a + q*time;
+					if (a.x*a.x*ellipseSqrFactorX + a.y*a.y*ellipseSqrFactorY > 1.0f || nextA.x*nextA.x*ellipseSqrFactorX + nextA.y*nextA.y*ellipseSqrFactorY > 1.0f) {
+						mn = time;
+					} else {
+						mx = time;
+					}
+				}
+
+				var finalAcceleration = (6*deltaPosition - 4*mx*currentVelocity)/(mx*mx);
+
+				// Boosting
+				{
+					// The trajectory calculated above has a tendency to use very wide arcs
+					// and that does unfortunately not look particularly good in some cases.
+					// Here we amplify the component of the acceleration that is perpendicular
+					// to our current velocity. This will make the agent turn towards the
+					// target quicker.
+					// How much amplification to use. Value is unitless.
+					const float Boost = 1;
+					finalAcceleration.y *= 1 + Boost;
+
+					// Clamp the velocity to the maximum acceleration.
+					// Note that the maximum acceleration constraint is shaped like an ellipse, not like a circle.
+					float ellipseMagnitude = finalAcceleration.x*finalAcceleration.x*ellipseSqrFactorX + finalAcceleration.y*finalAcceleration.y*ellipseSqrFactorY;
+					if (ellipseMagnitude > 1.0f) finalAcceleration /= Mathf.Sqrt(ellipseMagnitude);
+				}
+
+				return VectorMath.ComplexMultiply(finalAcceleration, forwardsVector);
+			} else {
+				// Here we try to move towards the next waypoint which has been modified slightly using our
+				// desired velocity at that point so that the agent will more smoothly round the corner.
+
+				// How much to strive for making sure we reach the target point with the target velocity. Unitless.
+				const float TargetVelocityWeight = 0.5f;
+
+				// Limit to how much to care about the target velocity. Value is in seconds.
+				// This prevents the character from moving away from the path too much when the target point is far away
+				const float TargetVelocityWeightLimit = 1.5f;
+				float targetSpeed;
+				var normalizedTargetVelocity = VectorMath.Normalize(targetVelocity, out targetSpeed);
+
+				var distance = deltaPosition.magnitude;
+				var targetPoint = deltaPosition - normalizedTargetVelocity * System.Math.Min(TargetVelocityWeight * distance * targetSpeed / (currentSpeed + targetSpeed), maxSpeed*TargetVelocityWeightLimit);
+
+				// How quickly the agent will try to reach the velocity that we want it to have.
+				// We need this to prevent oscillations and jitter which is what happens if
+				// we let the constant go towards zero. Value is in seconds.
+				const float TimeToReachDesiredVelocity = 0.1f;
+				// TODO: Clamp to ellipse using more accurate acceleration (use rotation speed as well)
+				var finalAcceleration = (targetPoint.normalized*maxSpeed - currentVelocity) * (1f/TimeToReachDesiredVelocity);
+
+				// Clamp the velocity to the maximum acceleration.
+				// Note that the maximum acceleration constraint is shaped like an ellipse, not like a circle.
+				float ellipseMagnitude = finalAcceleration.x*finalAcceleration.x*ellipseSqrFactorX + finalAcceleration.y*finalAcceleration.y*ellipseSqrFactorY;
+				if (ellipseMagnitude > 1.0f) finalAcceleration /= Mathf.Sqrt(ellipseMagnitude);
+
+				return VectorMath.ComplexMultiply(finalAcceleration, forwardsVector);
+			}
+		}
+	}
+}