holopy3/Assets/Plugins/RootMotion/FinalIK/IK Solvers/IKSolverFABRIK.cs

using UnityEngine;
using System.Collections;
using System;

	namespace RootMotion.FinalIK {

	/// <summary>
	/// Forward and Backward Reaching Inverse Kinematics solver.
	/// 
	/// This class is based on the "FABRIK: A fast, iterative solver for the inverse kinematics problem." paper by Aristidou, A., Lasenby, J.
	/// </summary>
	[System.Serializable]
	public class IKSolverFABRIK : IKSolverHeuristic {
		
		#region Main Interface

		/// <summary>
		/// Solving stage 1 of the %FABRIK algorithm.
		/// </summary>
		public void SolveForward(Vector3 position) {
			if (!initiated) {
				if (!Warning.logged) LogWarning("Trying to solve uninitiated FABRIK chain.");
				return;
			}
			
			OnPreSolve();
			
			ForwardReach(position);
		}
		
		/// <summary>
		/// Solving stage 2 of the %FABRIK algorithm.
		/// </summary>
		public void SolveBackward(Vector3 position) {
			if (!initiated) {
				if (!Warning.logged) LogWarning("Trying to solve uninitiated FABRIK chain.");
				return;
			}
			
			BackwardReach(position);
			
			OnPostSolve();
		}

		public override Vector3 GetIKPosition() {
			if (target != null) return target.position;
			return IKPosition;
		}

		/// <summary>
		/// Called before each iteration of the solver.
		/// </summary>
		public IterationDelegate OnPreIteration;

		#endregion Main Interface

		private bool[] limitedBones = new bool[0];
		private Vector3[] solverLocalPositions = new Vector3[0];

		protected override void OnInitiate() {
			if (firstInitiation || !Application.isPlaying) IKPosition = bones[bones.Length - 1].transform.position;

			for (int i = 0; i < bones.Length; i++) {
				bones[i].solverPosition = bones[i].transform.position;
				bones[i].solverRotation = bones[i].transform.rotation;
			}
			
			limitedBones = new bool[bones.Length];
			solverLocalPositions = new Vector3[bones.Length];
			
			InitiateBones();

			for (int i = 0; i < bones.Length; i++) {
				solverLocalPositions[i] = Quaternion.Inverse(GetParentSolverRotation(i)) * (bones[i].transform.position - GetParentSolverPosition(i));
			}
		}
		
		protected override void OnUpdate() {
			if (IKPositionWeight <= 0) return;
			IKPositionWeight = Mathf.Clamp(IKPositionWeight, 0f, 1f);
			
			OnPreSolve();

			if (target != null) IKPosition = target.position;
			if (XY) IKPosition.z = bones[0].transform.position.z;

			Vector3 singularityOffset = maxIterations > 1? GetSingularityOffset(): Vector3.zero;

			// Iterating the solver
			for (int i = 0; i < maxIterations; i++) {
				// Optimizations
				if (singularityOffset == Vector3.zero && i >= 1 && tolerance > 0 && positionOffset < tolerance * tolerance) break;
				lastLocalDirection = localDirection;

				if (OnPreIteration != null) OnPreIteration(i);
				
				Solve(IKPosition + (i == 0? singularityOffset: Vector3.zero));
			}
			
			OnPostSolve();
		}
		
		/*
		 * If true, the solver will work with 0 length bones
		 * */
		protected override bool boneLengthCanBeZero { get { return false; }} // Returning false here also ensures that the bone lengths will be calculated

		/*
		 * Interpolates the joint position to match the bone's length
		*/
		private Vector3 SolveJoint(Vector3 pos1, Vector3 pos2, float length) {
			if (XY) pos1.z = pos2.z;
			
			return pos2 + (pos1 - pos2).normalized * length;
		}

		/*
		 * Check if bones have moved from last solved positions
		 * */
		private void OnPreSolve() {
			chainLength = 0;

			for (int i = 0; i < bones.Length; i++) {
				bones[i].solverPosition = bones[i].transform.position;
				bones[i].solverRotation = bones[i].transform.rotation;

				if (i < bones.Length - 1) {
					bones[i].length = (bones[i].transform.position - bones[i + 1].transform.position).magnitude;
					bones[i].axis = Quaternion.Inverse(bones[i].transform.rotation) * (bones[i + 1].transform.position - bones[i].transform.position);

					chainLength += bones[i].length;
				}

				if (useRotationLimits) solverLocalPositions[i] = Quaternion.Inverse(GetParentSolverRotation(i)) * (bones[i].transform.position - GetParentSolverPosition(i));
			}
		}
		
		/*
		 * After solving the chain
		 * */
		private void OnPostSolve() {
			// Rotating bones to match the solver positions
			if (!useRotationLimits) MapToSolverPositions();
			else MapToSolverPositionsLimited();

			lastLocalDirection = localDirection;
		}
		
		private void Solve(Vector3 targetPosition) {
			// Forward reaching
			ForwardReach(targetPosition);

			// Backward reaching
			BackwardReach(bones[0].transform.position);
		}
		
		/*
		 * Stage 1 of FABRIK algorithm
		 * */
		private void ForwardReach(Vector3 position) {
			// Lerp last bone's solverPosition to position
			bones[bones.Length - 1].solverPosition = Vector3.Lerp(bones[bones.Length - 1].solverPosition, position, IKPositionWeight);

			for (int i = 0; i < limitedBones.Length; i++) limitedBones[i] = false;
			
			for (int i = bones.Length - 2; i > -1; i--) {
				// Finding joint positions
				bones[i].solverPosition = SolveJoint(bones[i].solverPosition, bones[i + 1].solverPosition, bones[i].length);
				
				// Limiting bone rotation forward
				LimitForward(i, i + 1);
			}
			
			// Limiting the first bone's rotation
			LimitForward(0, 0);
		}

		private void SolverMove(int index, Vector3 offset) {
			for (int i = index; i < bones.Length; i++) {
				bones[i].solverPosition += offset;
			}
		}

		private void SolverRotate(int index, Quaternion rotation, bool recursive) {
			for (int i = index; i < bones.Length; i++) {
				bones[i].solverRotation = rotation * bones[i].solverRotation;

				if (!recursive) return;
			}
		}

		private void SolverRotateChildren(int index, Quaternion rotation) {
			for (int i = index + 1; i < bones.Length; i++) {
				bones[i].solverRotation = rotation * bones[i].solverRotation;
			}
		}

		private void SolverMoveChildrenAroundPoint(int index, Quaternion rotation) {
			for (int i = index + 1; i < bones.Length; i++) {
				Vector3 dir = bones[i].solverPosition - bones[index].solverPosition;
				bones[i].solverPosition = bones[index].solverPosition + rotation * dir;
			}
		}

		private Quaternion GetParentSolverRotation(int index) {
			if (index > 0) return bones[index - 1].solverRotation;
			if (bones[0].transform.parent == null) return Quaternion.identity;
			return bones[0].transform.parent.rotation;
		}

		private Vector3 GetParentSolverPosition(int index) {
			if (index > 0) return bones[index - 1].solverPosition;
			if (bones[0].transform.parent == null) return Vector3.zero;
			return bones[0].transform.parent.position;
		}

		private Quaternion GetLimitedRotation(int index, Quaternion q, out bool changed) {
			changed = false;
			
			Quaternion parentRotation = GetParentSolverRotation(index);
			Quaternion localRotation = Quaternion.Inverse(parentRotation) * q;
			
			Quaternion limitedLocalRotation = bones[index].rotationLimit.GetLimitedLocalRotation(localRotation, out changed);
			
			if (!changed) return q;
			
			return parentRotation * limitedLocalRotation;
		}

		/*
		 * Applying rotation limit to a bone in stage 1 in a more stable way
		 * */
		private void LimitForward(int rotateBone, int limitBone) {
			if (!useRotationLimits) return;
			if (bones[limitBone].rotationLimit == null) return;

			// Storing last bone's position before applying the limit
			Vector3 lastBoneBeforeLimit = bones[bones.Length - 1].solverPosition;

			// Moving and rotating this bone and all its children to their solver positions
			for (int i = rotateBone; i < bones.Length - 1; i++) {
				if (limitedBones[i]) break;

				Quaternion fromTo = Quaternion.FromToRotation(bones[i].solverRotation * bones[i].axis, bones[i + 1].solverPosition - bones[i].solverPosition);
				SolverRotate(i, fromTo, false);
			}

			// Limit the bone's rotation
			bool changed = false;
			Quaternion afterLimit = GetLimitedRotation(limitBone, bones[limitBone].solverRotation, out changed);

			if (changed) {
				// Rotating and positioning the hierarchy so that the last bone's position is maintained
				if (limitBone < bones.Length - 1) {
					Quaternion change = QuaTools.FromToRotation(bones[limitBone].solverRotation, afterLimit);
					bones[limitBone].solverRotation = afterLimit;
					SolverRotateChildren(limitBone, change);
					SolverMoveChildrenAroundPoint(limitBone, change);

					// Rotating to compensate for the limit
					Quaternion fromTo = Quaternion.FromToRotation(bones[bones.Length - 1].solverPosition - bones[rotateBone].solverPosition, lastBoneBeforeLimit - bones[rotateBone].solverPosition);

					SolverRotate(rotateBone, fromTo, true);
					SolverMoveChildrenAroundPoint(rotateBone, fromTo);

					// Moving the bone so that last bone maintains it's initial position
					SolverMove(rotateBone, lastBoneBeforeLimit - bones[bones.Length - 1].solverPosition);
				} else {
					// last bone
					bones[limitBone].solverRotation = afterLimit;
				}
			}

			limitedBones[limitBone] = true;
		}
		
		/*
		 * Stage 2 of FABRIK algorithm
		 * */
		private void BackwardReach(Vector3 position) {
			if (useRotationLimits) BackwardReachLimited(position);
			else BackwardReachUnlimited(position);
		}
		
		/*
		 * Stage 2 of FABRIK algorithm without rotation limits
		 * */
		private void BackwardReachUnlimited(Vector3 position) {
			// Move first bone to position
			bones[0].solverPosition = position;
			
			// Finding joint positions
			for (int i = 1; i < bones.Length; i++) {
				bones[i].solverPosition = SolveJoint(bones[i].solverPosition, bones[i - 1].solverPosition, bones[i - 1].length);
			}
		}
		
		/*
		 * Stage 2 of FABRIK algorithm with limited rotations
		 * */
		private void BackwardReachLimited(Vector3 position) {
			// Move first bone to position
			bones[0].solverPosition = position;

			// Applying rotation limits bone by bone
			for (int i = 0; i < bones.Length - 1; i++) {
				// Rotating bone to look at the solved joint position
				Vector3 nextPosition = SolveJoint(bones[i + 1].solverPosition, bones[i].solverPosition, bones[i].length);

				Quaternion swing = Quaternion.FromToRotation(bones[i].solverRotation * bones[i].axis, nextPosition - bones[i].solverPosition);
				Quaternion targetRotation = swing * bones[i].solverRotation;

				// Rotation Constraints
				if (bones[i].rotationLimit != null) {
					bool changed = false;
					targetRotation = GetLimitedRotation(i, targetRotation, out changed);
				}

				Quaternion fromTo = QuaTools.FromToRotation(bones[i].solverRotation, targetRotation);
				bones[i].solverRotation = targetRotation;
				SolverRotateChildren(i, fromTo);

				// Positioning the next bone to its default local position
				bones[i + 1].solverPosition = bones[i].solverPosition + bones[i].solverRotation * solverLocalPositions[i + 1];
			}

			// Reconstruct solver rotations to protect from invalid Quaternions
			for (int i = 0; i < bones.Length; i++) {
				bones[i].solverRotation = Quaternion.LookRotation(bones[i].solverRotation * Vector3.forward, bones[i].solverRotation * Vector3.up);
			}
		}

		/*
		 * Rotate bones to match the solver positions when not using Rotation Limits
		 * */
		private void MapToSolverPositions() {
			bones[0].transform.position = bones[0].solverPosition;
			
			for (int i = 0; i < bones.Length - 1; i++) {
				if (XY) {
					bones[i].Swing2D(bones[i + 1].solverPosition);
				} else {
					bones[i].Swing(bones[i + 1].solverPosition);
				}
			}
		}

		/*
		 * Rotate bones to match the solver positions when using Rotation Limits
		 * */
		private void MapToSolverPositionsLimited() {
            bones[0].transform.position = bones[0].solverPosition;

			for (int i = 0; i < bones.Length; i++) {
				if (i < bones.Length - 1) bones[i].transform.rotation = bones[i].solverRotation;
			}
		}
	}
}