holopy3/Assets/SteamVR/Scripts/SteamVR_IK.cs

//======= Copyright (c) Valve Corporation, All rights reserved. ===============
//
// Purpose: Simple two bone ik solver.
//
//=============================================================================

using UnityEngine;

namespace Valve.VR
{
    public class SteamVR_IK : MonoBehaviour
    {
        public Transform target;
        public Transform start, joint, end;
        public Transform poleVector, upVector;

        public float blendPct = 1.0f;

        [HideInInspector]
        public Transform startXform, jointXform, endXform;

        void LateUpdate()
        {
            const float epsilon = 0.001f;
            if (blendPct < epsilon)
                return;

            var preUp = upVector ? upVector.up : Vector3.Cross(end.position - start.position, joint.position - start.position).normalized;

            var targetPosition = target.position;
            var targetRotation = target.rotation;

            Vector3 forward, up, result = joint.position;
            Solve(start.position, targetPosition, poleVector.position,
                (joint.position - start.position).magnitude,
                (end.position - joint.position).magnitude,
                ref result, out forward, out up);

            if (up == Vector3.zero)
                return;

            var startPosition = start.position;
            var jointPosition = joint.position;
            var endPosition = end.position;

            var startRotationLocal = start.localRotation;
            var jointRotationLocal = joint.localRotation;
            var endRotationLocal = end.localRotation;

            var startParent = start.parent;
            var jointParent = joint.parent;
            var endParent = end.parent;

            var startScale = start.localScale;
            var jointScale = joint.localScale;
            var endScale = end.localScale;

            if (startXform == null)
            {
                startXform = new GameObject("startXform").transform;
                startXform.parent = transform;
            }

            startXform.position = startPosition;
            startXform.LookAt(joint, preUp);
            start.parent = startXform;

            if (jointXform == null)
            {
                jointXform = new GameObject("jointXform").transform;
                jointXform.parent = startXform;
            }

            jointXform.position = jointPosition;
            jointXform.LookAt(end, preUp);
            joint.parent = jointXform;

            if (endXform == null)
            {
                endXform = new GameObject("endXform").transform;
                endXform.parent = jointXform;
            }

            endXform.position = endPosition;
            end.parent = endXform;

            startXform.LookAt(result, up);
            jointXform.LookAt(targetPosition, up);
            endXform.rotation = targetRotation;

            start.parent = startParent;
            joint.parent = jointParent;
            end.parent = endParent;

            end.rotation = targetRotation; // optionally blend?

            // handle blending in/out
            if (blendPct < 1.0f)
            {
                start.localRotation = Quaternion.Slerp(startRotationLocal, start.localRotation, blendPct);
                joint.localRotation = Quaternion.Slerp(jointRotationLocal, joint.localRotation, blendPct);
                end.localRotation = Quaternion.Slerp(endRotationLocal, end.localRotation, blendPct);
            }

            // restore scale so it doesn't blow out
            start.localScale = startScale;
            joint.localScale = jointScale;
            end.localScale = endScale;
        }

        public static bool Solve(
            Vector3 start, // shoulder / hip
            Vector3 end, // desired hand / foot position
            Vector3 poleVector, // point to aim elbow / knee toward
            float jointDist, // distance from start to elbow / knee
            float targetDist, // distance from joint to hand / ankle
            ref Vector3 result, // original and output elbow / knee position
            out Vector3 forward, out Vector3 up) // plane formed by root, joint and target
        {
            var totalDist = jointDist + targetDist;
            var start2end = end - start;
            var poleVectorDir = (poleVector - start).normalized;
            var baseDist = start2end.magnitude;

            result = start;

            const float epsilon = 0.001f;
            if (baseDist < epsilon)
            {
                // move jointDist toward jointTarget
                result += poleVectorDir * jointDist;

                forward = Vector3.Cross(poleVectorDir, Vector3.up);
                up = Vector3.Cross(forward, poleVectorDir).normalized;
            }
            else
            {
                forward = start2end * (1.0f / baseDist);
                up = Vector3.Cross(forward, poleVectorDir).normalized;

                if (baseDist + epsilon < totalDist)
                {
                    // calculate the area of the triangle to determine its height
                    var p = (totalDist + baseDist) * 0.5f; // half perimeter
                    if (p > jointDist + epsilon && p > targetDist + epsilon)
                    {
                        var A = Mathf.Sqrt(p * (p - jointDist) * (p - targetDist) * (p - baseDist));
                        var height = 2.0f * A / baseDist; // distance of joint from line between root and target

                        var dist = Mathf.Sqrt((jointDist * jointDist) - (height * height));
                        var right = Vector3.Cross(up, forward); // no need to normalized - already orthonormal

                        result += (forward * dist) + (right * height);
                        return true; // in range
                    }
                    else
                    {
                        // move jointDist toward jointTarget
                        result += poleVectorDir * jointDist;
                    }
                }
                else
                {
                    // move elboDist toward target
                    result += forward * jointDist;
                }
            }

            return false; // edge cases
        }
    }
}