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334 lines
11 KiB
C#

using UnityEngine;
using System.Collections;
namespace RootMotion.FinalIK {
/// <summary>
/// Using a spherical polygon to limit the range of rotation on universal and ball-and-socket joints. A reach cone is specified as a spherical polygon
/// on the surface of a a reach sphere that defines all positions the longitudinal segment axis beyond the joint can take.
///
/// This class is based on the "Fast and Easy Reach-Cone Joint Limits" paper by Jane Wilhelms and Allen Van Gelder.
/// Computer Science Dept., University of California, Santa Cruz, CA 95064. August 2, 2001
/// http://users.soe.ucsc.edu/~avg/Papers/jtl.pdf
///
/// </summary>
[HelpURL("http://www.root-motion.com/finalikdox/html/page14.html")]
[AddComponentMenu("Scripts/RootMotion.FinalIK/Rotation Limits/Rotation Limit Polygonal")]
public class RotationLimitPolygonal : RotationLimit {
// Open the User Manual URL
[ContextMenu("User Manual")]
private void OpenUserManual() {
Application.OpenURL("http://www.root-motion.com/finalikdox/html/page14.html");
}
// Open the Script Reference URL
[ContextMenu("Scrpt Reference")]
private void OpenScriptReference() {
Application.OpenURL("http://www.root-motion.com/finalikdox/html/class_root_motion_1_1_final_i_k_1_1_rotation_limit_polygonal.html");
}
// Link to the Final IK Google Group
[ContextMenu("Support Group")]
void SupportGroup() {
Application.OpenURL("https://groups.google.com/forum/#!forum/final-ik");
}
// Link to the Final IK Asset Store thread in the Unity Community
[ContextMenu("Asset Store Thread")]
void ASThread() {
Application.OpenURL("http://forum.unity3d.com/threads/final-ik-full-body-ik-aim-look-at-fabrik-ccd-ik-1-0-released.222685/");
}
#region Main Interface
/// <summary>
/// Limit of twist rotation around the main axis.
/// </summary>
[Range(0f, 180f)] public float twistLimit = 180;
/// <summary>
/// The number of smoothing iterations applied to the polygon.
/// </summary>
[Range(0, 3)] public int smoothIterations = 0;
/// <summary>
/// Sets the limit points and recalculates the reach cones.
/// </summary>
/// <param name='_points'>
/// _points.
/// </param>
public void SetLimitPoints(LimitPoint[] points) {
if (points.Length < 3) {
LogWarning("The polygon must have at least 3 Limit Points.");
return;
}
this.points = points;
BuildReachCones();
}
#endregion Main Interface
/*
* Limits the rotation in the local space of this instance's Transform.
* */
protected override Quaternion LimitRotation(Quaternion rotation) {
if (reachCones.Length == 0) Start();
// Subtracting off-limits swing
Quaternion swing = LimitSwing(rotation);
// Apply twist limits
return LimitTwist(swing, axis, secondaryAxis, twistLimit);
}
/*
* Tetrahedron composed of 2 Limit points, the origin and an axis point.
* */
[System.Serializable]
public class ReachCone {
public Vector3[] tetrahedron;
public float volume;
public Vector3 S, B;
public Vector3 o { get { return tetrahedron[0]; }}
public Vector3 a { get { return tetrahedron[1]; }}
public Vector3 b { get { return tetrahedron[2]; }}
public Vector3 c { get { return tetrahedron[3]; }}
public ReachCone(Vector3 _o, Vector3 _a, Vector3 _b, Vector3 _c) {
this.tetrahedron = new Vector3[4];
this.tetrahedron[0] = _o; // Origin
this.tetrahedron[1] = _a; // Axis
this.tetrahedron[2] = _b; // Limit Point 1
this.tetrahedron[3] = _c; // Limit Point 2
this.volume = 0;
this.S = Vector3.zero;
this.B = Vector3.zero;
}
public bool isValid { get { return volume > 0; }}
public void Calculate() {
Vector3 crossAB = Vector3.Cross(a, b);
volume = Vector3.Dot(crossAB, c) / 6.0f;
S = Vector3.Cross(a, b).normalized;
B = Vector3.Cross(b, c).normalized;
}
}
/*
* The points defining the polygon
* */
[System.Serializable]
public class LimitPoint {
public Vector3 point;
public float tangentWeight;
public LimitPoint() {
this.point = Vector3.forward;
this.tangentWeight = 1;
}
}
[HideInInspector] public LimitPoint[] points;
[HideInInspector] public Vector3[] P;
[HideInInspector] public ReachCone[] reachCones = new ReachCone[0];
void Start() {
if (points.Length < 3) ResetToDefault();
// Check if Limit Points are valid
for (int i = 0; i < reachCones.Length; i++) {
if (!reachCones[i].isValid) {
if (smoothIterations <= 0) {
int nextPoint = 0;
if (i < reachCones.Length - 1) nextPoint = i + 1;
else nextPoint = 0;
LogWarning("Reach Cone {point " + i + ", point " + nextPoint + ", Origin} has negative volume. Make sure Axis vector is in the reachable area and the polygon is convex.");
} else LogWarning("One of the Reach Cones in the polygon has negative volume. Make sure Axis vector is in the reachable area and the polygon is convex.");
}
}
axis = axis.normalized;
}
#region Precalculations
/*
* Apply the default initial setup of 4 Limit Points
* */
public void ResetToDefault() {
points = new LimitPoint[4];
for (int i = 0; i < points.Length; i++) points[i] = new LimitPoint();
Quaternion swing1Rotation = Quaternion.AngleAxis(45, Vector3.right);
Quaternion swing2Rotation = Quaternion.AngleAxis(45, Vector3.up);
points[0].point = (swing1Rotation * swing2Rotation) * axis;
points[1].point = (Quaternion.Inverse(swing1Rotation) * swing2Rotation) * axis;
points[2].point = (Quaternion.Inverse(swing1Rotation) * Quaternion.Inverse(swing2Rotation)) * axis;
points[3].point = (swing1Rotation * Quaternion.Inverse(swing2Rotation)) * axis;
BuildReachCones();
}
/*
* Recalculate reach cones if the Limit Points have changed
* */
public void BuildReachCones() {
smoothIterations = Mathf.Clamp(smoothIterations, 0, 3);
// Make another array for the points so that they could be smoothed without changing the initial points
P = new Vector3[points.Length];
for (int i = 0; i < points.Length; i++) P[i] = points[i].point.normalized;
for (int i = 0; i < smoothIterations; i++) P = SmoothPoints();
// Calculating the reach cones
reachCones = new ReachCone[P.Length];
for (int i = 0; i < reachCones.Length - 1; i++) {
reachCones[i] = new ReachCone(Vector3.zero, axis.normalized, P[i], P[i + 1]);
}
reachCones[P.Length - 1] = new ReachCone(Vector3.zero, axis.normalized, P[P.Length - 1], P[0]);
for (int i = 0; i < reachCones.Length; i++) reachCones[i].Calculate();
}
/*
* Automatically adds virtual limit points to smooth the polygon
* */
private Vector3[] SmoothPoints() {
// Create the new point array with double length
Vector3[] Q = new Vector3[P.Length * 2];
float scalar = GetScalar(P.Length); // Get the constant used for interpolation
// Project all the existing points on a plane that is tangent to the unit sphere at the Axis point
for (int i = 0; i < Q.Length; i+= 2) Q[i] = PointToTangentPlane(P[i / 2], 1);
// Interpolate the new points
for (int i = 1; i < Q.Length; i+= 2) {
Vector3 minus2 = Vector3.zero;
Vector3 plus1 = Vector3.zero;
Vector3 plus2 = Vector3.zero;
if (i > 1 && i < Q.Length - 2) {
minus2 = Q[i - 2];
plus2 = Q[i + 1];
} else if (i == 1) {
minus2 = Q[Q.Length - 2];
plus2 = Q[i + 1];
} else if (i == Q.Length - 1) {
minus2 = Q[i - 2];
plus2 = Q[0];
}
if (i < Q.Length - 1) plus1 = Q[i + 1];
else plus1 = Q[0];
int t = Q.Length / points.Length;
// Interpolation
Q[i] = (0.5f * (Q[i - 1] + plus1)) + (scalar * points[i / t].tangentWeight * (plus1 - minus2)) + (scalar * points[i / t].tangentWeight * (Q[i - 1] - plus2));
}
// Project the points from tangent plane to the sphere
for (int i = 0; i < Q.Length; i++) Q[i] = TangentPointToSphere(Q[i], 1);
return Q;
}
/*
* Returns scalar values used for interpolating smooth positions between limit points
* */
private float GetScalar(int k) {
// Values k (number of points) == 3, 4 and 6 are calculated by analytical geometry, values 5 and 7 were estimated by interpolation
if (k <= 3) return .1667f;
if (k == 4) return .1036f;
if (k == 5) return .0850f;
if (k == 6) return .0773f;
if (k == 7) return .0700f;
return .0625f; // Cubic spline fit
}
/*
* Project a point on the sphere to a plane that is tangent to the unit sphere at the Axis point
* */
private Vector3 PointToTangentPlane(Vector3 p, float r) {
float d = Vector3.Dot(axis, p);
float u = (2 * r * r) / ((r * r) + d);
return (u * p) + ((1 - u) * -axis);
}
/*
* Project a point on the tangent plane to the sphere
* */
private Vector3 TangentPointToSphere(Vector3 q, float r) {
float d = Vector3.Dot(q - axis, q - axis);
float u = (4 * r * r) / ((4 * r * r) + d);
return (u * q) + ((1 - u) * -axis);
}
#endregion Precalculations
#region Runtime calculations
/*
* Applies Swing limit to the rotation
* */
private Quaternion LimitSwing(Quaternion rotation) {
if (rotation == Quaternion.identity) return rotation; // Assuming initial rotation is in the reachable area
Vector3 L = rotation * axis; // Test this vector against the reach cones
int r = GetReachCone(L); // Get the reach cone to test against (can be only 1)
// Just in case we are running our application with invalid reach cones
if (r == -1) {
if (!Warning.logged) LogWarning("RotationLimitPolygonal reach cones are invalid.");
return rotation;
}
// Dot product of cone normal and rotated axis
float v = Vector3.Dot(reachCones[r].B, L);
if (v > 0) return rotation; // Rotation is reachable
// Find normal for a plane defined by origin, axis, and rotated axis
Vector3 rotationNormal = Vector3.Cross(axis, L);
// Find the line where this plane intersects with the reach cone plane
L = Vector3.Cross(-reachCones[r].B, rotationNormal);
// Rotation from current(illegal) swing rotation to the limited(legal) swing rotation
Quaternion toLimits = Quaternion.FromToRotation(rotation * axis, L);
// Subtract the illegal rotation
return toLimits * rotation;
}
/*
* Finding the reach cone to test against
* */
private int GetReachCone(Vector3 L) {
float p = 0;
float p1 = Vector3.Dot(reachCones[0].S, L);
for (int i = 0; i < reachCones.Length; i++) {
p = p1;
if (i < reachCones.Length - 1) p1 = Vector3.Dot(reachCones[i + 1].S, L);
else p1 = Vector3.Dot(reachCones[0].S, L);
if (p >= 0 && p1 < 0) return i;
}
return -1;
}
#endregion Runtime calculations
}
}