using UnityEngine;
using System.Collections;
using System.Collections.Generic;
using Dreamteck;
namespace Dreamteck.Splines {
//The Spline class defines a spline with world coordinates. It comes with various sampling methods
[System.Serializable]
public class Spline {
public enum Direction { Forward = 1, Backward = -1 }
public enum Type { CatmullRom, BSpline, Bezier, Linear };
public SplinePoint[] points = new SplinePoint[0];
public Type type = Type.Bezier;
public bool linearAverageDirection = true;
public AnimationCurve customValueInterpolation = null;
public AnimationCurve customNormalInterpolation = null;
public int sampleRate = 10;
///
/// Returns true if the spline is closed
///
public bool isClosed
{
get
{
return closed && points.Length >= 3;
}
}
///
/// The step size of the percent incrementation when evaluating a spline (based on percision)
///
public double moveStep
{
get {
if (type == Type.Linear) return 1f / (points.Length-1);
return 1f / (iterations-1);
}
set { }
}
///
/// The total count of samples for the spline (based on the sample rate)
///
public int iterations
{
get {
if (type == Type.Linear) return closed ? points.Length + 1 : points.Length;
int segments = closed ? points.Length : points.Length - 1;
return sampleRate * segments - segments + 1;
}
}
public float knotParametrization
{
get { return _knotParametrization; }
set
{
_knotParametrization = Mathf.Clamp01(value);
}
}
private static Vector3[] P = new Vector3[4];
private static Vector3 A1;
private static Vector3 A2;
private static Vector3 A3;
private static Vector3 B1;
private static Vector3 B2;
private static float t1;
private static float t2;
private static float t3;
[SerializeField]
private bool closed = false;
[SerializeField, Range(0f, 1f)]
private float _knotParametrization;
public Spline(Type type){
this.type = type;
points = new SplinePoint[0];
}
public Spline(Type type, int sampleRate)
{
this.type = type;
this.sampleRate = sampleRate;
points = new SplinePoint[0];
}
///
/// Calculate the length of the spline
///
/// Calculate from [0-1] default: 0f
/// Calculate to [0-1] default: 1f
/// Resolution multiplier for precision [0-1] default: 1f
///
public float CalculateLength(double from = 0.0, double to = 1.0, double resolution = 1.0)
{
if (points.Length == 0) return 0f;
resolution = DMath.Clamp01(resolution);
if (resolution == 0.0) return 0f;
from = DMath.Clamp01(from);
to = DMath.Clamp01(to);
if (to < from) to = from;
double percent = from;
Vector3 lastPos = EvaluatePosition(percent);
float sum = 0f;
while (true)
{
percent = DMath.Move(percent, to, moveStep / resolution);
Vector3 pos = EvaluatePosition(percent);
sum += (pos - lastPos).magnitude;
lastPos = pos;
if (percent == to) break;
}
return sum;
}
///
/// Project point on the spline. Returns evaluation percent.
///
/// 3D Point
/// Subdivisions default: 4
/// Sample from [0-1] default: 0f
/// Sample to [0-1] default: 1f
///
public double Project(Vector3 position, int subdivide = 4, double from = 0.0, double to = 1.0)
{
if (points.Length == 0) return 0.0;
if (closed && from == 0.0 && to == 1.0) //Handle looped splines
{
double closest = GetClosestPoint(subdivide, position, from, to, Mathf.RoundToInt(Mathf.Max(iterations / points.Length, 10)) * 5);
if (closest < moveStep)
{
double nextClosest = GetClosestPoint(subdivide, position, 0.5, to, Mathf.RoundToInt(Mathf.Max(iterations / points.Length, 10)) * 5);
if (Vector3.Distance(position, EvaluatePosition(nextClosest)) < Vector3.Distance(position, EvaluatePosition(closest))) return nextClosest;
}
return closest;
}
return GetClosestPoint(subdivide, position, from, to, Mathf.RoundToInt(Mathf.Max(iterations / points.Length, 10)) * 5);
}
///
/// Casts rays along the spline against all colliders in the scene
///
/// Hit information
/// The percent of evaluation where the hit occured
/// Layer mask for the raycast
/// Resolution multiplier for precision [0-1] default: 1f
/// Raycast from [0-1] default: 0f
/// Raycast to [0-1] default: 1f
/// Should hit triggers? (not supported in 5.1)
///
public bool Raycast(out RaycastHit hit, out double hitPercent, LayerMask layerMask, double resolution = 1.0, double from = 0.0, double to = 1.0, QueryTriggerInteraction hitTriggers = QueryTriggerInteraction.UseGlobal
)
{
resolution = DMath.Clamp01(resolution);
from = DMath.Clamp01(from);
to = DMath.Clamp01(to);
double percent = from;
Vector3 fromPos = EvaluatePosition(percent);
hitPercent = 0f;
if (resolution == 0f)
{
hit = new RaycastHit();
hitPercent = 0f;
return false;
}
while (true)
{
double prevPercent = percent;
percent = DMath.Move(percent, to, moveStep / resolution);
Vector3 toPos = EvaluatePosition(percent);
if (Physics.Linecast(fromPos, toPos, out hit, layerMask, hitTriggers))
{
double segmentPercent = (hit.point - fromPos).sqrMagnitude / (toPos - fromPos).sqrMagnitude;
hitPercent = DMath.Lerp(prevPercent, percent, segmentPercent);
return true;
}
fromPos = toPos;
if (percent == to) break;
}
return false;
}
///
/// Casts rays along the spline against all colliders in the scene and returns all hits. Order is not guaranteed.
///
/// Hit information
/// The percents of evaluation where each hit occured
/// Layer mask for the raycast
/// Resolution multiplier for precision [0-1] default: 1f
/// Raycast from [0-1] default: 0f
/// Raycast to [0-1] default: 1f
/// Should hit triggers? (not supported in 5.1)
///
public bool RaycastAll(out RaycastHit[] hits, out double[] hitPercents, LayerMask layerMask, double resolution = 1.0, double from = 0.0, double to = 1.0, QueryTriggerInteraction hitTriggers = QueryTriggerInteraction.UseGlobal
)
{
resolution = DMath.Clamp01(resolution);
from = DMath.Clamp01(from);
to = DMath.Clamp01(to);
double percent = from;
Vector3 fromPos = EvaluatePosition(percent);
List hitList = new List();
List percentList = new List();
if (resolution == 0f)
{
hits = new RaycastHit[0];
hitPercents = new double[0];
return false;
}
bool hasHit = false;
while (true)
{
double prevPercent = percent;
percent = DMath.Move(percent, to, moveStep / resolution);
Vector3 toPos = EvaluatePosition(percent);
RaycastHit[] h = Physics.RaycastAll(fromPos, toPos - fromPos, Vector3.Distance(fromPos, toPos), layerMask, hitTriggers);
for (int i = 0; i < h.Length; i++)
{
hasHit = true;
double segmentPercent = (h[i].point - fromPos).sqrMagnitude / (toPos - fromPos).sqrMagnitude;
percentList.Add(DMath.Lerp(prevPercent, percent, segmentPercent));
hitList.Add(h[i]);
}
fromPos = toPos;
if (percent == to) break;
}
hits = hitList.ToArray();
hitPercents = percentList.ToArray();
return hasHit;
}
///
/// Converts a point index to spline percent
///
/// The point index
///
public double GetPointPercent(int pointIndex)
{
if (closed)
{
return DMath.Clamp01((double)pointIndex / points.Length);
}
return DMath.Clamp01((double)pointIndex / (points.Length - 1));
}
///
/// Evaluate the spline and return position. This is simpler and faster than Evaluate.
///
/// Percent of evaluation [0-1]
public Vector3 EvaluatePosition(double percent)
{
if (points.Length == 0) return Vector3.zero;
Vector3 position = new Vector3();
EvaluatePosition(percent, ref position);
return position;
}
///
/// Evaluate the spline at the given time and return a SplineSample
///
/// Percent of evaluation [0-1]
public SplineSample Evaluate(double percent)
{
SplineSample result = new SplineSample();
Evaluate(percent, ref result);
return result;
}
///
/// Evaluate the spline at the position of a given point and return a SplineSample
///
/// Point index
public SplineSample Evaluate(int pointIndex)
{
SplineSample result = new SplineSample();
Evaluate(GetPointPercent(pointIndex), ref result);
return result;
}
///
/// Evaluate the splien at the given point and write the result to the "result" object
///
/// The result output
/// Point index
public void Evaluate(int pointIndex, ref SplineSample result)
{
Evaluate(GetPointPercent(pointIndex), ref result);
}
///
/// Evaluate the splien at the given time and write the result to the "result" object
///
/// The result output
/// Percent of evaluation [0-1]
public void Evaluate(double percent, ref SplineSample sample)
{
if (points.Length == 0)
{
sample = new SplineSample();
return;
}
percent = DMath.Clamp01(percent);
if (closed && points.Length <= 2)
{
closed = false;
}
if (points.Length == 1)
{
sample.position = points[0].position;
sample.up = points[0].normal;
sample.forward = Vector3.forward;
sample.size = points[0].size;
sample.color = points[0].color;
sample.percent = percent;
return;
}
double doubleIndex = (points.Length - 1) * percent;
if (closed)
{
doubleIndex = points.Length * percent;
}
int fromIndex = DMath.FloorInt(doubleIndex);
int toIndex = fromIndex + 1;
if (closed)
{
if (fromIndex >= points.Length - 1)
{
fromIndex = points.Length - 1;
}
if(toIndex > points.Length - 1)
{
toIndex = 0;
}
} else
{
if(toIndex > points.Length-1)
{
toIndex = points.Length - 1;
}
}
double getPercent = doubleIndex - fromIndex;
sample.percent = percent;
float valueInterpolation = (float)getPercent;
if (customValueInterpolation != null)
{
if (customValueInterpolation.length > 0)
{
valueInterpolation = customValueInterpolation.Evaluate(valueInterpolation);
}
}
float normalInterpolation = (float)getPercent;
if (customNormalInterpolation != null)
{
if (customNormalInterpolation.length > 0)
{
normalInterpolation = customNormalInterpolation.Evaluate(normalInterpolation);
}
}
sample.size = Mathf.Lerp(points[fromIndex].size, points[toIndex].size, valueInterpolation);
sample.color = Color.Lerp(points[fromIndex].color, points[toIndex].color, valueInterpolation);
sample.up = Vector3.Slerp(points[fromIndex].normal, points[toIndex].normal, normalInterpolation);
EvaluatePositionAndTangent(ref sample.position, ref sample.forward, percent);
if (type == Type.BSpline)
{
double step = 1.0 / (iterations - 1);
if (percent <= 1.0 - step && percent >= step)
{
sample.forward = EvaluatePosition(percent + step) - EvaluatePosition(percent - step);
}
else
{
Vector3 back = Vector3.zero, front = Vector3.zero;
if (closed)
{
if (percent < step) EvaluatePosition(1.0 - (step - percent), ref back);
else EvaluatePosition(percent - step, ref back);
if (percent > 1.0 - step) EvaluatePosition(step - (1.0 - percent), ref front);
else EvaluatePosition(percent + step, ref front);
sample.forward = front - back;
}
else
{
EvaluatePosition(percent - step, ref back);
back = sample.position - back;
EvaluatePosition(percent + step, ref front);
front = front - sample.position;
sample.forward = Vector3.Slerp(front, back, back.magnitude / front.magnitude);
}
}
}
sample.forward.Normalize();
}
[System.Obsolete("This override is obsolete. Use Evaluate(int pointIndex, ref SplineSample sample) instead")]
public void Evaluate(ref SplineSample sample, int pointIndex)
{
Evaluate(pointIndex, ref sample);
}
[System.Obsolete("This override is obsolete. Use Evaluate(double percent, ref SplineSample sample) instead")]
public void Evaluate(ref SplineSample sample, double percent)
{
Evaluate(percent, ref sample);
}
///
/// Evaluates the spline segment and writes the results to the array
///
/// Start position [0-1]
/// Target position [from-1]
///
public void Evaluate(ref SplineSample[] samples, double from = 0.0, double to = 1.0)
{
if (points.Length == 0) {
samples = new SplineSample[0];
return;
}
from = DMath.Clamp01(from);
to = DMath.Clamp(to, from, 1.0);
double fromValue = from * (iterations - 1);
double toValue = to * (iterations - 1);
int clippedIterations = DMath.CeilInt(toValue) - DMath.FloorInt(fromValue) + 1;
if (samples == null) samples = new SplineSample[clippedIterations];
else if (samples.Length != clippedIterations) samples = new SplineSample[clippedIterations];
double percent = from;
double ms = moveStep;
int index = 0;
while (true)
{
samples[index] = Evaluate(percent);
index++;
if (index >= samples.Length) break;
percent = DMath.Move(percent, to, ms);
}
}
///
/// Evaluates the spline segment and writes uniformly spaced results to the array
///
/// Start position [0-1]
/// Target position [from-1]
///
public void EvaluateUniform(ref SplineSample[] samples, ref double[] originalSamplePercents, double from = 0.0, double to = 1.0)
{
if (points.Length == 0)
{
samples = new SplineSample[0];
return;
}
from = DMath.Clamp01(from);
to = DMath.Clamp(to, from, 1.0);
double fromValue = from * (iterations - 1);
double toValue = to * (iterations - 1);
int clippedIterations = DMath.CeilInt(toValue) - DMath.FloorInt(fromValue) + 1;
if (samples == null || samples.Length != clippedIterations) samples = new SplineSample[clippedIterations];
if (originalSamplePercents == null || originalSamplePercents.Length != clippedIterations)
{
originalSamplePercents = new double[clippedIterations];
}
float lengthStep = CalculateLength(from, to) / (iterations - 1);
Evaluate(from, ref samples[0]);
samples[0].percent = originalSamplePercents[0] = from;
double lastPercent = from;
float moved = 0f;
for (int i = 1; i < samples.Length - 1; i++)
{
Evaluate(Travel(lastPercent, lengthStep, out moved, Direction.Forward), ref samples[i]);
lastPercent = samples[i].percent;
originalSamplePercents[i] = lastPercent;
samples[i].percent = DMath.Lerp(from, to, (double)i/ (samples.Length - 1));
}
Evaluate(to, ref samples[samples.Length - 1]);
samples[samples.Length - 1].percent = originalSamplePercents[originalSamplePercents.Length - 1] = to;
}
///
/// Evaluates the spline segment based on the spline's precision and returns only the position.
///
/// The position buffer
/// Start position [0-1]
/// Target position [from-1]
///
public void EvaluatePositions(ref Vector3[] positions, double from = 0.0, double to = 1.0)
{
if (points.Length == 0) {
positions = new Vector3[0];
return;
}
from = DMath.Clamp01(from);
to = DMath.Clamp(to, from, 1.0);
double fromValue = from * (iterations - 1);
double toValue = to * (iterations - 1);
int clippedIterations = DMath.CeilInt(toValue) - DMath.FloorInt(fromValue) + 1;
if (positions.Length != clippedIterations) positions = new Vector3[clippedIterations];
double percent = from;
double ms = moveStep;
int index = 0;
while (true)
{
positions[index] = EvaluatePosition(percent);
index++;
if (index >= positions.Length) break;
percent = DMath.Move(percent, to, ms);
}
}
///
/// Returns the percent from the spline at a given distance from the start point
///
/// The start point
/// /// The distance to travel
/// The direction towards which to move
///
public double Travel(double start, float distance, out float moved, Direction direction)
{
moved = 0f;
if (points.Length <= 1) return 0.0;
if (direction == Direction.Forward && start >= 1.0) return 1.0;
else if (direction == Direction.Backward && start <= 0.0) return 0.0; ;
if (distance == 0f) return DMath.Clamp01(start);
Vector3 pos = Vector3.zero;
EvaluatePosition(start, ref pos);
Vector3 lastPosition = pos;
double lastPercent = start;
int i = iterations - 1;
int nextSampleIndex = direction == Spline.Direction.Forward ? DMath.CeilInt(start * i) : DMath.FloorInt(start * i);
float lastDistance = 0f;
double percent = start;
while (true)
{
percent = (double)nextSampleIndex / i;
pos = EvaluatePosition(percent);
lastDistance = Vector3.Distance(pos, lastPosition);
lastPosition = pos;
moved += lastDistance;
if (moved >= distance) break;
lastPercent = percent;
if (direction == Spline.Direction.Forward)
{
if (nextSampleIndex == i) break;
nextSampleIndex++;
}
else
{
if (nextSampleIndex == 0) break;
nextSampleIndex--;
}
}
return DMath.Lerp(lastPercent, percent, 1f - (moved - distance) / lastDistance);
}
public double Travel(double start, float distance, Spline.Direction direction = Spline.Direction.Forward)
{
float moved;
return Travel(start, distance, out moved, direction);
}
public void EvaluatePosition(double percent, ref Vector3 position)
{
if (points.Length == 0)
{
position = Vector3.zero;
return;
}
if (points.Length == 1)
{
position = points[0].position;
return;
}
percent = DMath.Clamp01(percent);
double doubleIndex = (points.Length - 1) * percent;
if (closed)
{
doubleIndex = points.Length * percent;
}
int pointIndex = DMath.FloorInt(doubleIndex);
if (type == Type.Bezier)
{
pointIndex = Mathf.Clamp(pointIndex, 0, Mathf.Max(points.Length - 1, 0));
}
CalculatePosition(ref position, doubleIndex - pointIndex, pointIndex);
}
[System.Obsolete("This override is obsolete. Use EvaluatePosition(double percent, ref Vector3 position) instead")]
public void EvaluatePosition(ref Vector3 position, double percent)
{
EvaluatePosition(percent, ref position);
}
public void EvaluateTangent(double percent, ref Vector3 tangent)
{
if (points.Length < 2)
{
tangent = Vector3.forward;
return;
}
percent = DMath.Clamp01(percent);
double doubleIndex = (points.Length - 1) * percent;
if (closed)
{
doubleIndex = points.Length * percent;
}
int pointIndex = DMath.FloorInt(doubleIndex);
if (type == Type.Bezier)
{
pointIndex = Mathf.Clamp(pointIndex, 0, Mathf.Max(points.Length - 1, 0));
}
CalculateTangent(ref tangent, doubleIndex - pointIndex, pointIndex);
}
public void EvaluatePositionAndTangent(ref Vector3 position, ref Vector3 tangent, double percent)
{
if (points.Length == 0)
{
position = Vector3.zero;
tangent = Vector3.forward;
return;
}
if (points.Length == 1)
{
position = points[0].position;
tangent = Vector3.forward;
return;
}
percent = DMath.Clamp01(percent);
double doubleIndex = (points.Length - 1) * percent;
if (closed)
{
doubleIndex = points.Length * percent;
}
int pointIndex = DMath.FloorInt(doubleIndex);
if (type == Type.Bezier)
{
pointIndex = Mathf.Clamp(pointIndex, 0, Mathf.Max(points.Length - 1, 0));
}
CalculatePositionAndTangent(doubleIndex - pointIndex, pointIndex, ref position, ref tangent);
}
//Get closest point in spline segment. Used for projection
private double GetClosestPoint(int iterations, Vector3 point, double start, double end, int slices)
{
if (iterations <= 0)
{
float startDist = (point - EvaluatePosition(start)).sqrMagnitude;
float endDist = (point - EvaluatePosition(end)).sqrMagnitude;
if (startDist < endDist) return start;
else if (endDist < startDist) return end;
else return (start + end) / 2;
}
double closestPercent = 0.0;
float closestDistance = Mathf.Infinity;
double tick = (end - start) / slices;
double t = start;
Vector3 pos = Vector3.zero;
while (true)
{
EvaluatePosition(t, ref pos);
float dist = (point - pos).sqrMagnitude;
if (dist < closestDistance)
{
closestDistance = dist;
closestPercent = t;
}
if (t == end) break;
t = DMath.Move(t, end, tick);
}
double newStart = closestPercent - tick;
if (newStart < start) newStart = start;
double newEnd = closestPercent + tick;
if (newEnd > end) newEnd = end;
return GetClosestPoint(--iterations, point, newStart, newEnd, slices);
}
///
/// Break the closed spline
///
public void Break()
{
Break(0);
}
///
/// Break the closed spline at given point
///
///
public void Break(int at)
{
if (!closed) return;
if (at >= points.Length) return;
if (at < 0) return;
SplinePoint[] previousPoints = new SplinePoint[points.Length];
points.CopyTo(previousPoints, 0);
for (int i = at; i < previousPoints.Length; i++)
{
points[i - at] = previousPoints[i];
}
for (int i = 0; i < at; i++)
{
points[(points.Length - at) + i] = previousPoints[i];
}
closed = false;
}
///
/// Close the spline. This will cause the first and last points of the spline to merge
///
public void Close()
{
if (points.Length < 3)
{
Debug.LogError("Points need to be at least 3 to close the spline");
return;
}
closed = true;
}
///
/// Convert the spline to a Bezier path
///
public void CatToBezierTangents()
{
switch (type)
{
case Type.Linear:
for (int i = 0; i < points.Length; i++)
{
points[i].type = SplinePoint.Type.Broken;
points[i].SetTangentPosition(points[i].position);
points[i].SetTangent2Position(points[i].position);
}
break;
case Type.CatmullRom:
for (int i = 0; i < points.Length; i++)
{
points[i].type = SplinePoint.Type.SmoothMirrored;
double percent = GetPointPercent(i);
Vector3 tangent = Vector3.forward;
EvaluateTangent(percent, ref tangent);
if(_knotParametrization > 0f)
{
ComputeCatPoints(i);
points[i].SetTangent2Position(points[i].position + tangent.normalized * Vector3.Distance(P[0], P[2]) / 6f);
} else
{
points[i].SetTangent2Position(points[i].position + tangent / 3f);
}
}
break;
case Type.BSpline:
//No BSPline support yet
break;
}
type = Type.Bezier;
}
///
/// Evaluates the position of the spline using one of the algorithms
///
private void CalculatePosition(ref Vector3 position, double percent, int pointIndex)
{
switch (type)
{
case Type.CatmullRom:
ComputeCatPoints(pointIndex);
if (_knotParametrization < 0.000001f)
{
CalculateCatmullRomPositionFast(ref position, percent, pointIndex);
} else
{
CalculateCatmullRomComponents(percent);
CalculateCatmullRomPosition(percent, ref position);
}
break;
case Type.Bezier: CalculateBezierPosition(ref position, percent, pointIndex); break;
case Type.BSpline:
ComputeCatPoints(pointIndex);
CalculateBSplinePosition(ref position, percent, pointIndex); break;
case Type.Linear:
ComputeCatPoints(pointIndex);
CalculateLinearPosition(ref position, percent, pointIndex);
break;
}
}
///
/// Evaluates the direction of the spline using one of the algorithms
///
private void CalculateTangent(ref Vector3 tangent, double percent, int pointIndex)
{
switch (type)
{
case Type.CatmullRom:
ComputeCatPoints(pointIndex);
if (_knotParametrization < 0.000001f)
{
CalculateCatmullRomTangentFast(ref tangent, percent, pointIndex);
}
else
{
CalculateCatmullRomComponents(percent);
CalculateCatmullRomTangent(percent, ref tangent);
}
break;
case Type.Bezier:
CalculateBezierTangent(ref tangent, percent, pointIndex);
break;
case Type.Linear:
ComputeCatPoints(pointIndex);
CalculateLinearTangent(ref tangent, percent, pointIndex);
break;
}
}
///
/// Slightly faster than calling GetPoint and GetTangent separately
///
private void CalculatePositionAndTangent(double percent, int pointIndex, ref Vector3 position, ref Vector3 tangent)
{
switch (type)
{
case Type.CatmullRom:
ComputeCatPoints(pointIndex);
if (_knotParametrization < 0.000001f)
{
CalculateCatmullRomPositionFast(ref position, percent, pointIndex);
CalculateCatmullRomTangentFast(ref tangent, percent, pointIndex);
}
else
{
CalculateCatmullRomComponents(percent);
CalculateCatmullRomPosition(percent, ref position);
CalculateCatmullRomTangent(percent, ref tangent);
}
break;
case Type.Bezier:
CalculateBezierPosition(ref position, percent, pointIndex);
CalculateBezierTangent(ref tangent, percent, pointIndex);
break;
case Type.BSpline:
ComputeCatPoints(pointIndex);
CalculateBSplinePosition(ref position, percent, pointIndex);
break;
case Type.Linear:
ComputeCatPoints(pointIndex);
CalculateLinearPosition(ref position, percent, pointIndex);
CalculateLinearTangent(ref tangent, percent, pointIndex);
break;
}
}
private void CalculateLinearPosition(ref Vector3 position, double t, int i)
{
if (points.Length == 0)
{
position = Vector3.zero;
return;
}
position = Vector3.Lerp(P[1], P[2], (float)t);
}
private void CalculateLinearTangent(ref Vector3 tangent, double t, int i)
{
if (points.Length == 0)
{
tangent = Vector3.forward;
return;
}
if (linearAverageDirection) tangent = Vector3.Slerp(P[1] - P[0], P[2] - P[1], 0.5f);
else tangent = P[2] - P[1];
}
private void CalculateBSplinePosition(ref Vector3 position, double time, int i)
{
if (points.Length > 0) position = points[0].position;
if (points.Length > 1)
{
float tf = (float)DMath.Clamp01(time);
position = ((-P[0] + P[2]) / 2f
+ tf * ((P[0] - 2f * P[1] + P[2]) / 2f
+ tf * (-P[0] + 3f * P[1] - 3f * P[2] + P[3]) / 6f)) * tf
+ (P[0] + 4f * P[1] + P[2]) / 6f;
}
}
private void CalculateBezierPosition(ref Vector3 position, double t, int i)
{
if (points.Length > 0) position = points[0].position;
else return;
if (!closed && points.Length == 1) return;
t = DMath.Clamp01(t);
int it = i + 1;
if (it >= points.Length)
{
it = 0;
}
float ft = (float)t;
float nt = 1f - ft;
position = nt * nt * nt * points[i].position +
3f * nt * nt * ft * points[i].tangent2 +
3f * nt * ft * ft * points[it].tangent +
ft * ft * ft * points[it].position;
}
private void CalculateBezierTangent(ref Vector3 tangent, double t, int i)
{
if (points.Length > 0) tangent = points[0].tangent;
else return;
if (!closed && points.Length == 1) return;
t = DMath.Clamp01(t);
int it = i + 1;
if (it >= points.Length)
{
it = 0;
}
float ft = (float)t;
float nt = 1f - ft;
tangent = -3f * nt * nt * points[i].position +
3f * nt * nt * points[i].tangent2 -
6f * ft * nt * points[i].tangent2 -
3f * ft * ft * points[it].tangent +
6f * ft * nt * points[it].tangent +
3f * ft * ft * points[it].position;
}
private void CalculateCatmullRomComponents(double t)
{
const float t0 = 0f;
t1 = GetInterval(P[0], P[1]);
t2 = GetInterval(P[1], P[2]) + t1;
t3 = GetInterval(P[2], P[3]) + t2;
float tf = Mathf.LerpUnclamped(t1, t2, (float)t);
A1 = (t1 - tf) / (t1 - t0) * P[0] + (tf - t0) / (t1 - t0) * P[1];
A2 = (t2 - tf) / (t2 - t1) * P[1] + (tf - t1) / (t2 - t1) * P[2];
A3 = (t3 - tf) / (t3 - t2) * P[2] + (tf - t2) / (t3 - t2) * P[3];
B1 = (t2 - tf) / (t2 - t0) * A1 + (tf - t0) / (t2 - t0) * A2;
B2 = (t3 - tf) / (t3 - t1) * A2 + (tf - t1) / (t3 - t1) * A3;
float GetInterval(Vector3 a, Vector3 b)
{
return Mathf.Pow((a - b).sqrMagnitude, _knotParametrization * 0.5f);
}
}
private void CalculateCatmullRomPosition(double t, ref Vector3 position)
{
float tf = Mathf.LerpUnclamped(t1, t2, (float)t);
position = (t2 - tf) / (t2 - t1) * B1 + (tf - t1) / (t2 - t1) * B2;
}
private void CalculateCatmullRomTangent(double t, ref Vector3 tangent)
{
float tf = Mathf.LerpUnclamped(t1, t2, (float)t);
Vector3 A1p = (P[1] - P[0]) / t1;
Vector3 A2p = (P[2] - P[1]) / (t2 - t1);
Vector3 A3p = (P[3] - P[2]) / (t3 - t2);
Vector3 B1p = (A2 - A1) / t2 + (t2 - tf) / t2 * A1p + tf / t2 * A2p;
Vector3 B2p = (A3 - A2) / (t3 - t1) + (t3 - tf) / (t3 - t1) * A2p + (tf - t1) / (t3 - t1) * A3p;
tangent = (B2 - B1) / (t2 - t1) + (t2 - tf) / (t2 - t1) * B1p + (tf - t1) / (t2 - t1) * B2p;
}
private void CalculateCatmullRomPositionFast(ref Vector3 position, double t, int i)
{
float t1 = (float)t;
float t2 = t1 * t1;
float t3 = t2 * t1;
if (points.Length > 0)
{
position = points[0].position;
}
if (!closed && i >= points.Length) return;
if (points.Length > 1)
{
position = 0.5f * ((2f * P[1]) + (-P[0] + P[2]) * t1
+ (2f * P[0] - 5f * P[1] + 4f * P[2] - P[3]) * t2
+ (-P[0] + 3f * P[1] - 3f * P[2] + P[3]) * t3);
}
}
private void CalculateCatmullRomTangentFast(ref Vector3 tangent, double t, int i)
{
float t1 = (float)t;
float t2 = t1 * t1;
if (!closed && i >= points.Length) return;
if (points.Length > 1)
{
tangent = (6 * t2 - 6 * t1) * P[1]
+ (3 * t2 - 4 * t1 + 1) * (P[2] - P[0]) * 0.5f
+ (-6 * t2 + 6 * t1) * P[2]
+ (3 * t2 - 2 * t1) * (P[3] - P[1]) * 0.5f;
}
}
private void ComputeCatPoints(int i)
{
int p1 = i - 1;
int p2 = i;
int p3 = i + 1;
int p4 = i + 2;
if (closed)
{
if(p1 < 0)
{
p1 += points.Length;
}
if (p2 >= points.Length)
{
p2 -= points.Length;
}
if (p3 >= points.Length)
{
p3 -= points.Length;
}
if(p4 >= points.Length)
{
p4 -= points.Length;
}
P[0] = points[p1].position;
P[1] = points[p2].position;
P[2] = points[p3].position;
P[3] = points[p4].position;
} else
{
if(p1 < 0)
{
P[0] = points[0].position;
P[0] += (P[0] - points[1].position);
} else
{
P[0] = points[p1].position;
}
P[1] = points[p2].position;
if (p3 >= points.Length)
{
P[2] = points[points.Length - 1].position;
Vector3 pos = P[2];
P[2] += P[2] - points[points.Length - 2].position;
P[3] = P[2] + (P[2] - pos);
}
else
{
P[2] = points[p3].position;
if(p4 >= points.Length)
{
P[3] = P[2] + (P[2] - points[p3 - 1].position);
}
else
{
P[3] = points[p4].position;
}
}
}
}
public static void FormatFromTo(ref double from, ref double to, bool preventInvert = true)
{
from = DMath.Clamp01(from);
to = DMath.Clamp01(to);
if (preventInvert && from > to)
{
double tmp = from;
from = to;
to = tmp;
} else to = DMath.Clamp(to, 0.0, 1.0);
}
}
}