public static Vector2 Calculate(Vector2 p0, Vector2 p1, Vector2 p2, Vector2 p3, float t)
{
Vector2 a, b, c, d;
float ct = 0;
if (t < 1f / 3f)
{
a = p0;
b = p0;
c = p1;
d = p2;
ct = t * 3.0f;
}
else if (t > 2f / 3f)
{
a = p1;
b = p2;
c = p3;
d = p3;
ct = t * 3.0f - 2.0f;
}
else
{
a = p0;
b = p1;
c = p2;
d = p3;
ct = t * 3.0f - 1.0f;
}
return(SplineMaths.CalculateCatmullRom(a, b, c, d, ct));
}
public static Vector3 Calculate(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t)
{
Vector3 a, b, c, d;
float ct = 0;
if (t < 1f / 3f)
{
a = p0;
b = p0;
c = p1;
d = p2;
ct = t * 3.0f;
}
else if (t > 2f / 3f)
{
a = p1;
b = p2;
c = p3;
d = p3;
ct = t * 3.0f - 2.0f;
}
else
{
a = p0;
b = p1;
c = p2;
d = p3;
ct = t * 3.0f - 1.0f;
}
// return SplineMaths.CalculateHermite(p0, p1, p2, p3, t, -0.80f, 0);
// return SplineMaths.CalculateBezierPoint(p0, p1, p2, p3, t);
return(SplineMaths.CalculateCatmullRom(a, b, c, d, ct));
}
public static Vector3 Calculate(Vector3 p0, Vector3 p1, Vector3 p2, float t)
{
Vector3 a, b, c, d;
float ct = 0;
if (t < 0.5f)
{
a = p0;
b = p0;
c = p1;
d = p2;
ct = t * 2.0f;
}
else if (t > 0.5f)
{
a = p0;
b = p1;
c = p2;
d = p2;
ct = t * 2.0f - 1.0f;
}
else
{
return(p1);
}
return(SplineMaths.CalculateHermite(a, b, c, d, ct, -0.80f, 0));
// return SplineMaths.CalculateBezierPoint(a, b, c, d, ct);
// return SplineMaths.CalculateCatmullRom(a, b, c, d, ct);
}
//Sample nextNormIndex position on the entire curve based on time (0-1)
public Vector3 GetRightBoundaryPosition(float t)
{
float curveT = 1.0f / numberOfCurves;
int point = Mathf.FloorToInt(t / curveT);
float ct = Mathf.Clamp01((t - point * curveT) * numberOfCurves);
TrackBuildRPoint pointA = GetPoint(point);
TrackBuildRPoint pointB = GetPoint(point + 1);
return(SplineMaths.CalculateBezierPoint(ct, pointA.rightTrackBoundary, pointA.rightForwardControlPoint, pointB.rightBackwardControlPoint, pointB.rightTrackBoundary));
}
public Vector3 GetTrackCross(float t)
{
float curveT = 1.0f / numberOfCurves;
int point = Mathf.FloorToInt(t / curveT);
float ct = Mathf.Clamp01((t - point * curveT) * numberOfCurves);
float hermite = SplineMaths.CalculateHermite(ct);
TrackBuildRPoint pointA = GetPoint(point);
TrackBuildRPoint pointB = GetPoint(point + 1);
return(Vector3.Slerp(pointA.trackCross, pointB.trackCross, hermite));
}
public float GetTrackCrownAngle(float t)
{
float curveT = 1.0f / numberOfCurves;
int point = Mathf.FloorToInt(t / curveT);
float ct = Mathf.Clamp01((t - point * curveT) * numberOfCurves);
float hermite = SplineMaths.CalculateHermite(ct);
TrackBuildRPoint pointA = GetPoint(point);
TrackBuildRPoint pointB = GetPoint(point + 1);
return(Mathf.LerpAngle(pointA.crownAngle, pointB.crownAngle, hermite));
}
public Vector3 GetTrackDirection(float t)
{
float curveT = 1.0f / numberOfCurves;
int point = Mathf.FloorToInt(t / curveT);
float ct = Mathf.Clamp01((t - point * curveT) * numberOfCurves);
float hermite = SplineMaths.CalculateHermite(ct);
TrackBuildRPoint pointA = GetPoint(point);
TrackBuildRPoint pointB = GetPoint(point + 1);
Quaternion trackDirectionA = Quaternion.LookRotation(pointA.trackDirection);
Quaternion trackDirectionB = Quaternion.LookRotation(pointB.trackDirection);
Quaternion trackDirectionQ = Quaternion.Slerp(trackDirectionA, trackDirectionB, hermite);
return(trackDirectionQ * Vector3.forward);
}
//Sample nextNormIndex position on the entire curve based on time (0-1)
public Vector3 GetTrackPosition(float t)
{
if (realNumberOfPoints < 2)
{
Debug.LogError("Not enough points to define a curve");
return(Vector3.zero);
}
float curveT = 1.0f / numberOfCurves;
int point = Mathf.FloorToInt(t / curveT);
float ct = Mathf.Clamp01((t - point * curveT) * numberOfCurves);
TrackBuildRPoint pointA = GetPoint(point);
TrackBuildRPoint pointB = GetPoint(point + 1);
return(SplineMaths.CalculateBezierPoint(ct, pointA.position, pointA.forwardControlPoint, pointB.backwardControlPoint, pointB.position));
}
public void RecalculateCurves()
{
if (_points.Count < 2)//there is no track with only one point :o)
{
return;
}
if (isDirty)
{
_tangentsGenerated = false;
_lightmapGenerated = false;
_optimised = false;
}
//calculate approx bezier arc length per curve
for (int i = 0; i < realNumberOfPoints; i++)
{
TrackBuildRPoint pointA = GetPoint(i);
TrackBuildRPoint pointB = GetPoint(i + 1);
float thisArcLength = 0;
thisArcLength += Vector3.Distance(pointA.position, pointA.forwardControlPoint);
thisArcLength += Vector3.Distance(pointA.forwardControlPoint, pointB.backwardControlPoint);
thisArcLength += Vector3.Distance(pointB.backwardControlPoint, pointB.position);
_points[i].arcLength = thisArcLength;
if (thisArcLength == 0)
{
DestroyImmediate(pointA);
i--;
}
}
for (int i = 0; i < realNumberOfPoints; i++)
{
TrackBuildRPoint pointA = GetPoint(i);
TrackBuildRPoint pointB = GetPoint(i + 1);
TrackBuildRPoint pointC = GetPoint(i - 1);
pointA.nextPoint = pointB;
pointA.lastPoint = pointC;
pointA.pointName = "point " + i;
}
foreach (TrackBuildRPoint curve in _points)
{
if (!curve.curveIsDirty)//only recalculate modified points
{
continue;
}
if (curve.arcLength > 0)
{
TrackBuildRPoint pointA = curve;
TrackBuildRPoint pointB = curve.nextPoint;
//Build accurate arc length data into curve
curve.center = Vector3.zero;
int arcLengthResolution = Mathf.Max(Mathf.RoundToInt(curve.arcLength * 10), 1);
float alTime = 1.0f / arcLengthResolution;
float calculatedTotalArcLength = 0;
curve.storedArcLengthsFull = new float[arcLengthResolution];
curve.storedArcLengthsFull[0] = 0.0f;
Vector3 pA = curve.position;
for (int i = 0; i < arcLengthResolution - 1; i++)
{
curve.center += pA;
float altB = alTime * (i + 1) + alTime;
Vector3 pB = SplineMaths.CalculateBezierPoint(altB, curve.position, curve.forwardControlPoint, pointB.backwardControlPoint, pointB.position);
float arcLength = Vector3.Distance(pA, pB);
calculatedTotalArcLength += arcLength;
curve.storedArcLengthsFull[i + 1] = calculatedTotalArcLength;
pA = pB;//switch over values so we only calculate the bezier once
}
curve.arcLength = calculatedTotalArcLength;
curve.center /= arcLengthResolution;
int storedPointSize = Mathf.RoundToInt(calculatedTotalArcLength / meshResolution);
curve.storedPointSize = storedPointSize;
curve.normalisedT = new float[storedPointSize];
curve.targetSize = new float[storedPointSize];
curve.midPointPerc = new float[storedPointSize];
curve.prevNormIndex = new int[storedPointSize];
curve.nextNormIndex = new int[storedPointSize];
curve.clipArrayLeft = new bool[storedPointSize];
curve.clipArrayRight = new bool[storedPointSize];
//calculate normalised spline data
int normalisedIndex = 0;
curve.normalisedT[0] = 0;
for (int p = 1; p < storedPointSize; p++)
{
float t = p / (float)(storedPointSize - 1);
float targetLength = t * calculatedTotalArcLength;
curve.targetSize[p] = targetLength;
int it = 1000;
while (targetLength > curve.storedArcLengthsFull[normalisedIndex])
{
normalisedIndex++;
it--;
if (it < 0)
{
curve.normalisedT[p] = 0;
break;
}
}
normalisedIndex = Mathf.Min(normalisedIndex, arcLengthResolution);//ensure we've not exceeded the length
int prevNormIndex = Mathf.Max((normalisedIndex - 1), 0);
int nextNormIndex = normalisedIndex;
float lengthBefore = curve.storedArcLengthsFull[prevNormIndex];
float lengthAfter = curve.storedArcLengthsFull[nextNormIndex];
float midPointPercentage = (targetLength - lengthBefore) / (lengthAfter - lengthBefore);
curve.midPointPerc[p] = midPointPercentage;
curve.prevNormIndex[p] = prevNormIndex;
curve.nextNormIndex[p] = nextNormIndex;
float normalisedT = (normalisedIndex + midPointPercentage) / arcLengthResolution;//lerp between the values to get the exact normal T
curve.normalisedT[p] = normalisedT;
}
curve.sampledPoints = new Vector3[storedPointSize];
curve.sampledLeftBoundaryPoints = new Vector3[storedPointSize];
curve.sampledRightBoundaryPoints = new Vector3[storedPointSize];
curve.sampledWidths = new float[storedPointSize];
curve.sampledCrowns = new float[storedPointSize];
curve.sampledTrackDirections = new Vector3[storedPointSize];
curve.sampledTrackUps = new Vector3[storedPointSize];
curve.sampledTrackCrosses = new Vector3[storedPointSize];
curve.sampledAngles = new float[storedPointSize];
for (int p = 0; p < storedPointSize; p++)
{
float tN = curve.normalisedT[p];
float tH = SplineMaths.CalculateHermite(tN);
curve.sampledPoints[p] = SplineMaths.CalculateBezierPoint(tN, pointA.position, pointA.forwardControlPoint, pointB.backwardControlPoint, pointB.position);
curve.sampledLeftBoundaryPoints[p] = SplineMaths.CalculateBezierPoint(tN, pointA.leftTrackBoundary, pointA.leftForwardControlPoint, pointB.leftBackwardControlPoint, pointB.leftTrackBoundary);
curve.sampledRightBoundaryPoints[p] = SplineMaths.CalculateBezierPoint(tN, pointA.rightTrackBoundary, pointA.rightForwardControlPoint, pointB.rightBackwardControlPoint, pointB.rightTrackBoundary);
curve.sampledWidths[p] = Mathf.LerpAngle(pointA.width, pointB.width, tH);
curve.sampledCrowns[p] = Mathf.LerpAngle(pointA.crownAngle, pointB.crownAngle, tH);
curve.sampledTrackUps[p] = Quaternion.Slerp(pointA.trackUpQ, pointB.trackUpQ, tH) * Vector3.forward;
curve.clipArrayLeft[p] = true;
curve.clipArrayRight[p] = true;
}
}
}
for (int i = 0; i < numberOfCurves; i++)
{
TrackBuildRPoint curve = _points[i];
if (!curve.curveIsDirty)//only recalculate modified points
{
continue;
}
if (curve.arcLength > 0)
{
int lastCurveIndex = (i > 0) ? i - 1 : (_looped) ? numberOfCurves - 1 : 0;
int nextCurveIndex = (i < numberOfCurves - 1) ? i + 1 : (_looped) ? 0 : numberOfCurves - 1;
TrackBuildRPoint lastcurve = _points[lastCurveIndex];
TrackBuildRPoint nextcurve = _points[nextCurveIndex];
int storedPointSize = curve.storedPointSize;
for (int p = 0; p < storedPointSize; p++)
{
int pA = p - 1;
int pB = p;
int pC = p + 1;
if (pA < 0)
{
pA = 0;
}
if (pC >= storedPointSize)
{
pC = storedPointSize - 1;
}
Vector3 sampledPointA = curve.sampledPoints[pA];
Vector3 sampledPointB = curve.sampledPoints[pB];
Vector3 sampledPointC = curve.sampledPoints[pC];
if (p == 0 && lastcurve != null && lastcurve.sampledPoints.Length > 1)
{
sampledPointA = lastcurve.sampledPoints[lastcurve.storedPointSize - 2];//retrieve the penultimate point from the last curve
}
if (p == storedPointSize - 1 && nextcurve != null && nextcurve.sampledPoints.Length > 1)
{
sampledPointC = nextcurve.sampledPoints[1];//retrieve the second point from the next curve
}
Vector3 sampledTrackDirectionA = (sampledPointB - sampledPointA);
Vector3 sampledTrackDirectionB = (sampledPointC - sampledPointB);
Vector3 sampledTrackDirection = (sampledTrackDirectionA + sampledTrackDirectionB).normalized;
curve.sampledTrackDirections[pB] = sampledTrackDirection;
curve.sampledTrackCrosses[pB] = Vector3.Cross(curve.sampledTrackUps[pB], sampledTrackDirection);
curve.sampledAngles[pB] = Vector3.Angle(sampledTrackDirectionA, sampledTrackDirectionB) * -Mathf.Sign(Vector3.Dot((sampledTrackDirectionB - sampledTrackDirectionA), curve.sampledTrackCrosses[pB]));
curve.clipArrayLeft[pB] = true;
curve.clipArrayRight[pB] = true;
}
}
}
bool dirtyTextures = false;
foreach (TrackBuildRTexture texture in _textures)
{
if (texture.isDirty)
{
dirtyTextures = true;//if nextNormIndex point was dirty, ensure it's rerendered
}
texture.isDirty = false;
}
foreach (TrackBuildRPoint point in _points)
{
if (point.curveIsDirty || dirtyTextures)
{
point.shouldReRender = true;//if nextNormIndex point was dirty, ensure it's rerendered
}
}
//clean points
foreach (TrackBuildRPoint point in _points)
{
point.isDirty = false;//reset all points - data is no longer considered dirty
}
//recalculate track length
_trackLength = 0;
foreach (TrackBuildRPoint curve in _points)
{
_trackLength += curve.arcLength;
}
}
public void RecalculateCurves()
{
if (_points.Count < 2)//there is no track with only one point :o)
{
return;
}
if (isDirty)
{
_tangentsGenerated = false;
_lightmapGenerated = false;
_optimised = false;
}
//calculate approx bezier arc length per curve
float roughArcLength = 0;
for (int i = 0; i < realNumberOfPoints; i++)
{
TrackBuildRPoint pointA = GetPoint(i);
TrackBuildRPoint pointB = GetPoint(i + 1);
roughArcLength += Vector3.Distance(pointA.position, pointA.forwardControlPoint);
roughArcLength += Vector3.Distance(pointA.forwardControlPoint, pointB.backwardControlPoint);
roughArcLength += Vector3.Distance(pointB.backwardControlPoint, pointB.position);
_points[i].arcLength = roughArcLength;
if (roughArcLength == 0)
{
DestroyImmediate(pointA);
i--;
}
}
for (int i = 0; i < realNumberOfPoints; i++)
{
TrackBuildRPoint pointA = GetPoint(i);
TrackBuildRPoint pointB = GetPoint(i + 1);
TrackBuildRPoint pointC = GetPoint(i - 1);
pointA.nextPoint = pointB;
pointA.lastPoint = pointC;
pointA.pointName = "point " + i;
}
foreach (TrackBuildRPoint curve in _points)
{
if (!curve.curveIsDirty)//only recalculate modified points
{
continue;
}
if (curve.arcLength > 0)
{
TrackBuildRPoint pointA = curve;
TrackBuildRPoint pointB = curve.nextPoint;
//Build accurate arc length data into curve
curve.center = Vector3.zero;
Vector3 curveA = pointA.position;
Vector3 curveP = pointA.forwardControlPoint;
Vector3 curveQ = pointB.backwardControlPoint;
Vector3 curveB = pointB.position;
Vector3 curveALTB = pointA.leftTrackBoundary;
Vector3 curveARTB = pointA.rightTrackBoundary;
Vector3 curveBLTB = pointB.leftTrackBoundary;
Vector3 curveBRTB = pointB.rightTrackBoundary;
Vector3 curveALFCP = pointA.leftForwardControlPoint;
// Vector3 curveALBCP = pointA.leftBackwardControlPoint;
Vector3 curveARFCP = pointA.rightForwardControlPoint;
// Vector3 curveARBCP = pointA.rightBackwardControlPoint;
// Vector3 curveBLFCP = pointB.leftForwardControlPoint;
Vector3 curveBLBCP = pointB.leftBackwardControlPoint;
// Vector3 curveBRFCP = pointB.rightForwardControlPoint;
Vector3 curveBRBCP = pointB.rightBackwardControlPoint;
int _dataSize = Mathf.Max(Mathf.RoundToInt(curve.arcLength / meshResolution), 1);
float normilisePercentAmount = 1.0f / (_dataSize * 10);
float normalisePercent = 0;
float targetMovement = curve.arcLength / (_dataSize - 1);
List <float> normValues = new List <float>();
normValues.Add(0);
float currentLength = 0;
float targetLength = targetMovement;
float totalArcLength = 0;
Vector3 pA = curveA, pB;
for (; normalisePercent < 1.0f - normilisePercentAmount; normalisePercent += normilisePercentAmount)
{
pB = SplineMaths.CalculateBezierPoint(normalisePercent, curveA, curveP, curveQ, curveB);
float arcLength = Vector3.Distance(pA, pB);
if (currentLength + arcLength > targetLength)
{
float lerpPoint = (targetLength - currentLength) / arcLength;
float normValue = Mathf.Lerp(normalisePercent, normalisePercent + normilisePercentAmount, lerpPoint);
normValues.Add(normValue);
curve.center += pB;
currentLength = targetLength;
targetLength += targetMovement;
}
currentLength += arcLength;
totalArcLength += arcLength;
pA = pB;
}
normValues.Add(1);
int storedPointSize = normValues.Count;
curve.normalisedT = normValues.ToArray();
curve.arcLength = totalArcLength;
curve.center /= (storedPointSize - 2);
curve.storedPointSize = storedPointSize;
curve.clipArrayLeft = new bool[storedPointSize];
curve.clipArrayRight = new bool[storedPointSize];
curve.sampledPoints = new Vector3[storedPointSize];
curve.sampledLeftBoundaryPoints = new Vector3[storedPointSize];
curve.sampledRightBoundaryPoints = new Vector3[storedPointSize];
curve.sampledWidths = new float[storedPointSize];
curve.sampledCrowns = new float[storedPointSize];
curve.sampledTrackDirections = new Vector3[storedPointSize];
curve.sampledTrackUps = new Vector3[storedPointSize];
curve.sampledTrackCrosses = new Vector3[storedPointSize];
curve.sampledAngles = new float[storedPointSize];
for (int p = 0; p < storedPointSize; p++)
{
float tN = curve.normalisedT[p];
float tH = SplineMaths.CalculateHermite(tN);
curve.sampledPoints[p] = SplineMaths.CalculateBezierPoint(tN, curveA, curveP, curveQ, curveB);
curve.sampledLeftBoundaryPoints[p] = SplineMaths.CalculateBezierPoint(tN, curveALTB, curveALFCP, curveBLBCP, curveBLTB);
curve.sampledRightBoundaryPoints[p] = SplineMaths.CalculateBezierPoint(tN, curveARTB, curveARFCP, curveBRBCP, curveBRTB);
curve.sampledWidths[p] = Mathf.LerpAngle(pointA.width, pointB.width, tH);
curve.sampledCrowns[p] = Mathf.LerpAngle(pointA.crownAngle, pointB.crownAngle, tH);
curve.sampledTrackUps[p] = Quaternion.Slerp(pointA.trackUpQ, pointB.trackUpQ, tH) * Vector3.forward;
curve.clipArrayLeft[p] = true;
curve.clipArrayRight[p] = true;
}
}
}
for (int i = 0; i < numberOfCurves; i++)
{
TrackBuildRPoint curve = _points[i];
if (!curve.curveIsDirty)//only recalculate modified points
{
continue;
}
if (curve.arcLength > 0)
{
int lastCurveIndex = (i > 0) ? i - 1 : (_looped) ? numberOfCurves - 1 : 0;
int nextCurveIndex = (i < numberOfCurves - 1) ? i + 1 : (_looped) ? 0 : numberOfCurves - 1;
TrackBuildRPoint lastcurve = _points[lastCurveIndex];
TrackBuildRPoint nextcurve = _points[nextCurveIndex];
int storedPointSize = curve.storedPointSize;
for (int p = 0; p < storedPointSize; p++)
{
int pA = p - 1;
int pB = p;
int pC = p + 1;
if (pA < 0)
{
pA = 0;
}
if (pC >= storedPointSize)
{
pC = storedPointSize - 1;
}
Vector3 sampledPointA = curve.sampledPoints[pA];
Vector3 sampledPointB = curve.sampledPoints[pB];
Vector3 sampledPointC = curve.sampledPoints[pC];
if (p == 0 && lastcurve != null && lastcurve.sampledPoints.Length > 1)
{
sampledPointA = lastcurve.sampledPoints[lastcurve.storedPointSize - 2];//retrieve the penultimate point from the last curve
}
if (p == storedPointSize - 1 && nextcurve != null && nextcurve.sampledPoints.Length > 1)
{
sampledPointC = nextcurve.sampledPoints[1];//retrieve the second point from the next curve
}
Vector3 sampledTrackDirectionA = (sampledPointB - sampledPointA);
Vector3 sampledTrackDirectionB = (sampledPointC - sampledPointB);
Vector3 sampledTrackDirection = (sampledTrackDirectionA + sampledTrackDirectionB).normalized;
curve.sampledTrackDirections[pB] = sampledTrackDirection;
curve.sampledTrackCrosses[pB] = Vector3.Cross(curve.sampledTrackUps[pB], sampledTrackDirection);
curve.sampledAngles[pB] = Vector3.Angle(sampledTrackDirectionA, sampledTrackDirectionB) * -Mathf.Sign(Vector3.Dot((sampledTrackDirectionB - sampledTrackDirectionA), curve.sampledTrackCrosses[pB]));
curve.clipArrayLeft[pB] = true;
curve.clipArrayRight[pB] = true;
}
}
}
bool dirtyTextures = false;
foreach (TrackBuildRTexture texture in _textures)
{
if (texture.isDirty)
{
dirtyTextures = true;//if nextNormIndex point was dirty, ensure it's rerendered
}
texture.isDirty = false;
}
foreach (TrackBuildRPoint point in _points)
{
if (point.curveIsDirty || dirtyTextures)
{
point.shouldReRender = true;//if nextNormIndex point was dirty, ensure it's rerendered
}
}
//clean points
foreach (TrackBuildRPoint point in _points)
{
point.isDirty = false;//reset all points - data is no longer considered dirty
}
//recalculate track length
_trackLength = 0;
foreach (TrackBuildRPoint curve in _points)
{
_trackLength += curve.arcLength;
}
}
