public static bool RaycastShArc(Ray ray, out float t, Vector3 arcOrigin, Vector3 arcStartPoint, Vector3 arcPlaneNormal, float degreesFromStart, ArcEpsilon epsilon = new ArcEpsilon())
{
t = 0.0f;
degreesFromStart = ConvertToSh3DArcAngle(arcOrigin, arcStartPoint, arcPlaneNormal, degreesFromStart);
Plane arcPlane = new Plane(arcPlaneNormal, arcOrigin);
float rayEnter;
if (arcPlane.Raycast(ray, out rayEnter) &&
ShArcContains3DPoint(ray.GetPoint(rayEnter), false, arcOrigin,
arcStartPoint, arcPlaneNormal, degreesFromStart, epsilon))
{
t = rayEnter;
return(true);
}
if (epsilon.ExtrudeEps != 0.0f)
{
float dot = Vector3Ex.AbsDot(ray.direction, arcPlaneNormal);
if (dot < ExtrudeEpsThreshold.Get)
{
OBB arcOBB = CalcSh3DArcOBB(arcOrigin, arcStartPoint, arcPlaneNormal, degreesFromStart, epsilon);
return(BoxMath.Raycast(ray, arcOBB.Center, arcOBB.Size, arcOBB.Rotation));
}
}
return(false);
}
public static bool LgArcContains2DPoint(Vector2 point, Vector2 arcOrigin, Vector2 arcStartPoint, float degreesFromStart, ArcEpsilon epsilon = new ArcEpsilon())
{
epsilon.ExtrudeEps = 0.0f;
return(LgArcContains3DPoint(point.ToVector3(), false, arcOrigin.ToVector3(), arcStartPoint.ToVector3(), Vector3.forward, degreesFromStart, epsilon));
}
public static OBB CalcLg3DArcOBB(Vector3 arcOrigin, Vector3 arcStartPoint, Vector3 arcPlaneNormal, float degreesFromStart, ArcEpsilon epsilon = new ArcEpsilon())
{
if (Math.Abs(degreesFromStart) <= 180.0f)
{
return(CalcSh3DArcOBB(arcOrigin, arcStartPoint, arcPlaneNormal, degreesFromStart, epsilon));
}
Vector3 toStartPt = (arcStartPoint - arcOrigin);
Vector3 toEndPt = Quaternion.AngleAxis(degreesFromStart, arcPlaneNormal) * toStartPt;
Vector3 endPt = arcOrigin + toEndPt;
Vector3 fromStartToEnd = (endPt - arcStartPoint);
Vector3 midPt = arcStartPoint + fromStartToEnd * 0.5f;
Vector3 toMidPt = midPt - arcOrigin;
midPt += toMidPt.normalized * epsilon.AreaEps;
float radius = (arcOrigin - arcStartPoint).magnitude;
float obbDepth = radius + toMidPt.magnitude + 2.0f * epsilon.AreaEps;
Quaternion obbRotation = Quaternion.LookRotation(toMidPt.normalized, arcPlaneNormal);
Vector3 obbCenter = midPt - toMidPt.normalized * obbDepth * 0.5f;
OBB obb = new OBB(obbCenter, obbRotation);
float obbWidth = (radius + epsilon.AreaEps) * 2.0f;
float obbHeight = epsilon.ExtrudeEps * 2.0f;
obb.Size = new Vector3(obbWidth, obbHeight, obbDepth);
return(obb);
}
public static bool Is3DPointOnLgArcWire(Vector3 point, bool checkOnPlane, Vector3 arcOrigin, Vector3 arcStartPoint,
Vector3 arcPlaneNormal, float degreesFromStart, ArcEpsilon epsilon = new ArcEpsilon())
{
if (Mathf.Abs(degreesFromStart) <= 180.0f)
{
return(Is3DPointOnShArcWire(point, checkOnPlane, arcOrigin, arcStartPoint, arcPlaneNormal, degreesFromStart, epsilon));
}
Vector3 toStartPt = (arcStartPoint - arcOrigin);
Vector3 toPt = (point - arcOrigin);
float distToPt = toPt.magnitude;
float arcRadius = (arcOrigin - arcStartPoint).magnitude;
Plane arcPlane = new Plane(arcPlaneNormal, arcOrigin);
if (checkOnPlane && arcPlane.GetAbsDistanceToPoint(point) > epsilon.ExtrudeEps)
{
return(false);
}
Vector3 arcEndPoint = Quaternion.AngleAxis(degreesFromStart, arcPlaneNormal) * toStartPt + arcOrigin;
float distanceFromSegment = point.GetDistanceToSegment(arcOrigin, arcStartPoint);
if (distanceFromSegment <= epsilon.WireEps)
{
return(true);
}
distanceFromSegment = point.GetDistanceToSegment(arcOrigin, arcEndPoint);
if (distanceFromSegment <= epsilon.WireEps)
{
return(true);
}
degreesFromStart = ConvertToSh3DArcAngle(arcOrigin, arcStartPoint, arcPlaneNormal, degreesFromStart);
float startToPtAngle = Vector3Ex.SignedAngle(toStartPt, toPt, arcPlaneNormal);
if (Mathf.Sign(startToPtAngle) == Mathf.Sign(degreesFromStart) &&
Mathf.Abs(startToPtAngle) <= Mathf.Abs(degreesFromStart))
{
return(false);
}
return(distToPt >= arcRadius - epsilon.WireEps &&
distToPt <= arcRadius + epsilon.WireEps);
}
public static OBB CalcSh3DArcOBB(Vector3 arcOrigin, Vector3 arcStartPoint, Vector3 arcPlaneNormal, float degreesFromStart, ArcEpsilon epsilon = new ArcEpsilon())
{
degreesFromStart = ConvertToSh3DArcAngle(arcOrigin, arcStartPoint, arcPlaneNormal, degreesFromStart);
Vector3 toStartPt = (arcStartPoint - arcOrigin);
Vector3 toMidBorderPt = Quaternion.AngleAxis(degreesFromStart * 0.5f, arcPlaneNormal) * toStartPt;
Vector3 midBorderPt = arcOrigin + toMidBorderPt;
Quaternion obbRotation = Quaternion.LookRotation(toMidBorderPt.normalized, arcPlaneNormal);
Vector3 obbCenter = arcOrigin + toMidBorderPt * 0.5f;
OBB obb = new OBB(obbCenter, obbRotation);
Vector3 toEndPt = Quaternion.AngleAxis(degreesFromStart, arcPlaneNormal) * toStartPt;
float sizeEpsAdd = 2.0f * epsilon.AreaEps;
float obbWidth = Vector3Ex.AbsDot(toEndPt, obb.Right) + Vector3Ex.AbsDot(toStartPt, obb.Right) + sizeEpsAdd;
float obbDepth = midBorderPt.magnitude + sizeEpsAdd;
float obbHeight = epsilon.ExtrudeEps * 2.0f;
obb.Size = new Vector3(obbWidth, obbHeight, obbDepth);
return(obb);
}
public static bool LgArcContains3DPoint(Vector3 point, bool checkOnPlane, Vector3 arcOrigin, Vector3 arcStartPoint,
Vector3 arcPlaneNormal, float degreesFromStart, ArcEpsilon epsilon = new ArcEpsilon())
{
degreesFromStart %= 360.0f;
if (Mathf.Abs(degreesFromStart) <= 180.0f)
{
return(ShArcContains3DPoint(point, checkOnPlane, arcOrigin, arcStartPoint, arcPlaneNormal, degreesFromStart, epsilon));
}
Vector3 toPt = (point - arcOrigin);
Vector3 toStartPt = (arcStartPoint - arcOrigin);
degreesFromStart = ConvertToSh3DArcAngle(arcOrigin, arcStartPoint, arcPlaneNormal, degreesFromStart);
float startToPtAngle = Vector3Ex.SignedAngle(toStartPt, toPt, arcPlaneNormal);
bool isInsideShortestArc = Mathf.Sign(startToPtAngle) == Mathf.Sign(degreesFromStart) &&
Mathf.Abs(startToPtAngle) <= Mathf.Abs(degreesFromStart);
if (isInsideShortestArc && epsilon.AreaEps != 0.0f)
{
Vector3 arcEndPoint = Quaternion.AngleAxis(degreesFromStart, arcPlaneNormal) * toStartPt + arcOrigin;
float distanceFromSegment = point.GetDistanceToSegment(arcOrigin, arcStartPoint);
if (distanceFromSegment <= epsilon.AreaEps)
{
return(true);
}
distanceFromSegment = point.GetDistanceToSegment(arcOrigin, arcEndPoint);
if (distanceFromSegment <= epsilon.AreaEps)
{
return(true);
}
return(false);
}
float arcRadius = (arcOrigin - arcStartPoint).magnitude + epsilon.AreaEps;
return(toPt.magnitude <= arcRadius);
}
public static bool ShArcContains2DPoint(Vector2 point, Vector2 arcOrigin, Vector2 arcStartPoint, float degreesFromStart, ArcEpsilon epsilon = new ArcEpsilon())
{
degreesFromStart = ArcMath.ConvertToSh2DArcAngle(arcOrigin, arcStartPoint, degreesFromStart);
epsilon.ExtrudeEps = 0.0f;
return(ShArcContains3DPoint(point.ToVector3(), false, arcOrigin.ToVector3(), arcStartPoint.ToVector3(), Vector3.forward, degreesFromStart, epsilon));
}
public static bool ShArcContains3DPoint(Vector3 point, bool checkOnPlane, Vector3 arcOrigin, Vector3 arcStartPoint,
Vector3 arcPlaneNormal, float degreesFromStart, ArcEpsilon epsilon = new ArcEpsilon())
{
Vector3 toStartPt = (arcStartPoint - arcOrigin);
Vector3 toPt = (point - arcOrigin);
float arcRadius = (arcOrigin - arcStartPoint).magnitude + epsilon.AreaEps;
if (arcRadius < toPt.magnitude)
{
return(false);
}
Plane arcPlane = new Plane(arcPlaneNormal, arcOrigin);
if (checkOnPlane && arcPlane.GetAbsDistanceToPoint(point) > epsilon.ExtrudeEps)
{
return(false);
}
float startToPtAngle = Vector3Ex.SignedAngle(toStartPt, toPt, arcPlaneNormal);
if (Mathf.Sign(startToPtAngle) == Mathf.Sign(degreesFromStart) &&
Mathf.Abs(startToPtAngle) <= Mathf.Abs(degreesFromStart))
{
return(true);
}
if (epsilon.AreaEps != 0.0f)
{
Vector3 arcEndPoint = Quaternion.AngleAxis(degreesFromStart, arcPlaneNormal) * toStartPt + arcOrigin;
float distanceFromSegment = point.GetDistanceToSegment(arcOrigin, arcStartPoint);
if (distanceFromSegment <= epsilon.AreaEps)
{
return(true);
}
distanceFromSegment = point.GetDistanceToSegment(arcOrigin, arcEndPoint);
if (distanceFromSegment <= epsilon.AreaEps)
{
return(true);
}
}
return(false);
}