public static float ConvertToSh3DArcAngle(Vector3 arcOrigin, Vector3 arcStartPoint, Vector3 arcPlaneNormal, float degreesFromStart)
{
degreesFromStart %= 360.0f;
if (Mathf.Abs(degreesFromStart) > 180.0f)
{
Vector3 toStartPt = (arcStartPoint - arcOrigin);
Vector3 toEndPt = (Quaternion.AngleAxis(degreesFromStart, arcPlaneNormal) * toStartPt).normalized;
degreesFromStart = Vector3Ex.SignedAngle(toStartPt, toEndPt, arcPlaneNormal);
}
return(degreesFromStart);
}
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 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);
}
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 Quaternion Align(this Transform transform, Vector3 normAlignVector, TransformAxis alignmentAxis)
{
Vector3 axis = transform.up;
if (alignmentAxis != TransformAxis.PositiveY)
{
if (alignmentAxis == TransformAxis.PositiveX)
{
axis = transform.right;
}
else if (alignmentAxis == TransformAxis.NegativeX)
{
axis = -transform.right;
}
else if (alignmentAxis == TransformAxis.NegativeY)
{
axis = -transform.up;
}
else if (alignmentAxis == TransformAxis.PositiveZ)
{
axis = transform.forward;
}
else if (alignmentAxis == TransformAxis.NegativeZ)
{
axis = -transform.forward;
}
}
float alignment = Vector3.Dot(axis, normAlignVector);
if (1.0f - alignment < 1e-5f)
{
return(Quaternion.identity);
}
Vector3 rotAxis = Vector3.zero;
// Check if the alignment axis is aligned with the alignment vector in the opposite direction
if (alignment + 1.0f < 1e-5f)
{
if (alignmentAxis == TransformAxis.PositiveX)
{
rotAxis = transform.up;
}
else if (alignmentAxis == TransformAxis.NegativeX)
{
rotAxis = -transform.up;
}
else if (alignmentAxis == TransformAxis.PositiveY)
{
rotAxis = transform.right;
}
else if (alignmentAxis == TransformAxis.NegativeY)
{
rotAxis = -transform.right;
}
else if (alignmentAxis == TransformAxis.PositiveZ)
{
rotAxis = transform.up;
}
else if (alignmentAxis == TransformAxis.NegativeZ)
{
rotAxis = -transform.up;
}
}
else
{
rotAxis = Vector3.Normalize(Vector3.Cross(axis, normAlignVector));
}
float rotAngle = Vector3Ex.SignedAngle(axis, normAlignVector, rotAxis);
transform.Rotate(rotAxis, rotAngle, Space.World);
return(Quaternion.AngleAxis(rotAngle, rotAxis));
}