PndFtsTrackFinder::PndFtsMath Namespace Reference

Functions
float	LineValue (const Line &line, const float arg) noexcept
float	CircleValue (const Circle &circle, const float arg) noexcept
Line	PointsToLine (float abscissa1, float ordinate1, float abscissa2, float ordinate2) noexcept
Line	PointsToLine (const Point2D &point1, const Point2D &point2) noexcept
Line	XZStrawsToLine (const PndFtsStraw &straw1, const PndFtsStraw &straw2) noexcept
Line	XZPointsToLine (const XZPoint &point1, const XZPoint &point2) noexcept
Line	YZPointsToLine (const YZVirtualHit &point1, const YZVirtualHit &point2) noexcept
float	PointLineDistance (const Point2D &point, const Line &line) noexcept
float	StrawXZLineDistance (const PndFtsStraw &straw, const Line &line) noexcept
float	LineYZPointDistance (const YZVirtualHit &point, const Line &line) noexcept
XZPoint	TangencyPoint (const float r, const XZPoint &s, const XZPoint &p, const float sign) noexcept
Circle	LineStrawCircle (const Line &xzLine, const float zTangency, const PndFtsStraw &straw, const float isochrone=0.) noexcept
float	StrawCircleDistance (const PndFtsStraw &straw, const Circle &circle) noexcept
float	XZCircleXCoord (const Circle &circle, const float zCoord) noexcept

Function Documentation

CircleValue()

float PndFtsTrackFinder::PndFtsMath::CircleValue ( const Circle &  circle, const float  arg  )

inlinenoexcept

Definition at line 19 of file PndFtsMath.h.

References sqrt().

{
  //  const float val = std::sqrt(circle.fRadius * circle.fRadius - arg * arg);
  const float val = std::sqrt(circle.fRadius * circle.fRadius - (arg - circle.fOrigin.fZ) * (arg - circle.fOrigin.fZ));
  return circle.fOrigin.fX > 0 ? circle.fOrigin.fX - val : circle.fOrigin.fX + val;
}

LineStrawCircle()

Circle PndFtsTrackFinder::PndFtsMath::LineStrawCircle ( const Line &  xzLine, const float  zTangency, const PndFtsStraw &  straw, const float  isochrone = 0.  )

inlinenoexcept

Definition at line 86 of file PndFtsMath.h.

References f, PndFtsTrackFinder::Line::fSlope, PndFtsTrackFinder::PndFtsStraw::fX, PndFtsTrackFinder::PndFtsStraw::fZ, LineValue(), PointsToLine(), and sqrt().

{
  // INFO Constructs circle tangent to straw and xz_line in point with Z = z_tangency
  const float xTangency = LineValue(xzLine, zTangency);

  const Line tanOriLine{-1 / xzLine.fSlope, xTangency + zTangency / xzLine.fSlope};
  const Line tanStrawLine = PointsToLine(zTangency, xTangency, straw.fZ, straw.fX + isochrone);

  const XZPoint tanStrawMid{0.5f * (xTangency + straw.fX + isochrone), 0.5f * (zTangency + straw.fZ)};

  const Line midOriLine{-1 / tanStrawLine.fSlope, tanStrawMid.fX + tanStrawMid.fZ / tanStrawLine.fSlope};

  const float originZ = (midOriLine.fIntercept - tanOriLine.fIntercept) / (tanOriLine.fSlope - midOriLine.fSlope);
  const float originX = LineValue(midOriLine, originZ);

  const XZPoint origin{originX, originZ};
  const float radius = std::sqrt(std::pow(zTangency - origin.fZ, 2.f) + std::pow(xTangency - origin.fX, 2.f));

  return {radius, origin};
}

LineValue()

float PndFtsTrackFinder::PndFtsMath::LineValue ( const Line &  line, const float  arg  )

inlinenoexcept

Definition at line 14 of file PndFtsMath.h.

Referenced by LineStrawCircle().

{
  return arg * line.fSlope + line.fIntercept;
}

LineYZPointDistance()

float PndFtsTrackFinder::PndFtsMath::LineYZPointDistance ( const YZVirtualHit &  point, const Line &  line  )

inlinenoexcept

Definition at line 70 of file PndFtsMath.h.

References fabs(), and sqrt().

{
  // INFO y = slope * z + intercept
  return std::fabs(point.fY - line.fSlope * point.fZ - line.fIntercept) / std::sqrt(line.fSlope * line.fSlope + 1);
}

PointLineDistance()

float PndFtsTrackFinder::PndFtsMath::PointLineDistance ( const Point2D &  point, const Line &  line  )

inlinenoexcept

Definition at line 58 of file PndFtsMath.h.

References fabs(), and sqrt().

{
  // INFO y = slope * z + intercept
  return std::fabs(point.fOrdinate - line.fSlope * point.fAbscissa - line.fIntercept) / std::sqrt(line.fSlope * line.fSlope + 1);
}

PointsToLine() [1/2]

Line PndFtsTrackFinder::PndFtsMath::PointsToLine ( float  abscissa1, float  ordinate1, float  abscissa2, float  ordinate2  )

inlinenoexcept

Definition at line 26 of file PndFtsMath.h.

Referenced by LineStrawCircle(), PointsToLine(), XZPointsToLine(), XZStrawsToLine(), and YZPointsToLine().

{
  // INFO ordinate = slope * abscissa + intercept // no need to handle zero denominator case
  const float slope = (ordinate1 - ordinate2) / (abscissa1 - abscissa2);
  const float intercept = ordinate1 - abscissa1 * slope;
  return {slope, intercept};
}

PointsToLine() [2/2]

Line PndFtsTrackFinder::PndFtsMath::PointsToLine ( const Point2D &  point1, const Point2D &  point2  )

inlinenoexcept

Definition at line 34 of file PndFtsMath.h.

References PointsToLine().

{
  // INFO ordinate = slope * abscissa + intercept // no need to handle zero denominator case
  return PointsToLine(point1.fAbscissa, point1.fOrdinate, point2.fAbscissa, point2.fOrdinate);
}

StrawCircleDistance()

float PndFtsTrackFinder::PndFtsMath::StrawCircleDistance ( const PndFtsStraw &  straw, const Circle &  circle  )

inlinenoexcept

Definition at line 107 of file PndFtsMath.h.

References sqrt().

{
  const float strawOriDistSq = std::pow(straw.fX - circle.fOrigin.fX, 2.f) + std::pow(straw.fZ - circle.fOrigin.fZ, 2.f);
  const float strawOriDist = std::sqrt(strawOriDistSq);

  return std::abs(circle.fRadius - strawOriDist);
}

StrawXZLineDistance()

float PndFtsTrackFinder::PndFtsMath::StrawXZLineDistance ( const PndFtsStraw &  straw, const Line &  line  )

inlinenoexcept

Definition at line 64 of file PndFtsMath.h.

References fabs(), and sqrt().

{
  // INFO x = slope * z + intercept
  return std::fabs(straw.fX - line.fSlope * straw.fZ - line.fIntercept) / std::sqrt(line.fSlope * line.fSlope + 1);
}

TangencyPoint()

XZPoint PndFtsTrackFinder::PndFtsMath::TangencyPoint ( const float  r, const XZPoint &  s, const XZPoint &  p, const float  sign  )

inlinenoexcept

Definition at line 76 of file PndFtsMath.h.

References sign(), and sqrt().

{
  // INFO based on https://mathworld.wolfram.com/CircleTangentLine.html
  const float distSq = (p.fZ - s.fZ) * (p.fZ - s.fZ) + (p.fX - s.fX) * (p.fX - s.fX);
  const float distMinusRsq = std::sqrt(distSq - r * r);
  const float x = s.fX + r * (r * (p.fX - s.fX) - sign * (p.fZ - s.fZ) * distMinusRsq) / distSq;
  const float z = s.fZ + r * (r * (p.fZ - s.fZ) + sign * (p.fX - s.fX) * distMinusRsq) / distSq;
  return {x, z};
}

XZCircleXCoord()

float PndFtsTrackFinder::PndFtsMath::XZCircleXCoord ( const Circle &  circle, const float  zCoord  )

inlinenoexcept

Definition at line 115 of file PndFtsMath.h.

References sqrt().

{
  const double radiusSq = std::pow(circle.fRadius, 2);
  const double zDistSq = std::pow(zCoord - circle.fOrigin.fZ, 2);
  return static_cast<float>(std::sqrt(std::abs(radiusSq - zDistSq)));
}

XZPointsToLine()

Line PndFtsTrackFinder::PndFtsMath::XZPointsToLine ( const XZPoint &  point1, const XZPoint &  point2  )

inlinenoexcept

Definition at line 46 of file PndFtsMath.h.

References PointsToLine().

{
  // INFO x = slope * z + intercept // no need to handle zero denominator case
  return PointsToLine(point1.fZ, point1.fX, point2.fZ, point2.fX);
}

XZStrawsToLine()

Line PndFtsTrackFinder::PndFtsMath::XZStrawsToLine ( const PndFtsStraw &  straw1, const PndFtsStraw &  straw2  )

inlinenoexcept

Definition at line 40 of file PndFtsMath.h.

References PointsToLine().

{
  // INFO x = slope * z + intercept // no need to handle zero denominator case
  return PointsToLine(straw1.fZ, straw1.fX, straw2.fZ, straw2.fX);
}

YZPointsToLine()

Line PndFtsTrackFinder::PndFtsMath::YZPointsToLine ( const YZVirtualHit &  point1, const YZVirtualHit &  point2  )

inlinenoexcept

Definition at line 52 of file PndFtsMath.h.

References PointsToLine().

{
  // INFO y = slope * z + intercept // no need to handle zero denominator case
  return PointsToLine(point1.fZ, point1.fY, point2.fZ, point2.fY);
}