coordijk.hpp File Reference

#include "QueryEngine/ExtensionFunctions/h3lib/include/coordijk.h"
#include "QueryEngine/ExtensionFunctions/h3lib/include/constants.h"

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Functions
EXTENSION_INLINE bool	_setIJK (CoordIJK(ijk), int i, int j, int k)
EXTENSION_NOINLINE bool	_hex2dToCoordIJK (const Vec2d(v), CoordIJK(h))
EXTENSION_INLINE bool	_ijkToHex2d (const CoordIJK(h), Vec2d(v))
EXTENSION_INLINE int	_ijkMatches (const CoordIJK(c1), const CoordIJK(c2))
EXTENSION_INLINE bool	_ijkAdd (const CoordIJK(h1), const CoordIJK(h2), CoordIJK(sum))
EXTENSION_INLINE bool	_ijkSub (const CoordIJK(h1), const CoordIJK(h2), CoordIJK(diff))
EXTENSION_INLINE bool	_ijkScale (CoordIJK(c), int factor)
EXTENSION_NOINLINE bool	_ijkNormalize (CoordIJK(c))
EXTENSION_NOINLINE int	_unitIjkToDigit (const CoordIJK(ijk))
EXTENSION_NOINLINE bool	_upAp7 (CoordIJK(ijk))
EXTENSION_NOINLINE bool	_upAp7r (CoordIJK(ijk))
EXTENSION_NOINLINE bool	_downAp7 (CoordIJK(ijk))
EXTENSION_NOINLINE bool	_downAp7r (CoordIJK(ijk))
EXTENSION_NOINLINE bool	_neighbor (CoordIJK(ijk), int digit)
EXTENSION_NOINLINE bool	_ijkRotate60ccw (CoordIJK(ijk))
EXTENSION_NOINLINE bool	_ijkRotate60cw (CoordIJK(ijk))
EXTENSION_NOINLINE int	_rotate60ccw (int digit)
EXTENSION_NOINLINE int	_rotate60cw (int digit)

Function Documentation

EXTENSION_NOINLINE bool _downAp7

(

CoordIJK(ijk)

)

Find the normalized ijk coordinates of the hex centered on the indicated hex at the next finer aperture 7 counter-clockwise resolution. Works in place.

Parameters

ijk	The ijk coordinates.

Definition at line 325 of file coordijk.hpp.

References _ijkAdd(), _ijkNormalize(), _ijkScale(), CoordIJK, I_INDEX, J_INDEX, and K_INDEX.

Referenced by _faceIjkToH3(), and _h3ToFaceIjkWithInitializedFijk().

                                                {
  // res r unit vectors in res r+1
  CoordIJK(iVec) = {3, 0, 1};
  CoordIJK(jVec) = {1, 3, 0};
  CoordIJK(kVec) = {0, 1, 3};

  _ijkScale(iVec, ijk[I_INDEX]);
  _ijkScale(jVec, ijk[J_INDEX]);
  _ijkScale(kVec, ijk[K_INDEX]);

  _ijkAdd(iVec, jVec, ijk);
  _ijkAdd(ijk, kVec, ijk);

  _ijkNormalize(ijk);
  return true;
}

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EXTENSION_NOINLINE bool _downAp7r

(

CoordIJK(ijk)

)

Find the normalized ijk coordinates of the hex centered on the indicated hex at the next finer aperture 7 clockwise resolution. Works in place.

Parameters

ijk	The ijk coordinates.

Definition at line 348 of file coordijk.hpp.

References _ijkAdd(), _ijkNormalize(), _ijkScale(), CoordIJK, I_INDEX, J_INDEX, and K_INDEX.

Referenced by _faceIjkToH3(), _h3ToFaceIjk(), and _h3ToFaceIjkWithInitializedFijk().

                                                 {
  // res r unit vectors in res r+1
  CoordIJK(iVec) = {3, 1, 0};
  CoordIJK(jVec) = {0, 3, 1};
  CoordIJK(kVec) = {1, 0, 3};

  _ijkScale(iVec, ijk[I_INDEX]);
  _ijkScale(jVec, ijk[J_INDEX]);
  _ijkScale(kVec, ijk[K_INDEX]);

  _ijkAdd(iVec, jVec, ijk);
  _ijkAdd(ijk, kVec, ijk);

  _ijkNormalize(ijk);
  return true;
}

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EXTENSION_NOINLINE bool _hex2dToCoordIJK	(	const	Vec2dv,
		CoordIJK(h)
	)

Determine the containing hex in ijk+ coordinates for a 2D cartesian coordinate vector (from DGGRID).

Parameters

v	The 2D cartesian coordinate vector.
h	The ijk+ coordinates of the containing hex.

Definition at line 54 of file coordijk.hpp.

References _ijkNormalize(), I_INDEX, J_INDEX, K_INDEX, M_SIN60, X_INDEX, and Y_INDEX.

Referenced by _geoToFaceIjk().

                                                                      {
  double a1, a2;
  double x1, x2;
  int m1, m2;
  double r1, r2;

  // quantize into the ij system and then normalize
  h[K_INDEX] = 0;

  a1 = fabs(v[X_INDEX]);
  a2 = fabs(v[Y_INDEX]);

  // first do a reverse conversion
  x2 = a2 / M_SIN60;
  x1 = a1 + x2 / 2.0;

  // check if we have the center of a hex
  m1 = x1;
  m2 = x2;

  // otherwise round correctly
  r1 = x1 - m1;
  r2 = x2 - m2;

  if (r1 < 0.5) {
    if (r1 < 1.0 / 3.0) {
      if (r2 < (1.0 + r1) / 2.0) {
        h[I_INDEX] = m1;
        h[J_INDEX] = m2;
      } else {
        h[I_INDEX] = m1;
        h[J_INDEX] = m2 + 1;
      }
    } else {
      if (r2 < (1.0 - r1)) {
        h[J_INDEX] = m2;
      } else {
        h[J_INDEX] = m2 + 1;
      }

      if ((1.0 - r1) <= r2 && r2 < (2.0 * r1)) {
        h[I_INDEX] = m1 + 1;
      } else {
        h[I_INDEX] = m1;
      }
    }
  } else {
    if (r1 < 2.0 / 3.0) {
      if (r2 < (1.0 - r1)) {
        h[J_INDEX] = m2;
      } else {
        h[J_INDEX] = m2 + 1;
      }

      if ((2.0 * r1 - 1.0) < r2 && r2 < (1.0 - r1)) {
        h[I_INDEX] = m1;
      } else {
        h[I_INDEX] = m1 + 1;
      }
    } else {
      if (r2 < (r1 / 2.0)) {
        h[I_INDEX] = m1 + 1;
        h[J_INDEX] = m2;
      } else {
        h[I_INDEX] = m1 + 1;
        h[J_INDEX] = m2 + 1;
      }
    }
  }

  // now fold across the axes if necessary

  if (v[X_INDEX] < 0.0) {
    if ((h[J_INDEX] % 2) == 0)  // even
    {
      long long int axisi = h[J_INDEX] / 2;
      long long int diff = h[I_INDEX] - axisi;
      h[I_INDEX] = h[I_INDEX] - 2.0 * diff;
    } else {
      long long int axisi = (h[J_INDEX] + 1) / 2;
      long long int diff = h[I_INDEX] - axisi;
      h[I_INDEX] = h[I_INDEX] - (2.0 * diff + 1);
    }
  }

  if (v[Y_INDEX] < 0.0) {
    h[I_INDEX] = h[I_INDEX] - (2 * h[J_INDEX] + 1) / 2;
    h[J_INDEX] = -1 * h[J_INDEX];
  }

  _ijkNormalize(h);

  return true;
}

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EXTENSION_INLINE bool _ijkAdd	(	const	CoordIJKh1,
		const	CoordIJKh2,
		CoordIJK(sum)
	)

Add two ijk coordinates.

Parameters

h1	The first set of ijk coordinates.
h2	The second set of ijk coordinates.
sum	The sum of the two sets of ijk coordinates.

Definition at line 184 of file coordijk.hpp.

References I_INDEX, J_INDEX, and K_INDEX.

Referenced by _adjustOverageClassII(), _downAp7(), _downAp7r(), _ijkRotate60ccw(), _ijkRotate60cw(), and _neighbor().

                                                                                     {
  sum[I_INDEX] = h1[I_INDEX] + h2[I_INDEX];
  sum[J_INDEX] = h1[J_INDEX] + h2[J_INDEX];
  sum[K_INDEX] = h1[K_INDEX] + h2[K_INDEX];
  return true;
}

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EXTENSION_INLINE int _ijkMatches	(	const	CoordIJKc1,
		const	CoordIJKc2
	)

Returns whether or not two ijk coordinates contain exactly the same component values.

Parameters

c1	The first set of ijk coordinates.
c2	The second set of ijk coordinates.

Returns

1 if the two addresses match, 0 if they do not.

Definition at line 172 of file coordijk.hpp.

References I_INDEX, J_INDEX, and K_INDEX.

Referenced by _unitIjkToDigit().

                                                                         {
  return (c1[I_INDEX] == c2[I_INDEX] && c1[J_INDEX] == c2[J_INDEX] &&
          c1[K_INDEX] == c2[K_INDEX]);
}

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EXTENSION_NOINLINE bool _ijkNormalize

(

CoordIJK(c)

)

Normalizes ijk coordinates by setting the components to the smallest possible values. Works in place.

Parameters

c	The ijk coordinates to normalize.

Definition at line 224 of file coordijk.hpp.

References I_INDEX, J_INDEX, and K_INDEX.

Referenced by _adjustOverageClassII(), _downAp7(), _downAp7r(), _faceIjkToH3(), _hex2dToCoordIJK(), _ijkRotate60ccw(), _ijkRotate60cw(), _neighbor(), _unitIjkToDigit(), _upAp7(), and _upAp7r().

                                                   {
  // remove any negative values
  if (c[I_INDEX] < 0) {
    c[J_INDEX] -= c[I_INDEX];
    c[K_INDEX] -= c[I_INDEX];
    c[I_INDEX] = 0;
  }

  if (c[J_INDEX] < 0) {
    c[I_INDEX] -= c[J_INDEX];
    c[K_INDEX] -= c[J_INDEX];
    c[J_INDEX] = 0;
  }

  if (c[K_INDEX] < 0) {
    c[I_INDEX] -= c[K_INDEX];
    c[J_INDEX] -= c[K_INDEX];
    c[K_INDEX] = 0;
  }

  // remove the min value if needed
  int min = c[I_INDEX];
  if (c[J_INDEX] < min)
    min = c[J_INDEX];
  if (c[K_INDEX] < min)
    min = c[K_INDEX];
  if (min > 0) {
    c[I_INDEX] -= min;
    c[J_INDEX] -= min;
    c[K_INDEX] -= min;
  }

  return true;
}

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EXTENSION_NOINLINE bool _ijkRotate60ccw

(

CoordIJK(ijk)

)

Rotates ijk coordinates 60 degrees counter-clockwise. Works in place.

Parameters

ijk	The ijk coordinates.

Definition at line 385 of file coordijk.hpp.

References _ijkAdd(), _ijkNormalize(), _ijkScale(), CoordIJK, I_INDEX, J_INDEX, and K_INDEX.

Referenced by _adjustOverageClassII().

                                                       {
  // unit vector rotations
  CoordIJK(iVec) = {1, 1, 0};
  CoordIJK(jVec) = {0, 1, 1};
  CoordIJK(kVec) = {1, 0, 1};

  _ijkScale(iVec, ijk[I_INDEX]);
  _ijkScale(jVec, ijk[J_INDEX]);
  _ijkScale(kVec, ijk[K_INDEX]);

  _ijkAdd(iVec, jVec, ijk);
  _ijkAdd(ijk, kVec, ijk);

  _ijkNormalize(ijk);
  return true;
}

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EXTENSION_NOINLINE bool _ijkRotate60cw

(

CoordIJK(ijk)

)

Rotates ijk coordinates 60 degrees clockwise. Works in place.

Parameters

ijk	The ijk coordinates.

Definition at line 407 of file coordijk.hpp.

References _ijkAdd(), _ijkNormalize(), _ijkScale(), CoordIJK, I_INDEX, J_INDEX, and K_INDEX.

Referenced by _adjustOverageClassII().

                                                      {
  // unit vector rotations
  CoordIJK(iVec) = {1, 0, 1};
  CoordIJK(jVec) = {1, 1, 0};
  CoordIJK(kVec) = {0, 1, 1};

  _ijkScale(iVec, ijk[I_INDEX]);
  _ijkScale(jVec, ijk[J_INDEX]);
  _ijkScale(kVec, ijk[K_INDEX]);

  _ijkAdd(iVec, jVec, ijk);
  _ijkAdd(ijk, kVec, ijk);

  _ijkNormalize(ijk);
  return true;
}

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EXTENSION_INLINE bool _ijkScale	(	CoordIJK(c)	,
		int	factor
	)

Uniformly scale ijk coordinates by a scalar. Works in place.

Parameters

c	The ijk coordinates to scale.
factor	The scaling factor.

Definition at line 211 of file coordijk.hpp.

References I_INDEX, J_INDEX, and K_INDEX.

Referenced by _adjustOverageClassII(), _downAp7(), _downAp7r(), _ijkRotate60ccw(), and _ijkRotate60cw().

                                                         {
  c[I_INDEX] *= factor;
  c[J_INDEX] *= factor;
  c[K_INDEX] *= factor;
  return true;
}

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EXTENSION_INLINE bool _ijkSub	(	const	CoordIJKh1,
		const	CoordIJKh2,
		CoordIJK(diff)
	)

Subtract two ijk coordinates.

Parameters

h1	The first set of ijk coordinates.
h2	The second set of ijk coordinates.
diff	The difference of the two sets of ijk coordinates (h1 - h2).

Definition at line 198 of file coordijk.hpp.

References I_INDEX, J_INDEX, and K_INDEX.

Referenced by _adjustOverageClassII(), and _faceIjkToH3().

                                                                                      {
  diff[I_INDEX] = h1[I_INDEX] - h2[I_INDEX];
  diff[J_INDEX] = h1[J_INDEX] - h2[J_INDEX];
  diff[K_INDEX] = h1[K_INDEX] - h2[K_INDEX];
  return true;
}

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EXTENSION_INLINE bool _ijkToHex2d	(	const	CoordIJKh,
		Vec2d(v)
	)

Find the center point in 2D cartesian coordinates of a hex.

Parameters

h	The ijk coordinates of the hex.
v	The 2D cartesian coordinates of the hex center point.

Definition at line 155 of file coordijk.hpp.

References I_INDEX, J_INDEX, K_INDEX, M_SQRT3_2, X_INDEX, and Y_INDEX.

Referenced by _faceIjkToGeo().

                                                               {
  int i = h[I_INDEX] - h[K_INDEX];
  int j = h[J_INDEX] - h[K_INDEX];

  v[X_INDEX] = i - 0.5 * j;
  v[Y_INDEX] = j * M_SQRT3_2;
  return true;
}

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EXTENSION_NOINLINE bool _neighbor	(	CoordIJK(ijk)	,
		int	digit
	)

Find the normalized ijk coordinates of the hex in the specified digit direction from the specified ijk coordinates. Works in place.

Parameters

ijk	The ijk coordinates.
digit	The digit direction from the original ijk coordinates.

Definition at line 372 of file coordijk.hpp.

References _ijkAdd(), _ijkNormalize(), CENTER_DIGIT, and NUM_DIGITS.

Referenced by _h3ToFaceIjkWithInitializedFijk().

                                                            {
  if (digit > CENTER_DIGIT && digit < NUM_DIGITS) {
    _ijkAdd(ijk, UNIT_VECS[digit], ijk);
    _ijkNormalize(ijk);
  }
  return true;
}

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EXTENSION_NOINLINE int _rotate60ccw

(

int

digit

)

Rotates indexing digit 60 degrees counter-clockwise. Returns result.

Parameters

digit

Indexing digit (between 1 and 6 inclusive)

Definition at line 429 of file coordijk.hpp.

References I_AXES_DIGIT, IJ_AXES_DIGIT, IK_AXES_DIGIT, J_AXES_DIGIT, JK_AXES_DIGIT, and K_AXES_DIGIT.

Referenced by _h3Rotate60ccw(), and _h3RotatePent60ccw().

                                               {
  switch (Direction(digit)) {
    case K_AXES_DIGIT:
      return IK_AXES_DIGIT;
    case IK_AXES_DIGIT:
      return I_AXES_DIGIT;
    case I_AXES_DIGIT:
      return IJ_AXES_DIGIT;
    case IJ_AXES_DIGIT:
      return J_AXES_DIGIT;
    case J_AXES_DIGIT:
      return JK_AXES_DIGIT;
    case JK_AXES_DIGIT:
      return K_AXES_DIGIT;
    default:
      return digit;
  }
}

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EXTENSION_NOINLINE int _rotate60cw

(

int

digit

)

Rotates indexing digit 60 degrees clockwise. Returns result.

Parameters

digit

Indexing digit (between 1 and 6 inclusive)

Definition at line 453 of file coordijk.hpp.

References I_AXES_DIGIT, IJ_AXES_DIGIT, IK_AXES_DIGIT, J_AXES_DIGIT, JK_AXES_DIGIT, and K_AXES_DIGIT.

Referenced by _h3Rotate60cw(), and _h3RotatePent60cw().

                                              {
  switch (Direction(digit)) {
    case K_AXES_DIGIT:
      return JK_AXES_DIGIT;
    case JK_AXES_DIGIT:
      return J_AXES_DIGIT;
    case J_AXES_DIGIT:
      return IJ_AXES_DIGIT;
    case IJ_AXES_DIGIT:
      return I_AXES_DIGIT;
    case I_AXES_DIGIT:
      return IK_AXES_DIGIT;
    case IK_AXES_DIGIT:
      return K_AXES_DIGIT;
    default:
      return digit;
  }
}

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EXTENSION_INLINE bool _setIJK	(	CoordIJK(ijk)	,
		int	i,
		int	j,
		int	k
	)

Sets an IJK coordinate to the specified component values.

Parameters

ijk	The IJK coordinate to set.
i	The desired i component value.
j	The desired j component value.
k	The desired k component value.

Definition at line 40 of file coordijk.hpp.

References I_INDEX, J_INDEX, and K_INDEX.

Referenced by _adjustOverageClassII().

                                                                  {
  ijk[I_INDEX] = i;
  ijk[J_INDEX] = j;
  ijk[K_INDEX] = k;
  return true;
}

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EXTENSION_NOINLINE int _unitIjkToDigit

(

const

CoordIJKijk

)

Determines the H3 digit corresponding to a unit vector in ijk coordinates.

Parameters

ijk	The ijk coordinates; must be a unit vector.

Returns

The H3 digit (0-6) corresponding to the ijk unit vector, or INVALID_DIGIT on failure.

Definition at line 266 of file coordijk.hpp.

References _ijkMatches(), _ijkNormalize(), CENTER_DIGIT, CoordIJK, CoordIJK_clone, INVALID_DIGIT, and NUM_DIGITS.

Referenced by _faceIjkToH3().

                                                            {
  CoordIJK(c) = CoordIJK_clone(ijk);
  _ijkNormalize(c);

  Direction digit = INVALID_DIGIT;
  for (int i = CENTER_DIGIT; i < NUM_DIGITS; i++) {
    if (_ijkMatches(c, UNIT_VECS[i])) {
      digit = Direction(i);
      break;
    }
  }

  return digit;
}

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EXTENSION_NOINLINE bool _upAp7

(

CoordIJK(ijk)

)

Find the normalized ijk coordinates of the indexing parent of a cell in a counter-clockwise aperture 7 grid. Works in place.

Parameters

ijk	The ijk coordinates.

Definition at line 287 of file coordijk.hpp.

References _ijkNormalize(), I_INDEX, J_INDEX, and K_INDEX.

Referenced by _faceIjkToH3().

                                              {
  // convert to CoordIJ
  int i = ijk[I_INDEX] - ijk[K_INDEX];
  int j = ijk[J_INDEX] - ijk[K_INDEX];

  ijk[I_INDEX] = (int)lround((3 * i - j) / 7.0);
  ijk[J_INDEX] = (int)lround((i + 2 * j) / 7.0);
  ijk[K_INDEX] = 0;
  _ijkNormalize(ijk);

  return true;
}

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EXTENSION_NOINLINE bool _upAp7r

(

CoordIJK(ijk)

)

Find the normalized ijk coordinates of the indexing parent of a cell in a clockwise aperture 7 grid. Works in place.

Parameters

ijk	The ijk coordinates.

Definition at line 306 of file coordijk.hpp.

References _ijkNormalize(), I_INDEX, J_INDEX, and K_INDEX.

Referenced by _faceIjkToH3(), and _h3ToFaceIjk().

                                               {
  // convert to CoordIJ
  int i = ijk[I_INDEX] - ijk[K_INDEX];
  int j = ijk[J_INDEX] - ijk[K_INDEX];

  ijk[I_INDEX] = (int)lround((2 * i + j) / 7.0);
  ijk[J_INDEX] = (int)lround((3 * j - i) / 7.0);
  ijk[K_INDEX] = 0;
  _ijkNormalize(ijk);
  return true;
}

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