# arrayTools: Various array and rectangle tools

Routines for calculating bounding boxes, point in rectangle calculations and so on.

fontTools.misc.arrayTools.calcBounds(array)

  Calculate the bounding rectangle of a 2D points array.

  Parameters

    array – A sequence of 2D tuples.

  Returns

    A four-item tuple representing the bounding rectangle `(xMin, yMin, xMax, yMax)`.

fontTools.misc.arrayTools.calcIntBounds(array, round=<function otRound>)

  Calculate the integer bounding rectangle of a 2D points array.

  Values are rounded to closest integer towards `+Infinity` using the `fontTools.misc.fixedTools.otRound()` function by default, unless an optional `round` function is passed.

  Parameters

    - array – A sequence of 2D tuples.

    - round – A rounding function of type `f(x: float) -> int`.

  Returns

    `(xMin, yMin, xMax, yMax)`.

  Return type

    A four-item tuple of integers representing the bounding rectangle

fontTools.misc.arrayTools.updateBounds(bounds, p, min=<built-in function min>, max=<built-in function max>)

  Add a point to a bounding rectangle.

  Parameters

    - bounds – A bounding rectangle expressed as a tuple `(xMin, yMin, xMax, yMax)`.

    - p – A 2D tuple representing a point.

    - min – functions to compute the minimum and maximum.

    - max – functions to compute the minimum and maximum.

  Returns

    The updated bounding rectangle `(xMin, yMin, xMax, yMax)`.

fontTools.misc.arrayTools.pointInRect(p, rect)

  Test if a point is inside a bounding rectangle.

  Parameters

    - p – A 2D tuple representing a point.

    - rect – A bounding rectangle expressed as a tuple `(xMin, yMin, xMax, yMax)`.

  Returns

    `True` if the point is inside the rectangle, `False` otherwise.

fontTools.misc.arrayTools.pointsInRect(array, rect)

  Determine which points are inside a bounding rectangle.

  Parameters

    - array – A sequence of 2D tuples.

    - rect – A bounding rectangle expressed as a tuple `(xMin, yMin, xMax, yMax)`.

  Returns

    A list containing the points inside the rectangle.

fontTools.misc.arrayTools.vectorLength(vector)

  Calculate the length of the given vector.

  Parameters

    vector – A 2D tuple.

  Returns

    The Euclidean length of the vector.

fontTools.misc.arrayTools.asInt16(array)

  Round a list of floats to 16-bit signed integers.

  Parameters

    array – List of float values.

  Returns

    A list of rounded integers.

fontTools.misc.arrayTools.normRect(rect)

  Normalize a bounding box rectangle.

  This function “turns the rectangle the right way up”, so that the following holds:

      xMin <= xMax and yMin <= yMax

  Parameters

    rect – A bounding rectangle expressed as a tuple `(xMin, yMin, xMax, yMax)`.

  Returns

    A normalized bounding rectangle.

fontTools.misc.arrayTools.scaleRect(rect, x, y)

  Scale a bounding box rectangle.

  Parameters

    - rect – A bounding rectangle expressed as a tuple `(xMin, yMin, xMax, yMax)`.

    - x – Factor to scale the rectangle along the X axis.

    - Y – Factor to scale the rectangle along the Y axis.

  Returns

    A scaled bounding rectangle.

fontTools.misc.arrayTools.offsetRect(rect, dx, dy)

  Offset a bounding box rectangle.

  Parameters

    - rect – A bounding rectangle expressed as a tuple `(xMin, yMin, xMax, yMax)`.

    - dx – Amount to offset the rectangle along the X axis.

    - dY – Amount to offset the rectangle along the Y axis.

  Returns

    An offset bounding rectangle.

fontTools.misc.arrayTools.insetRect(rect, dx, dy)

  Inset a bounding box rectangle on all sides.

  Parameters

    - rect – A bounding rectangle expressed as a tuple `(xMin, yMin, xMax, yMax)`.

    - dx – Amount to inset the rectangle along the X axis.

    - dY – Amount to inset the rectangle along the Y axis.

  Returns

    An inset bounding rectangle.

fontTools.misc.arrayTools.sectRect(rect1, rect2)

  Test for rectangle-rectangle intersection.

  Parameters

    - rect1 – First bounding rectangle, expressed as tuples `(xMin, yMin, xMax, yMax)`.

    - rect2 – Second bounding rectangle.

  Returns

    A boolean and a rectangle. If the input rectangles intersect, returns `True` and the intersecting rectangle. Returns `False` and `(0, 0, 0, 0)` if the input rectangles don’t intersect.

fontTools.misc.arrayTools.unionRect(rect1, rect2)

  Determine union of bounding rectangles.

  Parameters

    - rect1 – First bounding rectangle, expressed as tuples `(xMin, yMin, xMax, yMax)`.

    - rect2 – Second bounding rectangle.

  Returns

    The smallest rectangle in which both input rectangles are fully enclosed.

fontTools.misc.arrayTools.rectCenter(rect)

  Determine rectangle center.

  Parameters

    rect – Bounding rectangle, expressed as tuples `(xMin, yMin, xMax, yMax)`.

  Returns

    A 2D tuple representing the point at the center of the rectangle.

fontTools.misc.arrayTools.rectArea(rect)

  Determine rectangle area.

  Parameters

    rect – Bounding rectangle, expressed as tuples `(xMin, yMin, xMax, yMax)`.

  Returns

    The area of the rectangle.

fontTools.misc.arrayTools.intRect(rect)

  Round a rectangle to integer values.

  Guarantees that the resulting rectangle is NOT smaller than the original.

  Parameters

    rect – Bounding rectangle, expressed as tuples `(xMin, yMin, xMax, yMax)`.

  Returns

    A rounded bounding rectangle.

class fontTools.misc.arrayTools.Vector(values, keep=False)
  count(value, /)

    Return number of occurrences of value.

  dot(other)

    Performs vector dot product, returning the sum of `a[0] * b[0], a[1] * b[1], ...`

  index(value, start=0, stop=9223372036854775807, /)

    Return first index of value.

    Raises ValueError if the value is not present.

  length()

    Return the length of the vector. Equivalent to abs(vector).

  normalized()

    Return the normalized vector of the vector.

  toInt()
  property values

fontTools.misc.arrayTools.pairwise(iterable, reverse=False)

  Iterate over current and next items in iterable.

  Parameters

    - iterable – An iterable

    - reverse – If true, iterate in reverse order.

  Returns

    A iterable yielding two elements per iteration.

  Example

      >>> tuple(pairwise([]))
      ()
      >>> tuple(pairwise([], reverse=True))
      ()
      >>> tuple(pairwise([0]))
      ((0, 0),)
      >>> tuple(pairwise([0], reverse=True))
      ((0, 0),)
      >>> tuple(pairwise([0, 1]))
      ((0, 1), (1, 0))
      >>> tuple(pairwise([0, 1], reverse=True))
      ((1, 0), (0, 1))
      >>> tuple(pairwise([0, 1, 2]))
      ((0, 1), (1, 2), (2, 0))
      >>> tuple(pairwise([0, 1, 2], reverse=True))
      ((2, 1), (1, 0), (0, 2))
      >>> tuple(pairwise(['a', 'b', 'c', 'd']))
      (('a', 'b'), ('b', 'c'), ('c', 'd'), ('d', 'a'))
      >>> tuple(pairwise(['a', 'b', 'c', 'd'], reverse=True))
      (('d', 'c'), ('c', 'b'), ('b', 'a'), ('a', 'd'))