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.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)

A math-like vector.

Represents an n-dimensional numeric vector. Vector objects support vector addition and subtraction, scalar multiplication and division, negation, rounding, and comparison tests.

values

Sequence of values stored in the vector.

toInt()

Synonym for round.

dot(other)

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

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'))