"""Routines for calculating bounding boxes, point in rectangle calculations and
so on.
"""
from fontTools.misc.roundTools import otRound
from fontTools.misc.vector import Vector as _Vector
import math
import warnings
[docs]
def calcBounds(array):
"""Calculate the bounding rectangle of a 2D points array.
Args:
array: A sequence of 2D tuples.
Returns:
A four-item tuple representing the bounding rectangle ``(xMin, yMin, xMax, yMax)``.
"""
if not array:
return 0, 0, 0, 0
xs = [x for x, y in array]
ys = [y for x, y in array]
return min(xs), min(ys), max(xs), max(ys)
[docs]
def calcIntBounds(array, round=otRound):
"""Calculate the integer bounding rectangle of a 2D points array.
Values are rounded to closest integer towards ``+Infinity`` using the
:func:`fontTools.misc.fixedTools.otRound` function by default, unless
an optional ``round`` function is passed.
Args:
array: A sequence of 2D tuples.
round: A rounding function of type ``f(x: float) -> int``.
Returns:
A four-item tuple of integers representing the bounding rectangle:
``(xMin, yMin, xMax, yMax)``.
"""
return tuple(round(v) for v in calcBounds(array))
[docs]
def updateBounds(bounds, p, min=min, max=max):
"""Add a point to a bounding rectangle.
Args:
bounds: A bounding rectangle expressed as a tuple
``(xMin, yMin, xMax, yMax), or None``.
p: A 2D tuple representing a point.
min,max: functions to compute the minimum and maximum.
Returns:
The updated bounding rectangle ``(xMin, yMin, xMax, yMax)``.
"""
(x, y) = p
if bounds is None:
return x, y, x, y
xMin, yMin, xMax, yMax = bounds
return min(xMin, x), min(yMin, y), max(xMax, x), max(yMax, y)
[docs]
def pointInRect(p, rect):
"""Test if a point is inside a bounding rectangle.
Args:
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.
"""
(x, y) = p
xMin, yMin, xMax, yMax = rect
return (xMin <= x <= xMax) and (yMin <= y <= yMax)
[docs]
def pointsInRect(array, rect):
"""Determine which points are inside a bounding rectangle.
Args:
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.
"""
if len(array) < 1:
return []
xMin, yMin, xMax, yMax = rect
return [(xMin <= x <= xMax) and (yMin <= y <= yMax) for x, y in array]
[docs]
def vectorLength(vector):
"""Calculate the length of the given vector.
Args:
vector: A 2D tuple.
Returns:
The Euclidean length of the vector.
"""
x, y = vector
return math.sqrt(x**2 + y**2)
[docs]
def asInt16(array):
"""Round a list of floats to 16-bit signed integers.
Args:
array: List of float values.
Returns:
A list of rounded integers.
"""
return [int(math.floor(i + 0.5)) for i in array]
[docs]
def 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
Args:
rect: A bounding rectangle expressed as a tuple
``(xMin, yMin, xMax, yMax)``.
Returns:
A normalized bounding rectangle.
"""
(xMin, yMin, xMax, yMax) = rect
return min(xMin, xMax), min(yMin, yMax), max(xMin, xMax), max(yMin, yMax)
[docs]
def scaleRect(rect, x, y):
"""Scale a bounding box rectangle.
Args:
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.
"""
(xMin, yMin, xMax, yMax) = rect
return xMin * x, yMin * y, xMax * x, yMax * y
[docs]
def offsetRect(rect, dx, dy):
"""Offset a bounding box rectangle.
Args:
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.
"""
(xMin, yMin, xMax, yMax) = rect
return xMin + dx, yMin + dy, xMax + dx, yMax + dy
[docs]
def insetRect(rect, dx, dy):
"""Inset a bounding box rectangle on all sides.
Args:
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.
"""
(xMin, yMin, xMax, yMax) = rect
return xMin + dx, yMin + dy, xMax - dx, yMax - dy
[docs]
def sectRect(rect1, rect2):
"""Test for rectangle-rectangle intersection.
Args:
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.
"""
(xMin1, yMin1, xMax1, yMax1) = rect1
(xMin2, yMin2, xMax2, yMax2) = rect2
xMin, yMin, xMax, yMax = (
max(xMin1, xMin2),
max(yMin1, yMin2),
min(xMax1, xMax2),
min(yMax1, yMax2),
)
if xMin >= xMax or yMin >= yMax:
return False, (0, 0, 0, 0)
return True, (xMin, yMin, xMax, yMax)
[docs]
def unionRect(rect1, rect2):
"""Determine union of bounding rectangles.
Args:
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.
"""
(xMin1, yMin1, xMax1, yMax1) = rect1
(xMin2, yMin2, xMax2, yMax2) = rect2
xMin, yMin, xMax, yMax = (
min(xMin1, xMin2),
min(yMin1, yMin2),
max(xMax1, xMax2),
max(yMax1, yMax2),
)
return (xMin, yMin, xMax, yMax)
[docs]
def rectCenter(rect):
"""Determine rectangle center.
Args:
rect: Bounding rectangle, expressed as tuples
``(xMin, yMin, xMax, yMax)``.
Returns:
A 2D tuple representing the point at the center of the rectangle.
"""
(xMin, yMin, xMax, yMax) = rect
return (xMin + xMax) / 2, (yMin + yMax) / 2
[docs]
def rectArea(rect):
"""Determine rectangle area.
Args:
rect: Bounding rectangle, expressed as tuples
``(xMin, yMin, xMax, yMax)``.
Returns:
The area of the rectangle.
"""
(xMin, yMin, xMax, yMax) = rect
return (yMax - yMin) * (xMax - xMin)
[docs]
def intRect(rect):
"""Round a rectangle to integer values.
Guarantees that the resulting rectangle is NOT smaller than the original.
Args:
rect: Bounding rectangle, expressed as tuples
``(xMin, yMin, xMax, yMax)``.
Returns:
A rounded bounding rectangle.
"""
(xMin, yMin, xMax, yMax) = rect
xMin = int(math.floor(xMin))
yMin = int(math.floor(yMin))
xMax = int(math.ceil(xMax))
yMax = int(math.ceil(yMax))
return (xMin, yMin, xMax, yMax)
[docs]
def quantizeRect(rect, factor=1):
"""
>>> bounds = (72.3, -218.4, 1201.3, 919.1)
>>> quantizeRect(bounds)
(72, -219, 1202, 920)
>>> quantizeRect(bounds, factor=10)
(70, -220, 1210, 920)
>>> quantizeRect(bounds, factor=100)
(0, -300, 1300, 1000)
"""
if factor < 1:
raise ValueError(f"Expected quantization factor >= 1, found: {factor!r}")
xMin, yMin, xMax, yMax = normRect(rect)
return (
int(math.floor(xMin / factor) * factor),
int(math.floor(yMin / factor) * factor),
int(math.ceil(xMax / factor) * factor),
int(math.ceil(yMax / factor) * factor),
)
[docs]
class Vector(_Vector):
def __init__(self, *args, **kwargs):
warnings.warn(
"fontTools.misc.arrayTools.Vector has been deprecated, please use "
"fontTools.misc.vector.Vector instead.",
DeprecationWarning,
)
[docs]
def pairwise(iterable, reverse=False):
"""Iterate over current and next items in iterable.
Args:
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'))
"""
if not iterable:
return
if reverse:
it = reversed(iterable)
else:
it = iter(iterable)
first = next(it, None)
a = first
for b in it:
yield (a, b)
a = b
yield (a, first)
def _test():
"""
>>> import math
>>> calcBounds([])
(0, 0, 0, 0)
>>> calcBounds([(0, 40), (0, 100), (50, 50), (80, 10)])
(0, 10, 80, 100)
>>> updateBounds((0, 0, 0, 0), (100, 100))
(0, 0, 100, 100)
>>> pointInRect((50, 50), (0, 0, 100, 100))
True
>>> pointInRect((0, 0), (0, 0, 100, 100))
True
>>> pointInRect((100, 100), (0, 0, 100, 100))
True
>>> not pointInRect((101, 100), (0, 0, 100, 100))
True
>>> list(pointsInRect([(50, 50), (0, 0), (100, 100), (101, 100)], (0, 0, 100, 100)))
[True, True, True, False]
>>> vectorLength((3, 4))
5.0
>>> vectorLength((1, 1)) == math.sqrt(2)
True
>>> list(asInt16([0, 0.1, 0.5, 0.9]))
[0, 0, 1, 1]
>>> normRect((0, 10, 100, 200))
(0, 10, 100, 200)
>>> normRect((100, 200, 0, 10))
(0, 10, 100, 200)
>>> scaleRect((10, 20, 50, 150), 1.5, 2)
(15.0, 40, 75.0, 300)
>>> offsetRect((10, 20, 30, 40), 5, 6)
(15, 26, 35, 46)
>>> insetRect((10, 20, 50, 60), 5, 10)
(15, 30, 45, 50)
>>> insetRect((10, 20, 50, 60), -5, -10)
(5, 10, 55, 70)
>>> intersects, rect = sectRect((0, 10, 20, 30), (0, 40, 20, 50))
>>> not intersects
True
>>> intersects, rect = sectRect((0, 10, 20, 30), (5, 20, 35, 50))
>>> intersects
1
>>> rect
(5, 20, 20, 30)
>>> unionRect((0, 10, 20, 30), (0, 40, 20, 50))
(0, 10, 20, 50)
>>> rectCenter((0, 0, 100, 200))
(50.0, 100.0)
>>> rectCenter((0, 0, 100, 199.0))
(50.0, 99.5)
>>> intRect((0.9, 2.9, 3.1, 4.1))
(0, 2, 4, 5)
"""
if __name__ == "__main__":
import sys
import doctest
sys.exit(doctest.testmod().failed)