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