| """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 |
| |
| |
| 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) |
| |
| |
| 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)) |
| |
| |
| 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)``. |
| 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 |
| xMin, yMin, xMax, yMax = bounds |
| return min(xMin, x), min(yMin, y), max(xMax, x), max(yMax, y) |
| |
| |
| 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) |
| |
| |
| 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] |
| |
| |
| 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) |
| |
| |
| 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] |
| |
| |
| 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) |
| |
| |
| 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 |
| |
| |
| 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 |
| |
| |
| 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 |
| |
| |
| 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) |
| |
| |
| 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) |
| |
| |
| 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 |
| |
| |
| 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) |
| |
| |
| 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) |
| |
| |
| 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), |
| ) |
| |
| |
| 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, |
| ) |
| |
| |
| 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) |