| # |
| # Various array and rectangle tools, but mostly rectangles, hence the |
| # name of this module (not). |
| # |
| |
| |
| from __future__ import print_function, division, absolute_import |
| from fontTools.misc.py23 import * |
| from fontTools.misc.fixedTools import otRound |
| from numbers import Number |
| import math |
| import operator |
| |
| def calcBounds(array): |
| """Return the bounding rectangle of a 2D points array as a tuple: |
| (xMin, yMin, xMax, yMax) |
| """ |
| if len(array) == 0: |
| 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): |
| """Return the integer bounding rectangle of a 2D points array as a |
| tuple: (xMin, yMin, xMax, yMax) |
| Values are rounded to closest integer towards +Infinity using otRound |
| function by default, unless an optional 'round' function is passed. |
| """ |
| return tuple(round(v) for v in calcBounds(array)) |
| |
| |
| def updateBounds(bounds, p, min=min, max=max): |
| """Return the bounding recangle of rectangle bounds and point (x, y).""" |
| (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): |
| """Return True when point (x, y) is inside rect.""" |
| (x, y) = p |
| xMin, yMin, xMax, yMax = rect |
| return (xMin <= x <= xMax) and (yMin <= y <= yMax) |
| |
| def pointsInRect(array, rect): |
| """Find out which points or array are inside rect. |
| Returns an array with a boolean for each point. |
| """ |
| 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): |
| """Return the length of the given vector.""" |
| x, y = vector |
| return math.sqrt(x**2 + y**2) |
| |
| def asInt16(array): |
| """Round and cast to 16 bit integer.""" |
| return [int(math.floor(i+0.5)) for i in array] |
| |
| |
| def normRect(rect): |
| """Normalize the rectangle so that the following holds: |
| xMin <= xMax and yMin <= yMax |
| """ |
| (xMin, yMin, xMax, yMax) = rect |
| return min(xMin, xMax), min(yMin, yMax), max(xMin, xMax), max(yMin, yMax) |
| |
| def scaleRect(rect, x, y): |
| """Scale the rectangle by x, y.""" |
| (xMin, yMin, xMax, yMax) = rect |
| return xMin * x, yMin * y, xMax * x, yMax * y |
| |
| def offsetRect(rect, dx, dy): |
| """Offset the rectangle by dx, dy.""" |
| (xMin, yMin, xMax, yMax) = rect |
| return xMin+dx, yMin+dy, xMax+dx, yMax+dy |
| |
| def insetRect(rect, dx, dy): |
| """Inset the rectangle by dx, dy on all sides.""" |
| (xMin, yMin, xMax, yMax) = rect |
| return xMin+dx, yMin+dy, xMax-dx, yMax-dy |
| |
| def sectRect(rect1, rect2): |
| """Return a boolean and a rectangle. If the input rectangles intersect, return |
| True and the intersecting rectangle. Return 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): |
| """Return the smallest rectangle in which both input rectangles are fully |
| enclosed. In other words, return the total bounding rectangle of both input |
| rectangles. |
| """ |
| (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(rect0): |
| """Return the center of the rectangle as an (x, y) coordinate.""" |
| (xMin, yMin, xMax, yMax) = rect0 |
| return (xMin+xMax)/2, (yMin+yMax)/2 |
| |
| def intRect(rect1): |
| """Return the rectangle, rounded off to integer values, but guaranteeing that |
| the resulting rectangle is NOT smaller than the original. |
| """ |
| (xMin, yMin, xMax, yMax) = rect1 |
| 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) |
| |
| |
| class Vector(object): |
| """A math-like vector.""" |
| |
| def __init__(self, values, keep=False): |
| self.values = values if keep else list(values) |
| |
| def __getitem__(self, index): |
| return self.values[index] |
| |
| def __len__(self): |
| return len(self.values) |
| |
| def __repr__(self): |
| return "Vector(%s)" % self.values |
| |
| def _vectorOp(self, other, op): |
| if isinstance(other, Vector): |
| assert len(self.values) == len(other.values) |
| a = self.values |
| b = other.values |
| return [op(a[i], b[i]) for i in range(len(self.values))] |
| if isinstance(other, Number): |
| return [op(v, other) for v in self.values] |
| raise NotImplementedError |
| |
| def _scalarOp(self, other, op): |
| if isinstance(other, Number): |
| return [op(v, other) for v in self.values] |
| raise NotImplementedError |
| |
| def _unaryOp(self, op): |
| return [op(v) for v in self.values] |
| |
| def __add__(self, other): |
| return Vector(self._vectorOp(other, operator.add), keep=True) |
| def __iadd__(self, other): |
| self.values = self._vectorOp(other, operator.add) |
| return self |
| __radd__ = __add__ |
| |
| def __sub__(self, other): |
| return Vector(self._vectorOp(other, operator.sub), keep=True) |
| def __isub__(self, other): |
| self.values = self._vectorOp(other, operator.sub) |
| return self |
| def __rsub__(self, other): |
| return other + (-self) |
| |
| def __mul__(self, other): |
| return Vector(self._scalarOp(other, operator.mul), keep=True) |
| def __imul__(self, other): |
| self.values = self._scalarOp(other, operator.mul) |
| return self |
| __rmul__ = __mul__ |
| |
| def __truediv__(self, other): |
| return Vector(self._scalarOp(other, operator.div), keep=True) |
| def __itruediv__(self, other): |
| self.values = self._scalarOp(other, operator.div) |
| return self |
| |
| def __pos__(self): |
| return Vector(self._unaryOp(operator.pos), keep=True) |
| def __neg__(self): |
| return Vector(self._unaryOp(operator.neg), keep=True) |
| def __round__(self): |
| return Vector(self._unaryOp(round), keep=True) |
| def toInt(self): |
| return self.__round__() |
| |
| def __eq__(self, other): |
| if type(other) == Vector: |
| return self.values == other.values |
| else: |
| return self.values == other |
| def __ne__(self, other): |
| return not self.__eq__(other) |
| |
| def __bool__(self): |
| return any(self.values) |
| __nonzero__ = __bool__ |
| |
| def __abs__(self): |
| return math.sqrt(sum([x*x for x in self.values])) |
| def dot(self, other): |
| a = self.values |
| b = other.values if type(other) == Vector else b |
| assert len(a) == len(b) |
| return sum([a[i] * b[i] for i in range(len(a))]) |
| |
| |
| def pairwise(iterable, reverse=False): |
| """Iterate over current and next items in iterable, optionally in |
| reverse order. |
| |
| >>> 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) |
