""" Extension to create and manipulate shapes """ # Copyright (c) 2019 Christof Hanke (christof.hanke@induhviduals.de) # License: MIT License import math def ngon(num_corners, edge_length=None, radius=None, rotation=0.): """ Returns the corners of a regular polygon as iterable of (x, y) tuples. The polygon size is determined by the `edge_length` or the `radius` argument. If both are given `edge_length` will be taken. Args: num_corners: count of polygon corners edge_length: length of polygon side radius: circum radius rotation: rotation angle in radians Returns: iterable of (x, y) tuples """ if num_corners < 3: raise ValueError('Argument `num_corners` has to be greater than 2.') if edge_length is not None: radius = edge_length / 2 / math.sin(math.pi / num_corners) elif radius is not None: if radius <= 0.: raise ValueError('Argument `radius` has to be greater than 0.') else: raise ValueError('Argument `edge_length` or `radius` required.') delta = 2 * math.pi / num_corners angle = rotation for _ in range(num_corners): yield (radius * math.cos(angle), radius * math.sin(angle)) angle += delta def star(spikes, r1, r2, rotation=0.): """ Create a star shape as iterable of (x, y) vertices. Argument `spikes` defines the count of star spikes, `r1` defines the radius of the "outer" vertices and `r2` defines the radius of the "inner" vertices, but this does not mean that `r1` has to greater than `r2`. Args: spikes: spike count r1: radius 1 r2: radius 2 rotation: rotation angle in radians Returns: iterable of (x, y) tuples """ if spikes < 3: raise ValueError('Argument `spikes` has to be greater than 2.') if r1 <= 0.: raise ValueError('Argument `r1` has to be greater than 0.') if r2 <= 0.: raise ValueError('Argument `r2` has to be greater than 0.') corners1 = ngon(spikes, radius=r1, rotation=rotation) corners2 = ngon(spikes, radius=r2, rotation=math.pi/spikes+rotation) for s1, s2 in zip(corners1, corners2): yield s1 yield s2 def translate(vertices, delta_x, delta_y): """ Translates `vertices` about `delta_x` and `delta_y` Args: vertices: iterable of (x, y) tuples delta_x: translation in x axis delta_y: translation in y axis Returns: iterable of (x, y) tuples """ for x, y in vertices: yield (x + delta_x, y + delta_y) def scale(vertices, scale_x, scale_y): """ Scales `vertices` about `scale_x` and `scale_y` Args: vertices: iterable of (x, y) tuples scale_x: scaling factor in x axis direction scale_y: scaling factor in y axis direction Returns: iterable of (x, y) tuples """ for x, y in vertices: yield (x * scale_x, y * scale_y) def rotate(vertices, delta): """ Rotates `vertices` about `delta` degrees around the origin (0, 0). Args: vertices: iterable of (x, y) tuples delta: rotation angle in radians Returns: iterable of (x, y) tuples """ for x, y in vertices: r = math.hypot(x, y) angle = math.atan2(y, x) + delta yield (r * math.cos(angle), r * math.sin(angle)) def centroid(vertices): """ Returns the centroid of a series of `vertices`. """ k, c_x, c_y = 0, 0, 0 for x, y in vertices: c_x += x c_y += y k += 1 return c_x / k, c_y / k