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More flexible space filling curve class
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Grant Sanderson
parent
b481eda8ac
commit
b2c5f71155
1 changed files with 169 additions and 74 deletions
243
hilbert.py
243
hilbert.py
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@ -8,16 +8,11 @@ from topics.geometry import Line, Point
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from helpers import *
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def flip(points, axis, angle = np.pi):
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def rotate(points, angle = np.pi, axis = OUT):
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if axis is None:
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return points
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if isinstance(axis, tuple):
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axes = axis
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else:
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axes = [axis]
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for ax in axes:
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matrix = rotation_matrix(angle, ax)
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points = np.dot(points, np.transpose(matrix))
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matrix = rotation_matrix(angle, axis)
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points = np.dot(points, np.transpose(matrix))
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return points
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@ -38,72 +33,139 @@ class SpaceFillingCurve(Mobject1D):
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def get_anchor_points(self):
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raise Exception("Not implemented")
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class LindenmayerCurve(SpaceFillingCurve):
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DEFAULT_CONFIG = {
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"axiom" : "A",
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"rule" : {},
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"scale_factor" : 2,
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"radius" : 3,
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"start_step" : RIGHT,
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"angle" : np.pi/2,
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}
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def expand_command_string(self, command):
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result = ""
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for letter in command:
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if letter in self.rule:
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result += self.rule[letter]
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else:
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result += letter
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return result
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def get_command_string(self):
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result = self.axiom
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for x in range(self.order):
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result = self.expand_command_string(result)
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return result
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def get_anchor_points(self):
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step = float(self.radius) * self.start_step
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step /= (self.scale_factor**self.order)
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curr = np.zeros(3)
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result = [curr]
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for letter in self.get_command_string():
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if letter is "+":
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step = rotate(step, self.angle)
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elif letter is "-":
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step = rotate(step, -self.angle)
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else:
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curr = curr + step
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result.append(curr)
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return np.array(result) - center_of_mass(result)
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class SelfSimilarSpaceFillingCurve(SpaceFillingCurve):
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DEFAULT_CONFIG = {
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"axis_offset_pairs" : [],
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"offsets" : [],
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"offset_index_to_rotation_axis" : {},
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"scale_factor" : 2,
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"radius_scale_factor" : 0.5,
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}
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def transform(self, points, offset):
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"""
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How to transform the copy of points shifted by
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offset. Generally meant to be extended in subclasses
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"""
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if offset in self.offset_index_to_rotation_axis:
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return rotate(
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points,
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axis = self.offset_index_to_rotation_axis[offset]
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)
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points /= self.scale_factor,
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points += offset*self.radius*self.radius_scale_factor
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return points
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def refine_into_subparts(self, points):
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transformed_copies = [
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flip(points/self.scale_factor, axis) + \
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offset*self.radius*self.radius_scale_factor
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for axis, offset in self.axis_offset_pairs
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self.transform(points, offset)
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for offset in self.offsets
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]
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return reduce(
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lambda a, b : np.append(a, b, axis = 0),
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lambda a, b : np.append(a, b, axis = 0),
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transformed_copies
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)
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def get_anchor_points(self):
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points = np.zeros((1, 3))
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for count in range(self.order):
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points = self.refine_into_subparts(
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points
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)
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points = self.refine_into_subparts(points)
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return points
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class HilbertCurve(SelfSimilarSpaceFillingCurve):
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DEFAULT_CONFIG = {
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"axis_offset_pairs" : [
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(RIGHT+UP, LEFT+DOWN ),
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(None, LEFT+UP ),
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(None, RIGHT+UP ),
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(RIGHT+DOWN, RIGHT+DOWN),
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"offsets" : [
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LEFT+DOWN,
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LEFT+UP,
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RIGHT+UP,
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RIGHT+DOWN,
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],
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}
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"offset_index_to_rotation_axis" : {
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0 : RIGHT+UP,
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3 : RIGHT+DOWN,
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},
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}
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class HilbertCurve3D(SelfSimilarSpaceFillingCurve):
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DEFAULT_CONFIG = {
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"axis_offset_pairs" : [ #TODO
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(None, LEFT+DOWN+OUT),
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(None, LEFT+UP+OUT),
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(None, LEFT+UP+IN),
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(None, LEFT+DOWN+IN),
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(None, RIGHT+DOWN+IN),
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(None, RIGHT+UP+IN),
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(None, RIGHT+UP+OUT),
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(None, RIGHT+DOWN+OUT),
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"offsets" : [
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LEFT+DOWN+OUT,
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LEFT+UP+OUT,
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LEFT+UP+IN,
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LEFT+DOWN+IN,
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RIGHT+DOWN+IN,
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RIGHT+UP+IN,
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RIGHT+UP+OUT,
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RIGHT+DOWN+OUT,
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],
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"offset_index_to_rotation_axis" : {}#TODO
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}
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class PeanoCurve(SelfSimilarSpaceFillingCurve):
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DEFAULT_CONFIG = {
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"start_color" : PURPLE,
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"end_color" : TEAL,
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"axis_offset_pairs" : [
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(None, LEFT+DOWN ),
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(UP, LEFT ),
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(None, LEFT+UP ),
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(RIGHT, UP ),
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(LEFT+UP, ORIGIN ),
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(RIGHT, DOWN ),
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(None, RIGHT+DOWN),
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(UP, RIGHT ),
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(None, RIGHT+UP ),
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"offsets" : [
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LEFT+DOWN,
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LEFT,
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LEFT+UP,
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UP,
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ORIGIN,
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DOWN,
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RIGHT+DOWN,
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RIGHT,
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RIGHT+UP,
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],
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"offset_index_to_rotation_axis" : {
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1 : UP,
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3 : RIGHT,
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4 : LEFT+UP,
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5 : RIGHT,
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6 : UP,
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},
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"scale_factor" : 3,
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"radius_scale_factor" : 2.0/3,
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}
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@ -112,57 +174,90 @@ class TriangleFillingCurve(SelfSimilarSpaceFillingCurve):
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DEFAULT_CONFIG = {
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"start_color" : MAROON,
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"end_color" : YELLOW,
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"axis_offset_pairs" : [
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(None, LEFT/4.+DOWN/6.),
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(RIGHT, ORIGIN),
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(None, RIGHT/4.+DOWN/6.),
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(UP, UP/3.),
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"offsets" : [
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LEFT/4.+DOWN/6.,
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ORIGIN,
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RIGHT/4.+DOWN/6.,
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UP/3.,
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],
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"offset_index_to_rotation_axis" : {
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1 : RIGHT,
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3 : UP,
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},
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"scale_factor" : 2,
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"radius_scale_factor" : 1.5,
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}
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class HexagonFillingCurve(SelfSimilarSpaceFillingCurve):
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DEFAULT_CONFIG = {
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"start_color" : WHITE,
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"end_color" : BLUE_D,
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"axis_offset_pairs" : [
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(None, 1.5*DOWN + 0.5*np.sqrt(3)*LEFT),
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(UP+np.sqrt(3)*RIGHT, 1.5*DOWN + 0.5*np.sqrt(3)*RIGHT),
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(np.sqrt(3)*UP+RIGHT, ORIGIN),
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((UP, RIGHT), np.sqrt(3)*LEFT),
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(None, 1.5*UP + 0.5*np.sqrt(3)*LEFT),
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(None, 1.5*UP + 0.5*np.sqrt(3)*RIGHT),
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(RIGHT, np.sqrt(3)*RIGHT),
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],
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"scale_factor" : 3,
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"radius_scale_factor" : 2/(3*np.sqrt(3)),
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}
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# class HexagonFillingCurve(SelfSimilarSpaceFillingCurve):
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# DEFAULT_CONFIG = {
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# "start_color" : WHITE,
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# "end_color" : BLUE_D,
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# "axis_offset_pairs" : [
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# (None, 1.5*DOWN + 0.5*np.sqrt(3)*LEFT),
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# (UP+np.sqrt(3)*RIGHT, 1.5*DOWN + 0.5*np.sqrt(3)*RIGHT),
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# (np.sqrt(3)*UP+RIGHT, ORIGIN),
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# ((UP, RIGHT), np.sqrt(3)*LEFT),
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# (None, 1.5*UP + 0.5*np.sqrt(3)*LEFT),
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# (None, 1.5*UP + 0.5*np.sqrt(3)*RIGHT),
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# (RIGHT, np.sqrt(3)*RIGHT),
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# ],
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# "scale_factor" : 3,
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# "radius_scale_factor" : 2/(3*np.sqrt(3)),
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# }
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# def refine_into_subparts(self, points):
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# return SelfSimilarSpaceFillingCurve.refine_into_subparts(
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# self,
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# rotate(points, np.pi/6, IN)
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# )
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def refine_into_subparts(self, points):
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return SelfSimilarSpaceFillingCurve.refine_into_subparts(
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self,
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flip(points, IN, np.pi/6)
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)
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class UtahFillingCurve(SelfSimilarSpaceFillingCurve):
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DEFAULT_CONFIG = {
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"start_color" : WHITE,
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"end_color" : BLUE_D,
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"axis_offset_pairs" : [
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(None, 1.5*DOWN + 0.5*np.sqrt(3)*LEFT),
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(UP+np.sqrt(3)*RIGHT, 1.5*DOWN + 0.5*np.sqrt(3)*RIGHT),
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(np.sqrt(3)*UP+RIGHT, ORIGIN),
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((UP, RIGHT), np.sqrt(3)*LEFT),
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(None, 1.5*UP + 0.5*np.sqrt(3)*LEFT),
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(None, 1.5*UP + 0.5*np.sqrt(3)*RIGHT),
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(RIGHT, np.sqrt(3)*RIGHT),
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],
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"scale_factor" : 3,
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"radius_scale_factor" : 2/(3*np.sqrt(3)),
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}
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class FlowSnake(LindenmayerCurve):
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DEFAULT_CONFIG = {
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"start_color" : YELLOW,
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"end_color" : GREEN,
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"axiom" : "A",
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"rule" : {
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"A" : "A-B--B+A++AA+B-",
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"B" : "+A-BB--B-A++A+B",
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},
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"radius" : 6, #TODO, this is innaccurate
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"scale_factor" : np.sqrt(7),
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"start_step" : RIGHT,
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"angle" : -np.pi/3,
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}
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def __init__(self, **kwargs):
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LindenmayerCurve.__init__(self, **kwargs)
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self.rotate(-self.order*np.pi/9)
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class Sierpinski(LindenmayerCurve):
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DEFAULT_CONFIG = {
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"start_color" : RED,
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"end_color" : WHITE,
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"axiom" : "A",
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"rule" : {
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"A" : "+B-A-B+",
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"B" : "-A+B+A-",
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},
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"radius" : 6, #TODO, this is innaccurate
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"scale_factor" : 2,
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"start_step" : RIGHT,
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"angle" : -np.pi/3,
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}
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class SnakeCurve(SpaceFillingCurve):
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DEFAULT_CONFIG = {
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"start_color" : BLUE,
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