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Possibly better alignment algorithm

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This commit is contained in:
Grant Sanderson
2016-04-10 19:19:13 -07:00
parent 26c5aa8e67
commit 25aa564cca
2 changed files with 124 additions and 85 deletions
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78
helpers.py
View File

@ -7,23 +7,56 @@ import random
import inspect
import string
import re
from scipy import linalg
from constants import *
def color_to_rgb(color):
return np.array(Color(color).get_rgb())
def color_to_int_rgb(color):
return (255*color_to_rgb(color)).astype('uint8')
def compass_directions(n = 4, start_vect = UP):
angle = 2*np.pi/n
return [
rotate_vector(start_vect, k*angle)
for k in range(n)
]
def get_smooth_handle_points(points, closed = False):
num_handles = len(points) - 1
dim = points.shape[1]
if num_handles < 1:
return np.zeros((0, dim)), np.zeros((0, dim))
#Must solve 2*num_handles equations to get the handles.
#l and u are the number of lower an upper diagonal rows
#in the matrix to solve.
l, u = 2, 1
#diag is a representation of the matrix in diagonal form
#See https://www.particleincell.com/2012/bezier-splines/
#for how to arive at these equations
diag = np.zeros((l+u+1, 2*num_handles))
diag[0,1::2] = -1
diag[0,2::2] = 1
diag[1,0::2] = 2
diag[1,1::2] = 1
diag[2,1:-2:2] = -2
diag[3,0:-3:2] = 1
#last
diag[2,-2] = 2
diag[1,-1] = -1
#This is the b as in Ax = b, where we are solving for x,
#and A is represented using diag. However, think of entries
#to x and b as being points in space, not numbers
b = np.zeros((2*num_handles, dim))
b[1::2] = 2*points[1:]
b[0] = points[0]
b[-1] = points[-1]
solve_func = lambda b : linalg.solve_banded(
(l, u), diag, b
)
if closed:
#Get equations to relate first and last points
matrix = diag_to_matrix((l, u), diag)
#last row handles second derivative
matrix[-1, [0, 1, -2, -1]] = [2, -1, 1, -2]
#first row handles first derivative
matrix[0,:] = np.zeros(matrix.shape[1])
matrix[0,[0, -1]] = [1, 1]
b[0] = 2*points[0]
b[-1] = np.zeros(dim)
solve_func = lambda b : linalg.solve(matrix, b)
handle_pairs = np.zeros((2*num_handles, dim))
for i in range(dim):
handle_pairs[:,i] = solve_func(b[:,i])
return handle_pairs[0::2], handle_pairs[1::2]
def diag_to_matrix(l_and_u, diag):
"""
@ -41,6 +74,21 @@ def diag_to_matrix(l_and_u, diag):
)
return matrix
from constants import *
def color_to_rgb(color):
return np.array(Color(color).get_rgb())
def color_to_int_rgb(color):
return (255*color_to_rgb(color)).astype('uint8')
def compass_directions(n = 4, start_vect = UP):
angle = 2*np.pi/n
return [
rotate_vector(start_vect, k*angle)
for k in range(n)
]
def bezier(points):
n = len(points) - 1

131
mobject/vectorized_mobject.py
View File

@ -1,4 +1,4 @@
from scipy import linalg
from .mobject import Mobject
@ -77,16 +77,10 @@ class VectorizedMobject(Mobject):
self.points = np.zeros((total_len, self.dim))
self.points[0] = anchors[0]
arrays = [handles1, handles2, anchors[1:]]
for index, array in zip(it.count(1), arrays):
self.points[index::3] = array
for index, array in enumerate(arrays):
self.points[index+1::3] = array
return self.points
def get_anchors_and_handles(self):
return [
self.points[i::3]
for i in range(3)
]
def set_points_as_corners(self, points):
if len(points) <= 1:
return self
@ -100,50 +94,8 @@ class VectorizedMobject(Mobject):
if len(points) <= 1:
return self
points = self.close_if_needed(points)
num_handles = len(points) - 1
#Must solve 2*num_handles equations to get the handles.
#l and u are the number of lower an upper diagonal rows
#in the matrix to solve.
l, u = 2, 1
#diag is a representation of the matrix in diagonal form
#See https://www.particleincell.com/2012/bezier-splines/
#for how to arive at these equations
diag = np.zeros((l+u+1, 2*num_handles))
diag[0,1::2] = -1
diag[0,2::2] = 1
diag[1,0::2] = 2
diag[1,1::2] = 1
diag[2,1:-2:2] = -2
diag[3,0:-3:2] = 1
diag[2,-2] = 1
diag[1,-1] = -2
#This is the b as in Ax = b, where we are solving for x,
#and A is represented using diag. However, think of entries
#to x and b as being points in space, not numbers
b = np.zeros((2*num_handles, self.dim))
b[1::2] = 2*points[1:]
b[0] = points[0]
b[-1] = points[-1]
solve_func = lambda b : linalg.solve_banded(
(l, u), diag, b
)
if self.is_closed():
#Get equations to relate first and last points
matrix = diag_to_matrix((l, u), diag)
#last row handles second derivative
matrix[-1, [0, 1]] = matrix[0, [0, 1]]
#first row handles first derivative
matrix[0,:] = np.zeros(matrix.shape[1])
matrix[0,[0, -1]] = [1, 1]
b[0] = 2*points[0]
b[-1] = np.zeros(self.dim)
solve_func = lambda b : linalg.solve(matrix, b)
handle_pairs = np.zeros((2*num_handles, self.dim))
for i in range(self.dim):
handle_pairs[:,i] = solve_func(b[:,i])
handles1 = handle_pairs[0::2]
handles2 = handle_pairs[1::2]
self.set_anchors_and_handles(points, handles1, handles2)
h1, h2 = get_smooth_handle_points(points, self.is_closed())
self.set_anchors_and_handles(points, h1, h2)
return self
def close_if_needed(self, points):
@ -167,8 +119,23 @@ class VectorizedMobject(Mobject):
raise Exception("Unknown mode")
return self
def change_mode(self, mode):
anchors, h1, h2 = self.get_anchors_and_handles()
self.set_points(anchors, mode = mode)
return self
def make_smooth(self):
return self.change_mode("smooth")
def make_jagged(self):
return self.change_mode("corners")
## Information about line
def component_curves_iter(self):
for i in range(0, len(self.points)-1, 3):
yield bezier(self.points[i:i+4])
def get_num_points(self):
return (len(self.points) - 1)/3 + 1
@ -179,27 +146,53 @@ class VectorizedMobject(Mobject):
cubic = bezier(self.points[index:index+4])
return cubic(interpoint_alpha)
def get_anchors_and_handles(self):
return [
self.points[i::3]
for i in range(3)
]
## Alignment
# def align_points_with_larger(self, larger_mobject):
# assert(isinstance(larger_mobject, VectorizedMobject))
# anchors, handles1, handles2 = self.get_anchors_and_handles()
# old_n = len(anchors)
# new_n = larger_mobject.get_num_points()
# #Buff up list of anchor points to appropriate length
# new_anchors = anchors[old_n*np.arange(new_n)/new_n]
# #At first, handles are on anchor points
# #the [2:] is because start has no handles
# new_points = new_anchors.repeat(3, axis = 0)[2:]
# #These indices indicate the spots between genuinely
# #different anchor points in new_points list
# indices = 3*(np.arange(old_n) * new_n / old_n)[1:]
# new_points[indices+1] = handles1
# new_points[indices+2] = handles2
# self.set_points(new_points, mode = "handles_included")
# return self
def align_points_with_larger(self, larger_mobject):
assert(isinstance(larger_mobject, VectorizedMobject))
anchors, handles1, handles2 = self.get_anchors_and_handles()
old_n = len(anchors)
new_n = larger_mobject.get_num_points()
#Buff up list of anchor points to appropriate length
new_anchors = anchors[old_n*np.arange(new_n)/new_n]
#At first, handles are on anchor points
#the [2:] is because start has no handles
new_points = new_anchors.repeat(3, axis = 0)[2:]
#These indices indicate the spots between genuinely
#different anchor points in new_points list
indices = 3*(np.arange(old_n) * new_n / old_n)[1:]
new_points[indices+1] = handles1
new_points[indices+2] = handles2
self.set_points(new_points, mode = "handles_included")
points = np.array([self.points[0]])
target_len = larger_mobject.get_num_points()-1
num_curves = self.get_num_points()-1
#curves are buckets, and we need to know how many new
#anchor points to put into each one
index_allocation = (np.arange(target_len) * num_curves)/target_len
for index, curve in enumerate(self.component_curves_iter()):
num_inter_points = sum(index_allocation == index)
step = 1./num_inter_points
alphas = np.arange(0, 1+step, step)
new_anchors = np.array(map(curve, alphas))
h1, h2 = get_smooth_handle_points(new_anchors)
new_points = np.array(
zip(h1, h2, new_anchors[1:])
)
new_points = new_points.reshape((new_points.size/3, 3))
points = np.append(points, new_points, 0)
self.set_points(points, "handles_included")
return self
def get_point_mobject(self):
return VectorizedPoint(self.get_center())
@ -218,8 +211,6 @@ class VectorizedMobject(Mobject):
))
class VectorizedPoint(VectorizedMobject):
CONFIG = {
"color" : BLACK,