I have this bezier curve diagram I created in Python but i need to redo it in Julia. I looked up alot of articles but still couldn’t learn how to do it. Please help by commenting on how to do it. It can be a part of this code or all of it.I know once I see the syntax…it will be easy for me to do on my own. I have attached the image i got when i run this code in Python. it can be a little different in Julia, am still okay with it.
import numpy as np
import matplotlib.pyplot as plt
import scipy.special
from scipy import comb
from scipy.stats import binom
from matplotlib.colors import hsv_to_rgb
import sys
import numpy as np
k = np.array([3, 4]);k
array([ 120., 210.])
comb(10, 3, exact=True)
comb(10, 3, exact=True, repetition=True)
# Save combinations into array
combs = []
for n in range(10):
ar = []
for k in range(n + 1):
ar.append(comb(n, k))
combs.append(ar)
def combinations(n, k):
if n < k: return .0
else:
return combs[n][k]
# Done
def bernstein_matrix_2(t, w):
return np.matmul(np.matmul([1, t**1, t**2], [[1, 0, 0], [-2, 2, 0], [1, -2, 1]]), w)
def bernstein_matrix_3(t, w):
return np.matmul(np.matmul([1, t, t**2, t**3], [[1, 0, 0, 0], [-3, 3, 0, 0], [3, -6, 3, 0], [-1, 3, -3, 1]]), w)
# Done
def bernstein_2(t, w):
return np.multiply((1-t)**2, w[0]) + np.multiply(2*t*(1-t), w[1]) + np.multiply(t**2 , w[2])
# Basis for Bernstein
def bbasis(t, n, i):
return combinations(n, i) * (1 - t)**(n - i) * t**(i)
# Done
def bernstein(t, w):
w = np.array(w).astype('float')
ret = np.array([0,0])
for i in range(len(w)):
ret = ret + w[i] * bbasis(t, len(w)-1, i)
return ret
# Derivaive for 2d vector
def deriv2(t, w):
return (np.array(w[1]) - np.array(w[0])) * 2 * (1 - t) + (np.array(w[2] - np.array(w[1]))) * 2 * t
# Derivaive for Nd vector
def deriv(t, w):
n = len(w) - 1
ret = np.array([0, 0])
for i in range(n):
ret = ret + (np.array(w[i+1]) - np.array(w[i])) * bbasis(t, n-1, i) * (n)
return ret
# De Casteljue
# rerurn all control points
def de_cast_all(t, w):
ret = []
n = len(w)
for k in range(0, n):
ar = []
for i in range(n - k):
ar.append(r(i, k, t, w))
ret.append(ar)
return ret
# De Casteljue
# rerurn point on Bezier curve
def de_cast(t, w):
return r(0, len(w)-1, t, w)
# De Casteljue
# recursive stuff
def r(i, k, t, w):
if k == 0: return np.array(w[i])
return (1 - t) * r(i, k-1, t, w) + t * r(i+1, k-1, t, w)
w_points = [[0, 0], [2, 3], [3, 0]]
bezier_matrix_points = []
bezier_bernstein_points = []
bernstein_points = []
for t in np.linspace(0, 1, 100):
bezier_matrix_points.append(bernstein_matrix_2(t, w_points))
bezier_bernstein_points.append(bernstein_2(t, w_points))
bernstein_points.append(bernstein(t, w_points))
fig = plt.figure(figsize=(18,18))
axs = [fig.add_subplot(1, 3, i) for i in range(1, 4)]
for ax in axs:
ax.grid()
ax.set_aspect('equal')
axs[0].set_title('Matrix 2')
axs[1].set_title('Bernstein 2')
axs[2].set_title('Bernstein N')
axs[0].plot([x[0] for x in bezier_matrix_points], [x[1] for x in bezier_matrix_points],
linewidth=4, color='r', label='Bezier curve')
axs[0].plot([x[0] for x in w_points], [x[1] for x in w_points],
marker='o', color='black', label='Control points')
axs[0].legend(fontsize=13, framealpha=1)
axs[1].plot([x[0] for x in bezier_bernstein_points], [x[1] for x in bezier_bernstein_points],
linewidth=4, color='g', label='Bezier curve')
axs[1].plot([x[0] for x in w_points], [x[1] for x in w_points],
marker='o', color='black', label='Control points')
axs[1].legend(fontsize=13, framealpha=1)
axs[2].plot([x[0] for x in bernstein_points], [x[1] for x in bernstein_points],
linewidth=4, color='b', label='Bezier curve')
axs[2].plot([x[0] for x in w_points], [x[1] for x in w_points],
marker='o', color='black', label='Control points')
axs[2].legend(fontsize=13, framealpha=1)
