Drawing Bézier curves with DrawBot

b2_01.py

# Load external packages
import sys
import os

mod_dir = os.path.expanduser('~/.pyenv/versions/3.6.4/lib/python3.6/site-packages')

if mod_dir not in sys.path:
    sys.path.append(mod_dir)

import numpy as np

# Define canvas size
CANVAS = 500

# Define control points
p0 = np.array([100, 100])
p1 = np.array([200, 450])
p2 = np.array([450, 100])

newPage(CANVAS, CANVAS)

# Draw lines
stroke(0.6)
line(p0, p1)
line(p1, p2)

# Draw points and notes
d = 5
r = d/2
notes_margin = np.array([10, r])
coord_margin = np.array([10, d*3])
stroke(0)
fill(0)
font('Input Mono Condensed', 10)

for i, point in enumerate([p0, p1, p2]):
    oval(*(point-r), d, d)
    text("P{}".format(i), point-notes_margin, align="right")
    text("({}, {})".format(point[0], point[1]), point-coord_margin, align="right")

save_dir = os.path.expanduser('~/Downloads')
file_name = 'b2_01.png'
saveImage(os.path.join(save_dir, file_name), imageResolution=200)

b2_02.py

# Load external packages
import sys
import os

mod_dir = os.path.expanduser('~/.pyenv/versions/3.6.4/lib/python3.6/site-packages')

if mod_dir not in sys.path:
    sys.path.append(mod_dir)

import numpy as np

# Define canvas size
CANVAS = 500

# Define control points
p0 = np.array([100, 100])
p1 = np.array([200, 450])
p2 = np.array([450, 100])

newPage(CANVAS, CANVAS)

# Draw lines
stroke(0.6)
line(p0, p1)
line(p1, p2)

# Draw points and notes
d = 5
r = d/2
notes_margin = np.array([10, r])
coord_margin = np.array([10, d*3])
stroke(0.6)
fill(0.6)
font('InputMonoCondensed Light', 10)

for i, point in enumerate([p0, p1, p2]):
    oval(*(point-r), d, d)
    text("P{}".format(i), point-notes_margin, align="right")
    text("({}, {})".format(point[0], point[1]), point-coord_margin, align="right")

# Draw additional points according to t
for i in range(1, 5, 1):
    t = i/5
    p01 = p0 + t*(p1-p0)
    p12 = p1 + t*(p2-p1)
    
    # Draw lines
    stroke(0.6)
    fill(0.6)
    line(p01, p12)
    
    # Draw points and notes
    stroke(0)
    fill(0)
    for j, point in enumerate([p01, p12]):
        oval(*(point-r), d, d)
        text("P{}{}{}".format(j, j+1, i), point-notes_margin, align="right")
        text("({:.0f}, {:.0f})".format(point[0], point[1]), point-coord_margin, align="right")


# Save image
save_dir = os.path.expanduser('~/Downloads')
file_name = 'b2_02.png'
saveImage(os.path.join(save_dir, file_name), imageResolution=200)

b2_03.py

# Load external packages
import sys
import os

mod_dir = os.path.expanduser('~/.pyenv/versions/3.6.4/lib/python3.6/site-packages')

if mod_dir not in sys.path:
    sys.path.append(mod_dir)

import numpy as np

# Define canvas size
CANVAS = 500

# Define control points
p0 = np.array([100, 100])
p1 = np.array([200, 450])
p2 = np.array([450, 100])

newPage(CANVAS, CANVAS)

# Draw lines
stroke(0.6)
line(p0, p1)
line(p1, p2)

# Draw points and notes
d = 5
r = d/2
notes_margin = np.array([10, r])
coord_margin = np.array([10, d*3])

font('InputMonoCondensed Light', 10)

for i, point in enumerate([p0, p1, p2]):
    stroke(0.6)
    fill(0.6)
    oval(*(point-r), d, d)
    if point is not p1:
        stroke(None)
        fill(None)
    text("P{}".format(i), point-notes_margin, align="right")
    text("({}, {})".format(point[0], point[1]), point-coord_margin, align="right")

# Draw additional points according to t
o = p0
t_range = [0, 6]
for i in range(*t_range, 1):
    t = i/(t_range[1]-1)
    p01 = p0 + t*(p1-p0)
    p12 = p1 + t*(p2-p1)
    
    # Draw lines
    stroke(0.6)
    fill(0.6)
    line(p01, p12)
    
    # Draw points and notes
    stroke(0.6)
    fill(0.6)
    
    if (i == t_range[0]) or (i == t_range[1]-1):
        stroke(None)
        fill(None)
    
    for j, point in enumerate([p01, p12]):
        oval(*(point-r), d, d)
        text("P{}{}{}".format(j, j+1, i), point-notes_margin, align="right")
        text("({:.0f}, {:.0f})".format(point[0], point[1]), point-coord_margin, align="right")
    
    # Draw points on bezier curve
    p = p01 + t*(p12 - p01)
    stroke(0)
    fill(0)
    oval(*(p-r), d, d)
    text("P({})".format(t), p-notes_margin, align="right")
    text("({:.0f}, {:.0f})".format(p[0], p[1]), p-coord_margin, align="right")
    
    line(o, p)
    o = p

# Save image
save_dir = os.path.expanduser('~/Downloads')
file_name = 'b2_03.png'
saveImage(os.path.join(save_dir, file_name), imageResolution=200)

b2_04.py

# Load external packages
import sys
import os

mod_dir = os.path.expanduser('~/.pyenv/versions/3.6.4/lib/python3.6/site-packages')

if mod_dir not in sys.path:
    sys.path.append(mod_dir)

import numpy as np

# Define canvas size and frames
CANVAS = 500
fps = 50
seconds = 3
total_frames = fps * seconds
duration = 1/fps

# Define control points
p0 = np.array([100, 100])
p1 = np.array([200, 450])
p2 = np.array([450, 100])

for frame in range(total_frames):
    newPage(CANVAS, CANVAS)
    
    if frame == total_frames - 1:
        frameDuration(1)
    else:
        frameDuration(duration)

    # Draw lines
    stroke(0.6)
    line(p0, p1)
    line(p1, p2)

    d = 5
    r = d/2
    notes_margin = np.array([10, r])
    coord_margin = np.array([10, d*3])

    font('InputMonoCondensed Light', 10)

    # Draw control points and notes
    for i, point in enumerate([p0, p1, p2]):
        stroke(0.6)
        fill(0.6)
        oval(*(point-r), d, d)
        text("P{}".format(i), point-notes_margin, align="right")
        text("({}, {})".format(point[0], point[1]), point-coord_margin, align="right")

    o = p0
    t_range = [0, frame+1]
    for i in range(*t_range, 1):
        t = i/(total_frames-1)
        p01 = p0 + t*(p1-p0)
        p12 = p1 + t*(p2-p1) 
    
        # Draw bezier curve
        p = p01 + t*(p12 - p01)
        stroke(0)
        fill(0)
    
        line(o, p)
        o = p
        
    text("t={:.4f}".format(t), (CANVAS-60, CANVAS-20), align="left")

# Save image
save_dir = os.path.expanduser('~/Downloads')
file_name = 'b2_04.gif'
saveImage(os.path.join(save_dir, file_name), imageResolution=200)

b3_01.py

# Load external packages
import sys
import os

mod_dir = os.path.expanduser('~/.pyenv/versions/3.6.4/lib/python3.6/site-packages')

if mod_dir not in sys.path:
    sys.path.append(mod_dir)

import numpy as np

# Define canvas size
CANVAS = 500

# Define control points
q0 = np.array([100, 100])
q1 = np.array([200, 450])
q2 = np.array([450, 100])
p0 = q0
p1 = q0 + (q1-q0) * (2/3)
p2 = q2 + (q1-q2) * (2/3)
p3 = q2

newPage(CANVAS, CANVAS)

# Draw lines
stroke(0.6)
line(p0, p1)
line(p1, p2)
line(p2, p3)

# Draw points and notes
d = 5
r = d/2
notes_margin = np.array([10, -r])
coord_margin = np.array([10, d*2])
stroke(0)
fill(0)
font('Input Mono Condensed', 10)

for i, point in enumerate([p0, p1, p2, p3]):
    oval(*(point-r), d, d)
    text("P{}".format(i), point-notes_margin, align="right")
    text("({:.0f}, {:.0f})".format(point[0], point[1]), point-coord_margin, align="right")

save_dir = os.path.expanduser('~/Downloads')
file_name = 'b3_01.png'
saveImage(os.path.join(save_dir, file_name), imageResolution=200)

b3_02.py

# Load external packages
import sys
import os

mod_dir = os.path.expanduser('~/.pyenv/versions/3.6.4/lib/python3.6/site-packages')

if mod_dir not in sys.path:
    sys.path.append(mod_dir)

import numpy as np

# Define canvas size
CANVAS = 500

# Define control points
q0 = np.array([100, 100])
q1 = np.array([200, 450])
q2 = np.array([450, 100])
p0 = q0
p1 = q0 + (q1-q0) * (2/3)
p2 = q2 + (q1-q2) * (2/3)
p3 = q2

newPage(CANVAS, CANVAS)

# Draw lines
stroke(0.6)
line(p0, p1)
line(p1, p2)
line(p2, p3)

# Draw points and notes
d = 5
r = d/2
notes_margin = np.array([10, -r])
coord_margin = np.array([10, d*2])
stroke(0.6)
fill(0.6)
font('InputMonoCondensed Light', 10)

for i, point in enumerate([p0, p1, p2, p3]):
    oval(*(point-r), d, d)
    text("P{}".format(i), point-notes_margin, align="right")
    # text("({:.0f}, {:.0f})".format(point[0], point[1]), point-coord_margin, align="right")

# Draw additional points according to t
for i in range(1, 5, 1):
    t = i/5
    p01 = p0 + t*(p1-p0)
    p12 = p1 + t*(p2-p1)
    p23 = p2 + t*(p3-p2)
    
    # Draw lines
    stroke(0.6)
    fill(0.6)
    line(p01, p12)
    line(p12, p23)
    
    # Draw points and notes
    stroke(0)
    fill(0)
    for j, point in enumerate([p01, p12, p23]):
        oval(*(point-r), d, d)
        # text("P{}{}{}".format(j, j+1, i), point-notes_margin, align="right")
        # text("({:.0f}, {:.0f})".format(point[0], point[1]), point-coord_margin, align="right")


# Save image
save_dir = os.path.expanduser('~/Downloads')
file_name = 'b3_02.png'
saveImage(os.path.join(save_dir, file_name), imageResolution=200)

b3_03.py

# Load external packages
import sys
import os

mod_dir = os.path.expanduser('~/.pyenv/versions/3.6.4/lib/python3.6/site-packages')

if mod_dir not in sys.path:
    sys.path.append(mod_dir)

import numpy as np

# Define canvas size
CANVAS = 500
	
# Define control points
q0 = np.array([100, 100])
q1 = np.array([200, 450])
q2 = np.array([450, 100])
p0 = q0
p1 = q0 + (q1-q0) * (2/3)
p2 = q2 + (q1-q2) * (2/3)
p3 = q2

newPage(CANVAS, CANVAS)

# Draw lines
stroke(0.6)
line(p0, p1)
line(p1, p2)
line(p2, p3)

# Draw points and notes
d = 5
r = d/2
notes_margin = np.array([10, -r])
coord_margin = np.array([10, d*2])

font('InputMonoCondensed Light', 10)

for i, point in enumerate([p0, p1, p2, p3]):
    stroke(0.6)
    fill(0.6)
    oval(*(point-r), d, d)
    text("P{}".format(i), point-notes_margin, align="right")
    # text("({:.0f}, {:.0f})".format(point[0], point[1]), point-coord_margin, align="right")

# Draw additional points according to t
t_range = [0, 6]
for i in range(*t_range, 1):
    t = i/(t_range[1]-1)
    p01 = p0 + t*(p1-p0)
    p12 = p1 + t*(p2-p1)
    p23 = p2 + t*(p3-p2)
    
    # Draw lines
    stroke(0.6)
    fill(0.6)
    line(p01, p12)
    line(p12, p23)
    
    if (i == t_range[0]) or (i == t_range[1]-1):
        stroke(None)
        fill(None)
    
    for j, point in enumerate([p01, p12, p23]):
        oval(*(point-r), d, d)
        # text("P{}{}{}".format(j, j+1, i), point-notes_margin, align="right")
        # text("({:.0f}, {:.0f})".format(point[0], point[1]), point-coord_margin, align="right")
    
    # Draw lines and points
    p0112 = p01 + t*(p12 - p01)
    p1223 = p12 + t*(p23 - p12)
    
    stroke(0)
    fill(0)
    line(p0112, p1223)
    
    for point in [p0112, p1223]:
        oval(*(point-r), d, d)
        # text("P({})".format(t), point-notes_margin, align="right")
        # text("({:.0f}, {:.0f})".format(p[0], p[1]), p-coord_margin, align="right")
    
# Save image
save_dir = os.path.expanduser('~/Downloads')
file_name = 'b3_03.png'
saveImage(os.path.join(save_dir, file_name), imageResolution=200)

b3_04.py

# Load external packages
import sys
import os

mod_dir = os.path.expanduser('~/.pyenv/versions/3.6.4/lib/python3.6/site-packages')

if mod_dir not in sys.path:
    sys.path.append(mod_dir)

import numpy as np

# Define canvas size
CANVAS = 500
	
# Define control points
q0 = np.array([100, 100])
q1 = np.array([200, 450])
q2 = np.array([450, 100])
p0 = q0
p1 = q0 + (q1-q0) * (2/3)
p2 = q2 + (q1-q2) * (2/3)
p3 = q2

newPage(CANVAS, CANVAS)

# Draw lines
stroke(0.6)
line(p0, p1)
line(p1, p2)
line(p2, p3)

# Draw points and notes
d = 5
r = d/2
notes_margin = np.array([10, -r])
coord_margin = np.array([10, d*2])

font('InputMonoCondensed Light', 10)

for i, point in enumerate([p0, p1, p2, p3]):
    stroke(0.6)
    fill(0.6)
    oval(*(point-r), d, d)
    if (point is not p1) and (point is not p2):
        stroke(None)
        fill(None)
    text("P{}".format(i), point-notes_margin, align="right")
    # text("({:.0f}, {:.0f})".format(point[0], point[1]), point-coord_margin, align="right")

# Draw additional points according to t
o = p0
t_range = [0, 6]
for i in range(*t_range, 1):
    t = i/(t_range[1]-1)
    p01 = p0 + t*(p1-p0)
    p12 = p1 + t*(p2-p1)
    p23 = p2 + t*(p3-p2)
    
    # Draw lines
    stroke(0.6)
    fill(0.6)
    line(p01, p12)
    line(p12, p23)
    
    if (i == t_range[0]) or (i == t_range[1]-1):
        stroke(None)
        fill(None)
    
    for j, point in enumerate([p01, p12, p23]):
        oval(*(point-r), d, d)
        # text("P{}{}{}".format(j, j+1, i), point-notes_margin, align="right")
        # text("({:.0f}, {:.0f})".format(point[0], point[1]), point-coord_margin, align="right")
    
    # Draw lines and points
    p0112 = p01 + t*(p12 - p01)
    p1223 = p12 + t*(p23 - p12)
    
    stroke(0.6)
    fill(0.6)
    line(p0112, p1223)
    
    if (i == t_range[0]) or (i == t_range[1]-1):
        stroke(None)
        fill(None)
    
    for point in [p0112, p1223]:
        oval(*(point-r), d, d)
        # text("P({})".format(t), point-notes_margin, align="right")
        # text("({:.0f}, {:.0f})".format(p[0], p[1]), p-coord_margin, align="right")
        
    p = p0112 + t*(p1223 - p0112)

    stroke(0)
    fill(0)
    oval(*(p-r), d, d)
    text("P({})".format(t), p-notes_margin, align="right")
    text("({:.0f}, {:.0f})".format(p[0], p[1]), p-coord_margin, align="right")

    line(o, p)
    o = p
    
# Save image
save_dir = os.path.expanduser('~/Downloads')
file_name = 'b3_04.png'
saveImage(os.path.join(save_dir, file_name), imageResolution=200)

b3_05.py

# Load external packages
import sys
import os

mod_dir = os.path.expanduser('~/.pyenv/versions/3.6.4/lib/python3.6/site-packages')

if mod_dir not in sys.path:
    sys.path.append(mod_dir)

import numpy as np

# Define canvas size and frames
CANVAS = 500
fps = 50
seconds = 3
total_frames = fps * seconds
duration = 1/fps

# Define control points
q0 = np.array([100, 100])
q1 = np.array([200, 450])
q2 = np.array([450, 100])
p0 = q0
p1 = q0 + (q1-q0) * (2/3)
p2 = q2 + (q1-q2) * (2/3)
p3 = q2

for frame in range(total_frames):
    newPage(CANVAS, CANVAS)
    
    if frame == total_frames - 1:
        frameDuration(1)
    else:
        frameDuration(duration)

    # Draw lines
    stroke(0.6)
    line(p0, p1)
    line(p1, p2)
    line(p2, p3)

    d = 5
    r = d/2
    notes_margin = np.array([10, -r])
    coord_margin = np.array([10, d*2])

    font('InputMonoCondensed Light', 10)

    # Draw control points and notes
    for i, point in enumerate([p0, p1, p2, p3]):
        stroke(0.6)
        fill(0.6)
        oval(*(point-r), d, d)
        text("P{}".format(i), point-notes_margin, align="right")
        text("({:.0f}, {:.0f})".format(point[0], point[1]), point-coord_margin, align="right")

    o = p0
    t_range = [0, frame+1]
    for i in range(*t_range, 1):
        t = i/(total_frames-1)
        p01 = p0 + t*(p1-p0)
        p12 = p1 + t*(p2-p1)
        p23 = p2 + t*(p3-p2)
        
        p0112 = p01 + t*(p12 - p01)
        p1223 = p12 + t*(p23 - p12)  
    
        # Draw bezier curve
        p = p0112 + t*(p1223 - p0112)
        stroke(0)
        fill(0)
    
        line(o, p)
        o = p
        
    text("t={:.4f}".format(t), (CANVAS-60, CANVAS-20), align="left")

# Save image
save_dir = os.path.expanduser('~/Downloads')
file_name = 'b3_05.gif'
saveImage(os.path.join(save_dir, file_name), imageResolution=200)