@mrrouge

ok if i got you right you want the function to return a value — in your case the height of the legs. this value could then be used in a while loop. while loops are quite helpful but might run forever if done incorrect. I adapted the code a bit so the legs function returns the length of the legs which is then added to the y value in the while loop. There is a check inside the while loop so it will run for a maximum of 3000 times.

# -------------
#  settings 

pw = ph = 500
amount_x = 10

cell_w = pw / amount_x

max_h  = 50
gap = max_h * .2

# -------------
#  fucntion(s)

def legs(pos, max_w, max_h):

    x, y = pos
    length = random() * max_h
    step_s = random() * max_w
    polygon((x - step_s, y) , (x, y + length), (x + step_s, y), close = False)
    
    return length

# -------------
#  drawings

newPage(pw, ph) 
fill(None)
stroke(0)
strokeWidth(2)

for x in range(amount_x):
    
    count = 0
    y = -random() * max_h
    while y < ph:
        y += legs((x * cell_w + cell_w/2, y), cell_w/2, max_h)
        y += gap
        count += 1
        
        if count > 3000: break 

and the while loop without the check:

for x in range(amount_x):
    y = -random() * max_h
    while y < ph:
        y += legs((x * cell_w + cell_w/2, y), cell_w/2, max_h)
        y += gap

Vera Molnar is a great computer generated arts pioneer and is still working. I could not resist to emulate and try to recode some of her artworks. Using drawbot to do so is great fun and pretty easy — one can only wonder about the struggles she had to overcome. With all due respect here is a link to github with my humble attempts.

if you are not in chile or argentina for the solar eclipse this code can gif you solace:

# -------------
#  settings 

pw = 800
ph = 500

dia = pw * .45
frames = 20

# -------------
#  function(s)

def a_page():
    newPage(pw, ph)
    rect(0, 0, pw, ph)
    radialGradient((pw/2, ph/2), (pw/2, ph/2), [(1, 0.8, 0), (0.9, 0.6, 0) ])
    oval(pw/2-dia/2, ph/2-dia/2, dia, dia)

def ip(a, b, f): return a + (b-a)*f

# -------------
#  drawings

for frame in range(frames):
    a_page() 
    
    f = frame / frames 
    x = ip(pw/4, pw/4*3, f)
    y = ip(0, ph, f)
    fill(0)
    if abs(x - pw/2) < .2:
        shadow((0, 0), dia/3, (1, 1, 1))
    oval(x - dia/2, y - dia/2, dia, dia)
    
# saveImage('solar_eclipse.gif')

@mrrouge
I am not quite sure if this is what you are asking for but you either need to translate(x,y) the maximum leg length or width or just draw the legs at the position you want them to. In your legs() function you do have the parameters x and y but they are not used inside the function.

Also I do recommend to use a variable if you repeatedly use the same value. So instead of randint(20, 100) you could use

min_val = 20
max_val = 100
randint(min_val, max_val)

I put together a simple “legs” drawing that might help.
Good luck

# -------------
#  settings 

pw = ph = 500
amount_x = 10
amount_y =  4

cell_w = pw / amount_x
cell_h = ph / amount_y

# -------------
#  fucntion(s)

def legs(pos, max_w, max_h):

    x, y = pos
    length = random() * max_h
    step_s = random() * max_w
    
    polygon((x - step_s, y - length) , pos, (x + step_s, y - length), close = False)


# -------------
#  drawings

newPage(pw, ph) 
fill(None)
stroke(0)
strokeWidth(2)

for x in range(amount_x):
    for y in range(amount_y):
        legs((x * cell_w + cell_w/2, y * cell_h + cell_h/2), cell_w/2, cell_h/2)

@Sabina

to center the text on the page you should set the align parameter to center and set the x coordinate of the text to half of the page width:

    text(txt, (width()/2, 70), align ='center')

@Anna hi
do you get error messages?
if so you should post them.
and maybe post some code.
what is going wrong and what would you like it to do?

i hope i am not missing this in the documentation …
I was wondering if there is a way to list all instances of a variable font? and then possibly get the values of the axes at these instances.
thanks j

You cannot draw a circle with Beziers.

When I first read this some time ago I was a bit confused.
Why is this not a circle. It sure looks like one.

After learning a bit more about curve descriptions and calculations I kind of agree but the quote should better say:

You cannot draw a perfect circle with Beziers.

Getting the best tangent values.

We have a formula to calculate points on a Bezier Curve.

x = (1-t)**3*p1[0] + 3*(1-t)**2*t*t1[0] + 3*(1-t)*t**2*t2[0] + t**3*p2[0]
y = (1-t)**3*p1[1] + 3*(1-t)**2*t*t1[1] + 3*(1-t)*t**2*t2[1] + t**3*p2[1]

p1 and p2 are the two endpoints and t1 and t2 the two tangent points. t is the factor (0-1) at which we want the point on the curve.

On a bezier curve with the following coördinates:

p1 = (1, 0)
p2 = (0, 1)
t1 = (1, tangent_val)
t2 = (tangent_val, 1)

we can calculate the tangent_val if we assume that the point at t=0.5 (halfway the curve) is exactly on the circle. Halfway of a quartercircle is 45 degrees so x and y are both at 1/sqrt(2). If we plug these numbers into the formula we can calculate the tangent value:

1/sqrt(2) = (1-.5)**3*1 + 3*(1-.5)**2*.5*1 + 3*(1-.5)*.5**2*tangent_val + .5**3*0
...
tangent_val = 4*(sqrt(2)-1)/3 ≈ 0.5522847493

With this tangent_val we can calculate other points on the bezier curve. Of which we can calculate the angle in respect to the center point at (0, 0). And with this angle we can use sine and cosine to get the point that would be on a circle.

We can also calculate the distance of the bezier point and see where the offset is the biggest. As we can see the difference is really tiny. With a radius of 1 the biggest off value is 1.0002725295591013 (not even one permille). The difference is hardly visible so I added only the top part of a really long bar chart to make it show.
See the image below:

Code

# -------------------
#  settings 

pw, ph = 595, 842 #A4
margin = 70

tang = 4*(sqrt(2)-1)/3
r = pw - 2 * margin

density = 90 # amount of points 
dia_ = 1 # diameter to draw the points 

r_plot = 100000 # this is a magnifying factor to make the tiny difference visible. 

r_plot_y = margin - r_plot   #radius plotting 
c_plot_y = ph - 3 * margin - r  # circle plotting 

# -------------------
#  functions  

def get_bezier_p(p1, t1, t2, p2, t):
    ''' get the point on a bezier curve at t (should be between 0 and 1) '''
    x = (1 - t)**3 * p1[0] + 3*(1 - t)**2 * t * t1[0] + 3*(1 - t)* t**2 * t2[0] + t**3 * p2[0]
    y = (1 - t)**3 * p1[1] + 3*(1 - t)**2 * t * t1[1] + 3*(1 - t)* t**2 * t2[1] + t**3 * p2[1]
    return x, y

def get_dist(p1, p2): 
    ''' returns the distance between two points (x, y)'''
    return sqrt((p2[0]-p1[0])**2 + (p2[1]-p1[1])**2)

# -------------------
#  drawings  

newPage(pw, ph)
fill(1)
rect(0, 0, pw, ph)
translate(margin, margin)

# draw the tangent points 
rect(r - dia_, c_plot_y + tang*r - dia_, dia_*2, dia_*2)
rect(tang*r -dia_, c_plot_y + r - dia_, dia_*2, dia_*2)

max_off = 1

for i in range(density+1):

    # -------
    #  bezier 

    # calculate the factor f 
    f = i/density
    fill(0)
    if i == 0 or i == (density): dia = dia_ * 4
    else: dia = dia_
    # get the coordinates for the point at factor f 
    x_b, y_b = get_bezier_p( (1, 0), (1, tang), (tang, 1), (0, 1), f )
    # get the distance of the point from the center at (0, 0)
    r_b = get_dist((0, 0), (x_b, y_b))
    max_off = max(max_off, r_b)
    # get the angle of the point 
    angle = atan2(y_b, x_b)
    # draw the point and a rect for the bar chart     
    oval(x_b * r - dia/2, c_plot_y + y_b * r - dia/2, dia, dia)
    rect((angle/(pi/2)) * r - dia_/2, r_plot_y, dia_, r_plot * r_b)

    # -------
    #  circle

    fill(1, 0, 0)

    # get the point on a circle 
    x_c, y_c = cos(angle), sin(angle)
    # draw the point and a rect for the bar chart     
    oval(x_c * r - dia/2, c_plot_y + y_c * r - dia/2, dia, dia)
    rect((angle/(pi/2)) * r - dia_/2, r_plot_y, dia_, r_plot)
        
    fill(.3)
    if i % 10 == 0:
        x_p, y_p = r * f, margin #* 1.5
        rect(x_p - .25, y_p, .5, 30)
        text('%d°' % (f * 90), (x_p-2, y_p * 1.5))

print (max_off)
text('%.6f' % max_off, (-50, max_off * r_plot - r_plot + margin - 2))
text('%.6f' % 1, (-50, margin - 2))
    

The maybe more interesting peculiarity of bezier curves is the difference between time and distance. We can compare the bezier distance at factor f (0-1) to the circle if we use the same factor to get the appropriate fraction of 90 degrees.

Code

# -------------------
#  settings 

pw, ph = 595, 842 #A4
margin = 70

tang = 4*(sqrt(2)-1)/3
r = pw - 2 * margin

density = 90 # amount of points 
dia_ = 1 # diameter to draw the points 

r_plot = 100000 # this is a magnifying factor to make the tiny difference visible. 

r_plot_y = margin - r_plot   #radius plotting 
c_plot_y = ph - 3 * margin - r  # circle plotting 

# -------------------
#  functions  

def get_bezier_p(p1, t1, t2, p2, t):
    ''' get the point on a bezier curve at t (should be between 0 and 1) '''
    x = (1 - t)**3 * p1[0] + 3*(1 - t)**2 * t * t1[0] + 3*(1 - t)* t**2 * t2[0] + t**3 * p2[0]
    y = (1 - t)**3 * p1[1] + 3*(1 - t)**2 * t * t1[1] + 3*(1 - t)* t**2 * t2[1] + t**3 * p2[1]
    return x, y

def get_dist(p1, p2): 
    ''' returns the distance between two points (x, y)'''
    return sqrt((p2[0]-p1[0])**2 + (p2[1]-p1[1])**2)

# -------------------
#  drawings  

newPage(pw, ph)
fill(1)
rect(0, 0, pw, ph)
translate(margin, margin)

# draw the tangent points 
rect(r - dia_, c_plot_y + tang*r - dia_, dia_*2, dia_*2)
rect(tang*r -dia_, c_plot_y + r - dia_, dia_*2, dia_*2)


for i in range(density+1):

    # -------
    #  bezier 

    # calculate the factor f 
    f = i/density
    fill(0)
    if i == 0 or i == (density): dia = dia_ * 4
    else: dia = dia_
    # get the coordinates for the point at factor f 
    x_b, y_b = get_bezier_p( (1, 0), (1, tang), (tang, 1), (0, 1), f )
    # get the distance of the point from the center at (0, 0)
    r_b = get_dist((0, 0), (x_b, y_b))
    # get the angle of the point 
    angle = atan2(y_b, x_b)
    # draw the point and a rect for the bar chart     
    oval(x_b * r - dia/2, c_plot_y + y_b * r - dia/2, dia, dia)
    rect((angle/(pi/2)) * r - dia_/2, r_plot_y, dia_, r_plot)

    # -------
    #  circle

    fill(1, 0, 0)

    # get the point on a circle 
    x_c, y_c = cos( pi/2*f ), sin( pi/2*f )
    # draw the point and a rect for the bar chart     
    oval(x_c * r - dia/2, c_plot_y + y_c * r - dia/2, dia, dia)
    rect(f * r - dia_/2, r_plot_y, dia_, r_plot)
        
    fill(.3)
    if i % 10 == 0:
        x_p, y_p = r * f, margin #* 1.5
        rect(x_p - .25, y_p, .5, 30)
        text('%d°' % (f * 90), (x_p-2, y_p * 1.5))

oh, yes!
that is of course a very nice solution.
will update some of the scripts in the next days.
thanks!

@frederik thank you!

There is one 'issue' that makes it difficult to abstract the code. And I was wondering if this could be implemented differently in drawbot.
when setting the fontVariations the axis tag cannot be a variable:
fontVariations( axisTag = someValue )

It would be quite convenient to do:

myAxis = 'wght' # or whatever
# ... do some stuff with myAxis
# ... and then just place the variable name
fontVariations( myAxis = someValue )

or to just iterate through axes without ever having to type the axistag.