Posts made by monomonnik

The code responsible for the rounding of the paths in a small animation I made.

DEBUG = False

# A path has points.
# A point has only an anchor [(x,y)], or has an anchor and in and out point [(x,y), (x,y), (x,y)].
# To close a path, repeat the first point at the last position.
jagged_line =[[(500,210)], [(400,250)], [(600,350)], [(450,600)], [(500,790)]]
rectangle =[[(220,220)], [(780,220)], [(780,780)], [(220,780)], [(220,220)]]
circle = [[(500.0, 800.0), (335.0, 800.0), (665.0, 800.0)], [(800.0, 500.0), (800.0, 665.0), (800.0, 335.0)], [(500.0, 200.0), (665.0, 200.0), (335.0, 200.0)], [(200.0, 500.0), (200.0, 335.0), (200.0, 665.0)], [(500.0, 800.0), (335.0, 800.0), (665.0, 800.0)]]


def draw(path):
    bez = BezierPath()
    bez.moveTo(path[0][0])
    for i in range(1, len(path)):
        p0 = path[i-1]
        p1 = path[i]
        if len(p0) == 1 and len(p1) == 1:
            # straight line between points
            bez.lineTo(p1[0])
        elif len(p0) == 3 and len(p1) == 1:
            # from curve point to straight point
            bez.curveTo(p0[2], p1[0], p1[0])
        elif len(p0) == 1 and len(p1) == 3:
            # from straight point to curve point
            bez.curveTo(p0[0], p1[1], p1[0])
        elif len(p0) == 3 and len(p1) == 3:
            # curve point on both sides
            bez.curveTo(p0[2], p1[1], p1[0])
    if path[-1] == path[0]:
        bez.closePath()
    drawPath(bez)


def round_corners(path, roundness):
    if len(path) > 2:
        new_path = []
        new_path.append(path[0])
        new_path.append(path[1])
        for i in range(1, len(path) - 1):
            p1 = new_path[i - 1]
            p2 = path[i]
            p3 = path[i + 1]
            p1, p2, p3 = round_segment(p1, p2, p3, roundness)
            new_path[i - 1] = p1
            new_path[i] = p2
            new_path.append(p3)
        # If the path is closed, we need (the handle of) the first point 
        if path[-1] == path[0]:
            p1 = new_path[-2]
            p2 = path[0]
            p3 = new_path[1]
            p1, p2, p3 = round_segment(p1, p2, p3, roundness)
            new_path[-2] = p1
            new_path[-1] = p2
            new_path[0] = p2
        return new_path
    else:
        return path


def round_segment(p1, p2, p3, roundness):
    if roundable(p1, p2, p3):
        p2_in, p2_out = create_handles(p1[0], p2[0], p3[0], roundness)
        p2 = [p2[0], p2_in, p2_out]
    return p1, p2, p3


def roundable(p1, p2, p3):
    # If two of the three points are in the same spot,
    # we can’t calculate a curve between two points.
    p1_anchor = p1[0]
    p2_anchor = p2[0]
    p3_anchor = p3[0]
    d12 = distance_between(p1_anchor, p2_anchor)
    d23 = distance_between(p2_anchor, p3_anchor)
    if d12 == 0 or d23 == 0:
        return False
    else:
        return True


def create_handles(A, B, C, smoothness):
    # A is the point before point B
    # B is the point to create the handles for
    # C is the point after point B
    d_AB = distance_between(A, B)
    d_BC = distance_between(B, C)
    # Create an isosceles triangle A, B, p4 based on triangle A, B, C.
    # Side B, p4 is the same length as side A, B.
    # Side B, p4 has the same direction as side B, C
    p4_x = ((C[0] - B[0]) * (d_AB / d_BC)) + B[0]
    p4_y = ((C[1] - B[1]) * (d_AB / d_BC)) + B[1]
    p4 = (p4_x, p4_y)
    
    if DEBUG:
        draw_handle(B, p4)
    
    # Calculate a point p5 on the base of the isosceles triangle,
    # exactly in between A and B.
    p5_x = A[0] + ((p4[0] - A[0]) / 2)
    p5_y = A[1] + ((p4[1] - A[1]) / 2)
    p5 = (p5_x, p5_y)

    if DEBUG:
        draw_point(p5, 10)
        draw_line(A, p4)

    # The line from the top of the isosceles triangle B to 
    # the point p5 on the base of that triangle
    # divides the corner p1, p2, p3 in two equal parts

    if DEBUG:
        draw_line(B, p5)

    # Direction of the handles is perpendicular
    vx = p5[0] - B[0]
    vy = p5[1] - B[1]
    handle_vx = 0
    handle_vy = 0 
    if vx == 0 and vy == 0:
        # The three points are on one line, so there will never be a curve.
        pass
    elif vx == 0:
        # prevent a possible division by 0
        handle_vx = 1
        handle_vy = 0
    elif vy == 0:
        # prevent a possible division by 0
        handle_vx = 0
        handle_vy = 1
    elif abs(vx) < abs(vy):
        handle_vx = 1
        handle_vy = vx / vy
    else:
        handle_vx = vy / vx
        handle_vy = 1

    # Define handles
    handle_a = (B[0] + handle_vx, B[1] - handle_vy)
    handle_b = (B[0] - handle_vx, B[1] + handle_vy)

    # The handle closest to point A will be the incoming handle of point B
    d_ha_A = distance_between(A, handle_a)
    d_hb_A = distance_between(A, handle_b)

    # I have to make this better. Also, where’s that 0.8 coming from? What was I thinking?
    incoming_handle_lenght = d_AB * smoothness
    outgoing_handle_length = d_BC * smoothness
    total_handle_length = incoming_handle_lenght + outgoing_handle_length
    max_handle_length = 0.8 * total_handle_length
    if incoming_handle_lenght > max_handle_length:
        outgoing_handle_length += incoming_handle_lenght - max_handle_length
        incoming_handle_lenght = max_handle_length
    if outgoing_handle_length > max_handle_length:
        incoming_handle_lenght += outgoing_handle_length - max_handle_length
        outgoing_handle_length = max_handle_length
    
    # finally, the in and out points
    if d_ha_A < d_hb_A:
        B_incoming = (B[0] + handle_vx * incoming_handle_lenght, B[1] - handle_vy * incoming_handle_lenght)
        B_outgoing = (B[0] - handle_vx * outgoing_handle_length, B[1] + handle_vy * outgoing_handle_length) 
    else:
        B_incoming = (B[0] - handle_vx * incoming_handle_lenght, B[1] + handle_vy * incoming_handle_lenght) 
        B_outgoing = (B[0] + handle_vx * outgoing_handle_length, B[1] - handle_vy * outgoing_handle_length)

    if DEBUG:
        draw_point(B_incoming, 6)
        draw_point(B_outgoing, 6)
        draw_line(B, B_incoming)
        draw_line(B, B_outgoing)
        draw_line(A, B)

    return B_incoming, B_outgoing


def distance_between(p1, p2):
    dx = p2[0] - p1[0]
    dy = p2[1] - p1[1]
    return pow((dx * dx + dy * dy), 0.5)


def draw_point(point, size):
    with savedState():
        fill(0, 0.7, 1)
        stroke(None)
        oval(point[0] - 0.5 * size, point[1] - 0.5 * size, size, size)


def draw_line(a, b):
    with savedState():
        fill(None)
        strokeWidth(1)
        stroke(0, 0.7, 1)
        line((100, 100), (900, 900))
        line(a, b)


def draw_handle(p, h):
    draw_point(p, 9)
    draw_line(p, h)


fill(None)

# Drawing the original shape and the rounded shape, slightly thicker.
stroke(1, 0, 0)
strokeWidth(2)
draw(jagged_line)
rounded_line = round_corners(jagged_line, 0.4)
strokeWidth(4)
draw(rounded_line)

# A rounding of 0.28 seems to get me as close to a circle as I can get.
stroke(0, 1, 0)
strokeWidth(2)
draw(rectangle)
rounded_rectangle = round_corners(rectangle, 0.28)
strokeWidth(4)
draw(rounded_rectangle)

# Rounding an oval by zero results in a rhombus.
stroke(0, 0, 1)
strokeWidth(2)
draw(circle)
rounded_circle = round_corners(circle, 0)
strokeWidth(4)
draw(rounded_circle)

This will make an animated gif with two frames, one frame with text, the other without, thus creating the illusion of flashing text.

w = 500
h = 500

newPage(w,h)
# Draw a black background
fill(0)
rect(0, 0, w, h)
# Draw gray text
fill(0.2)
font("Times-Italic", 190)
text("FLASH", (w/2, h/2), align="center")

newPage(w,h)
# Draw a black background
fill(0)
rect(0, 0, width(), height())

saveImage("rapid flashing.gif")

@pi That is exactly my solution. It’s not elegant, but it’s quick and it works.

Below is the Applescript I used. If you name your paths in Illustrator and put the names in pathNames it will copy the coordinates of the points and corresponding control points to an array you can paste in DrawBot.

on run
	set pathNames to {"segment_concave"}
	set pathsArray to "segment = ["
	
	tell application "Adobe Illustrator"
		activate
		set docRef to current document
		
		repeat with pathName in pathNames
			set pointsArray to "["
			set itemRef to path item pathName of docRef
			
			set pointsRef to every path point of itemRef
			repeat with pointRef in pointsRef
				-- anchor point
				set pointAsString to "["
				set x to my string_float(item 1 of anchor of pointRef)
				set y to my string_float(item 2 of anchor of pointRef)
				set pointAsString to pointAsString & "(" & x & "," & y & "), "
				
				-- left bcp
				set x to my string_float(item 1 of left direction of pointRef)
				set y to my string_float(item 2 of left direction of pointRef)
				set pointAsString to pointAsString & "(" & x & "," & y & "), "
				
				-- right bcp
				set x to my string_float(item 1 of right direction of pointRef)
				set y to my string_float(item 2 of right direction of pointRef)
				set pointAsString to pointAsString & "(" & x & "," & y & ")"
				
				set pointAsString to pointAsString & "]"
				set pointsArray to pointsArray & pointAsString & ", "
			end repeat
			set pointsArrayLength to length of pointsArray
			set pointsArray to (characters 1 through (pointsArrayLength - 2) of pointsArray) as string
			set pointsArray to pointsArray & "]"
			
			set pathsArray to pathsArray & pointsArray & ", "
		end repeat
		set pathsArrayLength to length of pathsArray
		set pathsArray to (characters 1 through (pathsArrayLength - 2) of pathsArray) as string
		set pathsArray to pathsArray & "]"
		
	end tell
	
	activate
	set the clipboard to pathsArray
	log pathsArray
end run



on string_float(s)
	set s to s as string
	set new_s to ""
	repeat with c in s
		if c as string is equal to "," then set c to "."
		set new_s to new_s & c as string
	end repeat
	return new_s
end string_float

Almost the same code, but instead of drawing a grid we draw 1000 circles randomly. As they have to stay in the same place, we save their locations in an array.

(Also in this script some nice code to have if you want to publish animated gifs; a way to reduce the colours in the gif.)

import random
import struct

frames = 24
page_size = 1000
number_of_circles = 1000
min_dot_size = 10
max_dot_size = 70
radius = 200


# create color table for gif
# https://stackoverflow.com/questions/6269765/what-does-the-b-character-do-in-front-of-a-string-literal
table = b""
greys = [0,85,170,255]
for i in greys:
    r = struct.pack(">B", i)
    g = struct.pack(">B", i)
    b = struct.pack(">B", i)
    table += r + g + b # + a


def draw_dot(center, diameter): 
    x = center[0] - diameter / 2
    y = center[1] - diameter / 2
    oval(x, y, diameter, diameter)


# Generate circles, randomly distributed
circles = []
for i in range(number_of_circles):
    x = random.randint(0,page_size)
    y = random.randint(0,page_size)
    circles.append((x,y))


for f in range(frames):
    percentage_animated = f / frames
    newPage()
    
    fill(0)
    rect(0, 0, page_size, page_size)

    for c in circles:
        x = c[0]
        y = c[1]
        distance = pow( (pow(x - page_size / 2, 2 ) + pow(y - page_size / 2, 2)), 0.5)
        distance = distance - percentage_animated * radius * 2
        distance = distance % (radius * 2)
        percentage = distance / radius
        if percentage > 1:
            percentage = 2 - percentage
        dot_size = min_dot_size + percentage * (max_dot_size - min_dot_size)
        fill(None)
        stroke(1)
        draw_dot((x,y), dot_size)
        
saveImage("animated.gif", imageGIFRGBColorTable = table)

frames = 24
page_size = 1000
grid_size = 20
grid_spacing = page_size / grid_size
min_dot_size = 10
max_dot_size = 50
radius = 100

def draw_dot(center, diameter): 
    x = center[0] - diameter / 2
    y = center[1] - diameter / 2
    oval(x, y, diameter, diameter)

for f in range(frames):
    percentage_animated = f / frames
    newPage()
    
    fill(0)
    rect(0, 0, page_size, page_size)

    for row in range(grid_size):
        for column in range(grid_size):
            x = row * grid_spacing + grid_spacing / 2
            y = column * grid_spacing + grid_spacing / 2
            # Calculate distance from (x,y) of the dot to the center of the page
            distance = pow( (pow(x - page_size / 2, 2 ) + pow(y - page_size / 2, 2)), 0.5)
            # The wave must seem to move, so for every frame in the 
            # animation, add a precentage of the length of the wave.
            # Add or substract to change direction.
            distance = distance - percentage_animated * radius * 2
            # Use modulo to get a distance between 0 and double the radius
            distance = distance % (radius * 2)
            # The wave has a lenghth of double the radius. In the 
            # first halve of the lenght, the dots get larger, in the 
            # second halve the dots get smaller.
            # So, we calculate a percentage between 0 and 2, and when
            # the percentage is larger than 1, we count backwards.
            percentage = distance / radius
            if percentage > 1:
                percentage = 2 - percentage
            dot_size = min_dot_size + percentage * (max_dot_size - min_dot_size)
            fill(1)
            draw_dot((x,y), dot_size)
        
saveImage("animated.gif")

A simple example of how to move the wave through a grid of dots. The position of the dots does not matter.

@frederik probably has a better and more robust solution for this also

2. I don’t think you need a radial grid.

If you base the timing of the animation of one hexagon on its distance to the center point, I believe you get the same effect as in your example.

1. Changing the bezier-handle is a simple as calculating a point between two extremes, based on a percentage, based on how far you are in your animation.

(Check out easings.net to create smoother animations)

frames = 12

def draw_segment(percentage):
    first_point = (-500, 0)
    first_control_point_convex = (-500, 185.191467285156)
    first_control_point_concave = (-350.388183585986, 86.410583482659)
    second_control_point_convex = (-399.316345214836, 346.863525390625)
    second_control_point_concave = (-249.704528786313,248.082641579087)
    second_point = (-249.704528808587, 433.274108886719)
    # Calculate in-between points based on percentage
    fcpcx = first_control_point_convex[0] + percentage * (first_control_point_concave[0] - first_control_point_convex[0])
    fcpcy = first_control_point_convex[1] + percentage * (first_control_point_concave[1] - first_control_point_convex[1])
    scpcx = second_control_point_convex[0] + percentage * (second_control_point_concave[0] - second_control_point_convex[0])
    scpcy = second_control_point_convex[1] + percentage * (second_control_point_concave[1] - second_control_point_convex[1])
    first_control_point = (fcpcx, fcpcy)
    second_control_point = (scpcx, scpcy)
    # Make and draw path
    bez = BezierPath()
    bez.moveTo(first_point)
    bez.curveTo(first_control_point, second_control_point, second_point)
    drawPath(bez)

def draw_hexagon(percentage):
    for i in range(6):
        with savedState():
            translate(500,500)
            scale(0.5, 0.5)
            rotate(i * 60, center=(0, 0))
            draw_segment(percentage)

for i in range(frames):
    newPage()

    fill(None)
    stroke(0)
    strokeWidth(10)

    percentage = i / frames
    draw_hexagon(percentage)

for i in range(frames, 0, -1):
    newPage()

    fill(None)
    stroke(0)
    strokeWidth(10)

    percentage = i / frames
    draw_hexagon(percentage)

saveImage("animated.gif")

1. Without doing too much math, and using some ugly constants, you can draw a segment of the hexagon.

Draw and rotate it six times, and you have the basis of the hexagon.

def draw_segment():
    # Coordinates based on a circle with diameter 1000 and center at 0,0
    first_point = (-500, 0)
    first_control_point = (-500, 185.191467285156)
    second_control_point = (-399.316345214836, 346.863525390625)
    second_point = (-249.704528808587, 433.274108886719)
    # Make and draw path
    bez = BezierPath()
    bez.moveTo(first_point)
    bez.curveTo(first_control_point, second_control_point, second_point)
    drawPath(bez)

def draw_hexagon():
    for i in range(6):
        with savedState():
            translate(500,500)
            scale(0.5, 0.5)
            rotate(i * 60, center=(0, 0))
            draw_segment()

newPage()

fill(None)
stroke(0)
strokeWidth(10)
draw_hexagon()

@pi I think it’s doable. What do you have so far? To which questions didn’t you find an answer?

@rohernandezz You don’t have ~/Library/Preferences/com.drawbot.plist ?

@MauriceMeilleur

An arbitrary amount of circles seemingly overlapping:

import random

number_of_circles = 10
radius = 100
wobble = 400
canvas_size = 1000

circles = []
drawn_circles = []
center = canvas_size / 2

# Create circles
for i in range(number_of_circles):
    x  = center - (wobble * 0.5) + random.random() * wobble
    y  = center - (wobble * 0.5) + random.random() * wobble
    circle = BezierPath()
    circle.oval(x - radius, y - radius, radius * 2, radius * 2)
    circles.append(circle)

# Check if circles overlap
for circle in circles:
    for i in range(len(drawn_circles)):
        intersecting_shape = circle.intersection(circles[i])
        if len(intersecting_shape.points) > 0:
            circle = circle.difference(circles[i])
    drawn_circles.append(circle)

# Draw circles, or what’s left of them
newPage(canvas_size, canvas_size)
fill(None)
stroke(0)
for circle in drawn_circles:
    drawPath(circle)

radius = 300
circle_size = 300
step = 3
x, y = 500, 500

fill(1)
stroke(0)

for d in range(0, 360, step):
    circle1 = BezierPath()
    circle1.oval(x - circle_size / 2, y - circle_size / 2, circle_size, circle_size)
    circle1.translate(0, radius)
    circle1.rotate(d, (x, y))

    circle2 = BezierPath()
    circle2.oval(x - circle_size / 2, y - circle_size / 2, circle_size, circle_size)
    circle2.translate(0, radius)
    circle2.rotate(d + step, (x, y))
    
    dif = circle2.difference(circle1)
    drawPath(dif)

In response to https://twitter.com/MauriceMeilleur/status/1242196482717110274

@frederik You opened a door to a whole new world for me. This is much simpler than I thought. And at the same time, I think it’s going to take me some time to get my head around all this pen-stuff. Thanks!

Is there an easy way to add anchor points to a path, like the Add Anchor Points command in Illustrator?

(I looked here and in the documentation, but I can’t find it.)

Thanks for the tip @gferreira

Running the script and saving to a gif is faster, only two seconds though. But not having to wait for the Drawbot app to finish is a great improvement.

I create animated gifs with Drawbot. They’re somewhat complex and take some time to proces and draw. After calculating, drawing, and saving all frames to a gif, Drawbot remains unresponsive. It seems it needs considerable time to draw the canvases in the app.

For example, for my last animation it took 69 seconds to calculate and save 78 frames to a gif, and then an extra 25 seconds for Drawbot to start drawing 78 canvases — the (actual, visible) drawing takes less than a second — and become responsive again.

I’m a little curious why this is. If the canvases can be saved as a gif, they should be already be there? Why should it take that much time to draw them on screen?

And, is it possible to only save as gif, and not draw the canvas in the Drawbot app?

Screen recording on youtube

Saving of the gif at 1:08

Drawbot draws canvases and becomes responsive at 1:34

The gif on twitter.