Intertwined

Draw intertwined threads, knots and knitting figures with PyCairo

Overall Idea

Threads (paths) are made of segments (Bezier curves) with their own z-depth.

Segments are drawn in z-depth order, so that threads look Intertwined.

Control points are either set explicitely by the caller, or computed according to specific rules.

Here are the drawing steps, starting from lowest z-depth, here for Braid.py.

Architecture

There are three classes, stacked in a layer model.

Canvas - the surface where to draw
Thread - a specific thread, attached to a canvas
Segment - a portion of a thread, with its own z-depth

API

The caller only interacts with Canvas, which exposes methods to create and move threads.

cv = Canvas(...)
t = cv.create_thread(...)
cv.arc_to(t, ...)
cv.arc_rel(t, ...)
cv.draw(...)

Whenever a thread is moved, a segment is added to the thread.

Segments are cubic Bezier curves, defined by two endpoints and two control points.

Control points logic

When not set by the caller, control points are calculated as follows:

• cp1: symetric to previous segement cp2 around segment origin
• cp2: from segment end towards segment cp1, same length as origin to cp1

No control points are set explicitely on 1st segment s1. Control point s1.cp2 is computed as half s.p_s.o. Control point s2.cp1 (red) is computed according to previous segment s1.cp2 (green). Control point s2.cp2 is computed as s2.p_s2.cp1 with samed length as s2.cp1.	t = cv.create_thread(o = (1,2)) cv.arc_rel(t, 5, -1, 1) cv.arc_rel(t, 2, 5, 1)
s1.cp1 is set, s1.cp2 is calculated accordingly. Orientation propagates to s2.cp1.	t = cv.create_thread(o = (1,2)) cv.arc_rel(t, 5, -1, 1, cp1=(1,-2)) cv.arc_rel(t, 2, 5, 1)
s1.cp2 is set, s2.cp1 is calculated accordingly.	t = cv.create_thread(o = (1,2)) cv.arc_rel(t, 5, -1, 1, cp2=(0,-2)) cv.arc_rel(t, 2, 5, 1)
Both control points are set for s1.	t = cv.create_thread(o = (1,2)) cv.arc_rel(t, 5, -1, 1, cp1=(1,-2), cp2=(0,-2)) cv.arc_rel(t, 2, 5, 1)

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Sample Drawings

Crochet.py

from Intertwined import *

cv = Canvas(47, 25)
        
v_offset = 6

for row in range(3):

    t = cv.create_thread(o = (1, 10 + (v_offset*row)))
    
    for col in range(3):

        cv.arc_rel(t,  8,  0, 1, cp1=(2, 2), cp2=(-2, 2))
        cv.arc_rel(t, -2, -8, 1, cp2=(-2, 2))
        cv.arc_rel(t,  8,  0, 0, cp2=(-2,-2))
        cv.arc_rel(t, -2,  8, 1, cp2=(-2,-2))
    
    cv.arc_rel(t,  8,  0, 1, cp2=(-2, 2))

cv.draw()

cv.surface.write_to_png("crochet.png")

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Knots.py

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Node.py

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Drawing Options

Draw Grid	cv.draw(draw_grid=True)
Stretch Grid	cv = Canvas(10, 8, col_size=20, row_size=30)
Draw Points	cv.draw(draw_points=True)
Draw Control Points	cv.draw(draw_cp=True)
Draw Depth	cv.draw(draw_depth=True)
Draw All	cv.draw(draw_grid=True, draw_points=True, draw_cp=True, draw_depth=True)