This is a python library for pattern cutting.
Vector class
A class for 2d cartesian coordinates. Its used for point coordinates and also for 2d vectors
from src.geometry.Vector import Vector
origin = Vector(0,0)
origin.label = "Origin"
You can use the render function to generate an SVG representation of the geometry
from src.render import render
render(origin)
Shape
A Shape object is defined by multiple points which are joined by line
segemnts to create a complicated line or shape.
from src.geometry.Shape import Shape
square = Shape([
Vector(0, 0),
Vector(100, 0),
Vector(100, 100),
Vector(0, 100),
Vector(0, 0)]
).with_label("a square").with_style("polygon")
render(square)
Using the style property, a polyline can be rendered as many different
kinds of shapes.
from layout import topToBottom
shape = Shape([Vector(0, 0), Vector(100, 50), Vector(200, -50), Vector(300, 0)])
render(
*topToBottom(
shape.with_style("line").with_label("line"),
shape.with_style("dashed").with_label("dashed"),
shape.with_style("arrow").with_label("arrow"),
shape.with_style("dashed_arrow").with_label("dashed_arrow"),
shape.with_style("pointset").with_label("pointset"),
shape.with_style("polygon").with_label("polygon"),
shape.with_style("tape").with_label("tape"),
shape.with_style("ruler").with_label("ruler")
)
)
You can draw measurement markers along a polyline:
render(
square,
*square.evenlySpacedMeasurements()
)
Or automatically detect corners:
corners = square.corners()
render(
square,
*[corner.with_label("Here is a corner!") for corner in corners]
)
You can slice out a certain portion of a line:
from layout import process
from src.geometry.Group import Group
P = square.at(25).point.with_label("P")
Q = square.at(175).point.with_label("Q")
render(
*process(
Group(
square,
P,
Q,
),
Group(
square.slice(25, 175),
P, Q
)
)
)
The circle class can be used to generate regular polygons with so many sides they look like a circle:
from src.geometry.Circle import Circle
circle = Circle(Vector(0, 0), 100)
triangle = circle.polyline(3)
hexagon = circle.polyline(6)
almostCircle = circle.polyline(50)
from layout import sideBySide
render(*sideBySide(triangle, hexagon, almostCircle))
We can put this together to get good approximations of measurements along a curve:
arc = circle.polyline(100).slice(0, 150)
render(
arc,
*arc.evenlySpacedMeasurements()
)
Bezier Curves
from src.geometry.Shape import dashed
from src.geometry.bezier import BezierCurve
p0 = Vector(0,0).with_label("p0")
p1 = Vector(0, 50).with_label("p1")
p2 = Vector(50, 50).with_label("p2")
p3 = Vector(50, 100).with_label("p3")
mycurve = BezierCurve(p0, p1, p2, p3)
render(
mycurve.demo()
)
Interpolating a Shape with Bezier Curves
myshape = Shape([Vector(0,0), Vector(0, 200), Vector(200,250), Vector(250, 150), Vector(300 , 300)])
render(
myshape.with_style("dashed"),
myshape.interpolate(),
)
This makes a lot of points apear, so it might be a good idea to resample the curve at lower resolution:
interpolated = myshape.interpolate()
downsampled = interpolated.resample(25)
render(
*topToBottom(
interpolated.with_style("pointset"),
downsampled.with_style("pointset").with_label("Re-sampled")
)
)
Demonstrating different curve speeds
gen = [myshape]
for i in range(0, 20):
next = myshape.interpolate((i+1) / 4)
gen.append(next)
render(*gen)
Finding the closest point on a polyline
We can find the closest point on a polyline to any given coordinate:
from src.geometry.Shape import dashed_arrow
shape = arc
X = Vector(90, 100)
Y = shape.closestPoint(X)
render(
shape,
X.with_label("X"),
Y.with_label("Y"),
dashed_arrow(X, Y)
)
You can use closest points in other methods too, such as slice
shape = arc
P = Vector(90, 100).with_label("P")
Q = Vector(100, 0).with_label("Q")
sliced = shape.slice(P, Q)
render(
*process(
Group(
P,
Q,
dashed_arrow(P, shape.at(P).point),
shape.with_label("Original"),
),
Group(
sliced.with_label("sliced"),
*sliced.points, P, Q
)
)
)
Replacing a section of a shape
Here are two shapes
a = Shape([Vector(-100, 200), Vector(200, -100)])
b = arc
render(a.with_label("a simple shape"), b.with_label("replacement"))
We can replace a region of one with the other
render(a.replace(b))
Tweening between shapes
Tweening lets you morph one shape smoothly into another:
from src.geometry.tween import tween, tween_demo
a = Shape([Vector(-100, 200), Vector(200, -100)])
b = arc
render(tween_demo(a, b))
A circle becoming a square,
render(tween_demo(square, circle.polyline(100)))
Turtle/Spirograph curves
import math
from src.spirograph import spiro
angle_over_length = lambda x : math.radians(x*.1)
spiral = spiro(angle_over_length, 10000)
render(spiral)
Adding darts
shape = Shape([Vector(0,0), Vector(100, 0)])
shape.addDart(Vector(50, 0), 50, 20)
render(shape)
shape = Shape([Vector(0,0), Vector(0, 100)])
shape.addDart(Vector(0, 50), 50, 20)
render(shape)
Collision detection
Collision detection is powered by the qwertyquerty/collision library.
from src.geometry.Shape import rectangle
example_shape = rectangle(0, 0, 100, 100)
example_points = [Vector(50, 50), Vector(150, 50)]
for p in example_points:
if example_shape.point_is_inside(p):
p.label = "Collision!"
else:
p.label = "No collision!"
render(example_shape, *example_points)
Lets try something a bit trickier:
from aldrich.tailored_skirt_block import tailored_skirt_block
from src.point_grid import point_grid_over_shape
example_shape = tailored_skirt_block()["back"]
points = []
for point in point_grid_over_shape(example_shape, margin=17):
if example_shape.point_is_inside(point):
points.append(point)
render(example_shape.with_style("all_guides"), *points)
Triangulation
Turning a polygon into triangles:
render(example_shape.earclip_mesh())data:application/object;charset=us-ascii;base64,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
Sewing up the darts:
mesh = example_shape.earclip_mesh()
sides = example_shape.sides()
mesh.add_seam(sides[7], sides[8].reverse())
mesh.add_seam(sides[4], sides[5].reverse())
render(mesh)data:application/object;charset=us-ascii;base64,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
Die Lemma dress block
One of the main applications of this library is to create outfits for East London drag queen Die Lemma.
A dress block for Die was created and digitised into this library:
from DieLemmaDressBlock import DieLemmaDressBlock
render(DieLemmaDressBlock)
Drawing parallels to a complex polyline:
render(
DieLemmaDressBlock,
DieLemmaDressBlock.parallel(50),
*[dashed_arrow(P, Q) for P,Q in zip(DieLemmaDressBlock.points, DieLemmaDressBlock.parallel(50).points)],
*DieLemmaDressBlock.points
)
or drawing inside the shape instead of outside,
render(
DieLemmaDressBlock,
DieLemmaDressBlock.parallel(-25),
*[dashed_arrow(P, Q) for P,Q in zip(DieLemmaDressBlock.points, DieLemmaDressBlock.parallel(-25).points)],
*DieLemmaDressBlock.points
)
Winnifred Aldrich pattern blocks
One application of this library is quickly producing pattern blocks from Winnfred Aldrich’s book. To do that, we have to be able to use describe body measurements:
from src.sizing.BodyMeasurements import example_body_measurements
print(example_body_measurements)Size 24.74583333333333:
waist = 725.0mm (-297.4mm)
hips = 900.0mm (-338.6mm)
waist_to_hip = 265.0mm (+39.9mm)
body_rise = 340.0mm (+8.3mm)
bust = 1182.4mm
low_waist = 1122.4mm
back_width = 417.2mm
chest = 414.7mm
shoulder = 140.1mm
neck_size = 443.2mm
dart = 108.2mm
top_arm = 379.5mm
wrist = 196.6mm
ankle = 276.6mm
high_ankle = 246.6mm
nape_to_waist = 435.5mm
front_shoulder_to_waist = 462.4mm
armscye_depth = 240.2mm
waist_to_knee = 616.9mm
waist_to_floor = 1103.7mm
sleeve_length = 608.4mm
sleeve_length_jersey = 568.4mm
cuff_size_shirts = 241.9mm
cuff_size_two_piece_sleeve = 153.4mm
trouser_bottom_width = 251.9mm
jeans_bottom_width = 210.0mmTrouser block
from TheClassicTailoredTrouserBlock import TheClassicTailoredTrouserBlock
render(TheClassicTailoredTrouserBlock())
Skirt block
from aldrich.tailored_skirt_block import tailored_skirt_block
render(tailored_skirt_block())
Here it is with the seam and hems marked,
from aldrich.tailored_skirt_block import tailored_skirt_pattern
render(tailored_skirt_pattern())Warning: creating french seam on two lines with different length: 612.9753811041546 and 613.3124368403252
I’m planning a long flared skirt.
render(tailored_skirt_pattern(skirt_length=940, flare=1.4))Warning: creating french seam on two lines with different length: 958.9489488731247 and 959.2860046092952
Warning: creating french seam on two lines with different length: 958.9489488731247 and 959.2860046092952
Working in 3D
Turn a 2d shape into 3d one (and back again to render it):
import numpy as np
square3d = square.to_3D()
render(
*[
square3d.rotate(pitch=angle).isometric() for angle in np.arange(0, 6.28, 0.3)
]
)
Tweening radially,
shape_1 = Shape([Vector(0,0), Vector(50, -100)])
shape_2 = Shape([Vector(0,0), Vector(50, -15), Vector(50, -200)])
render(*[
tween(shape_1, shape_2, phase).to_3D().rotate(pitch=phase * 3.14).isometric() for phase in np.arange(0, 1, .05)
])
The Mesh class
For cloth simulation, we need to create a triangular mesh:
from src.geometry.Mesh import mesh_grid
render(mesh_grid(300, 300))
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Interupting the mesh with a new point:
my_mesh = mesh_grid(300, 300)
my_mesh.interupt_point((105, 115))
render(my_mesh)data:application/object;charset=us-ascii;base64,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
I want to sew the sides of this together to make a tube.O
tube = mesh_grid(300, 300)
left_side = Shape([Vector(0,0), Vector(0, 250)])
right_side = Shape([Vector(250,0), Vector(250, 250)])
tube.add_seam(left_side, right_side)
render (tube)data:application/object;charset=us-ascii;base64,v 0 0 0.0
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v 100 0 0.0
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v 150 125 0.0
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v 0 150 0.0
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v 250.0 0.0 0.0
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v 250.0 40.0 0.0
v 0.0 50.0 0.0
v 250.0 50.0 0.0
v 0.0 60.0 0.0
v 250.0 60.0 0.0
v 0.0 70.0 0.0
v 250.0 70.0 0.0
v 0.0 80.0 0.0
v 249.99999999999997 80.0 0.0
v 0.0 90.0 0.0
v 250.0 90.0 0.0
v 0.0 100.0 0.0
v 250.0 100.0 0.0
v 0.0 110.0 0.0
v 250.0 110.0 0.0
v 0.0 120.0 0.0
v 250.0 120.0 0.0
v 0.0 130.0 0.0
v 250.0 130.0 0.0
v 0.0 140.0 0.0
v 250.0 140.0 0.0
v 0.0 150.0 0.0
v 250.0 150.0 0.0
v 0.0 160.0 0.0
v 250.0 160.0 0.0
v 0.0 170.0 0.0
v 250.0 170.0 0.0
v 0.0 180.0 0.0
v 250.0 180.0 0.0
v 0.0 190.0 0.0
v 250.0 190.0 0.0
v 0.0 200.0 0.0
v 250.0 200.0 0.0
v 0.0 210.0 0.0
v 250.0 210.0 0.0
v 0.0 220.0 0.0
v 250.0 220.0 0.0
v 0.0 230.0 0.0
v 250.0 230.0 0.0
v 0.0 240.0 0.0
v 250.0 240.0 0.0
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f 185 183 94
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Making a skirt for myself
I would like a skirt. To get one, I’ve measured my body a little bit:
joelle_waist = 725
joelle_hips = 900
joelle_waist_to_hips = 265I’ve also decided a few dimensions of the skirt I’d like to make:
skirt_length_below_the_hips = 380
skirt_bottom_circumference = 1200Here is a graph plotting the circumference of the skirt over height:
from src.geometry.Shape import measurement_from_y_axis
skirt_circumference_graph = Shape()
origin = Vector(0,0)
waist_point = Vector(joelle_waist, 0)
hips_point = Vector(joelle_hips, -joelle_waist_to_hips)
hem_point = Vector(skirt_bottom_circumference, -joelle_waist_to_hips - skirt_length_below_the_hips)
skirt_circumference_graph.lineTo(waist_point)
skirt_circumference_graph.lineTo(hips_point)
skirt_circumference_graph.lineTo(hem_point)
render(
skirt_circumference_graph.close_against_y_axis(),
origin,
measurement_from_y_axis(waist_point),
measurement_from_y_axis(hips_point),
measurement_from_y_axis(hem_point)
)
This is the circumference of the skirt over elevation. But I think what I need (in order to get the scrolled hem I’m looking for) is the radius. To keep it simple I’ll imagine the skirt as a circlular prism with radius varying across its length.
skirt_radius_graph = Shape([Vector(p.x / (2*math.pi), p.y) for p in skirt_circumference_graph.points])
render(skirt_radius_graph)
This is a reasonable approximation for the silhouette of the skirt.
Now I’ll add the scroll
skirt_radius_graph.continue_with_arc(175, 2*math.pi)
render(skirt_radius_graph)
Here’s what it should look like in 3d:
render(*[
skirt_radius_graph.to_3D().rotate(pitch=angle).isometric() for angle in np.arange(0, math.pi*2, .1)
])
Now I’ve found a silhouette I like, I’ll unwrap this by length onto the y-axis.
final_radius_graph = Shape()
for w in np.arange(0, skirt_radius_graph.length, 10):
x = skirt_radius_graph.pointAlong(w).x
p = Vector(x, -w)
final_radius_graph.lineTo(p)
render(final_radius_graph.close_against_y_axis())
Next we transform this back into a circumference graph
final_circumference_graph = Shape(
[Vector(x = p.x * 2*math.pi, y=p.y) for p in final_radius_graph.points]
)
render(final_circumference_graph.close_against_y_axis())
Wow mad. Finally, lets subdivide this into 10 pattern pieces:
pattern_shape = final_circumference_graph.close_against_y_axis().subdivide_by_width(10)
render(pattern_shape)
Now I just need to add some seam & hem allowances. While I’m at it, I’ll make a pattern for the boning channel.
from src.geometry.Shape import rectangle
pattern_piece = Group(
shape=pattern_shape,
right_side = pattern_shape.sides()[0].with_style("line"),
left_side = pattern_shape.sides()[2].with_style("line").reverse(),
right_allowance = pattern_shape.sides()[0].allowance(-20),
left_allowance = pattern_shape.sides()[2].allowance(-20),
center_line = pattern_shape.vertical_center_line(),
)
boning = rectangle(pattern_shape.x_center() - 6, pattern_shape.bottom, 12, pattern_shape.height).with_label("12mm boning channel")
render(
*sideBySide(
pattern_piece,
Group(
boning,
boning.allowance(-12)
)
)
)
Here is a demo of the construction in 3D:
pattern_piece_3d = pattern_piece.to_3D()
pieces = []
for phase in np.arange(0, 1, 1.0/10.0):
pieces.append(pattern_piece_3d.translate(z=1000).rotate(pitch=phase * 2 * math.pi).isometric())
from src.geometry.seam_lines import seam_lines
all = []
for i in range(len(pieces)):
a = pieces[i]
b = pieces[(i+1)%len(pieces)]
all.append(a)
all.append(seam_lines(a["left_side"], b["right_side"]))
render(*all)