"""2026-03-07
Divisões 04
Inspirado em sketch de Alexandre Villares
ericof.com|https://abav.lugaralgum.com/sketch-a-day/#sketch_2026_02_16
png
Sketch,py5,CreativeCoding
"""
from collections import deque
from dataclasses import dataclass
from dataclasses import field
from shapely import Polygon
from sketches.utils.draw import canvas
from sketches.utils.draw.cores.paletas import gera_paleta
from sketches.utils.helpers import sketches as helpers
import numpy as np
import py5
sketch = helpers.info_for_sketch(__file__, __doc__)
cor_fundo = py5.color(0)
paleta: deque[int] = gera_paleta("pastel", como_deque=True)
divisoes: int = 4
@dataclass
class InfoGrupo:
vs: list = field(default_factory=list)
shapes: list = field(default_factory=list)
areas: list = field(default_factory=list)
max_area: float = 0.0
shape: py5.Py5Shape | None = None
grupos: dict[int, InfoGrupo] = {}
intensidade: float = 0.0008
fator: float = 1.1
distorcao_va = 1.5
def start(idx: int, largura: int, altura: int):
"""Initialize a division group from a rectangle covering the internal canvas."""
vs = [np.array(pt) for pt in ((0, 0), (largura, 0), (largura, altura), (0, altura))]
shapes = []
shapes.append((0, 1, 2, 3))
areas = [shape_area((0, 1, 2, 3), vs)]
grupos[idx] = InfoGrupo(
shape=None, vs=vs, shapes=shapes, areas=areas, max_area=max(areas)
)
def _divide_quadrado(
shp: tuple[int, ...], vs: list, div: int = 2
) -> list[tuple[int, ...]]:
"""Divide a quadrilateral into triangles based on div.
div=2: split along the shorter diagonal → 2 triangles, no new points.
div=3: midpoint of the shorter diagonal added → 3 triangles; the two
half-triangles each have area S/4 and the intact half has S/2
(best achievable balance with a single added point).
div=4: centroid added → 4 triangles, each S/4 for parallelograms and
approximately equal for distorted quads.
"""
a, b, c, d = shp
ac = py5.dist(*vs[a], *vs[c])
bd = py5.dist(*vs[b], *vs[d])
if div == 2:
return [(a, b, c), (a, c, d)] if ac < bd else [(a, b, d), (b, c, d)]
if div == 3:
if ac < bd:
# Shorter diagonal is AC. Add its midpoint and fan from b,
# splitting triangle (a,b,c) while keeping (a,c,d) intact.
mi = len(vs)
vs.append((vs[a] + vs[c]) / 2)
return [(b, mi, a), (b, c, mi), (a, c, d)]
else:
# Shorter diagonal is BD. Add its midpoint and fan from a,
# splitting triangle (a,b,d) while keeping (b,c,d) intact.
mi = len(vs)
vs.append((vs[b] + vs[d]) / 2)
return [(a, b, mi), (a, mi, d), (b, c, d)]
# div == 4: add centroid and fan to all four edges → 4 triangles.
gi = len(vs)
vs.append((vs[a] + vs[b] + vs[c] + vs[d]) / 4)
return [(a, b, gi), (b, c, gi), (c, d, gi), (d, a, gi)]
def _divide_trinagulo(
shp: tuple[int, ...], vs: list, div: int = 2
) -> list[tuple[int, ...]]:
"""Divide a triangle into smaller triangles based on edge lengths."""
a, b, c = shp
ab = py5.dist(*vs[a], *vs[b])
bc = py5.dist(*vs[b], *vs[c])
new_shapes = []
if ab != bc:
abi = len(vs)
vs.append((vs[a] + vs[b]) / div)
bci = len(vs)
vs.append((vs[b] + vs[c]) / div)
aci = len(vs)
vs.append((vs[a] + vs[c]) / div)
new_shapes.append((a, abi, aci))
new_shapes.append((abi, b, bci, aci))
new_shapes.append((bci, c, aci))
else:
i = len(vs)
if ab > bc:
vs.append((vs[a] + vs[b]) / div)
new_shapes.append((a, i, c))
new_shapes.append((i, b, c))
if bc > ab:
vs.append((vs[b] + vs[c]) / div)
new_shapes.append((b, i, a))
new_shapes.append((i, c, a))
else:
vs.append((vs[a] + vs[c]) / div)
new_shapes.append((a, i, b))
new_shapes.append((i, c, b))
return new_shapes
SPLIT_SHAPE = {
3: _divide_trinagulo,
4: _divide_quadrado,
}
def split_shapes(idx: int):
"""Create the next subdivision level for the given group index."""
info = grupos.get(idx)
if info and info.shape:
# Não é necessário dividir novamente se já temos um grupo
# para essa quantidade de divisões
return
idx_anterior = idx - 1 if idx > 1 else 1
anterior = grupos[idx_anterior]
shapes = anterior.shapes
vs = list(anterior.vs)
new_shapes = []
while shapes:
shp = shapes.pop()
total = len(shp)
div = 2 if total == 3 else py5.random_int(2, 4)
split_fn = SPLIT_SHAPE.get(total)
if split_fn:
new_shapes.extend(split_fn(shp, vs, div))
areas = [shape_area(shp, vs) for shp in new_shapes]
info = InfoGrupo(
shape=None, vs=vs, shapes=new_shapes, areas=areas, max_area=max(areas)
)
grupos[idx] = info
group_shape(idx)
def distort(idx: int, intensity=intensidade, f=fator):
"""Apply radial distortion to the group's vertices based on center distance."""
info = grupos[idx]
vs = info.vs
meio = helpers.DIMENSOES.internal[0] / 2, helpers.DIMENSOES.internal[1] / 2
va = np.array(vs)
va -= np.array((meio[0], meio[1]))
distances = np.linalg.norm(va, axis=1)
scaling_factors = 1 + (intensity * (distances**f))
va = distorcao_va * va / scaling_factors[:, np.newaxis]
va += np.array(meio)
info.vs = va
_group_shape(info)
def _group_shape(info: InfoGrupo):
"""Build and store a py5 group shape from an `InfoGrupo` definition."""
grupo = py5.create_shape(py5.GROUP)
shapes = info.shapes
areas = info.areas
vs = info.vs
for shp, _ in zip(shapes, areas, strict=False):
poly = py5.create_shape()
pts = np.array(vs)[np.array(shp)]
with poly.begin_closed_shape():
poly.vertices(pts)
cor = paleta[0]
paleta.rotate()
poly.set_fill(cor)
poly.set_stroke_weight(4)
grupo.add_child(poly)
info.shape = grupo
def group_shape(idx: int):
"""Create a renderable group shape for a stored subdivision group."""
info = grupos[idx]
if info.shape:
# Já temos um shape para esse grupo, não precisamos recriar
print(f"Shape para {idx} divisões já existe. Pulando criação.")
return
_group_shape(info)
def shape_area(shp, vs):
"""Return the polygon area for a shape index tuple over a vertex list."""
return Polygon(np.array(vs)[np.array(shp)]).area
def setup():
"""Configure the sketch and precompute subdivision groups up to `divisoes`."""
py5.size(*helpers.DIMENSOES.external, py5.P3D)
for idx in range(1, divisoes + 1):
start(idx, *helpers.DIMENSOES.internal)
split_shapes(idx=idx)
def draw():
"""Render the current subdivision group and update frame overlay metadata."""
py5.background(cor_fundo)
info = grupos[divisoes]
grupo = info.shape
if grupo:
with py5.push():
py5.shape_mode(py5.CENTER)
py5.translate(*helpers.DIMENSOES.centro)
py5.shape(grupo)
fps = py5.get_frame_rate()
py5.window_title(f"Divisões: {divisoes} - Frame Rate: {fps:.2f}")
# Credits and go
canvas.sketch_frame(
sketch,
cor_fundo,
"large_transparent_white",
"transparent_white",
version=2,
)
def key_pressed():
"""Handle keyboard controls for saving, subdividing, and distortion."""
global divisoes
key = py5.key
if key == " ":
save_and_close()
elif key == "r":
start(*helpers.DIMENSOES.internal)
elif key == "a":
divisoes -= 1 if divisoes > 1 else 0
split_shapes(divisoes)
elif key == "d":
divisoes += 1
split_shapes(divisoes)
elif key == "w":
distort(divisoes)
def save_and_close():
"""Stop rendering, save the current frame, and exit the sketch."""
py5.no_loop()
canvas.save_sketch_image(sketch)
py5.exit_sketch()
if __name__ == "__main__":
py5.run_sketch()
