"""2026-03-09
Divisões 06
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 import lerp_color_rgba
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)
)
return grupos
def _divide_quadrado(
idx: int, 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])
gi = len(vs)
vs.append((vs[a] + vs[b] + vs[c] + vs[d]) / gi)
new_shapes = [(a, b, c), (a, c, d)] if ac < bd else [(a, b, d), (b, c, d)]
match div:
case 3:
s = new_shapes.pop(-1)
new_shapes.append((s[0], s[1], gi))
new_shapes.append((gi, s[1], s[2]))
case 4:
new_shapes = [(a, b, gi), (b, c, gi), (c, d, gi), (d, a, gi)]
case _:
new_shapes = new_shapes
print(f"{idx} - 4 -> {len(new_shapes)}")
return new_shapes
def _divide_trinagulo(
idx: int, 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])
ab_m = (vs[a] + vs[b]) / div
bc = py5.dist(*vs[b], *vs[c])
bc_m = (vs[b] + vs[c]) / div
ca = py5.dist(*vs[c], *vs[a])
ca_m = (vs[c] + vs[a]) / div
new_shapes = []
if ab == bc == ca:
bci = len(vs)
vs.append(bc_m)
new_shapes.append((a, b, bci))
new_shapes.append((bci, a, c))
elif ab == bc:
cai = len(vs)
vs.append(ca_m)
new_shapes.append((a, b, cai))
new_shapes.append((cai, a, c))
elif bc == ca:
abi = len(vs)
vs.append(ab_m)
new_shapes.append((a, c, abi))
new_shapes.append((abi, b, c))
else:
new_shapes.append((a, c, b))
new_shapes.append((b, a, c))
print(f"{idx} - 3 -> {len(new_shapes)}")
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(idx, 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
formas = list(zip(shapes, areas, strict=False))
for shp, _ in formas:
poly = py5.create_shape()
cor = paleta[0]
cor_proxima = paleta[1]
pts = np.array(vs)[np.array(shp)]
total = len(pts)
with poly.begin_closed_shape():
poly.vertices(pts)
cores = []
for i in range(total):
cor = lerp_color_rgba(cor, cor_proxima, i, (0, total))
cores.append(cor)
poly.set_fills(cores)
poly.set_stroke_weight(4)
grupo.add_child(poly)
paleta.rotate()
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):
grupos = start(idx, *helpers.DIMENSOES.internal)
split_shapes(idx=idx)
print(f"{idx} - {grupos[idx].shape.get_child_count()}")
def draw():
"""Render the current subdivision group and update frame overlay metadata."""
py5.background(cor_fundo)
info = grupos[divisoes]
if grupo := info.shape:
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()
