Determinant, Alan ve Yönelim

yonlu_alan_m2: 26.250000
alan_m2: 26.250000
ilk_donus: counterclockwise
ucgen_yelpazesi_m2: 26.250000
ters_sira_yonlu_alan_m2: -26.250000
oteleme_farki_m2: 0.000e+00
donusum_determinanti: 1.020000
donusmus_alan_orani: 1.020000
yakin_normalize_determinant: 2.500000e-09
yakin_sinif: uncertain
kesin_iki_kat_alan: 100000000

Kod dosyasını indir

# Kitaptaki kod blokları; bu dosya içinde sırayla çalıştırılır.
# --- 1. Robot bölgesi, dönüşüm ve kesin karşılaştırma ---
import numpy as np
from sympy import Matrix
from agbook import (
    determinant_2d, orientation_diagnostics, polygon_area,
    polygon_signed_area, triangle_area,
)

boundary = np.array([
    [0., 0.], [6., 0.], [7., 3.], [4.5, 5.], [1., 4.]
])
tolerance = 1.0e-10

signed_area = polygon_signed_area(boundary)
area = polygon_area(boundary)
fan_area = sum(
    triangle_area(boundary[0], boundary[i], boundary[i + 1])
    for i in range(1, len(boundary) - 1)
)
first_turn = orientation_diagnostics(
    *boundary[:3], relative_tolerance=tolerance
)
reversed_area = polygon_signed_area(boundary[::-1])
translated_area = polygon_signed_area(
    boundary + np.array([1.0e9, -2.0e9])
)

linear_map = np.array([[1.2, 0.3], [-0.2, 0.8]])
mapped = boundary @ linear_map.T
scale = determinant_2d(linear_map[:, 0], linear_map[:, 1])
mapped_ratio = polygon_area(mapped) / area

near = np.array([
    [0., 0.], [1.0e8, 1.0e8], [2.0e8, 2.0e8 + 1.]
])
near_result = orientation_diagnostics(
    *near, relative_tolerance=1.0e-8
)
exact = Matrix([
    [100000000, 100000000],
    [200000000, 200000001],
]).det()

print(f"yonlu_alan_m2: {signed_area:.6f}")
print(f"alan_m2: {area:.6f}")
print(f"ilk_donus: {first_turn.classification}")
print(f"ucgen_yelpazesi_m2: {fan_area:.6f}")
print(f"ters_sira_yonlu_alan_m2: {reversed_area:.6f}")
print(f"oteleme_farki_m2: {translated_area-signed_area:.3e}")
print(f"donusum_determinanti: {scale:.6f}")
print(f"donusmus_alan_orani: {mapped_ratio:.6f}")
print(f"yakin_normalize_determinant: "
      f"{near_result.normalized_determinant:.6e}")
print(f"yakin_sinif: {near_result.classification}")
print(f"kesin_iki_kat_alan: {exact}")

Kaydedilen çıktı

1. Robot bölgesi, dönüşüm ve kesin karşılaştırma
yonlu_alan_m2: 26.250000
alan_m2: 26.250000
ilk_donus: counterclockwise
ucgen_yelpazesi_m2: 26.250000
ters_sira_yonlu_alan_m2: -26.250000
oteleme_farki_m2: 0.000e+00
donusum_determinanti: 1.020000
donusmus_alan_orani: 1.020000
yakin_normalize_determinant: 2.500000e-09
yakin_sinif: uncertain
kesin_iki_kat_alan: 100000000

Kod dosyasını indir

# Kitaptaki kod blokları; bu dosya içinde sırayla çalıştırılır.
# --- 1. Alternatiflik ve kesme artıkları ---
import numpy as np
from agbook import determinant_2d

pairs = [
    (np.array([3., -1.]), np.array([2., 4.])),
    (np.array([2.5, 0.8]), np.array([0.6, 2.2])),
    (np.array([-5., 7.]), np.array([3., 1.])),
]
lam = 3.25
residuals = []
for u, v in pairs:
    residuals.append(
        determinant_2d(u, v) + determinant_2d(v, u)
    )
    residuals.append(
        determinant_2d(u, v + lam*u) - determinant_2d(u, v)
    )
print(f"max_mutlak_artik: {max(map(abs, residuals)):.3e}")

# --- 2. Çokgen sırası, kapanış ve öteleme ---
import numpy as np
from agbook import polygon_signed_area

p = np.array([
    [0., 0.], [6., 0.], [7., 3.], [4.5, 5.], [1., 4.]
])
closed = np.vstack([p, p[0]])
shifted = p + np.array([1.0e9, -2.0e9])
for name, vertices in (
    ("ozgun", p),
    ("ters", p[::-1]),
    ("kapali", closed),
    ("otelenmis", shifted),
):
    print(name, f"{polygon_signed_area(vertices):.6f}")

# --- 3. Üç tolerans ve kesin determinant ---
import numpy as np
from sympy import Matrix
from agbook import orientation_diagnostics

points = np.array([
    [0., 0.], [1.0e8, 1.0e8], [2.0e8, 2.0e8 + 1.]
])
for tau in (1.0e-6, 1.0e-8, 1.0e-10):
    result = orientation_diagnostics(
        *points, relative_tolerance=tau
    )
    print(f"{tau:.0e}", result.classification,
          f"{result.normalized_determinant:.6e}")
exact = Matrix([
    [100000000, 100000000],
    [200000000, 200000001],
]).det()
print("kesin", exact)

# --- 4. Taşmayı yakalama ve işaret için ölçekleme ---
import numpy as np
from agbook import determinant_2d

u = np.array([1.0e308, 1.0e308])
v = np.array([1.0e308, -1.0e308])
try:
    determinant_2d(u, v)
except OverflowError as error:
    print("overflow:", type(error).__name__)

scale = 1.0e308
scaled_det = determinant_2d(u/scale, v/scale)
print(f"scaled_determinant: {scaled_det:.1f}")
print("sign:", int(np.sign(scaled_det)))

Kaydedilen çıktı

1. Alternatiflik ve kesme artıkları
max_mutlak_artik: 1.776e-15

2. Çokgen sırası, kapanış ve öteleme
ozgun 26.250000
ters -26.250000
kapali 26.250000
otelenmis 26.250000

3. Üç tolerans ve kesin determinant
1e-06 uncertain 2.500000e-09
1e-08 uncertain 2.500000e-09
1e-10 counterclockwise 2.500000e-09
kesin 100000000

4. Taşmayı yakalama ve işaret için ölçekleme
overflow: OverflowError
scaled_determinant: -2.0
sign: -1