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以下輸出都是以 bezierkit 0.5.0rc1 實際執行程式碼的結果。

求值、分割與取樣

from bezierkit import BezierCurve, Point
from bezierkit.sampling import UniformSampler

curve = BezierCurve.cubic(
    Point(0, 0),
    Point(1, 2),
    Point(3, 2),
    Point(4, 0),
)

print(curve.at(0.5))
print(curve.derivative().at(0.5))

left, right = curve.split(0.3)
print(left.at(1.0) == right.at(0.0))

sample = UniformSampler(200).sample(curve)
print(len(sample.points), "sample points")

輸出：

Point(coords=(2.0, 1.5))
Point(coords=(4.5, 0.0))
True
200 sample points

curve.at(t) 在參數 t（範圍 [0, 1]）求出曲線上的點，curve.derivative() 回傳導數曲線， split 則把曲線切成兩段。取樣結果也提供 t、x 與 y 陣列。

由斜率建構曲線

PlanarSlopes 根據兩個端點，以及兩端各自想要的斜率（dy/dx）建構三次曲線。

from bezierkit import Point
from bezierkit.construction import PlanarSlopes

demand = PlanarSlopes(
    start=Point(0, 5),
    end=Point(5, 0),
    start_slope=-2,
    end_slope=-0.3,
).build()

print(demand.at(0.0), demand.at(1.0))

# 兩端的切線斜率（dy/dx）與指定值一致。
d = demand.derivative()
for t in (0.0, 1.0):
    dx, dy = d.at(t).coords
    print(f"t={t}: dy/dx = {dy / dx:.2f}")

輸出：

Point(coords=(0.0, 5.0)) Point(coords=(5.0, 0.0))
t=0.0: dy/dx = -2.00
t=1.0: dy/dx = -0.30

匯出 SVG 與 TikZ

PiecewiseBezier 把多段三次曲線首尾相接。SVG 與 TikZ 匯出器直接輸出三次曲線的幾何，不會先把它壓平。

from bezierkit import CubicBezierSegment, PiecewiseBezier, Point
from bezierkit.export.svg import to_svg_path_data
from bezierkit.export.tikz import to_tikz

path = PiecewiseBezier([
    CubicBezierSegment.from_line(Point(0, 0), Point(2, 0)),
    CubicBezierSegment.from_line(Point(2, 0), Point(2, 4)),
])
print(path.at(0.75))
print(to_svg_path_data(path, precision=5))
print(to_tikz(path, precision=5, options="thick"))

輸出：

Point(coords=(2.0, 2.0))
M 0.00000 0.00000 C 0.66667 0.00000 1.33333 0.00000 2.00000 0.00000 C 2.00000 1.33333 2.00000 2.66667 2.00000 4.00000
\draw[thick] (0.00000,0.00000) .. controls (0.66667,0.00000) and (1.33333,0.00000) .. (2.00000,0.00000) .. controls (2.00000,1.33333) and (2.00000,2.66667) .. (2.00000,4.00000);

命令列

安裝 cli 額外功能後，可以直接在 shell 對同一條曲線取樣：

bezierkit sample \
  --points "0,0" --points "1,2" --points "3,2" --points "4,0" \
  --count 5 --format csv

t,x,y
0.0,0.0,0.0
0.25,0.90625,1.125
0.5,2.0,1.5
0.75,3.09375,1.125
1.0,4.0,0.0

執行 bezierkit --help 可查看完整的指令樹。

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