README.md

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花瓣.py — one surface, four lines of math

17 lines of numpy + matplotlib, no 3D engine: a parametric surface over u ∈ [0, 1] × v ∈ [0, 2π], drawn with a single plot_surface call.

$$ \begin{aligned} r &= a(1-u^2)(1+bu) \\ x &= r\cos(v)\left(1 - k\cdot u\sin(v/2)\right) \\ z &= r\sin(v)\left(1 + k\cdot u\cos(v)\right) \\ y &= u \end{aligned} $$

with a = 1, b = 0.5, k = 0.3, u ∈ [0, 1], v ∈ [0, 2π].

r(u) alone is a body of revolution: it narrows to a point at u = 1 and swells towards the base. The k term is what breaks the symmetry — it pushes x and z sideways by an amount that depends on both u and v, so the cross-section stops being a circle. Nudge the parameters and the leaf turns into a petal.

Mesh: 20 × 32 samples, 640 quads. Coloured with matplotlib's viridis.

Run it

pip install numpy matplotlib
python "python/surface/花瓣.py"

The script opens matplotlib's own 3D window; the picture above was rendered separately with a fixed view and a dark background — see docs/provenance.md for exactly what was changed.