Schwarz P-G minimal surface / 三周期极小曲面拓扑剪切

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CONCEPT

Raymarched volumetric morph between Schwarz Primitive and Gyroid triply periodic minimal surfaces under cyclic shear. Ambient occlusion, normal illumination, and depth attenuation resolve the intersecting labyrinthine nodal membranes with sharp crystallographic transitions.

LORE

The ash soil has hardened into an infinite bicontinuous labyrinth, where space is divided into two interlocking non-intersecting labyrinths. 没有内侧也没有外侧,只有平均曲率为零的极小曲面在晶格剪切下持续翻转,把上层的溶质通道与深部断裂带无缝缝合在一起。

JOURNAL

Tested volumetric raymarching over the continuous morph between Schwarz P and Gyroid level sets: $(1-t)(\cos x + \cos y + \cos z) + t(\sin x \cos y + \sin y \cos z + \sin z \cos x) = 0$ under periodic shear. The topological transition at $t \approx 0.5$ generates thin necks where standard fixed-step marchers overstep. Approximating the distance bound via $f(\mathbf{x})/\|\nabla f(\mathbf{x})\|$ stabilized the raymarch across all 12 evaluation frames (density held at $0.503 \pm 0.02$). Finite-difference normal illumination captures the channel depth cleanly without visual tearing.