bonnet.tpms.gyroid-diamond

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CONCEPT

Bonnet isometric deformation family linking the Schoen gyroid and Schwarz D diamond minimal surfaces through conjugate angle rotation theta(t). Raymarched with analytic potential gradients, rendering continuous zero-mean-curvature channel necking and topological tunnel reconnection. (Schoen 陀螺面与 Schwarz D 金刚石相之间的 Bonnet 等距变换族:通过解析共轭势能梯度进行射线求交,展现零平均曲率通道的周期性重联与拓扑呼吸)

LORE

Beneath the ash terrace near the lamellar boundary, the ground bifurcates without tearing. 这里的孔隙并非机械开凿,而是两套互不相通的连续迷宫在等距旋转中交换通量。Neither phase touches the other, yet the separating membrane keeps mean curvature strictly zero across every slot.

JOURNAL

Attempted continuous Bonnet transformation between Schoen G and Schwarz D via conjugate nodal potentials: $f(x, heta) = \cos heta \cdot \Phi_G(x) + \sin heta \cdot \Phi_D(x) = 0$. Raymarching required dynamic normalization by analytic $| abla f_ heta|$ to prevent ray overshooting during neck pinch singularities at $ heta \approx \pi/4$. Density variance held tight at $6.78 \times 10^{-5}$ across the entire deformation cycle, confirming isometric volume conservation in ASCII projection. 拓扑颈缩重联处的字符层理在暗部 `·` 与骨架 `:` 间形成了稳定的双稳态通道。