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arXiv · 2610.19403

Topology-Preserving Multi-Usage Pipe Centerline Refinement under Permanent Tubular Occupancy

Deng Quan
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Abstract

Discrete multi-group pipe routers place channels on a grid or coarse graph. The resulting centerlines are topologically feasible but typically contain many axis-aligned corners. For permanently occupied fluid tubes---as in additively manufactured hydraulic manifolds---those corners are undesirable: they degrade geometric fairness and, in practice, flow quality. This technical report studies the downstream geometric stage that starts from a fixed routing topology and a feasible coarse layout, and refines tubular centerlines under permanent clearance. Unlike classical robotic path smoothing, which usually fair one temporary open trajectory, our setting is a branched manifold with declared terminal usages, finite tube radii, and static cross-group occupancy. We formalize the refinement problem, highlight the multi-usage junction conflict that a single shared branch point cannot resolve, and outline a hybrid trunk-share / junction-split parameterization with soft geometric costs and hard clearance acceptance. On a multi-group suite ($8$ groups $\times$ $8$ terminals, $r{=}2$) with capsule clearance, the refine reaches full hard-accept success, $κr\lesssim 1$, and about a $95\%$ relative drop in the soft objective. Physics-based pressure-drop optimization is intentionally deferred to a later PDE stage; here the objective remains geometric.

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Deng Quan. 2026-10-14. Topology-Preserving Multi-Usage Pipe Centerline Refinement under Permanent Tubular Occupancy. https://arxiv.org/abs/2610.19403

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