  We propose a novel computational framework for optimizing the toolpath
continuity in fabricating surface models on an extrusion-based 3D printer.
Toolpath continuity has been a critical issue for extrusion-based fabrications
that affects both quality and efficiency. Transfer moves cause non-smoothor
bumpy surfaces and get worse for materials with large inertia like clay. For
surface models, the effects of continuity are even more severe, in terms of
surface quality and model stability. In this paper, we introduce an original
criterion "one-path-patch" (OPP), for representing a shell surface patch that
can be traversed in one path considering fabrication constraints. We study the
properties of an OPP and the merging operations for OPPs, and propose a
bottom-up OPP merging procedure for decomposing the given shell surface into a
minimal number of OPPs and generating the "as-continuous-as-possible" (ACAP)
toolpath. Furthermore, we customize the path planning algorithm with a curved
layer printing scheme, which reduces the staircase defect and improves the
toolpath continuity via possibly connecting multiple segments. We evaluate the
ACAP algorithm for both ceramic and thermoplastic materials, and results
demonstrate that it improves the fabrication of surface models in both surface
quality and efficiency.
