A General Algorithm for 3-Axis Non Planar 3D Printing

Overview

Traditional 3-axis fused-filament fabrication (FFF) is fundamentally constrained by Euclidean planar slicing, which introduces discrete staircase artifacts and fixed-bead orientations that compromise both surface isotropy and structural integrity. While 5-axis motion systems offer a hardware solution to these geometric limitations, their adoption is stifled by high capital costs—often exceeding $10,000 to $50,000—and a lack of accessible control software. We present FlexSlicer, the first source-available field-warp framework with integration possibility with a production-grade slicing engine (PrusaSlicer), enabling high-order non-planar printing on commodity 3-axis hardware by reframing slicing as a differential manifold mapping problem. Unlike previous non-planar methods that rely on proprietary kernels or single-displacement heightfields (K=1), FlexSlicer introduces a depth-varying "FlexField" (K>1). This field is constructed by solving two sparse least-squares systems constrained by top-surface and secondary "terrace" targets, defining a smooth mapping function, z_real = z_s + D(x, y, z_s), between a flattened parametric slicing space and the physical build volume. To ensure physical feasibility, we integrate a 3-axis conical collision model via a Lipschitz (max-slope) projection, preventing toolhead interference without the O(N^3) overhead of volumetric mesh checking. FlexSlicer leverages mature 2D toolpath heuristics by warping the model, slicing it planarly, and inverse-warping the resulting G-code with dynamic extrusion compensation. By coupling this geometric field with an orientation tensor field for stress-guided infill, FlexSlicer produces objects with 3x greater topological variety and 30% higher resilience to cross-Z stress than standard methods. Operating 10x faster than Radial Basis Function (RBF) alternatives, FlexSlicer provides a high-performance, open-access software upgrade that bridges the gap between budget 3-axis hardware and industrial-grade surface quality.

Competition history

• CSEF 2026 Computational Science (Senior Division) · Entry S-07-29

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