Polycube layouts for 3D models effectively support a wide variety of methods such as hex-mesh construction, seamless texture mapping, spline fitting, and multi-block grid generation. Our study of polycube layouts is motivated by conformal mesh generation for aerospace modelling. In this setting, quality and correctness guarantees are of the utmost importance. However, currently the fully automatic construction of valid polycube layouts still poses significant challenges: state-of-the-art methods are generally not guaranteed to return a proper solution, even after post-processing, or they use a prohibitively large number of voxels that add detail indiscriminately. In this paper we present a robust, flexible, and efficient method to generate polycube layouts. Our approach is based on a dual representation for polycube layouts and builds a layout by iteratively adding dual loops. Our construction is robust by design: at any iterative step we maintain a valid polycube layout. We offer the flexibility of manual intervention if the user so desires: while our method is able to compute a complete polycube layout without user intervention, the user can interrupt after each iteration and target further refinement on both the local and the global level. Last but not least, our method is efficient and can be implemented using comparatively simple algorithmic building blocks. Our implementation is publicly available and we present its output for numerous benchmark models.

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