Methods and systems for generating polycubes and all-hexahedral meshes of an object

A method for generating a polycube representation of an input object, the method comprising:

• receiving, at a processor, an input volumetric representation of the input object;
• deforming, by the processor, the input volumetric representation to provide a deformed object representation;
• extracting, by the processor, a polycube representation of the object from the deformed object representation, the polycube representation comprising a solid figure made of cubes joined face to face, the solid figure comprising axis-aligned surface planes which having normal vectors that align with one of six directions (±X, ±Y, ±Z) aligned with a set of global Cartesian axes;
• wherein deforming, by the processor, the input volumetric representation to provide the deformed object representation comprises effecting, by the processor, a tradeoff between competing objectives of:
• deforming the input volumetric representation in a manner which provides surfaces having normal vectors closely aligned with one of the six directions aligned with the set of global Cartesian axes;
• and deforming the input volumetric representation in a manner which provides low-distortion deformations.