Our parametric material model learns a correction to a nominal material model from kinematic data alone, allowing us to accurately capture the nonlinearity of different constitutive material models. Left: classical nonlinear constitutive material. Middle: user designed elasticity and damping. Right: real world material.

We present an automatic algorithm for subtractive manufacturing of freeform 3D objects using high-speed machining (HSM) via CNC. A CNC machine operates a cylindrical cutter to carve off material from a 3D shape stock, following a tool path, to "expose" the target object. Our method decomposes the input object's surface into a small number of patches each of which is fully accessible and machinable by the CNC machine, in continuous fashion, under a fixed cutter-object setup configuration. This is achieved by covering the input surface with a minimum number of accessible regions and then extracting a set of machinable patches from each accessible region. For each patch obtained, we compute a continuous, space-filling, and iso-scallop tool path which conforms to the patch boundary, enabling efficient carving with high-quality surface finishing. The tool path is generated in the form of connected Fermat spirals , which have been generalized from a 2D fill pattern for layered manufacturing to work for curved surfaces. Furthermore, we develop a novel method to control the spacing of Fermat spirals based on directional surface curvature and adapt the heat method to obtain iso-scallop carving. We demonstrate automatic generation of accessible and machinable surface decompositions and iso-scallop Fermat spiral carving paths for freeform 3D objects. Comparisons are made to tool paths generated by commercial software in terms of real machining time and surface quality.

The fidelity of a deformation simulation is highly dependent upon the underlying constitutive material model. Commonly used linear and nonlinear constitutive material models contain many simplifications and only cover a tiny part of possible material behavior. In this work we propose a framework for learning customized models of deformable materials from sparse example surface trajectories. The key idea is to iteratively improve a correction to a nominal model of the elastic and damping properties of the object, which allows new forward simulations with the learned correction to more accurately predict the behavior of a given soft object. The challenge is that such data is sparse as it is typically available only on part of the surface. Sparse reduced space-time optimization identifies gentle control forces with which we extract necessary annotated data for model inference and to finally encapsulate the material correction into a compact parametric form. We demonstrate our method with a set of synthetic examples, as well as with data captured from real world homogeneous elastic objects.

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