Signed Distance (Sdf.m
)
Signed Distance Fields (SDFs) have been widely applied in various areas of computer graphics, including the representation of implicit surfaces12, collision detection in robotics34. In particular, SDFs have gained attention for their use in implicit modeling5, a technique for representing 3D shapes as continuous functions, rather than discrete mesh descriptions.
In Sorotoki, SDFs are implemented in the class Sdf.m
and can be used to construct general 2D and 3D geometries. They can also be utilized to model static or dynamic contact environments, generate 3D models of soft actuators that are suitable for 3D printing, and compute inertia tensors for continuum bodies in
Implicit modeling using SDFs.
We briefly outline the mathematical foundations underpinning the Sdf
class. As the name suggests, signed distance functions are a type of function that encodes distance information relative to an object defined implicitly. Adopting the notation used in Reiner1, given a domain
where
SDFs provide a simple and efficient way of determining the location of a set of points relative to a domain
Example: Unit-circle and evaluation
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-1.0000, -0.6464, -0.2929, 0.0607, 0.4142
Example: Unit-circle intersect
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Tim Reiner, Gregor M\ifmmode \ddot u\else ü\fi ckl, and Carsten Dachsbacher. Interactive modeling of implicit surfaces using a direct visualization approach with signed distance functions. Computers & Graphics, 35(3):596–603, 2011. doi:10.1016/j.cag.2011.03.010. ↩↩
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Zhiqin Chen and Hao Zhang. Learning Implicit Fields for Generative Shape Modeling. ArXiv e-prints, 2018. arXiv:1812.02822, doi:10.48550/arXiv.1812.02822. ↩
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Joseph Ortiz, Alexander Clegg, Jing Dong, Edgar Sucar, David Novotny, Michael Zollhoefer, and Mustafa Mukadam. iSDF: Real-Time Neural Signed Distance Fields for Robot Perception. ArXiv e-prints, 2022. arXiv:2204.02296, doi:10.48550/arXiv.2204.02296. ↩
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Puze Liu, Kuo Zhang, Davide Tateo, Snehal Jauhri, Jan Peters, and Georgia Chalvatzaki. Regularized Deep Signed Distance Fields for Reactive Motion Generation. ArXiv e-prints, 2022. arXiv:2203.04739, doi:10.48550/arXiv.2203.04739. ↩
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Lawrence Smith and Robert MacCurdy. SoRoForge: End-to-End Soft Actuator Design. IEEE Transactions on Automation Science and Engineering, pages 1–12, 2023. doi:10.1109/TASE.2023.3241866. ↩