## 6 Conclusions  
In this work, we described and evaluated gridhopping--a method for transforming shapes defined by signed distance bounds into triangle meshes. Its main advantages are simplicity, ease of implementation, and processing speed. We confirmed this in theory and experiments by comparing the method to the enumeration and continuation variants of the marching cubes algorithm [10], which are the standard approaches for polygonizing signed distance bounds in practical applications. We used both simple shapes defined by short equations/code and more complicated ones defined through neural networks. We also showed that these conclusions hold when the computations are performed on a CPU and on a GPU, which is a further confirmation of the practicality of the method.  
The main limitations of gridhopping are the Lipschitz continuity requirement; that it works only with abstract, mathematically defined shapes and not real-world data like point clouds; and the fact that it generates too many triangles for some simple shapes. Note that the last limitation also holds for marching cubes, as both methods produce identical triangle meshes. Furthermore, within the context of this paper, we would like to mention that the marching cubes-based pipelines (gridhopping included) might be competing with deep learning-based methods that generate triangle meshes [18; 21], especially if the texture is included [17]. However, these deep learning-based approaches are not practical in many situations due to their implementation complexity, large processing speed, and the requirement for high-quality training data to be effective. Therefore, gridhopping is still relevant for the wider engineering community.  
Our implementation of the gridhopping method is available at [[https://github.com/nenadmarkus/gridhopping](https://github.com/nenadmarkus/gridhopping)]([https://github.com/nenadmarkus/gridhopping](https://github.com/nenadmarkus/gridhopping)) (accessed on 26 February 2024).  
Figure 7: Same setting as in Figure 6 except the computations are performed on the GPU.  
**Author Contributions:** Conceptualization, methodology, software, writing: N.M. Review, editing, validation, funding acquisition: M.S. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was supported by the Croatian National Recovery and Resilience Plan (NPOO) under the project Research and Development of Multiple Innovative Products, Services and Business Models Aimed at Strengthening Sustainable Tourism and the Green and Digital Transition of Tourism (ROBOCAMP), with grant number NPOO.C1.6.R1-I2.01. Furthermore, work was supported by the European Union under the project Enhanced Pilot Interfaces & Interactions for fighter Cockpit (EPIIC) funded by European Defence Fund (EDF) Grant Agreement 101103592.  
**Data Availability Statement:** The original contributions presented in the study are included in the article, further inquiries can be directed to the authors.  
**Conflicts of Interest:** The authors declare no conflicts of interest. The funding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.