The simplex projection expands the capabilities of simplex plots (also known as ternary plots) to achieve a lossless visualization of 4D compositional data on a 2D canvas. Previously, this was only possible for 3D compositional data. We demonstrate how our approach can be applied to individual data points, point clouds, and continuous probability density functions on simplices. While we showcase our visualization technique specifically for 4D compositional data, we offer rigorous proofs that support its extension to compositional data of any (finite) dimensionality.

翻译：单形投影扩展了单形图（亦称三元图）的能力，实现了在二维画布上对四维组分数据进行无损可视化。此前，这一方法仅适用于三维组分数据。我们展示了如何将本方法应用于单形上的单个数据点、点云及连续概率密度函数。尽管我们专门针对四维组分数据展示了可视化技术，但提供了严谨的证明以支持其向任意（有限）维度组分数据的扩展。