2026/08/05 by Seth Dutter
Mathematics · #math.CV #math.AG #msc:14H50 #msc:14Q05 #msc:68U05
18 pages, 9 figures
arxiv created 2026/08/05 · arxiv updated 2026/08/06
We introduce a nonlinear map α:ℂ2→ℝ3 with the purpose of visualizing curves. Basic properties of α are proved, including preservation of orthogonality, recovery of the magnitudes of vectors in the preimage, and continuous extension of α to \widetildeα:ℙ2_ℂ→ℝ3. For plane curves Z⊂ℙ2_ℂ, it is proved that \widetildeα(Z) is the union of boundaries of star-shaped domains. Methods are established to descend finite-order automorphisms of smooth projective curves to rotations of their images in ℝ3. Efficient techniques for creating meshes and ray-traced images of \widetildeα(Z) are developed.