Updated task_categories and tags

README.md

@@ -43,37 +43,35 @@ Filenames follow the pattern:
 
 g{genus}\_{knot_type}\_{n_x},{n_y},{n_z}\_{φ_x},{φ_y},{φ_z}\_{f}\_{c}\_{a}\_r{r_min}\_{r_max}\_v{resolution}.stl
 
+Each component encodes geometric or topological information.
 
-**Example:**
+**For example:**
 
 g7_lissajous_3,5,8,0,pi2,0_03_1.1_0.2_r0.02_0.029_v90.stl
 
-
-Each component encodes specific geometric and topological information:
-
-- **`g7`**: The topological genus of the surface. Here, genus 7 (i.e., the surface has 7 holes).
-- **`lissajous` or `fibonacci`**: Parameterization type. Most examples are *Lissajous* (singular) knots; a few are *Fibonacci* knots.
-- **`3,5,8`**: Frequencies (`n_x`, `n_y`, `n_z`) used in the parametric equations of the curve, corresponding to the x, y, and z coordinates.
-- **`0,pi2,0`**: Phase shifts (`φ_x`, `φ_y`, `φ_z`) in each coordinate. Notation like `pi2` represents multiples of π (e.g., `pi2` = π/2, `pi3` = π/3, etc.).
-- **`03_1.1_0.2`**: Parameters of the cosine-based radius modulation for the tubular neighborhood around the curve:
+- `g7`: Topological genus of the surface. In this example, the genus is 7 (i.e., the surface has 7 holes).
+- `lissajous` or `fibonacci`: Knot type. Most elements were generated from *Lissajous* (singular) knots, but just a couple from *Fibonacci* knots.
+- `3,5,8`: The frequencies `n_x`, `n_y`, `n_z` used in the parametric equations of the curve, corresponding to the x, y, and z coordinates.
+- `0,pi2,0`: The phase shifts `φ_x`, `φ_y`, `φ_z` in each coordinate. Notation like `pi2` represents fractions of π (e.g., `pi2` = π/2, `pi3` = π/3, etc.).
+- `03_1.1_0.2`: Parameters of the (cosine-based) sinusoidal radius variation for the tubular neighborhood around the curve:
   - `03`: frequency `f`
   - `1.1`: constant term `c`
   - `0.2`: amplitude `a`
 
   Thus, the radius function is:
 
-  r(t) = 1.1 + 0.2cos(3t)
+  $r(t) = 1.1 + 0.2cos(3t)$
 
-  
-- **`r0.02_0.029`**: Minimum and maximum radius values of the tubular neighborhood.
-- **`v90`**: Voxel resolution per axis. While v90 nominally refers to a 90 × 90 × 90 voxel grid, an offset of at least 5 voxels per side (sometimes 10 or 15) was added to prevent surface clipping at the bounding box edges. As a result, the actual scalar field is discretized into 101 × 101 × 101 grid points (vertices), yielding 1,000,000 voxels in total. This expanded grid ensures sufficient padding around the surface geometry. 
-- **`.stl`**: File extension. This denotes the *smoothed* version of the surface mesh.
+- `r0.02_0.029`: Minimum and maximum radius of the tubular neighborhood.
+- `v90`: Voxel resolution per axis. While v90 nominally refers to a 90 × 90 × 90 voxel grid, an offset of 5 voxels per side was added to prevent surface clipping at the bounding box edges.
+As a result, the actual scalar field is discretized into 101 × 101 × 101 = 1,030,301 grid points, yielding 1,000,000 voxels in total.
+- `.stl`: File extension. This denotes the *smoothed* version of the surface mesh.
 
 Other file variants use suffixes to indicate their content:
 
-- **`_ns.stl`**: The non-smoothed surface mesh, output directly from the Marching Cubes algorithm (raw geometry).
-- **`_sf.txt`**: The scalar field used to generate the surface.
-- **`_bup.txt`**: The blow-up profile (e.g., radius function samples or analytical envelope).
+- `_ns.stl`: The non-smoothed surface mesh, output directly from the Marching Cubes algorithm (raw geometry).
+- `_sf.txt`: The scalar field used to generate the surface.
+- `_bup.txt`: The blow-up profile (e.g., radius function samples or analytical envelope).
 
 
 # Acknowledgements
@@ -81,4 +79,4 @@ Other file variants use suffixes to indicate their content:
 - The authors thank DGTIC-UNAM for access to the Miztli HPC resources, grant LANCAD-UNAM-DGTIC-430.
 - RF thanks CONAHCyT for a graduate fellowship. 
 - This work was supported by Universidad Nacional Autónoma de México Postdoctoral Program (POSDOC) for author EIVR, who also acknowledges the postdoctoral fellowship received during the production of this work.
-- VM acknowledges the support from project PAPIIT TA100924 "Investigación de sesgos inductivos en aprendizaje profundo y sus aplicaciones"
+- VM acknowledges the support from project PAPIIT TA100924 "Investigación de sesgos inductivos en aprendizaje profundo y sus aplicaciones."