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Appendix

While not essential, naming things carefully helps with structuring and tracking thoughts.

Naming policies

  1. Clear. The name should be self-explanatory without needing to see the thing. Avoid abbreviations and acronyms unless they are established mathematical notation.
  2. Mathematically true. The name should reflect what is actually happening in the formula — the underlying surface type, the operation, the parameter that varies. Don't describe the visual impression if a more precise term exists.
  3. No metaphor or poetic language. Names describe geometry and motion, not mood or feeling. "Oscillating" not "breathing". "Vertical compression" not "squash" if a more precise term fits.
  4. Distinct. No two names in the same category should be confusable or interchangeable. If two names could plausibly describe the same thing, at least one needs revision.
  5. Consistent patterns within families. If several items share the same base formula or the same motion type, that relationship must be visible in the name. Don't vary the word for the same concept across entries.
  6. [Modifier · base] structure for animated surfaces. Every animated surface name follows exactly [present-participle motion] [mathematical shape noun] — e.g., "Oscillating paraboloid", "Pulsing sphere". Word order is fixed; no exceptions without a documented reason (e.g., the surface is a recognised mathematical proper noun).
  7. Prefer established mathematical terminology for base shapes. If the mathematical literature has a name for the surface or structure (paraboloid, hyperboloid, gyroid, lemniscate), use it. Don't substitute an informal synonym ("bowl", "donut", "figure-eight") when a precise term exists.
  8. No root reuse across different phenomena. The same root word must not appear in names for conceptually unrelated things. If "ripple" names the static radially-decaying cosine surface, the same root cannot be used to describe animation on a torus or an outward-traveling wave.

Vocabularies

Base shape nouns

The mathematical name of the underlying surface. Used as the final noun in an animated surface name.

paraboloid Quadratic surface opening in one direction; includes elliptic and hyperbolic variants hyperboloid One-sheet ruled quadratic surface; x² + z² − y² = c ellipsoid Triaxially scaled sphere; all quadratic terms positive sphere Zero set of x² + y² + z² = r² torus Surface of revolution of a circle; defined by major and tube radii cone Ruled quadratic surface with a vertex; x² + z² = y² saddle Hyperbolic paraboloid or higher-degree saddle-type surface Gaussian Surface whose equation contains e^(−r²/σ²); bell-curve profile cubic Algebraic surface of degree 3 quartic Algebraic surface of degree 4

Proper mathematical names

Recognised names from the literature. Use as-is; do not paraphrase or translate.

gyroid Triply periodic minimal surface; cos(x)sin(y) + cos(y)sin(z) + cos(z)sin(x) = 0 Schwartz P Triply periodic minimal surface; cos(2x) + cos(2y) + cos(2z) = c Schoen I-WP Triply periodic surface; cos(2x)cos(2y) + cos(2y)cos(2z) + cos(2z)cos(2x) = c lemniscate Figure-eight curve of revolution; (x²+y²+z²)² = a²(x²−z²) Chmutov T₄ Degree-4 surface from Chebyshev polynomials T₄; T₄(x)+T₄(y)+T₄(z) = 0

Animation participles

Present-participle words describing what the time parameter is doing. Used as the leading modifier in an animated surface name.

oscillating A scalar parameter alternates sign periodically; e.g., amplitude goes positive → negative → positive pulsing A magnitude varies periodically while staying positive; e.g., radius or height swells and contracts traveling A spatial feature (wave front, peak) translates through space; the surface moves, not just deforms rotating Angular position increases monotonically; the surface or a feature spins drifting A parameter shifts slowly and continuously without periodicity; no return to origin tilting The orientation angle of the surface varies; a rotation that reverses rather than spins continuously alternating The surface transitions between two discrete configurations; a binary oscillation

Spatial qualifiers

Adjectives or adverbs that specify the geometry of a feature — used when the base noun alone is ambiguous.

radial Depends only on r = √(x²+z²); rotationally symmetric about the vertical axis axial Varies along the primary (vertical) axis; independent of angle angular Depends on azimuthal angle θ; periodic in θ transverse Perpendicular to the primary axis or wave direction sinusoidal Profile follows a sin or cos function; use when the wave shape itself is the defining feature triply periodic Repeating in all three spatial directions; reserved for minimal surfaces and their relatives