Add Helix and PolarRepeat

CHANGELOG.md

@@ -7,6 +7,15 @@ format follows [Keep a Changelog](https://keepachangelog.com/en/1.1.0/).
 
 ### Added
 
+- `Helix(start, radius, pitch, turns, wire_radius, axis=..., left_handed=...)`: a helical
+  wire of round cross-section with hemispherical ends, e.g. the winding of an RF coil. Its
+  level set is the distance from the centreline (Newton steps along it from the
+  linearised minima of the nearest turns), exact within a wire radius of the wire and a
+  bound farther away; `centreline(t)`, `wire_length`, volume and surface area.
+- `PolarRepeat(source, count, axis=..., origin=...)`: ``count`` copies of a 3D shape about
+  an axis, evaluated by folding the point's angle into the first sector, so its cost does
+  not grow with ``count`` (the slits of a Faraday shield: ``tube - PolarRepeat(slit, 24)``;
+  the cut cells of 24 slits as fast as of one).
 - A Numerics section in the docs (header and sidebar): an overview of the geometry
   (`docs/src/content/docs/numerics/index.mdx`, with the main cards) and one page per module,
   from the shapes to the grids (starlight-theme's `methodcard: { pages: true }`).

docs/src/content/docs/getting-started/geometry-api.md

@@ -146,6 +146,8 @@ and where `level_set_exact` is true it is the Euclidean signed distance.
 | `Aperture2D` | exact while the plates do not touch |
 | `Cylinder`, `Tube`, `Cone`, `Torus` (any axis, with or without fillets) | exact |
 | `SlantedTube` | the larger of the uncut tube's and the cut plane's: exact on the faces, a bound near the cut's rim |
+| `Helix` | the distance from the centreline minus the wire's radius: exact within a wire radius of the wire, a bound farther away |
+| `PolarRepeat` (copies about an axis) | the source's, the least over the point's sector and its two neighbours: a bound |
 | `a \| b`, `a & b`, `a - b` | `min(a, b)`, `max(a, b)`, `max(a, -b)`: a bound, not exact |
 | rotations, translations, reflections, uniform scaling | exact if the source is |
 | nonuniform scaling, shears | the source's times the smallest stretch: a bound |

docs/src/content/docs/numerics/index.mdx

@@ -42,6 +42,8 @@ distances of boxes, segments, capped cones and tori:
   [Tube](/simgeometry/numerics/objects-tube/), [Cone](/simgeometry/numerics/objects-cone/),
   [Torus](/simgeometry/numerics/objects-torus/), and the
   [SlantedTube](/simgeometry/numerics/objects-slanted-tube/), a bound near its cut;
+- the [Helix](/simgeometry/numerics/objects-helix/), a helical wire (an RF coil), its
+  distance found by Newton steps along the centreline;
 - [Booleans, affine transforms and sections](/simgeometry/numerics/operations/), whose level
   sets are bounds, and [collections](/simgeometry/numerics/collection/) of labelled objects.
 

src/simgeometry/__init__.py

@@ -16,6 +16,7 @@
     Cylinder,
     FunctionObject2D,
     FunctionObject3D,
+    Helix,
     Line,
     Polygon,
     Polyline,
@@ -26,6 +27,7 @@
     Triangle,
     Tube,
 )
+from simgeometry.operations import PolarRepeat
 from simgeometry.simulation_domain import SimulationDomain
 
 # simgeometry's regions stay off unless the application enables the "simgeometry" tag.
@@ -38,6 +40,7 @@
 __all__ = [
     "GeometryCollection",
     "Grid",
+    "PolarRepeat",
     "SimulationDomain",
     "Aperture2D",
     "Aperture3D",
@@ -47,6 +50,7 @@
     "Cylinder",
     "FunctionObject2D",
     "FunctionObject3D",
+    "Helix",
     "Line",
     "Polygon",
     "Polyline",

src/simgeometry/objects/__init__.py

@@ -9,6 +9,7 @@
 from simgeometry.objects.cuboid import Cuboid
 from simgeometry.objects.cylinder import Cylinder
 from simgeometry.objects.function_object import FunctionObject2D, FunctionObject3D
+from simgeometry.objects.helix import Helix
 from simgeometry.objects.line import Line
 from simgeometry.objects.polygon import Polygon
 from simgeometry.objects.polyline import Polyline
@@ -31,6 +32,7 @@
     "Cylinder",
     "FunctionObject2D",
     "FunctionObject3D",
+    "Helix",
     # 1D objects
     "Line",
     "Polygon",