Free Torus Field Grid Generator

Every ellipse is squashed vertically to 0.36 of its width, and every one uses the same factor. That single number is the viewpoint: 0.36 is the sine of about 21 degrees, so the diagram is drawn as if you were looking down on the ring from a little over twenty degrees above its plane.

Rings describe the cross-section. A handful gives you a clean schematic that reads instantly as a torus; many gives you a field, where the eye stops counting and starts seeing a continuous surface. That is the choice the control is really offering — diagram or texture.

Spokes describe the sweep. They run from the inner bound to the outer at equal angles, and without them the rings are just nested ovals with no reason to be related. Two or three spokes are enough to establish the surface; a dozen makes it a wireframe. The counts are independent, and the most readable diagrams usually have more rings than spokes.

The torus is a real and important surface. It is the shape of a magnetic field around a current loop, of a smoke ring, of the plasma confinement in a tokamak, and it is a standard object in topology — the surface of genus one, the first thing after a sphere. All of that is well documented and none of it is in dispute.

The torus field overlay page separates the two, beside the rest of the other sacred-geometry figures. What is added in the sacred-geometry literature — that the torus is the fundamental pattern of energy in living systems, that human hearts or auras generate toroidal fields with the properties claimed — is not supported by the physics it borrows its vocabulary from. The magnetic field of a current loop is toroidal because of Ampère's law; that fact does not extend to the claims built on top of it.

This page draws the diagram and stops there. The figure is genuinely useful as an illustration — for a field around a loop, for a flow that returns on itself, for anything with a hole in the middle and a circulation around it — and it does not need the additional claims to earn its place.

For a flat ring diagram rather than a surface, the polar grid generator is the measured version, and the radial grid tool the ornamental one. For technical figures, keep the rings low and the spokes lower. Three or four rings and three spokes reads as a torus at a glance and leaves room for labels; anything denser competes with the annotation you are adding. Then export SVG so the figure can be dropped into a document and scaled without the curves degrading.

For decorative or pattern work the opposite applies — push both counts up until the surface becomes a moiré, which is where the figure stops being a diagram and starts being an image. Because both counts are independent, the interference pattern between them is controllable, which is a genuinely useful thing to have on a slider.

A torus is defined by two radii, and their ratio is the whole of its character. This overlay fixes them: the major radius is 0.55 of the figure's size and the minor is 0.42, which puts the hole at 0.13 and the rim at 0.97. That gives a fairly fat ring with a small hole — the proportions of a bagel rather than a hoop.

It is worth knowing that this is a fixed choice rather than a property of tori in general. Push the minor radius toward the major and the hole closes entirely, giving a horn torus whose inner surface meets itself at a point. Push it further and you get a self-intersecting spindle torus. Pull it the other way and you approach a thin ring, which is what most field diagrams in physics actually depict.

For most illustration the fixed ratio is what you want, because it reads unambiguously as a torus at any size and needs no explanation. Where it matters is if you are illustrating a specific physical case — a thin current loop, whose field is a far slenderer ring than this. There the honest options are to note the schematic nature of the figure in your caption, or to draw that case in a modelling tool. This page says so plainly rather than letting a fixed proportion be read as a measurement of anything.

One last practical note. Because every ring shares the same foreshortening, the diagram scales cleanly — doubling the size doubles every radius and leaves the apparent viewpoint untouched. That is worth knowing if you are producing a figure at two sizes for print and screen, since it means one export can be scaled rather than two being drawn.