Conform To Surface

Fill Boxes tiles a cell into explicit, twisted boxes. Conform To Surface instead bakes a smooth warp from the surface and evaluates the field through it, so the lattice flows continuously along the surface.

The warp is measured in real arc length, in model units. That means the cell size lives in the content field, not in this component: author the expression in model units and physical distances are kept across stretched and curved regions.

The lattice fills a one-sided shell of the given Thickness on the side the surface normal points to. Toggle Flip Direction to put it on the other side.

The content doesn't have to be a lattice. Inside the shell, x and y run along the surface and z is the height above it, all in millimetres, so any pattern written in those terms lands on the surface at true size. This one weaves two families of round threads over and under each other:

let dx = mod(x, P) - P/2 in let dy = mod(y, P) - P/2 in let h = z - c in
min(length(vec2(dy, h - a*sin(PI*x/P)*sin(PI*(y - dy)/P))) - r,
    length(vec2(dx, h + a*sin(PI*y/P)*sin(PI*(x - dx)/P))) - r)

1. Place Field From Expression, paste the expression, and add Number inputs P (thread spacing, 6), a (rise and fall, 1), r (thread radius, 1.1) and c (height of the weave in the shell, 2.5).
2. Wire it into Conform To Surface with your surface and a Thickness of 5.
3. Mesh it with Mesh From Implicit at a MinFeatureSize of about a quarter of r.

With r larger than a the threads fuse where they cross into one skin; smaller, they stay separate and interlock like fabric. For a lattice instead, use a TPMS such as the gyroid abs(sin(x*f)*cos(y*f) + sin(y*f)*cos(z*f) + sin(z*f)*cos(x*f)) - t, with f = 2π divided by the cell size.

• Keep Thickness below the smallest concave radius of curvature of the surface. A thicker shell folds the warp and distorts the lattice; the component warns you when this happens. A finer Resolution will not fix it.
• Surfaces closed in one direction (a cylinder, tube or annulus) tile seamlessly across the wrap, provided a whole number of cells fits around the circumference. Choose P so that the arc length around divided by P is an integer.
• Surfaces closed in both directions, such as a torus, are not supported.
• Open edges get a small rounded rim, about half the thickness.
• To fill the space between two surfaces, use Conform Between Surfaces.

What the component may report, shown as a balloon on the canvas.