Shell extraction

A thin wall around a mesh’s surface; here Lucy, rotated upright, with a quarter cut away. The source is at Examples/Shell/main.cpp.

Fig. 26 Lucy hollowed into a shell, a quarter cut away.

Important

The default mesh comes from the common-3d-test-models git submodule. Clone with --recurse-submodules, or run git submodule update --init in the repository (see Obtaining EBGeometry); otherwise pass a mesh of your own as the first argument.

Placing the mesh

Lucy stands along \(z\) in the file. Rotate turns her about \(x\) so that she stands along \(y\) and about \(y\) so that she faces the camera; Scale and Translate then give her height 2 and stand her on \(y = 0\).

Hollowing it

Annular(e, d) keeps the points within \(d\) of the surface (see Value operations): a wall \(2d\) thick centered on it, the kind of thin wall an embedded-boundary grid often needs from a closed surface mesh. A Difference with a box removes the quarter towards the camera:

using Tape = EBGeometry::Tape<T, EBGeometry::TapeFeature::ExactOffsets>;

const Tape shell(pool, Difference(Annular(statue, T(0.5) * thickness), quarter));

The tape type lists TapeFeature::ExactOffsets, so that rays trace the shell exactly (see below). A tape compiles such an optional feature only when its type lists it (see Tape features), so tapes that do not need it are not slowed by it.

The program prints the solid’s and the shell’s values at two points inside the statue: negative in the solid, positive in the shell, whose inside is now hollow.

Looking at it

The example ends with Render::view(shell, pool, argc, argv), a window on the shell with its quarter cut away. Its rays trace the shell exactly, from the mesh’s faces offset by the wall’s half-thickness, rather than marching its value (see Rays and segments); this holds through the Scale, Translate and Rotate that placed the mesh.

The window needs SDL2 and is built with make VIEWER=SDL2 or cmake -DEBGEOMETRY_VIEWER=SDL2 (see The viewer window (EBGEOMETRY_VIEWER)); otherwise, and with --no-view or without a display, view() prints why and returns. Drag to orbit and scroll to zoom; the window lists its other keys (see The viewer’s keys).

Building and running

See Building for how to compile it with CMake, GNU Make, or a direct compiler invocation. Built for a GPU (see Running on a GPU), the window renders on the device.

cd Examples/Shell
./Shell.ex