Clipping and capping

clip(mesh, origin, normal, keep="below", cap=True) cuts a surface by a plane, keeps one side with the cells that cross it split at the plane, and caps the cut so a closed part stays closed (roadmap 7.8.3). crop keeps or drops whole cells and slice returns only the section; this is the operation between them. It is named clip because cut is already the level-set cutting operation and CLI verb.

import meshioplusplus

lower, report = meshioplusplus.clip(part, (0, 0, 10), (0, 0, 1), return_report=True)
report["num_loops"], report["num_cap_triangles"]
upper = meshioplusplus.clip(part, (0, 0, 10), (0, 0, 1), keep="above")

Option	Default	Meaning
origin, normal		the plane; d = (x - origin) . normal, a zero normal is refused
keep	"below"	"below" keeps d < 0, "above" keeps d >= 0
cap	true	triangulate the cut's closed loops

The input is a surface: triangles, quads and polygons, simplexified as slice simplexifies them; a volume block is refused by name. A triangle wholly on the kept side stays, one across the plane is split at the crossings slice computes (the sorted-edge formula, so the cut boundary is slice's section bit for bit), and the rest go. The cut's crossings are chained (chained sections); each closed loop is triangulated by the planar CDT on the crossings themselves, with no new points, nested loops by the even-odd rule, the cap facing out of the kept side. Open chains (a cut through an open surface's border) are counted, not capped.

The result is one triangle block. Point data is interpolated at the crossings (Float64) and kept elsewhere; cell data is the parent cell's, NaN (floating) or -1 (integer) on the cap, which the Int64 cell data clip:cap marks with 1. The report gives num_kept, num_split, num_cap_triangles, num_loops, num_open_chains and warnings.

A closed sphere clipped at its equator gives a closed hemisphere whose volume is half the sphere's, and the two halves' volumes add up to the sphere's to 1e-12 (tests/cpp/test_clip.cpp, tests/python/test_scan_edit.py).

Surfaces

C++ clip (operations/clip.hpp), Python meshioplusplus.clip (C++ core only), both CLIs (clip IN OUT [--origin x,y,z] [--normal x,y,z] [--keep below|above] [--no-cap] [--json]), the Clip pipeline step (Origin, Normal, Keep, Cap), C mio_clip(mesh, origin, normal, keep_below, cap, &report) (mio_clip_report, 72 bytes; mio_clip_warnings), Fortran, Julia, R, Octave/MATLAB, WASM clip and the MCP tool clip.