# gf_slice¶

Synopsis

sl = gf_slice(sliceop, {slice sl|{mesh m| mesh_fem mf, vec U}, int refine}[, mat CVfids])
sl = gf_slice('streamlines', mesh_fem mf, mat U, mat S)
sl = gf_slice('points', mesh m, mat Pts)
sl = gf_slice('load', string filename[, mesh m])


Description :

General constructor for slice objects.

Creation of a mesh slice. Mesh slices are very similar to a P1-discontinuous mesh_fem on which interpolation is very fast. The slice is built from a mesh object, and a description of the slicing operation, for example:

sl = gf_slice({'planar',+1,[0;0],[1;0]}, m, 5);


cuts the original mesh with the half space {y>0}. Each convex of the original mesh m is simplexified (for example a quadrangle is splitted into 2 triangles), and each simplex is refined 5 times.

Slicing operations can be:

• cutting with a plane, a sphere or a cylinder
• intersection or union of slices
• isovalues surfaces/volumes
• “points”, “streamlines” (see below)

If the first argument is a mesh_fem mf instead of a mesh, and if it is followed by a mf-field u (with size(u,1) == gf_mesh_fem_get(mesh_fem MF, ‘nbdof’)), then the deformation u will be applied to the mesh before the slicing operation.

The first argument can also be a slice.

Command list :

sl = gf_slice(sliceop, {slice sl|{mesh m| mesh_fem mf, vec U}, int refine}[, mat CVfids])

Create a slice using sliceop operation.

sliceop operation is specified with Matlab CELL arrays (i.e. with braces) . The first element is the name of the operation, followed the slicing options:

• {‘none’} : Does not cut the mesh.

• {‘planar’, int orient, vec p, vec n} : Planar cut. p and n define a half-space, p being a point belong to the boundary of the half-space, and n being its normal. If orient is equal to -1 (resp. 0, +1), then the slicing operation will cut the mesh with the “interior” (resp. “boundary”, “exterior”) of the half-space. orient may also be set to +2 which means that the mesh will be sliced, but both the outer and inner parts will be kept.

• {‘ball’, int orient, vec c, scalar r} : Cut with a ball of center c and radius r.

• {‘cylinder’, int orient, vec p1, vec p2, scalar r} : Cut with a cylinder whose axis is the line (p1, p2) and whose radius is r.

• {‘isovalues’, int orient, mesh_fem mf, vec U, scalar s} : Cut using the isosurface of the field U (defined on the mesh_fem mf). The result is the set {x such that :math:U(x) leq s} or {x such that U(x)=s} or {x such that U(x) >= s} depending on the value of orient.

• {‘boundary’[, SLICEOP]} : Return the boundary of the result of SLICEOP, where SLICEOP is any slicing operation. If SLICEOP is not specified, then the whole mesh is considered (i.e. it is equivalent to {‘boundary’,{‘none’}}).

• {‘explode’, mat Coef} : Build an ‘exploded’ view of the mesh: each convex is shrinked ($$0 < \text{Coef} \leq 1$$). In the case of 3D convexes, only their faces are kept.

• {‘union’, SLICEOP1, SLICEOP2} : Returns the union of slicing operations.

• {‘intersection’, SLICEOP1, SLICEOP2} : Returns the intersection of slicing operations, for example:

sl = gf_slice({intersection',{'planar',+1,[0;0;0],[0;0;1]},
{'isovalues',-1,mf2,u2,0}},mf,u,5)

• {‘comp’, SLICEOP} : Returns the complementary of slicing operations.

• {‘diff’, SLICEOP1, SLICEOP2} : Returns the difference of slicing operations.

• {‘mesh’, mesh m} : Build a slice which is the intersection of the sliced mesh with another mesh. The slice is such that all of its simplexes are stricly contained into a convex of each mesh.

sl = gf_slice('streamlines', mesh_fem mf, mat U, mat S)

Compute streamlines of the (vector) field U, with seed points given by the columns of S.

sl = gf_slice('points', mesh m, mat Pts)

Return the “slice” composed of points given by the columns of Pts (useful for interpolation on a given set of sparse points, see gf_compute('interpolate on',sl)).

sl = gf_slice('load', string filename[, mesh m])

Load the slice (and its linked mesh if it is not given as an argument) from a text file.