tf

tf places the interior nodes of a face or a block by transfinite interpolation, which carries the node spacing of the boundary edges into the interior.

Syntax

tf imin jmin kmin imax jmax kmax

The six numbers are a region, as for lin. The region must be a face or a block. An edge or a vertex is refused.

What it does

Like lin, tf treats a region that spans several simple faces or blocks as one, and it never moves a boundary node. Unlike lin, it places each interior node by the relative arc length along the boundary edges, so the spacing you gave the edges shapes the interior. James does no smoothing afterwards. If the boundary folds the arc-length map, the elements come out inverted, and the part’s warning about inverted elements says so. A node that tf moves is projected again onto the surfaces that constrain it.

When James applies it

Step 10 for a face region and step 16 for a block region, after the default interpolations and the projections that come before them. tf is legal only in the Part phase. James refuses it in the Control and Merge phases (E0412).

Rules James adds

A region that is an edge or a vertex is an error (E0701).
Under intyp 2 the default interpolation of every simple face and block is already transfinite, so a tf on one simple region changes nothing there. Under the default, intyp 1, it does change it. The page of intyp describes the setting.
On a cylinder part, James interpolates the angle as an ordinary number, as for lin.

Diagnostics

E0701: the region is an edge or a vertex.
E0102: a reduced index lies outside the part.
E0106: a range of the region is written high to low.

Example

The script tests/corpus/063-tf-edge-rejected/input.tg, which make test runs:

block 1 5 9; 1 4; 1 3;
0 1 2;
0 .5;
0 .3;
tf 1 1 1 3 1 1
endpart

The region 1 1 1 3 1 1 has its j pair and its k pair equal, so it is an edge along i. James prints this and exits with 1, as tests/corpus/063-tf-edge-rejected/expected.diag.txt holds:

input.tg:5:1: error [E0701]: region is an edge or a vertex, but tf/tfi requires a face or a solid block
james: 1 error, 0 warnings

tf