Drawing a solid - Sketch
Description: Sketch

Next: Special objects, Previous: Drawing options, Up: Introduction by example

### 2.3 Drawing a solid

Let's try something more exciting. `Sketch` has no notion of a solid, but polygonal faces can be used to represent the boundary of a solid. To the previous example, let's add three more triangular polygons to make the faces of an irregular tetrahedron.

      % vertices of the tetrahedron
      def p1 (0,0,1) def p2 (1,0,0)
      def p3 (0,1,0) def p4 (-.3,-.5,-.8)

      % faces of the tetrahedron.
      polygon(p1)(p2)(p3) % original front polygon
      polygon(p1)(p4)(p2) % bottom
      polygon(p1)(p3)(p4) % left
      polygon(p3)(p2)(p4) % rear

      % line to pierce the tetrahedron
      line[linecolor=red](-1,-1,-1)(2,2,2)

This example uses definitions, which begin with `def`. These define or give names to points, which are then available as references by enclosing the names in parentheses, e.g. `(foo)`. The parentheses denote that the names refer to points; they are required. There can be no white space between them and the name.

As you can see, comments start with `%` as in TeX and extend to the end of the line (though `#` will work as well). White space, including spaces, tabs and blank lines, has no effect in the `sketch` language.

If we look inside the TeX file produced by `sketch`, there will be only three polygons. The fourth has been culled because it is a “back face” of the tetrahedron, invisible to our view. It is unnecessary, and so it is removed.

In some drawings, polygons act as zero-thickness solid surfaces with both sides visible rather than as the faces of solid objects, where back faces can be culled. For zero-thickness solids, culling is a problem. One solution is to use a pair of `sketch` polygons for each zero-thickness face, identical except with opposite vertex orders. This is unwieldy and expensive. A better way is to set the `sketch` internal option `cull` to `false` in the usual `PSTricks` manner.

      polygon[cull=false](p1)(p2)(p3)

The following shows the same helix shape drawn first with `cull=true` (the default) and then `cull=false`.

We'll soon see how to produce these helixes with a few lines of `sketch` language code.

It may be tempting to turn culling off gratuitously so that vertex order can be ignored. This is not a good idea because output file size and TeX and Postscript processing time both depend on the number of output polygons. Culling usually improves performance by a factor of two. On the other hand, globally setting `cull=false` is reasonable while debugging. See Global options and Limits on error detection.