While working on a project in higher category theory, a branch of mathematics, I was lead to draw surface diagrams like the ones you can find in these papers; for example page 22-23, page 13.* Intuitively, you can think of them as objects in three-dimensional space made up of various sheets of paper (of different shape, and sometimes with its boundary partially jagged) glued together at parts of their boundary. On to these "surfaces" one draws "lines" (1-cells).
I am looking for a software that can model these three-dimensional objects. I have the following (ideal, but not all necessary) requirements:
- One should be able to view the objects from all sides,
- One should be able to zoom in and out,
- One should be able to colour, and label certain regions,
- The "programming" of the objects should not be too time-consuming. Ideally, one can create a ?-shaped sheet, bend it and place it somewhere in space. The other such shapes should be easily glued to this sheet by specifying the "gluing boundary",
- The lines one draws onto the sheets should be depicted on both sides of the sheet,
- Ideally, it is freeware …
Does any candidate software come to mind?
*A self-drawn example is this one:
