How can I draw random polygons (triangles) in Inkscape like on the picture above? Well, I can do them manually, but maybe there is a tool for that?
This method will give you random polygons, but you'll have to fill them yourself.
Use the spray tool to spray some random dots. In the settings for the spray tool, select the "prevent overlapping shapes" option and set an offset so you don't get the dots too close.
Select all (CTRL+A)
Extensions > Generate from Path > Voranoi Diagram
Set the diagram type to: "Delaunay Triangulation"
To select triangles, use the Edit Paths by Nodes tool (F2).
Apply a fill
To apply a pattern fill, first copy and paste one of the triangles in place (CTRL+C to copy, then CTRL+Alt+V to paste in place)
Choose a pattern fill.
- Adjust the scale and position of the pattern fill with the Edit Paths by Nodes tool (F2), by clicking and dragging on the controls at the top of the page.
You can define your own custom patterns in Inkscape if the standard set aren't doing it for you. Just make a pattern of your own, select all of it, and click Object > Pattern > Objects to pattern
Here I've applied a pattern I made to a triangle as a pattern fill.
The spray tool is for randomly distributed objects, for instance triangles.
Make a base triangle. Then select it into the clipboard. Choose the spray tool. Experiment with the settings (size, rotation, number) and create a bunch of them.
What you won't get, AFAIK, is random fill patterns.