Plain weave can curve and undulate if you bend the weft as you weave using a wave stick. It's a tool you can make yourself or buy and it's a whole lot of fun!
Ashford Wavy Weaving Shuttle - Mielke's Fiber Arts
Little Looms
46 Wall Hangings and Tapestry Weaving ideas
WEAVING INSTRUCTIONS - PART 6 - WAVY LINES
Weaving Technique, Making Angles (and Waves)
Weaving Curves, hills and waves: Weaving Shapes - Fibers and Design
RailReed – RailReed - adjust warp density while you weave
Building a TriLoom, Pt 1
28 amazing weaving patterns - Gathered
Two braids with weave – Artofit