Overlapping Poly to Random Marching Triangles

I modified my SVG overlapping rectangles to be overlapping triangles, and it is as ugly as you would imagine. I will make polygons with a random number of sides and vertices, three or more. For this I will want to go around the circle, starting at a random point and ending when we get past that point, and also to place points at some random distance from the center of my polygon. Each polygon is then a triangle fan and I can calculate the area by adding up the areas of the triangles. Now we are starting to the point of this, to fill a world map with landmass equal to or at least closely approximating the area of the worlds’ landmass.

Back to the New Model World Map; we presumably have an orbit, stellar luminosity and therefore insolation in AUs, Sols and Earths respectively, as well a planetary mass, density and derive gravity and surface area. We can just randomly set what I usually call the hydrographic ratio. We need a fraction which is land and the rest is sea, or ice if the mean surface temperatures are even vaguely Earthlike, which isn’t guaranteed. For the world and the map, we can simply splat out land polygons, detect and subtract overlap, until we have drawn a world map with more or less enough land. We would then need to worry about local surface temps, precipitation, etc. to find arable land for colony sites or native civilizations. For that I will probably want to build adjacent polygons out of a little something I am calling random marching triangles; you make a small triangle, push out a new triangle off a random side, rinse and repeat. I need it to tend to double back on itself and close off triangle fans, but also push out projecting bits.