Sunday, September 26, 2021

I’ve been on this oval-shaped world polygon div kick for a while, where the 2D shape represents a ‘world peach’ polyhedron, with the edges of the oval-shaped polygon coming together at a seam ‘down the back’ of the ‘world peach’. The number of steps down that seam should have something to do with the size of the world so that the triangles we subdivide the world surface into should be more or less the same, not exactly but similar. For a circumference of 40,000 km and 20, 1000 km, steps from pole to pole we want roughly that many steps between each side of the seam… The shortcut we’re taking is to make these points separated by the width of a circle, but we can double that for an oval and not worry about making a sinusoidal shape; it makes no difference to me, I will sleep soundly without worrying about it!

I’ve tried to do this several times, but I will get it done this time! Anyway, we know how big the world is, how many thousands of kilometers in circumference, and we round down to half as many thousands, on average 20 for an earth-sized world of 40,000 km circumference. So we have 20 rows from pole to pole, zero wide at the top and at the bottom, the north and south poles, and then we can find the distance between the ends of the rows, which is zero for the first and last points at the North and South poles. In making points within a CSS polygon shape the top is 0; since we’re building something inside a circle 50 units in radius, this is (0, -50); the next would be (-10,-45), (10, -45), 20 units wide, 20/100*40 is 8 triangles in that north polar triangle fan. The next would be (-30, -40), (30, -40), 60 units wide or 24 for 2 bottom triangles, a top triangle and final bottom triangle, repeated eight times. The next row would be about 28 triangles wide…

I’m not getting anywhere with this right now, time to get to bed!!!


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