使用分形布朗运动创建无缝世界地图
我正在使用分形布朗运动创建高度图。然后，我根据高度为其着色并将其映射到球体。我的问题是高度图不能无缝包裹。我已经使用了 Diamond Square 算法，并且使用它可以很容易地使事情变得无缝，但我似乎无法弄清楚如何使用 fBm 来做到这一点，并且我似乎无法在网络上找到它的解释。
为了澄清，“无缝”是指当我将其映射到球体时，它会在球体上创建无缝地图。
I'm creating heightmaps using Fractal Brownian Motion. I'm then coloring it based on the heights and mapping it to a sphere. My problem is that the heightmap doesn't wrap seamlessly. I've used the Diamond Square algorithm and it's pretty easy to make things seamless using it, but I can't seem to figure out how to do it with fBm and I seem to be having trouble finding an explanation for it on the web.
To clarify, by "seamless", I mean that when I map it to a sphere, it creates a seamless map on the sphere.
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不是计算高度图上每个像素的高度图，而是根据球体上的每个点计算 3D 空间中的高度图，然后将其映射到图像像素。除非您从球体开始计算，否则您将很难将像这样的 2D 矩形高度图包装到球体上，而不会在极点处得到难看的结果。
fBM 概括为 3 维，因此给定球体上的一个点，您可以获得该点的高度，然后您可以进行数学运算，将该值映射到高度图图像中应存储的位置。
Instead of calculating the heightmap per pixel on the heightmap, calculate the heightmap in 3D space based on each point on the sphere and then map that to an image pixel. You're going to have trouble wrapping a 2D, rectangular heightmap like that onto a sphere without getting ugly results at the poles unless you start your calculations from the sphere.
fBM generalizes to 3 dimensions, so given a point on the sphere you can get the height at that point, and then you can do the math to map that value to where it should be stored in the heightmap image.
或者您可以使用传统的地图投影之一。圆柱投影 (x, y)->(x, sin y) 将为您提供一条仅一条子午线的接缝，您可以将其旋转到后面。或者您可以通过一种或另一种方式“消除锯齿”边缘。
对于立体投影 (x,y,z)->(x/(z+1),y/(z+1))，只有一个酸点（投影点本身）。
Or you could use one of the traditional map projections. A cylindrical projection (x, y)->(x, sin y) would give you a seam of just one meridian, which you could rotate to the back. Or you could "antialias" the edge by one or another means.
With a stereographic projection (x,y,z)->(x/(z+1),y/(z+1)), there's only one sour point (the projection point itself).