Maybe I'm going about this the wrong way, but I'm trying to model a huge area (up to 200 km or more) mainly as background to an area about 3 km long and 2 km wide, supposedly on the surface of an Earthlike planet. There is a river just off-center, curving south past the area of interest. There are bluffs about 5-9 km apart on either side of the river valley. The river branches just north of the area of interest. There is a small hill at the northern extreme. (I haven't even started modeling the thing I want to model. This is just the setting I want to place it in.)
The reason for the huge model is that I might want to do aerial renders of the final model (as if from a drone 500-2000 meters up), and at that altitude, if the camera view includes the horizon, the curvature of the Earth will have a noticeable effect. (A flat or infinite plain will look different.)
To mimic the curvature, I used Geometry Nodes to distort a series of grids. The first grid is a 6-km square. The second is a 12-km square with a 6-km square hole in the center. The third is a 24-km square with a 12-km square hole in it. Etc. The number of vetices per grid is adjustable, independent for each grid.
To create the curvature of a grid, I take the x and y position of each vertex, calculate (from the sine) the angle it forms relative to (0,0,0) and (0,0,-6378,000), then use 1-cosine times 6378,000 to calculate the z displacement (always a negative number, except at 0,0,0). I enforce shade smooth on the bent grid from within Geometry Nodes.
Here's my problem: at certain angles, the renders of even mildly reflective areas of the grid produce artifacts that appear as curved lines. This happens even on the center grid, the smallest of them all. Increasing the number of vertices makes the lines sharper and more obvious. Decreasing the number of vertices spreads the artifact out, making them less obvious, but does not get rid of them. They're still there.
I don't understand why I'm seeing these artifacts. They appear in the same place regardless of how much or little I subdivide the grid.
The following examples show renders using 901 or 201 subdivisions per side. The artifacts are less obvious with fewer subdivisions, but still present, and more jagged, with linear edges that clearly look unnatural. Also, they're in the same place, as if the only thing that matters is the distance to the center point. Changing the sun's position can hide the artifacts on areas like the "grass," but they almost always show up on the water. Looking at the model at a larger scale, I can sometimes see a series of these artifacts, like concentric rings.
Any ideas as to what is causing these artifacts or how to eliminate them?
So, my bad. Rendering is not the issue. The problem is with the mesh. My Geometry Node solution to bending a flat grid into a region of a sphere is not producing a smoothly curving surface. It is instead producing a series of concentric horizontal surfaces that move downward at discrete intervals. (Each vertical adjustment is 0.380 meters.)
I'm guessing that my math calculations are being truncated. Math precision in Blender is limited to about 7 decimal places, and my calculations are probably running up against that limitation.
The following rendering shows how the concentric rings are being caused by tiny but abrupt changes in elevation, which show up in the proper lighting.
So back to the original issue, how to produce a mesh with a very small but smooth curvature.