Morph terrain levels into each other so neighbours meet without cracks

Tiles drawn at the same level met exactly, but a finer tile beside a coarser one has
samples on their shared edge that the coarser one skips, and the ground between them
could open up. This closes the gap the standard way (CDLOD): each vertex slides towards
the next coarser level as its distance nears the end of its level's range, so that by the
end of the band a tile is, vertex for vertex, the coarser tile beyond it. Levels also stop
popping when they change.

The mip chain is point sampled, so the next level's grid is this level's even samples. An
odd vertex slides onto its even neighbour and takes its height, and the grid, whose
diagonals all run the same way at every level, collapses exactly into the coarser
triangulation. No second texture and no neighbour information is needed; the morph is
computed per vertex from its distance to the camera, the same distance the level is
chosen by.

Two things the geometry demands, both settled by tools/terraincook/seamcheck.py, which
walks random camera positions over 128 m, 256 m and 12.8 km tiles and counts every edge
vertex where the finer side has not finished morphing or the coarser side has started:

- the band ends a rescan's worth of travel (a quarter tile) short of the level's range.
  Levels are chosen where the camera stood at the last rescan, the morph follows it every
  frame, and a band ending at the range itself left gaps at every level boundary;
- the band is a fifth of the range wide, and level ranges are counted in tiles (four for
  the finest level) rather than fixed metres, which keeps the coarser tile's band clear of
  any edge a finer tile reaches, whatever the tile size.

The script finds no gap with these values. In the game on baltyk, a low view differs from
the unmorphed shader only in a strip of distant ground at the horizon, and nearer than
the first band the picture is identical.

The cooker's comment claimed tile seams were identical at every level; that held only
for neighbours at the same level, and now says so.

rendering/terrainstatus.cppm

@@ -19,14 +19,42 @@ export module eu07.rendering.terrainstatus;
 
 export {
 
-// distance out to which a terrain tile is drawn at its finest level; each further level
-// doubles it
-inline constexpr double terrain_finest_range { 512.0 };
+// distance out to which a terrain tile is drawn at its finest level, in tile sides; each
+// further level doubles it. four sides is 512 m for the usual 128 m tile. the ranges are
+// measured in tiles rather than metres because the morphing below only closes the seams
+// when a level's range is several tiles long, whatever the tile size
+inline constexpr double terrain_finest_tiles { 4.0 };
 
-// the distance up to which a level is used
+// how far the camera may move before the tiles in range and their levels are worked out
+// again, in tile sides
+inline constexpr double terrain_rescan_tiles { 0.25 };
+
+// the distance up to which a level is used, for tiles of the given side
 inline double
-terrain_level_distance( std::uint32_t const Level ) {
-    return terrain_finest_range * std::pow( 2.0, Level );
+terrain_level_distance( std::uint32_t const Level, double const Tilesize ) {
+    return terrain_finest_tiles * Tilesize * std::pow( 2.0, Level );
+}
+
+// A tile morphs into the next level over a band at the far end of its level's range. Two
+// neighbours at levels L and L+1 then meet exactly when, all along their shared edge, the
+// finer tile has finished morphing and the coarser one has not started. The band ends a
+// rescan's worth of travel short of the range, because levels are chosen where the camera
+// was at the last rescan while the morph follows the camera every frame; and it is a fifth
+// of the range wide, which keeps the coarser tile's band, a whole range further out, clear of
+// any edge a finer tile can reach. Both were settled by a geometric test over random camera
+// positions and three tile sizes, which finds no gap with these values and finds them at
+// every level boundary with a band ending at the range itself.
+inline constexpr double terrain_morph_band { 0.2 };
+
+// the distances, from the camera, over which a level L tile morphs into level L+1
+inline double
+terrain_morph_end( std::uint32_t const Level, double const Tilesize ) {
+    return terrain_level_distance( Level, Tilesize ) - terrain_rescan_tiles * Tilesize;
+}
+
+inline double
+terrain_morph_begin( std::uint32_t const Level, double const Tilesize ) {
+    return terrain_morph_end( Level, Tilesize ) - terrain_morph_band * terrain_level_distance( Level, Tilesize );
 }
 
 // what one terrain field's streamer is doing, kept by the field and read by the debug panel