37 lines
2.1 KiB
Go
37 lines
2.1 KiB
Go
package fluvial
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// Deterministic per-cell jitter, and why a router needs one.
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//
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// D8 lets a cell drain to one of eight neighbours, so every channel is a chain of 0, 45 and 90 degree
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// segments. In mountains the slope hides it. On a plain it is the dominant artefact, and for a specific
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// reason: across a filled flat the only gradient present is the priority-flood's own epsilon, one millimetre
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// a cell, applied in the order the flood happened to reach the cells. The router then faithfully follows the
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// flood's traversal geometry and draws it as rivers — ruler-straight diagonals, the polygonal network that
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// killed the first attempt at flat plains.
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//
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// The fix is to stop the epsilon being uniform. A hash of the cell index scatters it by plus or minus half,
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// which is far below anything that matters to the solve (a millimetre against metre-scale relief) and far
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// above the difference the flood's ordering would otherwise leave, so the descent direction on a flat is
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// decided by the hash rather than by scan order. The same hash breaks near-ties between two equally steep
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// neighbours, which is the other place a fixed direction order leaks a grid axis into the result.
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//
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// It is a hash rather than a random source because cross-cutting rule 12 is determinism from a seed: the
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// value for a cell must not depend on how many cells were visited before it, on which goroutine ran, or on
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// how many steps the solve has taken.
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// hash01 is splitmix64 finalised to the unit interval. Cheap, no state, and well enough distributed that
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// neighbouring indices get unrelated values — which is the whole requirement here.
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func hash01(seed uint64, i int32) float32 {
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x := seed ^ (uint64(uint32(i)) * 0x9e3779b97f4a7c15)
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x ^= x >> 30
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x *= 0xbf58476d1ce4e5b9
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x ^= x >> 27
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x *= 0x94d049bb133111eb
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x ^= x >> 31
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return float32(x>>11) / float32(1<<53)
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}
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// SetSeed ties the jitter to the run's seed, so two seeds do not share the same flat-routing geometry.
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// Zero is a perfectly good seed; it is the default and nothing depends on it being set.
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func (g *Grid) SetSeed(seed int64) { g.seed = uint64(seed)*0x9e3779b97f4a7c15 + 0x243f6a8885a308d3 }
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