veloren/world/src/sim/erosion.rs

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use super::{diffusion, downhill, uphill};
use crate::{config::CONFIG, util::RandomField};
use common::{
terrain::{
neighbors, uniform_idx_as_vec2, vec2_as_uniform_idx, MapSizeLg, TerrainChunkSize,
NEIGHBOR_DELTA,
},
vol::RectVolSize,
};
use tracing::{debug, error, warn};
// use faster::*;
use itertools::izip;
use noise::NoiseFn;
use num::{Float, Zero};
use ordered_float::NotNan;
#[cfg(feature = "simd")] use packed_simd::m32;
use rayon::prelude::*;
use std::{
cmp::{Ordering, Reverse},
collections::BinaryHeap,
f32, f64, fmt, mem,
time::Instant,
u32,
};
use vek::*;
pub type Alt = f64;
pub type Compute = f64;
pub type Computex8 = [Compute; 8];
/* code used by sharp in future
/// Compute the water flux at all chunks, given a list of chunk indices sorted
/// by increasing height.
pub fn get_drainage(
map_size_lg: MapSizeLg,
newh: &[u32],
downhill: &[isize],
_boundary_len: usize,
) -> Box<[f32]> {
// FIXME: Make the below work. For now, we just use constant flux.
// Initially, flux is determined by rainfall. We currently treat this as the
// same as humidity, so we just use humidity as a proxy. The total flux
// across the whole map is normalize to 1.0, and we expect the average flux
// to be 0.5. To figure out how far from normal any given chunk is, we use
// its logit. NOTE: If there are no non-boundary chunks, we just set
// base_flux to 1.0; this should still work fine because in that case
// there's no erosion anyway. let base_flux = 1.0 / ((map_size_lg.chunks_len())
// as f32);
let base_flux = 1.0;
let mut flux = vec![base_flux; map_size_lg.chunks_len()].into_boxed_slice();
newh.iter().rev().for_each(|&chunk_idx| {
let chunk_idx = chunk_idx as usize;
let downhill_idx = downhill[chunk_idx];
if downhill_idx >= 0 {
flux[downhill_idx as usize] += flux[chunk_idx];
}
});
flux
}
*/
/// Compute the water flux at all chunks for multiple receivers, given a list of
/// chunk indices sorted by increasing height and weights for each receiver.
pub fn get_multi_drainage(
map_size_lg: MapSizeLg,
mstack: &[u32],
mrec: &[u8],
mwrec: &[Computex8],
_boundary_len: usize,
) -> Box<[Compute]> {
// FIXME: Make the below work. For now, we just use constant flux.
// Initially, flux is determined by rainfall. We currently treat this as the
// same as humidity, so we just use humidity as a proxy. The total flux
// across the whole map is normalize to 1.0, and we expect the average flux
// to be 0.5. To figure out how far from normal any given chunk is, we use
// its logit. NOTE: If there are no non-boundary chunks, we just set
// base_flux to 1.0; this should still work fine because in that case
// there's no erosion anyway.
let base_area = 1.0;
let mut area = vec![base_area; map_size_lg.chunks_len()].into_boxed_slice();
mstack.iter().for_each(|&ij| {
let ij = ij as usize;
let wrec_ij = &mwrec[ij];
let area_ij = area[ij];
mrec_downhill(map_size_lg, mrec, ij).for_each(|(k, ijr)| {
area[ijr] += area_ij * wrec_ij[k];
});
});
area
/*
a=dx*dy*precip
do ij=1,nn
ijk=mstack(ij)
do k =1,mnrec(ijk)
a(mrec(k,ijk))=a(mrec(k,ijk))+a(ijk)*mwrec(k,ijk)
enddo
enddo
*/
}
/// Kind of water on this tile.
#[derive(Clone, Copy, Debug, PartialEq)]
pub enum RiverKind {
Ocean,
Lake {
/// In addition to a downhill node (pointing to, eventually, the bottom
/// of the lake), each lake also has a "pass" that identifies
/// the direction out of which water should flow from this lake
/// if it is minimally flooded. While some lakes may be too full for
/// this to be the actual pass used by their enclosing lake, we
/// still use this as a way to make sure that lake connections
/// to rivers flow in the correct direction.
neighbor_pass_pos: Vec2<i32>,
},
/// River should be maximal.
River {
/// Dimensions of the river's cross-sectional area, as m × m (rivers are
/// approximated as an open rectangular prism in the direction
/// of the velocity vector).
cross_section: Vec2<f32>,
},
}
impl RiverKind {
pub fn is_ocean(&self) -> bool { matches!(*self, RiverKind::Ocean) }
pub fn is_river(&self) -> bool { matches!(*self, RiverKind::River { .. }) }
pub fn is_lake(&self) -> bool { matches!(*self, RiverKind::Lake { .. }) }
}
impl PartialOrd for RiverKind {
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
match (*self, *other) {
(RiverKind::Ocean, RiverKind::Ocean) => Some(Ordering::Equal),
(RiverKind::Ocean, _) => Some(Ordering::Less),
(_, RiverKind::Ocean) => Some(Ordering::Greater),
(RiverKind::Lake { .. }, RiverKind::Lake { .. }) => None,
(RiverKind::Lake { .. }, _) => Some(Ordering::Less),
(_, RiverKind::Lake { .. }) => Some(Ordering::Greater),
(RiverKind::River { .. }, RiverKind::River { .. }) => None,
}
}
}
/// From velocity and cross_section we can calculate the volumetric flow rate,
/// as the cross-sectional area times the velocity.
///
/// TODO: we might choose to include a curve for the river, as long as it didn't
/// allow it to cross more than one neighboring chunk away. For now we defer
/// this to rendering time.
///
/// NOTE: This structure is 57 (or more likely 64) bytes, which is kind of big.
#[derive(Clone, Debug, Default)]
pub struct RiverData {
/// A velocity vector (in m / minute, i.e. voxels / second from a game
/// perspective).
///
/// TODO: To represent this in a better-packed way, use u8s instead (as
/// "f8s").
pub(crate) velocity: Vec3<f32>,
/// The computed derivative for the segment of river starting at this chunk
/// (and flowing downhill). Should be 0 at endpoints. For rivers with
/// more than one incoming segment, we weight the derivatives by flux
/// (cross-sectional area times velocity) which is correlated
/// with mass / second; treating the derivative as "velocity" with respect
/// to length along the river, we treat the weighted sum of incoming
/// splines as the "momentum", and can divide it by the total incoming
/// mass as a way to find the velocity of the center of mass. We can
/// then use this derivative to find a "tangent" for the incoming river
/// segment at this point, and as the linear part of the interpolating
/// spline at this point.
///
/// Note that we aren't going to have completely smooth curves here anyway,
/// so we will probably end up applying a dampening factor as well
/// (maybe based on the length?) to prevent extremely wild oscillations.
pub(crate) spline_derivative: Vec2<f32>,
/// If this chunk is part of a river, this should be true. We can't just
/// compute this from the cross section because once a river becomes
/// visible, we want it to stay visible until it reaches its sink.
pub river_kind: Option<RiverKind>,
/// We also have a second record for recording any rivers in nearby chunks
/// that manage to intersect this chunk, though this is unlikely to
/// happen in current gameplay. This is because river areas are allowed
/// to cross arbitrarily many chunk boundaries, if they are wide enough.
/// In such cases we may choose to render the rivers as particularly deep in
/// those places.
pub(crate) neighbor_rivers: Vec<u32>,
}
impl RiverData {
pub fn is_ocean(&self) -> bool {
self.river_kind
.as_ref()
.map(RiverKind::is_ocean)
.unwrap_or(false)
}
pub fn is_river(&self) -> bool {
self.river_kind
.as_ref()
.map(RiverKind::is_river)
.unwrap_or(false)
}
pub fn is_lake(&self) -> bool {
self.river_kind
.as_ref()
.map(RiverKind::is_lake)
.unwrap_or(false)
}
pub fn near_river(&self) -> bool { self.is_river() || !self.neighbor_rivers.is_empty() }
pub fn near_water(&self) -> bool { self.near_river() || self.is_lake() || self.is_ocean() }
}
/// Draw rivers and assign them heights, widths, and velocities. Take some
/// liberties with the constant factors etc. in order to make it more likely
/// that we draw rivers at all.
pub fn get_rivers<F: fmt::Debug + Float + Into<f64>, G: Float + Into<f64>>(
map_size_lg: MapSizeLg,
continent_scale_hack: f64,
newh: &[u32],
water_alt: &[F],
downhill: &[isize],
indirection: &[i32],
drainage: &[G],
) -> Box<[RiverData]> {
// For continuity-preserving quadratic spline interpolation, we (appear to) need
// to build up the derivatives from the top down. Fortunately this
// computation seems tractable.
let mut rivers = vec![RiverData::default(); map_size_lg.chunks_len()].into_boxed_slice();
let neighbor_coef = TerrainChunkSize::RECT_SIZE.map(|e| e as f64);
// (Roughly) area of a chunk, times minutes per second.
// NOTE: Clearly, this should "actually" be 1/60 (or maybe 1/64, if you want to
// retain powers of 2).
//
// But since we want rivers to form more often than they do in real life, we use
// this as a way to control the frequency of river formation. As grid_scale
// increases, mins_per_sec should decrease, until it hits 1 / 60 or 1/ 64.
// For example, if grid_scale is multiplied by 4, mins_per_sec should be
// multiplied by 1 / (4.0 * 4.0).
let mins_per_sec = 1.0 / (continent_scale_hack * continent_scale_hack)/*1.0 / 16.0*//*1.0 / 64.0*/;
let chunk_area_factor = neighbor_coef.x * neighbor_coef.y * mins_per_sec;
// NOTE: This technically makes us discontinuous, so we should be cautious about
// using this.
let derivative_divisor = 1.0;
newh.iter().rev().for_each(|&chunk_idx| {
let chunk_idx = chunk_idx as usize;
let downhill_idx = downhill[chunk_idx];
if downhill_idx < 0 {
// We are in the ocean.
debug_assert!(downhill_idx == -2);
rivers[chunk_idx].river_kind = Some(RiverKind::Ocean);
return;
}
let downhill_idx = downhill_idx as usize;
let downhill_pos = uniform_idx_as_vec2(map_size_lg, downhill_idx);
let dxy = (downhill_pos - uniform_idx_as_vec2(map_size_lg, chunk_idx)).map(|e| e as f64);
let neighbor_dim = neighbor_coef * dxy;
// First, we calculate the river's volumetric flow rate.
let chunk_drainage = drainage[chunk_idx].into();
// Volumetric flow rate is just the total drainage area to this chunk, times
// rainfall height per chunk per minute, times minutes per second
// (needed in order to use this as a m³ volume).
// TODO: consider having different rainfall rates (and including this
// information in the computation of drainage).
let volumetric_flow_rate =
chunk_drainage * chunk_area_factor * CONFIG.rainfall_chunk_rate as f64;
let downhill_drainage = drainage[downhill_idx].into();
// We know the drainage to the downhill node is just chunk_drainage - 1.0 (the
// amount of rainfall this chunk is said to get), so we don't need to
// explicitly remember the incoming mass. How do we find a slope for
// endpoints where there is no incoming data? Currently, we just assume
// it's set to 0.0. TODO: Fix this when we add differing amounts of
// rainfall.
let incoming_drainage = downhill_drainage - 1.0;
let get_river_spline_derivative =
|neighbor_dim: Vec2<f64>, spline_derivative: Vec2<f32>| {
// "Velocity of center of mass" of splines of incoming flows.
let river_prev_slope = spline_derivative.map(|e| e as f64);
// NOTE: We need to make sure the slope doesn't get *too* crazy.
// ((dpx - cx) - 4 * MAX).abs() = bx
// NOTE: This will fail if the distance between chunks in any direction
// is exactly TerrainChunkSize::RECT * 4.0, but hopefully this should not be
// possible. NOTE: This isn't measuring actual distance, you can
// go farther on diagonals.
let max_deriv = neighbor_dim - neighbor_coef * 2.0 * 2.0.sqrt();
let extra_divisor = river_prev_slope
.map2(max_deriv, |e, f| (e / f).abs())
.reduce_partial_max();
// Set up the river's spline derivative. For each incoming river at pos with
// river_spline_derivative bx, we can compute our interpolated slope as:
// d_x = 2 * (chunk_pos - pos - bx) + bx
// = 2 * (chunk_pos - pos) - bx
//
// which is exactly twice what was weighted by uphill nodes to get our
// river_spline_derivative in the first place.
//
// NOTE: this probably implies that the distance shouldn't be normalized, since
// the distances aren't actually equal between x and y... we'll
// see what happens.
(if extra_divisor > 1.0 {
river_prev_slope / extra_divisor
} else {
river_prev_slope
})
.map(|e| e as f32)
};
let river = &rivers[chunk_idx];
let river_spline_derivative =
get_river_spline_derivative(neighbor_dim, river.spline_derivative);
let indirection_idx = indirection[chunk_idx];
// Find the lake we are flowing into.
let lake_idx = if indirection_idx < 0 {
// If we're a lake bottom, our own indirection is negative.
let pass_idx = (-indirection_idx) as usize;
// NOTE: Must exist since this lake had a downhill in the first place.
let neighbor_pass_idx = downhill[pass_idx] as usize/*downhill_idx*/;
let mut lake_neighbor_pass = &mut rivers[neighbor_pass_idx];
// We definitely shouldn't have encountered this yet!
debug_assert!(lake_neighbor_pass.velocity == Vec3::zero());
// TODO: Rethink making the lake neighbor pass always a river or lake, no matter
// how much incoming water there is? Sometimes it looks weird
// having a river emerge from a tiny pool.
lake_neighbor_pass.river_kind = Some(RiverKind::River {
cross_section: Vec2::default(),
});
chunk_idx
} else {
indirection_idx as usize
};
// Find the pass this lake is flowing into (i.e. water at the lake bottom gets
// pushed towards the point identified by pass_idx).
let pass_idx = if downhill[lake_idx] < 0 {
// Flows into nothing, so this lake is its own pass.
lake_idx
} else {
(-indirection[lake_idx]) as usize
};
// Add our spline derivative to the downhill river (weighted by the chunk's
// drainage). NOTE: Don't add the spline derivative to the lake side of
// the pass for our own lake, because we don't want to preserve weird
// curvature from before we hit the lake in the outflowing river (this
// will not apply to one-chunk lakes, which are their own pass).
if pass_idx != downhill_idx {
// TODO: consider utilizing height difference component of flux as well;
// currently we just discard it in figuring out the spline's slope.
let downhill_river = &mut rivers[downhill_idx];
let weighted_flow = (neighbor_dim * 2.0 - river_spline_derivative.map(|e| e as f64))
/ derivative_divisor
* chunk_drainage
/ incoming_drainage;
downhill_river.spline_derivative += weighted_flow.map(|e| e as f32);
}
let neighbor_pass_idx = downhill[pass_idx];
// Find our own water height.
let chunk_water_alt = water_alt[chunk_idx];
if neighbor_pass_idx >= 0 {
// We may be a river. But we're not sure yet, since we still could be
// underwater. Check the lake height and see if our own water height is within
// ε of it.
let lake_water_alt = water_alt[lake_idx];
if chunk_water_alt == lake_water_alt {
// Not a river.
// Check whether we we are the lake side of the pass.
// NOTE: Safe because this is a lake.
let (neighbor_pass_pos, river_spline_derivative) = if pass_idx == chunk_idx {
// This is a pass, so set our flow direction to point to the neighbor pass
// rather than downhill.
// NOTE: Safe because neighbor_pass_idx >= 0.
(
uniform_idx_as_vec2(map_size_lg, downhill_idx),
river_spline_derivative,
)
} else {
// Try pointing towards the lake side of the pass.
(
uniform_idx_as_vec2(map_size_lg, pass_idx),
river_spline_derivative,
)
};
let mut lake = &mut rivers[chunk_idx];
lake.spline_derivative = river_spline_derivative;
lake.river_kind = Some(RiverKind::Lake {
neighbor_pass_pos: neighbor_pass_pos
* TerrainChunkSize::RECT_SIZE.map(|e| e as i32),
});
return;
}
// Otherwise, we must be a river.
} else {
// We are flowing into the ocean.
debug_assert!(neighbor_pass_idx == -2);
// But we are not the ocean, so we must be a river.
}
// Now, we know we are a river *candidate*. We still don't know whether we are
// actually a river, though. There are two ways for that to happen:
// (i) We are already a river.
// (ii) Using the GaucklerManningStrickler formula for cross-sectional
// average velocity of water, we establish that the river can be
// "big enough" to appear on the Veloren map.
//
// This is very imprecise, of course, and (ii) may (and almost certainly will)
// change over time.
//
// In both cases, we preemptively set our child to be a river, to make sure we
// have an unbroken stream. Also in both cases, we go to the effort of
// computing an effective water velocity vector and cross-sectional
// dimensions, as well as figuring out the derivative of our
// interpolating spline (since this percolates through the whole river
// network).
let downhill_water_alt = water_alt[downhill_idx];
let neighbor_distance = neighbor_dim.magnitude();
let dz = (downhill_water_alt - chunk_water_alt).into();
let slope = dz.abs() / neighbor_distance;
if slope == 0.0 {
// This is not a river--how did this even happen?
let pass_idx = (-indirection_idx) as usize;
error!(
"Our chunk (and downhill, lake, pass, neighbor_pass): {:?} (to {:?}, in {:?} via \
{:?} to {:?}), chunk water alt: {:?}, lake water alt: {:?}",
uniform_idx_as_vec2(map_size_lg, chunk_idx),
uniform_idx_as_vec2(map_size_lg, downhill_idx),
uniform_idx_as_vec2(map_size_lg, lake_idx),
uniform_idx_as_vec2(map_size_lg, pass_idx),
if neighbor_pass_idx >= 0 {
Some(uniform_idx_as_vec2(map_size_lg, neighbor_pass_idx as usize))
} else {
None
},
water_alt[chunk_idx],
water_alt[lake_idx]
);
panic!("Should this happen at all?");
}
let slope_sqrt = slope.sqrt();
// Now, we compute a quantity that is proportional to the velocity of the chunk,
// derived from the Manning formula, equal to
// volumetric_flow_rate / slope_sqrt * CONFIG.river_roughness.
let almost_velocity = volumetric_flow_rate / slope_sqrt * CONFIG.river_roughness as f64;
// From this, we can figure out the width of the chunk if we know the height.
// For now, we hardcode the height to 0.5, but it should almost
// certainly be much more complicated than this.
// let mut height = 0.5f32;
// We approximate the river as a rectangular prism. Theoretically, we need to
// solve the following quintic equation to determine its width from its
// height:
//
// h^5 * w^5 = almost_velocity^3 * (w + 2 * h)^2.
//
// This is because one of the quantities in the Manning formula (the unknown) is
// R_h = (area of cross-section / h)^(2/3).
//
// Unfortunately, quintic equations do not in general have algebraic solutions,
// and it's not clear (to me anyway) that this one does in all cases.
//
// In practice, for high ratios of width to height, we can approximate the
// rectangular prism's perimeter as equal to its width, so R_h as equal
// to height. This greatly simplifies the calculation. For simplicity,
// we do this even for low ratios of width to height--I found that for
// most real rivers, at least big ones, this approximation is
// "good enough." We don't need to be *that* realistic :P
//
// NOTE: Derived from a paper on estimating river width.
let mut width = 5.0
* (CONFIG.river_width_to_depth as f64
* (CONFIG.river_width_to_depth as f64 + 2.0).powf(2.0 / 3.0))
.powf(3.0 / 8.0)
* volumetric_flow_rate.powf(3.0 / 8.0)
* slope.powf(-3.0 / 16.0)
* (CONFIG.river_roughness as f64).powf(3.0 / 8.0);
width = width.max(0.0);
let mut height = if width == 0.0 {
CONFIG.river_min_height as f64
} else {
(almost_velocity / width).powf(3.0 / 5.0)
};
// We can now weight the river's drainage by its direction, which we use to help
// improve the slope of the downhill node.
let river_direction = Vec3::new(neighbor_dim.x, neighbor_dim.y, dz.signum() * dz);
// Now, we can check whether this is "really" a river.
// Currently, we just check that width and height are at least 0.5 and
// CONFIG.river_min_height.
let river = &rivers[chunk_idx];
let is_river = river.is_river() || width >= 0.5 && height >= CONFIG.river_min_height as f64;
let mut downhill_river = &mut rivers[downhill_idx];
if is_river {
// Provisionally make the downhill chunk a river as well.
downhill_river.river_kind = Some(RiverKind::River {
cross_section: Vec2::default(),
});
// Additionally, if the cross-sectional area for this river exceeds the max
// river width, the river is overflowing the two chunks adjacent to
// it, which we'd prefer to avoid since only its two immediate
// neighbors (orthogonal to the downhill direction) are guaranteed
// uphill of it. Solving this properly most likely requires
// modifying the erosion model to take channel width into account,
// which is a formidable task that likely requires rethinking the
// current grid-based erosion model (or at least, requires tracking some
// edges that aren't implied by the grid graph). For now, we will solve this
// problem by making the river deeper when it hits the max width,
// until it consumes all the available energy in this part of the
// river.
let max_width = TerrainChunkSize::RECT_SIZE.x as f64 * CONFIG.river_max_width as f64;
if width > max_width {
width = max_width;
height = (almost_velocity / width).powf(3.0 / 5.0);
}
}
// Now we can compute the river's approximate velocity magnitude as well, as
let velocity_magnitude =
1.0 / CONFIG.river_roughness as f64 * height.powf(2.0 / 3.0) * slope_sqrt;
// Set up the river's cross-sectional area.
let cross_section = Vec2::new(width as f32, height as f32);
// Set up the river's velocity vector.
let mut velocity = river_direction;
velocity.normalize();
velocity *= velocity_magnitude;
let mut river = &mut rivers[chunk_idx];
// NOTE: Not trying to do this more cleverly because we want to keep the river's
// neighbors. TODO: Actually put something in the neighbors.
river.velocity = velocity.map(|e| e as f32);
river.spline_derivative = river_spline_derivative;
river.river_kind = if is_river {
Some(RiverKind::River { cross_section })
} else {
None
};
});
rivers
}
/// Precompute the maximum slope at all points.
///
/// TODO: See if allocating in advance is worthwhile.
fn get_max_slope(
map_size_lg: MapSizeLg,
h: &[Alt],
rock_strength_nz: &(impl NoiseFn<[f64; 3]> + Sync),
height_scale: impl Fn(usize) -> Alt + Sync,
) -> Box<[f64]> {
let min_max_angle = (15.0 / 360.0 * 2.0 * f64::consts::PI).tan();
let max_max_angle = (60.0 / 360.0 * 2.0 * f64::consts::PI).tan();
let max_angle_range = max_max_angle - min_max_angle;
h.par_iter()
.enumerate()
.map(|(posi, &z)| {
let wposf = uniform_idx_as_vec2(map_size_lg, posi).map(|e| e as f64)
* TerrainChunkSize::RECT_SIZE.map(|e| e as f64);
let height_scale = height_scale(posi);
let wposz = z as f64 / height_scale as f64;
// Normalized to be between 6 and and 54 degrees.
let div_factor = (2.0 * TerrainChunkSize::RECT_SIZE.x as f64) / 8.0;
let rock_strength = rock_strength_nz.get([wposf.x, wposf.y, wposz * div_factor]);
let rock_strength = rock_strength.max(-1.0).min(1.0) * 0.5 + 0.5;
// Logistic regression. Make sure x ∈ (0, 1).
let logit = |x: f64| x.ln() - (-x).ln_1p();
// 0.5 + 0.5 * tanh(ln(1 / (1 - 0.1) - 1) / (2 * (sqrt(3)/pi)))
let logistic_2_base = 3.0f64.sqrt() * f64::consts::FRAC_2_PI;
// Assumes μ = 0, σ = 1
let logistic_cdf = |x: f64| (x / logistic_2_base).tanh() * 0.5 + 0.5;
// We do log-odds against center, so that our log odds are 0 when x = 0.25,
// lower when x is lower, and higher when x is higher.
//
// (NOTE: below sea level, we invert it).
//
// TODO: Make all this stuff configurable... but honestly, it's so complicated
// that I'm not sure anyone would be able to usefully tweak them on
// a per-map basis? Plus it's just a hacky heuristic anyway.
let center = 0.4;
let dmin = center - 0.05;
let dmax = center + 0.05;
let log_odds = |x: f64| logit(x) - logit(center);
let rock_strength = logistic_cdf(
1.0 * logit(rock_strength.min(1.0f64 - 1e-7).max(1e-7))
+ 1.0
* log_odds(
(wposz / CONFIG.mountain_scale as f64)
.abs()
.min(dmax)
.max(dmin),
),
);
// NOTE: If you want to disable varying rock strength entirely, uncomment this
// line. let max_slope = 3.0.sqrt() / 3.0;
rock_strength * max_angle_range + min_max_angle //max_slope
})
.collect::<Vec<_>>()
.into_boxed_slice()
}
// simd alternative
#[cfg(not(feature = "simd"))]
#[derive(Copy, Clone)]
#[allow(non_camel_case_types)]
struct m32(u32);
#[cfg(not(feature = "simd"))]
impl m32 {
#[inline]
fn new(x: bool) -> Self { if x { Self(u32::MAX) } else { Self(u32::MIN) } }
#[inline]
fn test(&self) -> bool { self.0 != 0 }
}
/// Erode all chunks by amount.
///
/// Our equation is:
///
/// dh(p) / dt = uplift(p)k * A(p)^m * slope(p)^n
///
/// where A(p) is the drainage area at p, m and n are constants
/// (we choose m = 0.4 and n = 1), and k is a constant. We choose
///
/// k = 2.244 * uplift.max() / (desired_max_height)
///
/// since this tends to produce mountains of max height desired_max_height;
/// and we set desired_max_height = 1.0 to reflect limitations of mountain
/// scale.
///
/// This algorithm does this in four steps:
///
/// 1. Sort the nodes in h by height (so the lowest node by altitude is first
/// in the list, and the highest node by altitude is last).
/// 2. Iterate through the list in *reverse.* For each node, we compute its
/// drainage area as the sum of the drainage areas of its "children" nodes
/// (i.e. the nodes with directed edges to this node). To do this
/// efficiently, we start with the "leaves" (the highest nodes), which
/// have no neighbors higher than them, hence no directed edges to them.
/// We add their area to themselves, and then to all neighbors that they
/// flow into (their "ancestors" in the flow graph); currently, this just
/// means the node immediately downhill of this node. As we go lower, we
/// know that all our "children" already had their areas computed, which
/// means that we can repeat the process in order to derive all the final
/// areas.
/// 3. Now, iterate through the list in *order.* Whether we used the filling
/// method to compute a "filled" version of each depression, or used the lake
/// connection algorithm described in [1], each node is guaranteed to have
/// zero or one drainage edges out, representing the direction of water flow
/// for that node. For nodes i with zero drainage edges out (boundary nodes
/// and lake bottoms) we set the slope to 0 (so the change in altitude is
/// uplift(i))
/// For nodes with at least one drainage edge out, we take advantage of the
/// fact that we are computing new heights in order and rewrite our equation
/// as (letting j = downhill[i], A[i] be the computed area of point i,
/// p(i) be the x-y position of point i,
/// flux(i) = k * A[i]^m / ((p(i) - p(j)).magnitude()), and δt = 1):
///
/// h[i](t + dt) = h[i](t) + δt * (uplift[i] + flux(i) * h[j](t + δt)) / (1 +
/// flux(i) * δt).
///
/// Since we compute heights in ascending order by height, and j is downhill
/// from i, h[j] will always be the *new* h[j](t + δt), while h[i] will still
/// not have been computed yet, so we only need to visit each node once.
///
/// Afterwards, we also apply a hillslope diffusion process using an ADI
/// (alternating direction implicit) method:
///
/// https://github.com/fastscape-lem/fastscapelib-fortran/blob/master/src/Diffusion.f90
///
/// We also borrow the implementation for sediment transport from
///
/// https://github.com/fastscape-lem/fastscapelib-fortran/blob/master/src/StreamPowerLaw.f90
///
/// The approximate equation for soil production function (predicting the rate
/// at which bedrock turns into soil, increasing the distance between the
/// basement and altitude) is taken from equation (11) from [2]. This (among
/// numerous other sources) also includes at least one prediction that hillslope
/// diffusion should be nonlinear, which we sort of attempt to approximate.
///
/// [1] Guillaume Cordonnier, Jean Braun, Marie-Paule Cani,
/// Bedrich Benes, Eric Galin, et al..
/// Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion.
/// Computer Graphics Forum, Wiley, 2016, Proc. EUROGRAPHICS 2016, 35 (2),
/// pp.165-175. ⟨10.1111/cgf.12820⟩. ⟨hal-01262376⟩
///
/// [2] William E. Dietrich, Dino G. Bellugi, Leonard S. Sklar,
/// Jonathan D. Stock
/// Geomorphic Transport Laws for Predicting Landscape Form and Dynamics.
/// Prediction in Geomorphology, Geophysical Monograph 135.
/// Copyright 2003 by the American Geophysical Union
/// 10.1029/135GM09
fn erode(
// Underlying map dimensions.
map_size_lg: MapSizeLg,
// Height above sea level of topsoil
h: &mut [Alt],
// Height above sea level of bedrock
b: &mut [Alt],
// Height above sea level of water
wh: &mut [Alt],
max_uplift: f32,
max_g: f32,
kdsed: f64,
_seed: &RandomField,
rock_strength_nz: &(impl NoiseFn<[f64; 3]> + Sync),
uplift: impl Fn(usize) -> f32 + Sync,
n_f: impl Fn(usize) -> f32 + Sync,
m_f: impl Fn(usize) -> f32 + Sync,
kf: impl Fn(usize) -> f64 + Sync,
kd: impl Fn(usize) -> f64,
g: impl Fn(usize) -> f32 + Sync,
epsilon_0: impl Fn(usize) -> f32 + Sync,
alpha: impl Fn(usize) -> f32 + Sync,
is_ocean: impl Fn(usize) -> bool + Sync,
// scaling factors
height_scale: impl Fn(f32) -> Alt + Sync,
k_da_scale: impl Fn(f64) -> f64,
threadpool: &rayon::ThreadPool,
) {
let compute_stats = true;
debug!("Done draining...");
// NOTE: To experimentally allow erosion to proceed below sea level, replace 0.0
// with -<Alt as Float>::infinity().
let min_erosion_height = 0.0; // -<Alt as Float>::infinity();
// NOTE: The value being divided by here sets the effective maximum uplift rate,
// as everything is scaled to it!
let dt = max_uplift as f64 / 1e-3;
debug!(?dt, "");
// Minimum sediment thickness before we treat erosion as sediment based.
let sediment_thickness = |_n| /*6.25e-5*/1.0e-4 * dt;
let neighbor_coef = TerrainChunkSize::RECT_SIZE.map(|e| e as f64);
let chunk_area = neighbor_coef.x * neighbor_coef.y;
let min_length = neighbor_coef.reduce_partial_min();
let max_stable = min_length * min_length / dt;
// Debris flow area coefficient (m^(-2q)).
let q = 0.2;
// NOTE: Set to 1.0 to make (assuming n = 1) the erosion equation linear during
// each stream power iteration. This will result in significant speedups,
// at the cost of less interesting erosion behavior (linear vs. nonlinear).
let q_ = 1.5;
let k_da = 2.5 * k_da_scale(q);
let nx = usize::from(map_size_lg.chunks().x);
let ny = usize::from(map_size_lg.chunks().y);
let dx = TerrainChunkSize::RECT_SIZE.x as f64;
let dy = TerrainChunkSize::RECT_SIZE.y as f64;
#[rustfmt::skip]
// ε₀ and α are part of the soil production approximate
// equation:
//
// -∂z_b / ∂t = ε₀ * e^(-αH)
//
// where
// z_b is the elevation of the soil-bedrock interface (i.e. the basement),
// ε₀ is the production rate of exposed bedrock (H = 0),
// H is the soil thickness normal to the ground surface,
// and α is a parameter (units of 1 / length).
//
// Note that normal depth at i, for us, will be interpreted as the soil depth vector,
// sed_i = ((0, 0), h_i - b_i),
// projected onto the ground surface slope vector,
// ground_surface_i = ((p_i - p_j), h_i - h_j),
// yielding the soil depth vector
// H_i = sed_i - sed_i ⋅ ground_surface_i / (ground_surface_i ⋅ ground_surface_i) * ground_surface_i
//
// = ((0, 0), h_i - b_i) -
// (0 * ||p_i - p_j|| + (h_i - b_i) * (h_i - h_j)) / (||p_i - p_j||^2 + (h_i - h_j)^2)
// * (p_i - p_j, h_i - h_j)
// = ((0, 0), h_i - b_i) -
// ((h_i - b_i) * (h_i - h_j)) / (||p_i - p_j||^2 + (h_i - h_j)^2)
// * (p_i - p_j, h_i - h_j)
// = (h_i - b_i) *
// (((0, 0), 1) - (h_i - h_j) / (||p_i - p_j||^2 + (h_i - h_j)^2) * (p_i - p_j, h_i - h_j))
// H_i_fact = (h_i - h_j) / (||p_i - p_j||^2 + (h_i - h_j)^2)
// H_i = (h_i - b_i) * ((((0, 0), 1) - H_i_fact * (p_i - p_j, h_i - h_j)))
// = (h_i - b_i) * (-H_i_fact * (p_i - p_j), 1 - H_i_fact * (h_i - h_j))
// ||H_i|| = (h_i - b_i) * √(H_i_fact^2 * ||p_i - p_j||^2 + (1 - H_i_fact * (h_i - h_j))^2)
// = (h_i - b_i) * √(H_i_fact^2 * ||p_i - p_j||^2 + 1 - 2 * H_i_fact * (h_i - h_j) +
// H_i_fact^2 * (h_i - h_j)^2)
// = (h_i - b_i) * √(H_i_fact^2 * (||p_i - p_j||^2 + (h_i - h_j)^2) +
// 1 - 2 * H_i_fact * (h_i - h_j))
// = (h_i - b_i) * √((h_i - h_j)^2 / (||p_i - p_j||^2 + (h_i - h_j)^2) * (||p_i - p_j||^2 + (h_i - h_j)^2) +
// 1 - 2 * (h_i - h_j)^2 / (||p_i - p_j||^2 + (h_i - h_j)^2))
// = (h_i - b_i) * √((h_i - h_j)^2 - 2(h_i - h_j)^2 / (||p_i - p_j||^2 + (h_i - h_j)^2) + 1)
//
// where j is i's receiver and ||p_i - p_j|| is the horizontal displacement between them. The
// idea here is that we first compute the hypotenuse between the horizontal and vertical
// displacement of ground (getting the horizontal component of the triangle), and then this is
// taken as one of the non-hypotenuse sides of the triangle whose other non-hypotenuse side is
// the normal height H_i, while their square adds up to the vertical displacement (h_i - b_i).
// If h and b have different slopes, this may not work completely correctly, but this is
// probably fine as an approximation.
// Spatio-temporal variation in net precipitation rate ((m / year) / (m / year)) (ratio of
// precipitation rate at chunk relative to mean precipitation rate p₀).
let p = 1.0;
// Dimensionless multiplier for stream power erosion constant when land becomes
// sediment.
let k_fs_mult_sed = 4.0;
// Dimensionless multiplier for G when land becomes sediment.
let g_fs_mult_sed = 1.0;
let ((dh, newh, maxh, mrec, mstack, mwrec, area), (mut max_slopes, h_t)) = threadpool.join(
|| {
let mut dh = downhill(
map_size_lg,
|posi| h[posi],
|posi| is_ocean(posi) && h[posi] <= 0.0,
);
debug!("Computed downhill...");
let (boundary_len, _indirection, newh, maxh) =
get_lakes(map_size_lg, |posi| h[posi], &mut dh);
debug!("Got lakes...");
let (mrec, mstack, mwrec) = get_multi_rec(
map_size_lg,
|posi| h[posi],
&dh,
&newh,
wh,
nx,
ny,
dx as Compute,
dy as Compute,
maxh,
threadpool,
);
debug!("Got multiple receivers...");
// TODO: Figure out how to switch between single-receiver and multi-receiver
// drainage, as the former is much less computationally costly.
// let area = get_drainage(map_size_lg, &newh, &dh, boundary_len);
let area = get_multi_drainage(map_size_lg, &mstack, &mrec, &*mwrec, boundary_len);
debug!("Got flux...");
(dh, newh, maxh, mrec, mstack, mwrec, area)
},
|| {
threadpool.join(
|| {
let max_slope = get_max_slope(map_size_lg, h, rock_strength_nz, |posi| {
height_scale(n_f(posi))
});
debug!("Got max slopes...");
max_slope
},
|| h.to_vec().into_boxed_slice(),
)
},
);
assert!(h.len() == dh.len() && dh.len() == area.len());
// max angle of slope depends on rock strength, which is computed from noise
// function. TODO: Make more principled.
let mid_slope = (30.0 / 360.0 * 2.0 * f64::consts::PI).tan();
type SimdType = f32;
type MaskType = m32;
// Precompute factors for Stream Power Law.
let czero = <SimdType as Zero>::zero();
let (k_fs_fact, k_df_fact) = threadpool.join(
|| {
dh.par_iter()
.enumerate()
.map(|(posi, &posj)| {
let mut k_tot = [czero; 8];
if posj < 0 {
// Egress with no outgoing flows, no stream power.
k_tot
} else {
let old_b_i = b[posi];
let sed = (h_t[posi] - old_b_i) as f64;
let n = n_f(posi);
// Higher rock strength tends to lead to higher erodibility?
let kd_factor = 1.0;
let k_fs = kf(posi) / kd_factor;
let k = if sed > sediment_thickness(n) {
// Sediment
k_fs_mult_sed * k_fs
} else {
// Bedrock
k_fs
} * dt;
let n = n as f64;
let m = m_f(posi) as f64;
let mwrec_i = &mwrec[posi];
mrec_downhill(map_size_lg, &mrec, posi).for_each(|(kk, posj)| {
let dxy = (uniform_idx_as_vec2(map_size_lg, posi)
- uniform_idx_as_vec2(map_size_lg, posj))
.map(|e| e as f64);
let neighbor_distance = (neighbor_coef * dxy).magnitude();
let knew = (k
* (p as f64
* chunk_area
* (area[posi] as f64 * mwrec_i[kk] as f64))
.powf(m)
/ neighbor_distance.powf(n))
as SimdType;
k_tot[kk] = knew;
});
k_tot
}
})
.collect::<Vec<[SimdType; 8]>>()
},
|| {
dh.par_iter()
.enumerate()
.map(|(posi, &posj)| {
let mut k_tot = [czero; 8];
let uplift_i = uplift(posi) as f64;
debug_assert!(uplift_i.is_normal() && uplift_i > 0.0 || uplift_i == 0.0);
if posj < 0 {
// Egress with no outgoing flows, no stream power.
k_tot
} else {
let area_i = area[posi] as f64;
let max_slope = max_slopes[posi];
let chunk_area_pow = chunk_area.powf(q);
let old_b_i = b[posi];
let sed = (h_t[posi] - old_b_i) as f64;
let n = n_f(posi);
let g_i = if sed > sediment_thickness(n) {
// Sediment
(g_fs_mult_sed * g(posi)) as f64
} else {
// Bedrock
g(posi) as f64
};
// Higher rock strength tends to lead to higher curvature?
let kd_factor = (max_slope / mid_slope).powi(2);
let k_da = k_da * kd_factor;
let mwrec_i = &mwrec[posi];
mrec_downhill(map_size_lg, &mrec, posi).for_each(|(kk, posj)| {
let mwrec_kk = mwrec_i[kk] as f64;
#[rustfmt::skip]
// Working equation:
// U = uplift per time
// D = sediment deposition per time
// E = fluvial erosion per time
// 0 = U + D - E - k_df * (1 + k_da * (mrec_kk * A)^q) * (∂B/∂p)^(q_)
//
// k_df = (U + D - E) / (1 + k_da * (mrec_kk * A)^q) / (∂B/∂p)^(q_)
//
// Want: ∂B/∂p = max slope at steady state, i.e.
// ∂B/∂p = max_slope
// Then:
// k_df = (U + D - E) / (1 + k_da * (mrec_kk * A)^q) / max_slope^(q_)
// Letting
// k = k_df * Δt
// we get:
// k = (U + D - E)Δt / (1 + k_da * (mrec_kk * A)^q) / (ΔB)^(q_)
//
// Now ∂B/∂t under constant uplift, without debris flow (U + D - E), is
// U + D - E = U - E + G/(p̃A) * ∫_A((U - ∂h/∂t) * dA)
//
// Observing that at steady state ∂h/∂t should theoretically
// be 0, we can simplify to:
// U + D = U + G/(p̃A) * ∫_A(U * dA)
//
// Upper bounding this at uplift = max_uplift/∂t for the whole prior
// drainage area, and assuming we account for just mrec_kk of
// the combined uplift and deposition, we get:
//
// U + D ≤ mrec_kk * U + G/p̃ * max_uplift/∂t
// (U + D - E)Δt ≤ (mrec_kk * uplift_i + G/p̃ * mrec_kk * max_uplift - EΔt)
//
// therefore
// k * (1 + k_da * (mrec_kk * A)^q) * max_slope^(q_) ≤ (mrec_kk * (uplift_i + G/p̃ * max_uplift) - EΔt)
// i.e.
// k ≤ (mrec_kk * (uplift_i + G/p̃ * max_uplift) - EΔt) / (1 + k_da * (mrec_kk * A)^q) / max_slope^q_
//
// (eliminating EΔt maintains the sign, but it's somewhat imprecise;
// we can address this later, e.g. by assigning a debris flow / fluvial erosion ratio).
let chunk_neutral_area = 0.1e6; // 1 km^2 * (1000 m / km)^2 = 1e6 m^2
let k = (mwrec_kk * (uplift_i + max_uplift as f64 * g_i / p as f64))
/ (1.0 + k_da * (mwrec_kk * chunk_neutral_area).powf(q))
/ max_slope.powf(q_);
let dxy = (uniform_idx_as_vec2(map_size_lg, posi)
- uniform_idx_as_vec2(map_size_lg, posj))
.map(|e| e as f64);
let neighbor_distance = (neighbor_coef * dxy).magnitude();
let knew = (k
* (1.0 + k_da * chunk_area_pow * (area_i * mwrec_kk).powf(q))
/ neighbor_distance.powf(q_))
as SimdType;
k_tot[kk] = knew;
});
k_tot
}
})
.collect::<Vec<[SimdType; 8]>>()
},
);
debug!("Computed stream power factors...");
let mut lake_water_volume: Box<[Compute]> =
vec![0.0_f64; map_size_lg.chunks_len()].into_boxed_slice();
let mut elev: Box<[Compute]> = vec![0_f64; map_size_lg.chunks_len()].into_boxed_slice();
let mut h_p: Box<[Compute]> = vec![0_f64; map_size_lg.chunks_len()].into_boxed_slice();
let mut deltah: Box<[Compute]> = vec![0_f64; map_size_lg.chunks_len()].into_boxed_slice();
// calculate the elevation / SPL, including sediment flux
let tol1: Compute = 1.0e-4_f64 * (maxh as Compute + 1.0);
let tol2: Compute = 1.0e-3_f64 * (max_uplift as Compute + 1.0);
let tol = tol1.max(tol2);
let mut err = 2.0 * tol;
// Some variables for tracking statistics, currently only for debugging
// purposes.
let mut minh = <Alt as Float>::infinity();
let mut maxh = 0.0;
let mut nland = 0usize;
let mut ncorr = 0usize;
let mut sums = 0.0;
let mut sumh = 0.0;
let mut sumsed = 0.0;
let mut sumsed_land = 0.0;
let mut ntherm = 0usize;
// ln of product of actual slopes (only where actual is above critical).
let mut prods_therm = 0.0;
// ln of product of critical slopes (only where actual is above critical).
let mut prodscrit_therm = 0.0;
let avgz = |x, y: usize| if y == 0 { f64::INFINITY } else { x / y as f64 };
let geomz = |x: f64, y: usize| {
if y == 0 {
f64::INFINITY
} else {
(x / y as f64).exp()
}
};
// Gauss-Seidel iteration
let mut lake_silt: Box<[Compute]> = vec![0.0_f64; map_size_lg.chunks_len()].into_boxed_slice();
let mut lake_sill = vec![-1isize; map_size_lg.chunks_len()].into_boxed_slice();
let mut n_gs_stream_power_law = 0;
// NOTE: Increasing this can theoretically sometimes be necessary for
// convergence, but in practice it is fairly unlikely that you should need
// to do this (especially if you stick to g ∈ [0, 1]).
let max_n_gs_stream_power_law = 99;
let mut mstack_inv = vec![0usize; dh.len()];
let mut h_t_stack = vec![Zero::zero(); dh.len()];
let mut dh_stack = vec![0isize; dh.len()];
let mut h_stack = vec![Zero::zero(); dh.len()];
let mut b_stack = vec![Zero::zero(); dh.len()];
let mut area_stack = vec![Zero::zero(); dh.len()];
assert!(mstack.len() == dh.len());
assert!(b.len() == dh.len());
assert!(h_t.len() == dh.len());
let mstack_inv = &mut *mstack_inv;
mstack.iter().enumerate().for_each(|(stacki, &posi)| {
let posi = posi as usize;
mstack_inv[posi] = stacki;
dh_stack[stacki] = dh[posi];
h_t_stack[stacki] = h_t[posi];
h_stack[stacki] = h[posi];
b_stack[stacki] = b[posi];
area_stack[stacki] = area[posi];
});
while err > tol && n_gs_stream_power_law < max_n_gs_stream_power_law {
debug!("Stream power iteration #{:?}", n_gs_stream_power_law);
// Reset statistics in each loop.
maxh = 0.0;
minh = <Alt as Float>::infinity();
nland = 0usize;
ncorr = 0usize;
sums = 0.0;
sumh = 0.0;
sumsed = 0.0;
sumsed_land = 0.0;
ntherm = 0usize;
prods_therm = 0.0;
prodscrit_therm = 0.0;
let start_time = Instant::now();
// Keep track of how many iterations we've gone to test for convergence.
n_gs_stream_power_law += 1;
threadpool.join(
|| {
// guess/update the elevation at t+Δt (k)
(&mut *h_p, &*h_stack)
.into_par_iter()
.for_each(|(h_p, h_)| {
*h_p = (*h_) as Compute;
});
},
|| {
// calculate erosion/deposition of sediment at each node
(&*mstack, &mut *deltah, &*h_t_stack, &*h_stack)
.into_par_iter()
.for_each(|(&posi, deltah, &h_t_i, &h_i)| {
let posi = posi as usize;
let uplift_i = uplift(posi) as Alt;
let delta = (h_t_i + uplift_i - h_i) as Compute;
*deltah = delta;
});
},
);
debug!(
"(Done precomputation, time={:?}ms).",
start_time.elapsed().as_millis()
);
#[rustfmt::skip]
// sum the erosion in stack order
//
// After:
// deltah_i = Σ{j ∈ {i} upstream_i(t)}(h_j(t, FINAL) + U_j * Δt - h_i(t + Δt, k))
let start_time = Instant::now();
izip!(&*mstack, &*dh_stack, &h_t_stack, &*h_p)
.enumerate()
.for_each(|(stacki, (&posi, &posj, &h_t_i, &h_p_i))| {
let posi = posi as usize;
let deltah_i = deltah[stacki];
if posj < 0 {
lake_silt[stacki] = deltah_i;
} else {
let uplift_i = uplift(posi) as Alt;
let uphill_deltah_i = deltah_i - ((h_t_i + uplift_i) as Compute - h_p_i);
let lposi = lake_sill[stacki];
if lposi == stacki as isize {
if uphill_deltah_i <= 0.0 {
lake_silt[stacki] = 0.0;
} else {
lake_silt[stacki] = uphill_deltah_i;
}
}
let mwrec_i = &mwrec[posi];
mrec_downhill(map_size_lg, &mrec, posi).for_each(|(k, posj)| {
let stack_posj = mstack_inv[posj];
deltah[stack_posj] += deltah_i * mwrec_i[k];
});
}
});
debug!(
"(Done sediment transport computation, time={:?}ms).",
start_time.elapsed().as_millis()
);
#[rustfmt::skip]
// do ij=nn,1,-1
// ijk=stack(ij)
// ijr=rec(ijk)
// if (ijr.ne.ijk) then
// dh(ijk)=dh(ijk)-(ht(ijk)-hp(ijk))
// if (lake_sill(ijk).eq.ijk) then
// if (dh(ijk).le.0.d0) then
// lake_sediment(ijk)=0.d0
// else
// lake_sediment(ijk)=dh(ijk)
// endif
// endif
// dh(ijk)=dh(ijk)+(ht(ijk)-hp(ijk))
// dh(ijr)=dh(ijr)+dh(ijk)
// else
// lake_sediment(ijk)=dh(ijk)
// endif
// enddo
let start_time = Instant::now();
(
&*mstack,
&mut *elev,
&*dh_stack,
&*h_t_stack,
&*area_stack,
&*deltah,
&*h_p,
&*b_stack,
)
.into_par_iter()
.for_each(
|(&posi, elev, &dh_i, &h_t_i, &area_i, &deltah_i, &h_p_i, &b_i)| {
let posi = posi as usize;
let uplift_i = uplift(posi) as Alt;
if dh_i < 0 {
*elev = (h_t_i + uplift_i) as Compute;
} else {
let old_h_after_uplift_i = (h_t_i + uplift_i) as Compute;
let area_i = area_i as Compute;
let uphill_silt_i = deltah_i - (old_h_after_uplift_i - h_p_i);
let old_b_i = b_i;
let sed = (h_t_i - old_b_i) as f64;
let n = n_f(posi);
let g_i = if sed > sediment_thickness(n) {
(g_fs_mult_sed * g(posi)) as Compute
} else {
g(posi) as Compute
};
// Make sure deposition coefficient doesn't result in more deposition than
// there actually was material to deposit. The
// current assumption is that as long as we
// are storing at most as much sediment as there actually was along the
// river, we are in the clear.
let g_i_ratio = g_i / (p * area_i);
// One side of nonlinear equation (23):
//
// h_i(t) + U_i * Δt + G / (p̃ * Ã_i) * Σ
// {j ∈ upstream_i(t)}(h_j(t, FINAL)
// + U_j * Δt - h_j(t + Δt, k))
//
// where
//
// Ã_i = A_i / (∆x∆y) = N_i,
// number of cells upstream of cell i.
*elev = old_h_after_uplift_i + uphill_silt_i * g_i_ratio;
}
},
);
debug!(
"(Done elevation estimation, time={:?}ms).",
start_time.elapsed().as_millis()
);
let start_time = Instant::now();
// TODO: Consider taking advantage of multi-receiver flow here.
// Iterate in ascending height order.
let mut sum_err: Compute = 0.0_f64;
itertools::izip!(&*mstack, &*elev, &*b_stack, &*h_t_stack, &*dh_stack, &*h_p)
.enumerate()
.rev()
.for_each(|(stacki, (&posi, &elev_i, &b_i, &h_t_i, &dh_i, &h_p_i))| {
let iteration_error = 0.0;
let posi = posi as usize;
let old_elev_i = elev_i as f64;
let old_b_i = b_i;
let old_ht_i = h_t_i;
let sed = (old_ht_i - old_b_i) as f64;
let posj = dh_i;
if posj < 0 {
if posj == -1 {
panic!("Disconnected lake!");
}
if h_t_i > 0.0 {
warn!("Ocean above zero?");
}
// Egress with no outgoing flows.
// wh for oceans is always at least min_erosion_height.
let uplift_i = uplift(posi) as Alt;
wh[posi] = min_erosion_height.max(h_t_i + uplift_i);
lake_sill[stacki] = posi as isize;
lake_water_volume[stacki] = 0.0;
} else {
let posj = posj as usize;
// Has an outgoing flow edge (posi, posj).
// flux(i) = k * A[i]^m / ((p(i) - p(j)).magnitude()), and δt = 1
// h[i](t + dt) = (h[i](t) + δt * (uplift[i] + flux(i) * h[j](t + δt))) / (1 +
// flux(i) * δt). NOTE: posj has already been computed since
// it's downhill from us. Therefore, we can rely on wh being
// set to the water height for that node.
// let h_j = h[posj_stack] as f64;
let wh_j = wh[posj] as f64;
let old_h_i = h_stack[stacki] as f64;
let mut new_h_i = old_h_i;
// Only perform erosion if we are above the water level of the previous node.
// NOTE: Can replace wh_j with h_j here (and a few other places) to allow
// erosion underwater, producing very different looking
// maps!
if old_elev_i > wh_j
/* h_j */
{
let dtherm = 0.0f64;
let h0 = old_elev_i + dtherm;
// hi(t + ∂t) = (hi(t) + ∂t(ui + kp^mAi^m(hj(t + ∂t)/||pi - pj||))) / (1 +
// ∂t * kp^mAi^m / ||pi - pj||)
let n = n_f(posi) as f64;
// Fluvial erosion.
let k_df_fact = &k_df_fact[posi];
let k_fs_fact = &k_fs_fact[posi];
if (n - 1.0).abs() <= 1.0e-3 && (q_ - 1.0).abs() <= 1.0e-3 {
let mut f = h0;
let mut df = 1.0;
mrec_downhill(map_size_lg, &mrec, posi).for_each(|(kk, posj)| {
let posj_stack = mstack_inv[posj];
let h_j = h_stack[posj_stack] as f64;
// This can happen in cases where receiver kk is neither uphill of
// nor downhill from posi's direct receiver.
// NOTE: Fastscape does h_t[posi] + uplift(posi) as f64 >= h_t[posj]
// + uplift(posj) as f64
// NOTE: We also considered using old_elev_i > wh[posj] here.
if old_elev_i > h_j {
let elev_j = h_j;
let fact = k_fs_fact[kk] as f64 + k_df_fact[kk] as f64;
f += fact * elev_j;
df += fact;
}
});
new_h_i = f / df;
} else {
// Local Newton-Raphson
// TODO: Work out how (if possible) to make this converge for tiny n.
let omega1 = 0.875f64 * n;
let omega2 = 0.875f64 / q_;
let omega = omega1.max(omega2);
let tolp = 1.0e-3;
let mut errp = 2.0 * tolp;
let mut rec_heights = [0.0; 8];
let mut mask = [MaskType::new(false); 8];
mrec_downhill(map_size_lg, &mrec, posi).for_each(|(kk, posj)| {
let posj_stack = mstack_inv[posj];
let h_j = h_stack[posj_stack];
// NOTE: Fastscape does h_t[posi] + uplift(posi) as f64 >= h_t[posj]
// + uplift(posj) as f64
// NOTE: We also considered using old_elev_i > wh[posj] here.
if old_elev_i > h_j as f64 {
mask[kk] = MaskType::new(true);
rec_heights[kk] = h_j as SimdType;
}
});
while errp > tolp {
let mut f = new_h_i - h0;
let mut df = 1.0;
izip!(&mask, &rec_heights, k_fs_fact, k_df_fact).for_each(
|(&mask_kk, &rec_heights_kk, &k_fs_fact_kk, &k_df_fact_kk)| {
if mask_kk.test() {
let h_j = rec_heights_kk;
let elev_j = h_j;
let dh = 0.0.max(new_h_i as SimdType - elev_j);
let powf = |a: SimdType, b| a.powf(b);
let dh_fs_sample = k_fs_fact_kk as SimdType
* powf(dh, n as SimdType - 1.0);
let dh_df_sample = k_df_fact_kk as SimdType
* powf(dh, q_ as SimdType - 1.0);
// Want: h_i(t+Δt) = h0 - fact * (h_i(t+Δt) -
// h_j(t+Δt))^n
// Goal: h_i(t+Δt) - h0 + fact * (h_i(t+Δt) -
// h_j(t+Δt))^n = 0
f += ((dh_fs_sample + dh_df_sample) * dh) as f64;
// ∂h_i(t+Δt)/∂n = 1 + fact * n * (h_i(t+Δt) -
// h_j(t+Δt))^(n - 1)
df += (n as SimdType * dh_fs_sample
+ q_ as SimdType * dh_df_sample)
as f64;
}
},
);
// hn = h_i(t+Δt, k) - (h_i(t+Δt, k) - (h0 - fact * (h_i(t+Δt, k) -
// h_j(t+Δt))^n)) / ∂h_i/∂n(t+Δt, k)
let hn = new_h_i - f / df;
// errp = |(h_i(t+Δt, k) - (h0 - fact * (h_i(t+Δt, k) -
// h_j(t+Δt))^n)) / ∂h_i/∂n(t+Δt, k)|
errp = (hn - new_h_i).abs();
// h_i(t+∆t, k+1) = ...
new_h_i = new_h_i * (1.0 - omega) + hn * omega;
}
/* omega=0.875d0/n
tolp=1.d-3
errp=2.d0*tolp
h0=elev(ijk)
do while (errp.gt.tolp)
f=h(ijk)-h0
df=1.d0
if (ht(ijk).gt.ht(ijr)) then
fact = kfint(ijk)*dt*a(ijk)**m/length(ijk)**n
f=f+fact*max(0.d0,h(ijk)-h(ijr))**n
df=df+fact*n*max(0.d0,h(ijk)-h(ijr))**(n-1.d0)
endif
hn=h(ijk)-f/df
errp=abs(hn-h(ijk))
h(ijk)=h(ijk)*(1.d0-omega)+hn*omega
enddo */
}
lake_sill[stacki] = posi as isize;
lake_water_volume[stacki] = 0.0;
// If we dipped below the receiver's water level, set our height to the
// receiver's water level.
// NOTE: If we want erosion to proceed underwater, use h_j here instead of
// wh_j.
if new_h_i <= wh_j
/* h_j */
{
if compute_stats {
ncorr += 1;
}
// NOTE: Why wh_j?
// Because in the next round, if the old height is still wh_j or under,
// it will be set precisely equal to the
// estimated height, meaning it effectively
// "vanishes" and just deposits sediment to its receiver.
// (This is probably related to criteria for block Gauss-Seidel, etc.).
// NOTE: If we want erosion to proceed underwater, use h_j here instead
// of wh_j.
new_h_i = wh_j;
} else if compute_stats && new_h_i > 0.0 {
let dxy = (uniform_idx_as_vec2(map_size_lg, posi)
- uniform_idx_as_vec2(map_size_lg, posj))
.map(|e| e as f64);
let neighbor_distance = (neighbor_coef * dxy).magnitude();
let dz = (new_h_i - wh_j).max(0.0);
let mag_slope = dz / neighbor_distance;
nland += 1;
sumsed_land += sed;
sumh += new_h_i;
sums += mag_slope;
}
} else {
new_h_i = old_elev_i;
let posj_stack = mstack_inv[posj];
let lposj = lake_sill[posj_stack];
lake_sill[stacki] = lposj;
if lposj >= 0 {
let lposj = lposj as usize;
lake_water_volume[lposj] += (wh_j - old_elev_i) as Compute;
}
}
// Set max_slope to this node's water height (max of receiver's water height and
// this node's height).
wh[posi] = wh_j.max(new_h_i) as Alt;
h_stack[stacki] = new_h_i as Alt;
}
if compute_stats {
sumsed += sed;
let h_i = h_stack[stacki];
if h_i > 0.0 {
minh = h_i.min(minh);
}
maxh = h_i.max(maxh);
}
// Add sum of squares of errors.
sum_err +=
(iteration_error + h_stack[stacki] as Compute - h_p_i as Compute).powi(2);
});
debug!(
"(Done erosion computation, time={:?}ms)",
start_time.elapsed().as_millis()
);
err = (sum_err / mstack.len() as Compute).sqrt();
debug!("(RMSE: {:?})", err);
if max_g == 0.0 {
err = 0.0;
}
if n_gs_stream_power_law == max_n_gs_stream_power_law {
warn!(
"Beware: Gauss-Seidel scheme not convergent: err={:?}, expected={:?}",
err, tol
);
}
}
(&*mstack_inv, &mut *h)
.into_par_iter()
.enumerate()
.for_each(|(posi, (&stacki, h))| {
assert!(posi == mstack[stacki] as usize);
*h = h_stack[stacki];
});
// update the basement
//
// NOTE: Despite this not quite applying since basement order and height order
// differ, we once again borrow the implicit FastScape stack order. If this
// becomes a problem we can easily compute a separate stack order just for
// basement. TODO: Consider taking advantage of multi-receiver flow here.
b.par_iter_mut()
.zip_eq(h.par_iter())
.enumerate()
.for_each(|(posi, (b, &h_i))| {
let old_b_i = *b;
let uplift_i = uplift(posi) as Alt;
// First, add uplift...
let mut new_b_i = old_b_i + uplift_i;
let posj = dh[posi];
// Sediment height normal to bedrock. NOTE: Currently we can actually have
// sediment and bedrock slope at different heights, meaning there's
// no uniform slope. There are probably more correct ways to
// account for this, such as averaging, integrating, or doing things
// by mass / volume instead of height, but for now we use the time-honored
// technique of ignoring the problem.
let vertical_sed = (h_i - new_b_i).max(0.0) as f64;
let h_normal = if posj < 0 {
// Egress with no outgoing flows; for now, we assume this means normal and
// vertical coincide.
vertical_sed
} else {
let posj = posj as usize;
let h_j = h[posj];
let dxy = (uniform_idx_as_vec2(map_size_lg, posi)
- uniform_idx_as_vec2(map_size_lg, posj))
.map(|e| e as f64);
let neighbor_distance_squared = (neighbor_coef * dxy).magnitude_squared();
let dh = (h_i - h_j) as f64;
// H_i_fact = (h_i - h_j) / (||p_i - p_j||^2 + (h_i - h_j)^2)
let h_i_fact = dh / (neighbor_distance_squared + dh * dh);
let h_i_vertical = 1.0 - h_i_fact * dh;
// ||H_i|| = (h_i - b_i) * √((H_i_fact^2 * ||p_i - p_j||^2 + (1 - H_i_fact *
// (h_i - h_j))^2))
vertical_sed
* (h_i_fact * h_i_fact * neighbor_distance_squared
+ h_i_vertical * h_i_vertical)
.sqrt()
};
// Rate of sediment production: -∂z_b / ∂t = ε₀ * e^(-αH)
let p_i = epsilon_0(posi) as f64 * dt * f64::exp(-alpha(posi) as f64 * h_normal);
new_b_i -= p_i as Alt;
// Clamp basement so it doesn't exceed height.
new_b_i = new_b_i.min(h_i);
*b = new_b_i;
});
debug!("Done updating basement and applying soil production...");
// update the height to reflect sediment flux.
if max_g > 0.0 {
// If max_g = 0.0, lake_silt will be too high during the first iteration since
// our initial estimate for h is very poor; however, the elevation
// estimate will have been unaffected by g.
(&mut *h, &*mstack_inv)
.into_par_iter()
.enumerate()
.for_each(|(posi, (h, &stacki))| {
let lposi = lake_sill[stacki];
if lposi >= 0 {
let lposi = lposi as usize;
if lake_water_volume[lposi] > 0.0 {
// +max(0.d0,min(lake_sediment(lake_sill(ij)),
// lake_water_volume(lake_sill(ij))))/
// lake_water_volume(lake_sill(ij))*(water(ij)-h(ij))
*h += (0.0.max(lake_silt[stacki].min(lake_water_volume[lposi]))
/ lake_water_volume[lposi]
* (wh[posi] - *h) as Compute) as Alt;
}
}
});
}
// do ij=1,nn
// if (lake_sill(ij).ne.0) then
// if (lake_water_volume(lake_sill(ij)).gt.0.d0) h(ij)=h(ij) &
// +max(0.d0,min(lake_sediment(lake_sill(ij)),
// lake_water_volume(lake_sill(ij))))/ &
// lake_water_volume(lake_sill(ij))*(water(ij)-h(ij))
// endif
// enddo
debug!(
"Done applying stream power (max height: {:?}) (avg height: {:?}) (min height: {:?}) (avg \
slope: {:?})\n (above talus angle, geom. mean slope [actual/critical/ratio]: {:?} \
/ {:?} / {:?})\n (old avg sediment thickness [all/land]: {:?} / {:?})\n \
(num land: {:?}) (num thermal: {:?}) (num corrected: {:?})",
maxh,
avgz(sumh, nland),
minh,
avgz(sums, nland),
geomz(prods_therm, ntherm),
geomz(prodscrit_therm, ntherm),
geomz(prods_therm - prodscrit_therm, ntherm),
avgz(sumsed, newh.len()),
avgz(sumsed_land, nland),
nland,
ntherm,
ncorr,
);
// Apply thermal erosion.
maxh = 0.0;
minh = <Alt as Float>::infinity();
sumh = 0.0;
sums = 0.0;
sumsed = 0.0;
sumsed_land = 0.0;
nland = 0usize;
ncorr = 0usize;
ntherm = 0usize;
prods_therm = 0.0;
prodscrit_therm = 0.0;
newh.iter().for_each(|&posi| {
let posi = posi as usize;
let old_h_i = h[posi] as f64;
let old_b_i = b[posi] as f64;
let sed = (old_h_i - old_b_i) as f64;
let max_slope = max_slopes[posi];
let n = n_f(posi);
max_slopes[posi] = if sed > sediment_thickness(n) && kdsed > 0.0 {
// Sediment
kdsed
} else {
// Bedrock
kd(posi)
};
let posj = dh[posi];
if posj < 0 {
// Egress with no outgoing flows.
if posj == -1 {
panic!("Disconnected lake!");
}
// wh for oceans is always at least min_erosion_height.
wh[posi] = min_erosion_height.max(old_h_i as Alt);
} else {
let posj = posj as usize;
// Find the water height for this chunk's receiver; we only apply thermal
// erosion for chunks above water.
let wh_j = wh[posj] as f64;
let mut new_h_i = old_h_i;
if wh_j < old_h_i {
// NOTE: Currently assuming that talus angle is not eroded once the substance is
// totally submerged in water, and that talus angle if part of the substance is
// in water is 0 (or the same as the dry part, if this is set to wh_j), but
// actually that's probably not true.
let old_h_j = h[posj] as f64;
let h_j = old_h_j;
// Test the slope.
// Hacky version of thermal erosion: only consider lowest neighbor, don't
// redistribute uplift to other neighbors.
let (posk, h_k) = (posj, h_j);
let (posk, h_k) = if h_k < h_j { (posk, h_k) } else { (posj, h_j) };
let dxy = (uniform_idx_as_vec2(map_size_lg, posi)
- uniform_idx_as_vec2(map_size_lg, posk))
.map(|e| e as f64);
let neighbor_distance = (neighbor_coef * dxy).magnitude();
let dz = (new_h_i - h_k).max(0.0);
let mag_slope = dz / neighbor_distance;
if mag_slope >= max_slope {
let dtherm = 0.0;
new_h_i -= dtherm;
if new_h_i <= wh_j {
if compute_stats {
ncorr += 1;
}
} else if compute_stats && new_h_i > 0.0 {
let dz = (new_h_i - h_j).max(0.0);
let slope = dz / neighbor_distance;
sums += slope;
nland += 1;
sumh += new_h_i;
sumsed_land += sed;
}
if compute_stats {
ntherm += 1;
prodscrit_therm += max_slope.ln();
prods_therm += mag_slope.ln();
}
} else {
// Poorly emulating nonlinear hillslope transport as described by
// http://eps.berkeley.edu/~bill/papers/112.pdf.
// sqrt(3)/3*32*32/(128000/2)
// Also Perron-2011-Journal_of_Geophysical_Research__Earth_Surface.pdf
let slope_ratio = (mag_slope / max_slope).powi(2);
let slope_nonlinear_factor =
slope_ratio * ((3.0 - slope_ratio) / (1.0 - slope_ratio).powi(2));
max_slopes[posi] += (max_slopes[posi] * slope_nonlinear_factor).min(max_stable);
if compute_stats && new_h_i > 0.0 {
sums += mag_slope;
// Just use the computed rate.
nland += 1;
sumh += new_h_i;
sumsed_land += sed;
}
}
}
// Set wh to this node's water height (max of receiver's water height and
// this node's height).
wh[posi] = wh_j.max(new_h_i) as Alt;
}
if compute_stats {
sumsed += sed;
let h_i = h[posi];
if h_i > 0.0 {
minh = h_i.min(minh);
}
maxh = h_i.max(maxh);
}
});
debug!(
"Done applying thermal erosion (max height: {:?}) (avg height: {:?}) (min height: {:?}) \
(avg slope: {:?})\n (above talus angle, geom. mean slope [actual/critical/ratio]: \
{:?} / {:?} / {:?})\n (avg sediment thickness [all/land]: {:?} / {:?})\n \
(num land: {:?}) (num thermal: {:?}) (num corrected: {:?})",
maxh,
avgz(sumh, nland),
minh,
avgz(sums, nland),
geomz(prods_therm, ntherm),
geomz(prodscrit_therm, ntherm),
geomz(prods_therm - prodscrit_therm, ntherm),
avgz(sumsed, newh.len()),
avgz(sumsed_land, nland),
nland,
ntherm,
ncorr,
);
// Apply hillslope diffusion.
diffusion(
nx,
ny,
nx as f64 * dx,
ny as f64 * dy,
dt,
(),
h,
b,
|posi| max_slopes[posi],
-1.0,
);
debug!("Done applying diffusion.");
debug!("Done eroding.");
}
/// The Planchon-Darboux algorithm for extracting drainage networks.
///
/// http://horizon.documentation.ird.fr/exl-doc/pleins_textes/pleins_textes_7/sous_copyright/010031925.pdf
///
/// See https://github.com/mewo2/terrain/blob/master/terrain.js
pub(crate) fn fill_sinks<F: Float + Send + Sync>(
map_size_lg: MapSizeLg,
h: impl Fn(usize) -> F + Sync,
is_ocean: impl Fn(usize) -> bool + Sync,
) -> Box<[F]> {
// NOTE: We are using the "exact" version of depression-filling, which is slower
// but doesn't change altitudes.
let epsilon = F::zero();
let infinity = F::infinity();
let range = 0..map_size_lg.chunks_len();
let oldh = range
.into_par_iter()
.map(&h)
.collect::<Vec<_>>()
.into_boxed_slice();
let mut newh = oldh
.par_iter()
.enumerate()
.map(|(posi, &h)| {
let is_near_edge = is_ocean(posi);
if is_near_edge {
debug_assert!(h <= F::zero());
h
} else {
infinity
}
})
.collect::<Vec<_>>()
.into_boxed_slice();
loop {
let mut changed = false;
(0..newh.len()).for_each(|posi| {
let nh = newh[posi];
let oh = oldh[posi];
if nh == oh {
return;
}
for nposi in neighbors(map_size_lg, posi) {
let onbh = newh[nposi];
let nbh = onbh + epsilon;
// If there is even one path downhill from this node's original height, fix
// the node's new height to be equal to its original height, and break out of
// the loop.
if oh >= nbh {
newh[posi] = oh;
changed = true;
break;
}
// Otherwise, we know this node's original height is below the new height of all
// of its neighbors. Then, we try to choose the minimum new
// height among all this node's neighbors that is (plus a
// constant epsilon) below this node's new height.
//
// (If there is no such node, then the node's new height must be (minus a
// constant epsilon) lower than the new height of every
// neighbor, but above its original height. But this can't be
// true for *all* nodes, because if this is true for any
// node, it is not true of any of its neighbors. So all neighbors must either
// be their original heights, or we will have another iteration
// of the loop (one of its neighbors was changed to its minimum
// neighbor). In the second case, in the next round, all
// neighbor heights will be at most nh + epsilon).
if nh > nbh && nbh > oh {
newh[posi] = nbh;
changed = true;
}
}
});
if !changed {
return newh;
}
}
}
/// Algorithm for finding and connecting lakes. Assumes newh and downhill have
/// already been computed. When a lake's value is negative, it is its own lake
/// root, and when it is 0, it is on the boundary of Ω.
///
/// Returns a 4-tuple containing:
/// - The first indirection vector (associating chunk indices with their lake's
/// root node).
/// - A list of chunks on the boundary (non-lake egress points).
/// - The second indirection vector (associating chunk indices with their lake's
/// adjacency list).
/// - The adjacency list (stored in a single vector), indexed by the second
/// indirection vector.
pub fn get_lakes<F: Float>(
map_size_lg: MapSizeLg,
h: impl Fn(usize) -> F,
downhill: &mut [isize],
) -> (usize, Box<[i32]>, Box<[u32]>, F) {
// Associates each lake index with its root node (the deepest one in the lake),
// and a list of adjacent lakes. The list of adjacent lakes includes the
// lake index of the adjacent lake, and a node index in the adjacent lake
// which has a neighbor in this lake. The particular neighbor should be the
// one that generates the minimum "pass height" encountered so far, i.e. the
// chosen pair should minimize the maximum of the heights of the nodes in the
// pair.
// We start by taking steps to allocate an indirection vector to use for storing
// lake indices. Initially, each entry in this vector will contain 0. We
// iterate in ascending order through the sorted newh. If the node has
// downhill == -2, it is a boundary node Ω and we store it in the boundary
// vector. If the node has downhill == -1, it is a fresh lake, and we store 0
// in it. If the node has non-negative downhill, we use the downhill index
// to find the next node down; if the downhill node has a lake entry < 0,
// then downhill is a lake and its entry can be negated to find an
// (over)estimate of the number of entries it needs. If the downhill
// node has a non-negative entry, then its entry is the lake index for this
// node, so we should access that entry and increment it, then set our own
// entry to it.
let mut boundary = Vec::with_capacity(downhill.len());
let mut indirection = vec![/*-1i32*/0i32; map_size_lg.chunks_len()].into_boxed_slice();
let mut newh = Vec::with_capacity(downhill.len());
// Now, we know that the sum of all the indirection nodes will be the same as
// the number of nodes. We can allocate a *single* vector with 8 * nodes
// entries, to be used as storage space, and augment our indirection vector
// with the starting index, resulting in a vector of slices. As we go, we
// replace each lake entry with its index in the new indirection buffer,
// allowing
let mut lakes = vec![(-1, 0); /*(indirection.len() - boundary.len())*/indirection.len() * 8];
let mut indirection_ = vec![0u32; indirection.len()];
// First, find all the lakes.
let mut lake_roots = Vec::with_capacity(downhill.len()); // Test
(&*downhill)
.iter()
.enumerate()
.filter(|(_, &dh_idx)| dh_idx < 0)
.for_each(|(chunk_idx, &dh)| {
if dh == -2 {
// On the boundary, add to the boundary vector.
boundary.push(chunk_idx);
// Still considered a lake root, though.
} else if dh == -1 {
lake_roots.push(chunk_idx);
} else {
panic!("Impossible.");
}
// Find all the nodes uphill from this lake. Since there is only one outgoing
// edge in the "downhill" graph, this is guaranteed never to visit a
// node more than once.
let start = newh.len();
let indirection_idx = (start * 8) as u32;
// New lake root
newh.push(chunk_idx as u32);
let mut cur = start;
while cur < newh.len() {
let node = newh[cur as usize];
uphill(map_size_lg, downhill, node as usize).for_each(|child| {
// lake_idx is the index of our lake root.
indirection[child] = chunk_idx as i32;
indirection_[child] = indirection_idx;
newh.push(child as u32);
});
cur += 1;
}
// Find the number of elements pushed.
let length = (cur - start) * 8;
// New lake root (lakes have indirection set to -length).
indirection[chunk_idx] = -(length as i32);
indirection_[chunk_idx] = indirection_idx;
});
assert_eq!(newh.len(), downhill.len());
debug!("Old lake roots: {:?}", lake_roots.len());
let newh = newh.into_boxed_slice();
let mut maxh = -F::infinity();
// Now, we know that the sum of all the indirection nodes will be the same as
// the number of nodes. We can allocate a *single* vector with 8 * nodes
// entries, to be used as storage space, and augment our indirection vector
// with the starting index, resulting in a vector of slices. As we go, we
// replace each lake entry with its index in the new indirection buffer,
// allowing
newh.iter().for_each(|&chunk_idx_| {
let chunk_idx = chunk_idx_ as usize;
let lake_idx_ = indirection_[chunk_idx];
let lake_idx = lake_idx_ as usize;
let height = h(chunk_idx_ as usize);
// While we're here, compute the max elevation difference from zero among all
// nodes.
maxh = maxh.max(height.abs());
// For every neighbor, check to see whether it is already set; if the neighbor
// is set, its height is ≤ our height. We should search through the
// edge list for the neighbor's lake to see if there's an entry; if not,
// we insert, and otherwise we get its height. We do the same thing in
// our own lake's entry list. If the maximum of the heights we get out
// from this process is greater than the maximum of this chunk and its
// neighbor chunk, we switch to this new edge.
neighbors(map_size_lg, chunk_idx).for_each(|neighbor_idx| {
let neighbor_height = h(neighbor_idx);
let neighbor_lake_idx_ = indirection_[neighbor_idx];
let neighbor_lake_idx = neighbor_lake_idx_ as usize;
if neighbor_lake_idx_ < lake_idx_ {
// We found an adjacent node that is not on the boundary and has already
// been processed, and also has a non-matching lake. Therefore we can use
// split_at_mut to get disjoint slices.
let (lake, neighbor_lake) = {
// println!("Okay, {:?} < {:?}", neighbor_lake_idx, lake_idx);
let (neighbor_lake, lake) = lakes.split_at_mut(lake_idx);
(lake, &mut neighbor_lake[neighbor_lake_idx..])
};
// We don't actually need to know the real length here, because we've reserved
// enough spaces that we should always either find a -1 (available slot) or an
// entry for this chunk.
'outer: for pass in lake.iter_mut() {
if pass.0 == -1 {
// println!("One time, in my mind, one time... (neighbor lake={:?}
// lake={:?})", neighbor_lake_idx, lake_idx_);
*pass = (chunk_idx_ as i32, neighbor_idx as u32);
// Should never run out of -1s in the neighbor lake if we didn't find
// the neighbor lake in our lake.
*neighbor_lake
.iter_mut()
.find(|neighbor_pass| neighbor_pass.0 == -1)
.unwrap() = (neighbor_idx as i32, chunk_idx_);
// panic!("Should never happen; maybe didn't reserve enough space in
// lakes?")
break;
} else if indirection_[pass.1 as usize] == neighbor_lake_idx_ {
for neighbor_pass in neighbor_lake.iter_mut() {
// Should never run into -1 while looping here, since (i, j)
// and (j, i) should be added together.
if indirection_[neighbor_pass.1 as usize] == lake_idx_ {
let pass_height = h(neighbor_pass.1 as usize);
let neighbor_pass_height = h(pass.1 as usize);
if height.max(neighbor_height)
< pass_height.max(neighbor_pass_height)
{
*pass = (chunk_idx_ as i32, neighbor_idx as u32);
*neighbor_pass = (neighbor_idx as i32, chunk_idx_);
}
break 'outer;
}
}
// Should always find a corresponding match in the neighbor lake if
// we found the neighbor lake in our lake.
let indirection_idx = indirection[chunk_idx];
let lake_chunk_idx = if indirection_idx >= 0 {
indirection_idx as usize
} else {
chunk_idx as usize
};
let indirection_idx = indirection[neighbor_idx];
let neighbor_lake_chunk_idx = if indirection_idx >= 0 {
indirection_idx as usize
} else {
neighbor_idx as usize
};
panic!(
"For edge {:?} between lakes {:?}, couldn't find partner for pass \
{:?}. Should never happen; maybe forgot to set both edges?",
(
(
chunk_idx,
uniform_idx_as_vec2(map_size_lg, chunk_idx as usize)
),
(
neighbor_idx,
uniform_idx_as_vec2(map_size_lg, neighbor_idx as usize)
)
),
(
(
lake_chunk_idx,
uniform_idx_as_vec2(map_size_lg, lake_chunk_idx as usize),
lake_idx_
),
(
neighbor_lake_chunk_idx,
uniform_idx_as_vec2(
map_size_lg,
neighbor_lake_chunk_idx as usize
),
neighbor_lake_idx_
)
),
(
(pass.0, uniform_idx_as_vec2(map_size_lg, pass.0 as usize)),
(pass.1, uniform_idx_as_vec2(map_size_lg, pass.1 as usize))
),
);
}
}
}
});
});
// Now it's time to calculate the lake connections graph T_L covering G_L.
let mut candidates = BinaryHeap::with_capacity(indirection.len());
// let mut pass_flows : Vec<i32> = vec![-1; indirection.len()];
// We start by going through each pass, deleting the ones that point out of
// boundary nodes and adding ones that point into boundary nodes from
// non-boundary nodes.
lakes.iter_mut().for_each(|edge| {
let edge: &mut (i32, u32) = edge;
// Only consider valid elements.
if edge.0 == -1 {
return;
}
// Check to see if this edge points out *from* a boundary node.
// Delete it if so.
let from = edge.0 as usize;
let indirection_idx = indirection[from];
let lake_idx = if indirection_idx < 0 {
from
} else {
indirection_idx as usize
};
if downhill[lake_idx] == -2 {
edge.0 = -1;
return;
}
// This edge is not pointing out from a boundary node.
// Check to see if this edge points *to* a boundary node.
// Add it to the candidate set if so.
let to = edge.1 as usize;
let indirection_idx = indirection[to];
let lake_idx = if indirection_idx < 0 {
to
} else {
indirection_idx as usize
};
if downhill[lake_idx] == -2 {
// Find the pass height
let pass = h(from).max(h(to));
candidates.push(Reverse((
NotNan::new(pass).unwrap(),
(edge.0 as u32, edge.1),
)));
}
});
let mut pass_flows_sorted: Vec<usize> = Vec::with_capacity(indirection.len());
// Now all passes pointing to the boundary are in candidates.
// As long as there are still candidates, we continue...
// NOTE: After a lake is added to the stream tree, the lake bottom's indirection
// entry no longer negates its maximum number of passes, but the lake side
// of the chosen pass. As such, we should make sure not to rely on using it
// this way afterwards. provides information about the number of candidate
// passes in a lake.
while let Some(Reverse((_, (chunk_idx, neighbor_idx)))) = candidates.pop() {
// We have the smallest candidate.
let lake_idx = indirection_[chunk_idx as usize] as usize;
let indirection_idx = indirection[chunk_idx as usize];
let lake_chunk_idx = if indirection_idx >= 0 {
indirection_idx as usize
} else {
chunk_idx as usize
};
if downhill[lake_chunk_idx] >= 0 {
// Candidate lake has already been connected.
continue;
}
assert_eq!(downhill[lake_chunk_idx], -1);
// Candidate lake has not yet been connected, and is the lowest candidate.
// Delete all other outgoing edges.
let max_len = -if indirection_idx < 0 {
indirection_idx
} else {
indirection[indirection_idx as usize]
} as usize;
// Add this chunk to the tree.
downhill[lake_chunk_idx] = neighbor_idx as isize;
// Also set the indirection of the lake bottom to the negation of the
// lake side of the chosen pass (chunk_idx).
// NOTE: This can't overflow i32 because map_size_lg.chunks_len() should fit
// in an i32.
indirection[lake_chunk_idx] = -(chunk_idx as i32);
// Add this edge to the sorted list.
pass_flows_sorted.push(lake_chunk_idx);
// pass_flows_sorted.push((chunk_idx as u32, neighbor_idx as u32));
for edge in &mut lakes[lake_idx..lake_idx + max_len] {
if *edge == (chunk_idx as i32, neighbor_idx as u32) {
// Skip deleting this edge.
continue;
}
// Delete the old edge, and remember it.
let edge = mem::replace(edge, (-1, 0));
if edge.0 == -1 {
// Don't fall off the end of the list.
break;
}
// Don't add incoming pointers from already-handled lakes or boundary nodes.
let indirection_idx = indirection[edge.1 as usize];
let neighbor_lake_idx = if indirection_idx < 0 {
edge.1 as usize
} else {
indirection_idx as usize
};
if downhill[neighbor_lake_idx] != -1 {
continue;
}
// Find the pass height
let pass = h(edge.0 as usize).max(h(edge.1 as usize));
// Put the reverse edge in candidates, sorted by height, then chunk idx, and
// finally neighbor idx.
candidates.push(Reverse((
NotNan::new(pass).unwrap(),
(edge.1, edge.0 as u32),
)));
}
}
debug!("Total lakes: {:?}", pass_flows_sorted.len());
// Perform the bfs once again.
#[derive(Clone, Copy, PartialEq)]
enum Tag {
UnParsed,
InQueue,
WithRcv,
}
let mut tag = vec![Tag::UnParsed; map_size_lg.chunks_len()];
// TODO: Combine with adding to vector.
let mut filling_queue = Vec::with_capacity(downhill.len());
let mut newh = Vec::with_capacity(downhill.len());
(&*boundary)
.iter()
.chain(pass_flows_sorted.iter())
.for_each(|&chunk_idx| {
// Find all the nodes uphill from this lake. Since there is only one outgoing
// edge in the "downhill" graph, this is guaranteed never to visit a
// node more than once.
let mut start = newh.len();
// First, find the neighbor pass (assuming this is not the ocean).
let neighbor_pass_idx = downhill[chunk_idx];
let first_idx = if neighbor_pass_idx < 0 {
// This is the ocean.
newh.push(chunk_idx as u32);
start += 1;
chunk_idx
} else {
// This is a "real" lake.
let neighbor_pass_idx = neighbor_pass_idx as usize;
// Let's find our side of the pass.
let pass_idx = -indirection[chunk_idx];
// NOTE: Since only lakes are on the boundary, this should be a valid array
// index.
assert!(pass_idx >= 0);
let pass_idx = pass_idx as usize;
// Now, we should recompute flow paths so downhill nodes are contiguous.
/* // Carving strategy: reverse the path from the lake side of the pass to the
// lake bottom, and also set the lake side of the pass's downhill to its
// neighbor pass.
let mut to_idx = neighbor_pass_idx;
let mut from_idx = pass_idx;
// NOTE: Since our side of the lake pass must be in the same basin as chunk_idx,
// and chunk_idx is the basin bottom, we must reach it before we reach an ocean
// node or other node with an invalid index.
while from_idx != chunk_idx {
// Reverse this (from, to) edge by first replacing to_idx with from_idx,
// then replacing from_idx's downhill with the old to_idx, and finally
// replacing from_idx with from_idx's old downhill.
//
// println!("Reversing (lake={:?}): to={:?}, from={:?}, dh={:?}", chunk_idx, to_idx, from_idx, downhill[from_idx]);
from_idx = mem::replace(
&mut downhill[from_idx],
mem::replace(
&mut to_idx,
// NOTE: This cast should be valid since the node is either a path on the way
// to a lake bottom, or a lake bottom with an actual pass outwards.
from_idx
) as isize,
) as usize;
}
// Remember to set the actual lake's from_idx properly!
downhill[from_idx] = to_idx as isize; */
// TODO: Enqueue onto newh simultaneously with filling (this could help prevent
// needing a special tag just for checking if we are already enqueued).
// Filling strategy: nodes are assigned paths based on cost.
{
assert!(tag[pass_idx] == Tag::UnParsed);
filling_queue.push(pass_idx);
tag[neighbor_pass_idx] = Tag::WithRcv;
tag[pass_idx] = Tag::InQueue;
let outflow_coords = uniform_idx_as_vec2(map_size_lg, neighbor_pass_idx);
let elev = h(neighbor_pass_idx).max(h(pass_idx));
while let Some(node) = filling_queue.pop() {
let coords = uniform_idx_as_vec2(map_size_lg, node);
let mut rcv = -1;
let mut rcv_cost = -f64::INFINITY; /*f64::EPSILON;*/
let outflow_distance = (outflow_coords - coords).map(|e| e as f64);
neighbors(map_size_lg, node).for_each(|ineighbor| {
if indirection[ineighbor] != chunk_idx as i32
&& ineighbor != chunk_idx
&& ineighbor != neighbor_pass_idx
|| h(ineighbor) > elev
{
return;
}
let dxy = (uniform_idx_as_vec2(map_size_lg, ineighbor) - coords)
.map(|e| e as f64);
let neighbor_distance = /*neighbor_coef * */dxy;
let tag = &mut tag[ineighbor];
match *tag {
Tag::WithRcv => {
// TODO: Remove outdated comment.
//
// vec_to_outflow ⋅ (vec_to_neighbor / |vec_to_neighbor|) =
// ||vec_to_outflow||cos Θ
// where θ is the angle between vec_to_outflow and
// vec_to_neighbor.
//
// Which is also the scalar component of vec_to_outflow in the
// direction of vec_to_neighbor.
let cost = outflow_distance
.dot(neighbor_distance / neighbor_distance.magnitude());
if cost > rcv_cost {
rcv = ineighbor as isize;
rcv_cost = cost;
}
},
Tag::UnParsed => {
filling_queue.push(ineighbor);
*tag = Tag::InQueue;
},
_ => {},
}
});
assert!(rcv != -1);
downhill[node] = rcv;
tag[node] = Tag::WithRcv;
}
}
// Use our side of the pass as the initial node in the stack order.
// TODO: Verify that this stack order will not "double reach" any lake chunks.
neighbor_pass_idx
};
// New lake root
let mut cur = start;
let mut node = first_idx;
loop {
uphill(map_size_lg, downhill, node as usize).for_each(|child| {
// lake_idx is the index of our lake root.
// Check to make sure child (flowing into us) is in the same lake.
if indirection[child] == chunk_idx as i32 || child == chunk_idx {
newh.push(child as u32);
}
});
if cur == newh.len() {
break;
}
node = newh[cur] as usize;
cur += 1;
}
});
assert_eq!(newh.len(), downhill.len());
(boundary.len(), indirection, newh.into_boxed_slice(), maxh)
}
/// Iterate through set neighbors of multi-receiver flow.
pub fn mrec_downhill(
map_size_lg: MapSizeLg,
mrec: &[u8],
posi: usize,
) -> impl Clone + Iterator<Item = (usize, usize)> {
let pos = uniform_idx_as_vec2(map_size_lg, posi);
let mrec_i = mrec[posi];
NEIGHBOR_DELTA
.iter()
.enumerate()
.filter(move |&(k, _)| (mrec_i >> k as isize) & 1 == 1)
.map(move |(k, &(x, y))| {
(
k,
vec2_as_uniform_idx(map_size_lg, Vec2::new(pos.x + x as i32, pos.y + y as i32)),
)
})
}
/// Algorithm for computing multi-receiver flow.
///
/// * `map_size_lg`: Size of the underlying map.
/// * `h`: altitude
/// * `downhill`: single receiver
/// * `newh`: single receiver stack
/// * `wh`: buffer into which water height will be inserted.
/// * `nx`, `ny`: resolution in x and y directions.
/// * `dx`, `dy`: grid spacing in x- and y-directions
/// * `maxh`: maximum |height| among all nodes.
///
///
/// Updates the water height to a nearly planar surface, and returns a 3-tuple
/// containing:
/// * A bitmask representing which neighbors are downhill.
/// * Stack order for multiple receivers (from top to bottom).
/// * The weight for each receiver, for each node.
pub fn get_multi_rec<F: fmt::Debug + Float + Sync + Into<Compute>>(
map_size_lg: MapSizeLg,
h: impl Fn(usize) -> F + Sync,
downhill: &[isize],
newh: &[u32],
wh: &mut [F],
nx: usize,
ny: usize,
dx: Compute,
dy: Compute,
_maxh: F,
threadpool: &rayon::ThreadPool,
) -> (Box<[u8]>, Box<[u32]>, Box<[Computex8]>) {
let nn = nx * ny;
let dxdy = Vec2::new(dx, dy);
/* // set bc
let i1 = 0;
let i2 = nx;
let j1 = 0;
let j2 = ny;
let xcyclic = false;
let ycyclic = false; */
/*
write (cbc,'(i4)') ibc
i1=1
i2=nx
j1=1
j2=ny
if (cbc(4:4).eq.'1') i1=2
if (cbc(2:2).eq.'1') i2=nx-1
if (cbc(1:1).eq.'1') j1=2
if (cbc(3:3).eq.'1') j2=ny-1
xcyclic=.FALSE.
ycyclic=.FALSE.
if (cbc(4:4).ne.'1'.and.cbc(2:2).ne.'1') xcyclic=.TRUE.
if (cbc(1:1).ne.'1'.and.cbc(3:3).ne.'1') ycyclic=.TRUE.
*/
assert_eq!(nn, wh.len());
// fill the local minima with a nearly planar surface
// See https://matthew-brett.github.io/teaching/floating_error.html;
// our absolute error is bounded by β^(e-(p-1)), where e is the exponent of the
// largest value we care about. In this case, since we are summing up to nn
// numbers, we are bounded from above by nn * |maxh|; however, we only need
// to invoke this when we actually encounter a number, so we compute it
// dynamically. for nn + |maxh|
// TODO: Consider that it's probably not possible to have a downhill path the
// size of the whole grid... either measure explicitly (maybe in get_lakes)
// or work out a more precise upper bound (since using nn * 2 * (maxh +
// epsilon) makes f32 not work very well).
let deltah = F::epsilon() + F::epsilon();
newh.iter().for_each(|&ijk| {
let ijk = ijk as usize;
let h_i = h(ijk);
let ijr = downhill[ijk];
wh[ijk] = if ijr >= 0 {
let ijr = ijr as usize;
let wh_j = wh[ijr];
if wh_j >= h_i {
let deltah = deltah * wh_j.abs();
wh_j + deltah
} else {
h_i
}
} else {
h_i
};
});
let mut wrec = Vec::<Computex8>::with_capacity(nn);
let mut mrec = Vec::with_capacity(nn);
let mut don_vis = Vec::with_capacity(nn);
// loop on all nodes
(0..nn)
.into_par_iter()
.map(|ij| {
// TODO: SIMDify? Seems extremely amenable to that.
let wh_ij = wh[ij];
let mut mrec_ij = 0u8;
let mut ndon_ij = 0u8;
let neighbor_iter = |posi| {
let pos = uniform_idx_as_vec2(map_size_lg, posi);
NEIGHBOR_DELTA
.iter()
.map(move |&(x, y)| Vec2::new(pos.x + x, pos.y + y))
.enumerate()
.filter(move |&(_, pos)| {
pos.x >= 0 && pos.y >= 0 && pos.x < nx as i32 && pos.y < ny as i32
})
.map(move |(k, pos)| (k, vec2_as_uniform_idx(map_size_lg, pos)))
};
neighbor_iter(ij).for_each(|(k, ijk)| {
let wh_ijk = wh[ijk];
if wh_ij > wh_ijk {
// Set neighboring edge lower than this one as being downhill.
// NOTE: relying on at most 8 neighbors.
mrec_ij |= 1 << k;
} else if wh_ijk > wh_ij {
// Avoiding ambiguous cases.
ndon_ij += 1;
}
});
(mrec_ij, (ndon_ij, ndon_ij))
})
.unzip_into_vecs(&mut mrec, &mut don_vis);
let czero = <Compute as Zero>::zero();
let (wrec, stack) = threadpool.join(
|| {
(0..nn)
.into_par_iter()
.map(|ij| {
let mut sumweight = czero;
let mut wrec = [czero; 8];
let mut nrec = 0;
mrec_downhill(map_size_lg, &mrec, ij).for_each(|(k, ijk)| {
let lrec_ijk = ((uniform_idx_as_vec2(map_size_lg, ijk)
- uniform_idx_as_vec2(map_size_lg, ij))
.map(|e| e as Compute)
* dxdy)
.magnitude();
let wrec_ijk = (wh[ij] - wh[ijk]).into() / lrec_ijk;
// NOTE: To emulate single-direction flow, uncomment this line.
// let wrec_ijk = if ijk as isize == downhill[ij] { <Compute as One>::one()
// } else { <Compute as Zero>::zero() };
wrec[k] = wrec_ijk;
sumweight += wrec_ijk;
nrec += 1;
});
let slope = sumweight / (nrec as Compute).max(1.0);
let p_mfd_exp = 0.5 + 0.6 * slope;
sumweight = czero;
wrec.iter_mut().for_each(|wrec_k| {
let wrec_ijk = wrec_k.powf(p_mfd_exp);
sumweight += wrec_ijk;
*wrec_k = wrec_ijk;
});
if sumweight > czero {
wrec.iter_mut().for_each(|wrec_k| {
*wrec_k /= sumweight;
});
}
wrec
})
.collect_into_vec(&mut wrec);
wrec
},
|| {
let mut stack = Vec::with_capacity(nn);
let mut parse = Vec::with_capacity(nn);
// we go through the nodes
(0..nn).for_each(|ij| {
let (ndon_ij, _) = don_vis[ij];
// when we find a "summit" (ie a node that has no donors)
// we parse it (put it in a stack called parse)
if ndon_ij == 0 {
parse.push(ij);
}
// we go through the parsing stack
while let Some(ijn) = parse.pop() {
// we add the node to the stack
stack.push(ijn as u32);
mrec_downhill(map_size_lg, &mrec, ijn).for_each(|(_, ijr)| {
let (_, ref mut vis_ijr) = don_vis[ijr];
if *vis_ijr >= 1 {
*vis_ijr -= 1;
if *vis_ijr == 0 {
parse.push(ijr);
}
}
});
}
});
assert_eq!(stack.len(), nn);
stack
},
);
(
mrec.into_boxed_slice(),
stack.into_boxed_slice(),
wrec.into_boxed_slice(),
)
}
/// Perform erosion n times.
pub fn do_erosion(
map_size_lg: MapSizeLg,
_max_uplift: f32,
n_steps: usize,
seed: &RandomField,
rock_strength_nz: &(impl NoiseFn<[f64; 3]> + Sync),
oldh: impl Fn(usize) -> f32 + Sync,
oldb: impl Fn(usize) -> f32 + Sync,
is_ocean: impl Fn(usize) -> bool + Sync,
uplift: impl Fn(usize) -> f64 + Sync,
n: impl Fn(usize) -> f32 + Sync,
theta: impl Fn(usize) -> f32 + Sync,
kf: impl Fn(usize) -> f64 + Sync,
kd: impl Fn(usize) -> f64 + Sync,
g: impl Fn(usize) -> f32 + Sync,
epsilon_0: impl Fn(usize) -> f32 + Sync,
alpha: impl Fn(usize) -> f32 + Sync,
// scaling factors
height_scale: impl Fn(f32) -> Alt + Sync,
k_d_scale: f64,
k_da_scale: impl Fn(f64) -> f64,
threadpool: &rayon::ThreadPool,
) -> (Box<[Alt]>, Box<[Alt]> /* , Box<[Alt]> */) {
debug!("Initializing erosion arrays...");
let oldh_ = (0..map_size_lg.chunks_len())
.into_par_iter()
.map(|posi| oldh(posi) as Alt)
.collect::<Vec<_>>()
.into_boxed_slice();
// Topographic basement (The height of bedrock, not including sediment).
let mut b = (0..map_size_lg.chunks_len())
.into_par_iter()
.map(|posi| oldb(posi) as Alt)
.collect::<Vec<_>>()
.into_boxed_slice();
// Stream power law slope exponent--link between channel slope and erosion rate.
let n = (0..map_size_lg.chunks_len())
.into_par_iter()
.map(&n)
.collect::<Vec<_>>()
.into_boxed_slice();
// Stream power law concavity index (θ = m/n), turned into an exponent on
// drainage (which is a proxy for discharge according to Hack's Law).
let m = (0..map_size_lg.chunks_len())
.into_par_iter()
.map(|posi| theta(posi) * n[posi])
.collect::<Vec<_>>()
.into_boxed_slice();
// Stream power law erodability constant for fluvial erosion (bedrock)
let kf = (0..map_size_lg.chunks_len())
.into_par_iter()
.map(&kf)
.collect::<Vec<_>>()
.into_boxed_slice();
// Stream power law erodability constant for hillslope diffusion (bedrock)
let kd = (0..map_size_lg.chunks_len())
.into_par_iter()
.map(&kd)
.collect::<Vec<_>>()
.into_boxed_slice();
// Deposition coefficient
let g = (0..map_size_lg.chunks_len())
.into_par_iter()
.map(&g)
.collect::<Vec<_>>()
.into_boxed_slice();
let epsilon_0 = (0..map_size_lg.chunks_len())
.into_par_iter()
.map(&epsilon_0)
.collect::<Vec<_>>()
.into_boxed_slice();
let alpha = (0..map_size_lg.chunks_len())
.into_par_iter()
.map(&alpha)
.collect::<Vec<_>>()
.into_boxed_slice();
let mut wh = vec![0.0; map_size_lg.chunks_len()].into_boxed_slice();
// TODO: Don't do this, maybe?
// (To elaborate, maybe we should have varying uplift or compute it some other
// way).
let uplift = (0..oldh_.len())
.into_par_iter()
.map(|posi| uplift(posi) as f32)
.collect::<Vec<_>>()
.into_boxed_slice();
let sum_uplift = uplift
.into_par_iter()
.cloned()
.map(|e| e as f64)
.sum::<f64>();
debug!("Sum uplifts: {:?}", sum_uplift);
let max_uplift = uplift
.into_par_iter()
.cloned()
.max_by(|a, b| a.partial_cmp(b).unwrap())
.unwrap();
let max_g = g
.into_par_iter()
.cloned()
.max_by(|a, b| a.partial_cmp(b).unwrap())
.unwrap();
debug!("Max uplift: {:?}", max_uplift);
debug!("Max g: {:?}", max_g);
// Height of terrain, including sediment.
let mut h = oldh_;
// Bedrock transport coefficients (diffusivity) in m^2 / year, for sediment.
// For now, we set them all to be equal
// on land, but in theory we probably want to at least differentiate between
// soil, bedrock, and sediment.
let kdsed = 1.5e-2 / 4.0;
let kdsed = kdsed * k_d_scale;
let n = |posi: usize| n[posi];
let m = |posi: usize| m[posi];
let kd = |posi: usize| kd[posi];
let kf = |posi: usize| kf[posi];
let g = |posi: usize| g[posi];
let epsilon_0 = |posi: usize| epsilon_0[posi];
let alpha = |posi: usize| alpha[posi];
(0..n_steps).for_each(|i| {
debug!("Erosion iteration #{:?}", i);
erode(
map_size_lg,
&mut h,
&mut b,
&mut wh,
max_uplift,
max_g,
kdsed,
seed,
rock_strength_nz,
|posi| uplift[posi],
n,
m,
kf,
kd,
g,
epsilon_0,
alpha,
&is_ocean,
&height_scale,
&k_da_scale,
threadpool,
);
});
(h, b)
}