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use super::{
neighbors, quadratic_nearest_point, river_spline_coeffs, uniform_idx_as_vec2,
vec2_as_uniform_idx, TerrainChunkSize, NEIGHBOR_DELTA, TERRAIN_CHUNK_BLOCKS_LG,
};
use crate::vol::RectVolSize;
use common_base::prof_span;
use core::{f32, f64, iter, ops::RangeInclusive};
use vek::*;
/// Base two logarithm of the maximum size of the precomputed world, in meters,
/// along the x (E/W) and y (N/S) dimensions.
///
/// NOTE: Each dimension is guaranteed to be a power of 2, so the logarithm is
/// exact. This is so that it is possible (at least in theory) for compiler or
/// runtime optimizations exploiting this are possible. For example, division
/// by the chunk size can turn into a bit shift.
///
/// NOTE: As an invariant, this value is at least [TERRAIN_CHUNK_BLOCKS_LG].
///
/// NOTE: As an invariant, `(1 << [MAX_WORLD_BLOCKS_LG])` fits in an i32.
///
/// TODO: Add static assertions for the above invariants.
///
/// Currently, we define the maximum to be 19 (corresponding to 2^19 m) for both
/// directions. This value was derived by backwards reasoning from the following
/// conservative estimate of the maximum landmass area (using an approximation
/// of 1024 blocks / km instead of 1000 blocks / km, which will result in an
/// estimate that is strictly lower than the real landmass):
///
/// Max area (km²)
/// ≌ (2^19 blocks * 1 km / 1024 blocks)^2
/// = 2^((19 - 10) * 2) km²
/// = 2^18 km²
/// = 262,144 km²
///
/// which is roughly the same area as the entire United Kingdom, and twice the
/// horizontal extent of Dwarf Fortress's largest map. Besides the comparison
/// to other games without infinite or near-infinite maps (like Dwarf Fortress),
/// there are other reasons to choose this as a good maximum size:
///
/// * It is large enough to include geological features of fairly realistic
/// scale. It may be hard to do justice to truly enormous features like the
/// Amazon River, and natural temperature variation not related to altitude
/// would probably not produce climate extremes on an Earth-like planet, but
/// it can comfortably fit enormous river basins, Everest-scale mountains,
/// large islands and inland lakes, vast forests and deserts, and so on.
///
/// * It is large enough that making it from one side of the map to another will
/// take a *very* long time. We show this with two examples. In each
/// example, travel is either purely horizontal or purely vertical (to
/// minimize distance traveled) across the whole map, and we assume there are
/// no obstacles or slopes.
///
/// In example 1, a human is walking at the (real-time) speed of the fastest
/// marathon runners (around 6 blocks / real-time s). We assume the human can
/// maintain this pace indefinitely without stopping. Then crossing the map
/// will take about:
///
/// 2^19 blocks * 1 real-time s / 6 blocks * 1 real-time min / 60 real-time s
/// * 1 real-time hr / 60 real-time min * 1 real-time days / 24 hr = 2^19 / 6 /
/// 60 / 60 / 24 real-time days ≌ 1 real-time day.
///
/// That's right--it will take a full day of *real* time to cross the map at
/// an apparent speed of 6 m / s. Moreover, since in-game time passes at a
/// rate of 1 in-game min / 1 in-game s, this would also take *60 days* of
/// in-game time.
///
/// Still though, this is the rate of an ordinary human. And besides that, if
/// we instead had a marathon runner traveling at 6 m / in-game s, it would
/// take just 1 day of in-game time for the runner to cross the map, or a mere
/// 0.4 hr of real time. To show that this rate of travel is unrealistic (and
/// perhaps make an eventual argument for a slower real-time to in-game time
/// conversion rate), our second example will consist of a high-speed train
/// running at 300 km / real-time h (the fastest real-world high speed train
/// averages under 270 k m / h, with 300 km / h as the designed top speed).
/// For a train traveling at this apparent speed (in real time), crossing the
/// map would take:
///
/// 2^19 blocks * 1 km / 1000 blocks * 1 real-time hr / 300 km
/// = 2^19 / 1000 / 300 real-time hr
/// ≌ 1.75 real-time hr
///
/// = 2^19 / 1000 / 300 real-time hr * 60 in-game hr / real-time hr
/// * 1 in-game days / 24 in-game hr
/// = 2^19 / 1000 / 300 * 60 / 24 in-game days
/// ≌ 4.37 in-game days
///
/// In other words, something faster in real-time than any existing high-speed
/// train would be over 4 times slower (in real-time) than our hypothetical
/// top marathon runner running at 6 m / s in in-game speed. This suggests
/// that the gap between in-game time and real-time is probably much too large
/// for most purposes; however, what it definitely shows is that even
/// extremely fast in-game transport across the world will not trivialize its
/// size.
///
/// It follows that cities or towns of realistic scale, player housing,
/// fields, and so on, will all fit comfortably on a map of this size, while
/// at the same time still being reachable by non-warping, in-game mechanisms
/// (such as high-speed transit). It also provides plenty of room for mounts
/// of varying speeds, which can help ensure that players don't feel cramped or
/// deliberately slowed down by their own speed.
///
/// * It is small enough that it is (barely) plausible that we could still
/// generate maps for a world of this size using detailed and realistic
/// erosion algorithms. At 1/4 of this map size along each dimension,
/// generation currently takes around 5 hours on a good computer, and one
/// could imagine (since the bottleneck step appears to be roughly O(n)) that
/// with a smart implementation generation times of under a week could be
/// achievable.
///
/// * The map extends further than the resolution of human eyesight under
/// Earthlike conditions, even from tall mountains across clear landscapes.
/// According to one calculation, even from Mt. Everest in the absence of
/// cloud cover, you could only see for about 339 km before the Earth's
/// horizon prevented you from seeing further, and other sources suggest that
/// in practice the limit is closer to 160 km under realistic conditions. This
/// implies that making the map much larger in a realistic way would require
/// incorporating curvature, and also implies that any features that cannot
/// fit on the map would not (under realistic atmospheric conditions) be fully
/// visible from any point on Earth. Therefore, even if we cannot represent
/// features larger than this accurately, nothing should be amiss from a
/// visual perspective, so this should not significantly impact the player
/// experience.
pub const MAX_WORLD_BLOCKS_LG: Vec2<u32> = Vec2 { x: 19, y: 19 };
/// Base two logarithm of a world size, in chunks, per dimension
/// (each dimension must be a power of 2, so the logarithm is exact).
///
/// NOTE: As an invariant, each dimension must be between 0 and
/// `[MAX_WORLD_BLOCKS_LG] - [TERRAIN_CHUNK_BLOCKS_LG]`.
///
/// NOTE: As an invariant, `(1 << ([DEFAULT_WORLD_CHUNKS_LG] +
/// [TERRAIN_CHUNK_BLOCKS_LG]))` fits in an i32 (derived from the invariant
/// on [MAX_WORLD_BLOCKS_LG]).
///
/// NOTE: As an invariant, each dimension (in chunks) must fit in a i16.
///
/// NOTE: As an invariant, the product of dimensions (in chunks) must fit in a
/// usize.
///
/// These invariants are all checked on construction of a `MapSizeLg`.
#[derive(Clone, Copy, Debug)]
pub struct MapSizeLg(Vec2<u32>);
impl MapSizeLg {
// FIXME: We cannot use is_some() here because it is not currently marked as a
// `const fn`. Since being able to use conditionals in constant expressions has
// not technically been stabilized yet, Clippy probably doesn't check for this
// case yet. When it can, or when is_some() is stabilized as a `const fn`,
// we should deal with this.
/// Construct a new `MapSizeLg`, returning an error if the needed invariants
/// do not hold and the vector otherwise.
///
/// TODO: In the future, we may use unsafe code to assert to the compiler
/// that these invariants indeed hold, safely opening up optimizations
/// that might not otherwise be available at runtime.
#[inline(always)]
#[allow(clippy::result_unit_err)]
pub const fn new(map_size_lg: Vec2<u32>) -> Result<Self, ()> {
// Assertion on dimensions: must be between
// 0 and ([MAX_WORLD_BLOCKS_LG] - [TERRAIN_CHUNK_BLOCKS_LG])
let is_le_max = map_size_lg.x <= MAX_WORLD_BLOCKS_LG.x - TERRAIN_CHUNK_BLOCKS_LG
&& map_size_lg.y <= MAX_WORLD_BLOCKS_LG.y - TERRAIN_CHUNK_BLOCKS_LG;
// Assertion on dimensions: chunks must fit in a i16.
let chunks_in_range =
/* 1u15.checked_shl(map_size_lg.x).is_some() &&
1u15.checked_shl(map_size_lg.y).is_some(); */
map_size_lg.x <= 15 &&
map_size_lg.y <= 15;
if is_le_max && chunks_in_range {
// Assertion on dimensions: blocks must fit in a i32.
let blocks_in_range =
/* 1i32.checked_shl(map_size_lg.x + TERRAIN_CHUNK_BLOCKS_LG).is_some() &&
1i32.checked_shl(map_size_lg.y + TERRAIN_CHUNK_BLOCKS_LG).is_some(); */
map_size_lg.x + TERRAIN_CHUNK_BLOCKS_LG < 32 &&
map_size_lg.y + TERRAIN_CHUNK_BLOCKS_LG < 32;
// Assertion on dimensions: product of dimensions must fit in a usize.
let chunks_product_in_range =
1usize.checked_shl(map_size_lg.x + map_size_lg.y).is_some();
if blocks_in_range && chunks_product_in_range {
// Cleared all invariants.
Ok(MapSizeLg(map_size_lg))
} else {
Err(())
}
} else {
Err(())
}
}
#[inline(always)]
/// Acquire the `MapSizeLg`'s inner vector.
pub const fn vec(self) -> Vec2<u32> { self.0 }
#[inline(always)]
/// Get the size of this map in chunks.
pub const fn chunks(self) -> Vec2<u16> { Vec2::new(1 << self.0.x, 1 << self.0.y) }
/// Get the size of an array of the correct size to hold all chunks.
pub const fn chunks_len(self) -> usize { 1 << (self.0.x + self.0.y) }
#[inline(always)]
/// Determine whether a chunk position is in bounds.
pub const fn contains_chunk(&self, chunk_key: Vec2<i32>) -> bool {
let map_size = self.chunks();
chunk_key.x >= 0
&& chunk_key.y >= 0
&& chunk_key.x == chunk_key.x & ((map_size.x as i32) - 1)
&& chunk_key.y == chunk_key.y & ((map_size.y as i32) - 1)
}
}
impl From<MapSizeLg> for Vec2<u32> {
#[inline(always)]
fn from(size: MapSizeLg) -> Self { size.vec() }
}
pub struct MapConfig<'a> {
/// Base two logarithm of the chunk dimensions of the base map.
/// Has no default; set explicitly during initial orthographic projection.
pub map_size_lg: MapSizeLg,
/// Dimensions of the window being written to.
///
/// Defaults to `1 << [MapConfig::map_size_lg]`.
pub dimensions: Vec2<usize>,
/// x, y, and z of top left of map.
///
/// Default x and y are 0.0; no reasonable default for z, so set during
/// initial orthographic projection.
pub focus: Vec3<f64>,
/// Altitude is divided by gain and clamped to [0, 1]; thus, decreasing gain
/// makes smaller differences in altitude appear larger.
///
/// No reasonable default for z; set during initial orthographic projection.
pub gain: f32,
/// `fov` is used for shading purposes and refers to how much impact a
/// change in the z direction has on the perceived slope relative to the
/// same change in x and y.
///
/// It is stored as cos θ in the range (0, 1\] where θ is the FOV
/// "half-angle" used for perspective projection. At 1.0, we treat it
/// as the limit value for θ = 90 degrees, and use an orthographic
/// projection.
///
/// Defaults to 1.0.
///
/// FIXME: This is a hack that tries to incorrectly implement a variant of
/// perspective projection (which generates ∂P/∂x and ∂P/∂y for screen
/// coordinate P by using the hyperbolic function \[assuming frustum of
/// \[l, r, b, t, n, f\], rh coordinates, and output from -1 to 1 in
/// s/t, 0 to 1 in r, and NDC is left-handed \[so visible z ranges from
/// -n to -f\]\]):
///
/// P.s(x, y, z) = -1 + 2(-n/z x - l) / ( r - l)
/// P.t(x, y, z) = -1 + 2(-n/z y - b) / ( t - b)
/// P.r(x, y, z) = 0 + -f(-n/z - 1) / ( f - n)
///
/// Then arbitrarily using W_e_x = (r - l) as the width of the projected
/// image, we have W_e_x = 2 n_e tan θ ⇒ tan Θ = (r - l) / (2n_e), for a
/// perspective projection
///
/// (where θ is the half-angle of the FOV).
///
/// Taking the limit as θ → 90, we show that this degenerates to an
/// orthogonal projection:
///
/// lim{n → ∞}(-f(-n / z - 1) / (f - n)) = -(z - -n) / (f - n).
///
/// (Proof not currently included, but has been formalized for the P.r case
/// in Coq-tactic notation; the proof can be added on request, but is
/// large and probably not well-suited to Rust documentation).
///
/// For this reason, we feel free to store `fov` as cos θ in the range (0,
/// 1\].
///
/// However, `fov` does not actually work properly yet, so for now we just
/// treat it as a visual gimmick.
pub fov: f64,
/// Scale is like gain, but for x and y rather than z.
///
/// Defaults to (1 << world_size_lg).x / dimensions.x (NOTE: fractional, not
/// integer, division!).
pub scale: f64,
/// Vector that indicates which direction light is coming from, if shading
/// is turned on.
///
/// Right-handed coordinate system: light is going left, down, and
/// "backwards" (i.e. on the map, where we translate the y coordinate on
/// the world map to z in the coordinate system, the light comes from -y
/// on the map and points towards +y on the map). In a right
/// handed coordinate system, the "camera" points towards -z, so positive z
/// is backwards "into" the camera.
///
/// "In world space the x-axis will be pointing east, the y-axis up and the
/// z-axis will be pointing south"
///
/// Defaults to (-0.8, -1.0, 0.3).
pub light_direction: Vec3<f64>,
/// If Some, uses the provided horizon map.
///
/// Defaults to None.
pub horizons: Option<&'a [(Vec<f32>, Vec<f32>); 2]>,
/// If true, only the basement (bedrock) is used for altitude; otherwise,
/// the surface is used.
///
/// Defaults to false.
pub is_basement: bool,
/// If true, water is rendered; otherwise, the surface without water is
/// rendered, even if it is underwater.
///
/// Defaults to true.
pub is_water: bool,
/// When `is_water` is true, controls whether an ice layer should appear on
/// that water.
///
/// Defaults to true.
pub is_ice: bool,
/// If true, 3D lighting and shading are turned on. Otherwise, a plain
/// altitude map is used.
///
/// Defaults to true.
pub is_shaded: bool,
/// If true, the red component of the image is also used for temperature
/// (redder is hotter). Defaults to false.
pub is_temperature: bool,
/// If true, the blue component of the image is also used for humidity
/// (bluer is wetter).
///
/// Defaults to false.
pub is_humidity: bool,
/// Record debug information.
///
/// Defaults to false.
pub is_debug: bool,
/// If true, contour lines are drawn on top of the base rbg
///
/// Defaults to false.
pub is_contours: bool,
/// If true, a yellow/terracotta heightmap shading is applied to the
/// terrain and water is a faded blue.
///
/// Defaults to false
pub is_height_map: bool,
/// Applies contour lines as well as color modifications
///
/// Defaults to false
pub is_stylized_topo: bool,
}
pub const QUADRANTS: usize = 4;
pub struct MapDebug {
pub quads: [[u32; QUADRANTS]; QUADRANTS],
pub rivers: u32,
pub lakes: u32,
pub oceans: u32,
}
/// Connection kind (per edge). Currently just supports rivers, but may be
/// extended to support paths or at least one other kind of connection.
#[derive(Clone, Copy, Debug)]
pub enum ConnectionKind {
/// Connection forms a visible river.
River,
}
/// Map connection (per edge).
#[derive(Clone, Copy, Debug)]
pub struct Connection {
/// The kind of connection this is (e.g. river or path).
pub kind: ConnectionKind,
/// Assumed to be the "b" part of a 2d quadratic function.
pub spline_derivative: Vec2<f32>,
/// Width of the connection.
pub width: f32,
}
/// Per-chunk data the map needs to be able to sample in order to correctly
/// render.
#[derive(Clone, Debug)]
pub struct MapSample {
/// the base RGB color for a particular map pixel using the current settings
/// (i.e. the color *without* lighting).
pub rgb: Rgb<u8>,
/// Surface altitude information
/// (correctly reflecting settings like is_basement and is_water)
pub alt: f64,
/// Downhill chunk (may not be meaningful on ocean tiles, or at least edge
/// tiles)
pub downhill_wpos: Vec2<i32>,
/// Connection information about any connections to/from this chunk (e.g.
/// rivers).
///
/// Connections at each index correspond to the same index in
/// NEIGHBOR_DELTA.
pub connections: Option<[Option<Connection>; 8]>,
}
impl<'a> MapConfig<'a> {
/// Constructs the configuration settings for an orthographic projection of
/// a map from the top down, rendering (by default) the complete map to
/// an image such that the chunk:pixel ratio is 1:1.
///
/// Takes two arguments: the base two logarithm of the horizontal map extent
/// (in chunks), and the z bounds of the projection.
pub fn orthographic(map_size_lg: MapSizeLg, z_bounds: RangeInclusive<f32>) -> Self {
assert!(z_bounds.start() <= z_bounds.end());
// NOTE: Safe cast since map_size_lg is restricted by the prior assert.
let dimensions = map_size_lg.chunks().map(usize::from);
Self {
map_size_lg,
dimensions,
focus: Vec3::new(0.0, 0.0, f64::from(*z_bounds.start())),
gain: z_bounds.end() - z_bounds.start(),
fov: 1.0,
scale: 1.0,
light_direction: Vec3::new(-1.2, -1.0, 0.8),
horizons: None,
is_basement: false,
is_water: true,
is_ice: true,
is_shaded: true,
is_temperature: false,
is_humidity: false,
is_debug: false,
is_contours: false,
is_height_map: false,
is_stylized_topo: false,
}
}
/// Get the base 2 logarithm of the underlying map size.
pub fn map_size_lg(&self) -> MapSizeLg { self.map_size_lg }
/// Generates a map image using the specified settings. Note that it will
/// write from left to write from (0, 0) to dimensions - 1, inclusive,
/// with 4 1-byte color components provided as (r, g, b, a). It is up
/// to the caller to provide a function that translates this information
/// into the correct format for a buffer and writes to it.
///
/// sample_pos is a function that, given a chunk position, returns enough
/// information about the chunk to attempt to render it on the map.
/// When in doubt, try using `MapConfig::sample_pos` for this.
///
/// sample_wpos is a simple function that, given a *column* position,
/// returns the approximate altitude at that column. When in doubt, try
/// using `MapConfig::sample_wpos` for this.
pub fn generate(
&self,
sample_pos: impl Fn(Vec2<i32>) -> MapSample,
sample_wpos: impl Fn(Vec2<i32>) -> f32,
mut write_pixel: impl FnMut(Vec2<usize>, (u8, u8, u8, u8)),
) -> MapDebug {
prof_span!("MapConfig::generate");
let MapConfig {
map_size_lg,
dimensions,
focus,
gain,
fov,
scale,
light_direction,
horizons,
is_shaded,
is_stylized_topo,
// is_debug,
..
} = *self;
let light_direction = Vec3::new(
light_direction.x,
light_direction.y,
0.0, // we currently ignore light_direction.z.
);
let light_shadow_dir = usize::from(light_direction.x < 0.0);
let horizon_map = horizons.map(|horizons| &horizons[light_shadow_dir]);
let light = light_direction.normalized();
let /*mut */quads = [[0u32; QUADRANTS]; QUADRANTS];
let /*mut */rivers = 0u32;
let /*mut */lakes = 0u32;
let /*mut */oceans = 0u32;
let focus_rect = Vec2::from(focus);
let chunk_size = TerrainChunkSize::RECT_SIZE.map(|e| e as f64);
/* // NOTE: Asserting this to enable LLVM optimizations. Ideally we should come up
// with a principled way to do this (especially one with no runtime
// cost).
assert!(
map_size_lg
.vec()
.cmple(&(MAX_WORLD_BLOCKS_LG - TERRAIN_CHUNK_BLOCKS_LG))
.reduce_and()
); */
let world_size = map_size_lg.chunks();
(0..dimensions.y * dimensions.x).for_each(|chunk_idx| {
let i = chunk_idx % dimensions.x;
let j = chunk_idx / dimensions.x;
let wposf = focus_rect + Vec2::new(i as f64, j as f64) * scale;
let pos = wposf.map(|e: f64| e as i32);
let wposf = wposf * chunk_size;
let chunk_idx = if pos.reduce_partial_min() >= 0
&& pos.x < world_size.x as i32
&& pos.y < world_size.y as i32
{
Some(vec2_as_uniform_idx(map_size_lg, pos))
} else {
None
};
let MapSample {
rgb,
alt,
downhill_wpos,
..
} = sample_pos(pos);
let alt = alt as f32;
let wposi = pos * TerrainChunkSize::RECT_SIZE.map(|e| e as i32);
let mut rgb = rgb.map(|e| e as f64 / 255.0);
// Material properties:
//
// For each material in the scene,
// k_s = (RGB) specular reflection constant
let mut k_s = Rgb::new(1.0, 1.0, 1.0);
// k_d = (RGB) diffuse reflection constant
let mut k_d = rgb;
// k_a = (RGB) ambient reflection constant
let mut k_a = rgb;
// α = (per-material) shininess constant
let mut alpha = 4.0; // 4.0;
// Compute connections
let mut has_river = false;
// NOTE: consider replacing neighbors with local_cells, since it is more
// accurate (though I'm not sure if it can matter for these
// purposes).
chunk_idx
.into_iter()
.flat_map(|chunk_idx| {
neighbors(map_size_lg, chunk_idx).chain(iter::once(chunk_idx))
})
.for_each(|neighbor_posi| {
let neighbor_pos = uniform_idx_as_vec2(map_size_lg, neighbor_posi);
let neighbor_wpos = neighbor_pos.map(|e| e as f64) * chunk_size;
let MapSample { connections, .. } = sample_pos(neighbor_pos);
NEIGHBOR_DELTA
.iter()
.zip(connections.iter().flatten())
.for_each(|(&delta, connection)| {
let connection = if let Some(connection) = connection {
connection
} else {
return;
};
let downhill_wpos = neighbor_wpos
+ Vec2::from(delta).map(|e: i32| e as f64) * chunk_size;
let coeffs = river_spline_coeffs(
neighbor_wpos,
connection.spline_derivative,
downhill_wpos,
);
let (_t, _pt, dist) = if let Some((t, pt, dist)) =
quadratic_nearest_point(
&coeffs,
wposf,
Vec2::new(neighbor_wpos, downhill_wpos),
) {
(t, pt, dist)
} else {
let ndist = wposf.distance_squared(neighbor_wpos);
let ddist = wposf.distance_squared(downhill_wpos);
if ndist <= ddist {
(0.0, neighbor_wpos, ndist)
} else {
(1.0, downhill_wpos, ddist)
}
};
let connection_dist =
(dist.sqrt() - (connection.width as f64 * 0.5).max(1.0)).max(0.0);
if connection_dist == 0.0 {
match connection.kind {
ConnectionKind::River => {
has_river = true;
},
}
}
});
});
// Color in connections.
let water_color_factor = 2.0;
let g_water = 32.0 * water_color_factor;
let b_water = 64.0 * water_color_factor;
if has_river {
// Rudimentary ice check
if !rgb.map(|e| e > 0.35).reduce_and() {
let water_rgb = Rgb::new(0, ((g_water) * 1.0) as u8, ((b_water) * 1.0) as u8)
.map(|e| e as f64 / 255.0);
rgb = water_rgb;
k_s = Rgb::new(1.0, 1.0, 1.0);
k_d = water_rgb;
k_a = water_rgb;
alpha = 0.255;
}
}
let downhill_alt = sample_wpos(downhill_wpos);
let cross_pos = wposi
+ ((downhill_wpos - wposi)
.map(|e| e as f32)
.rotated_z(f32::consts::FRAC_PI_2)
.map(|e| e as i32));
let cross_alt = sample_wpos(cross_pos);
// TODO: Fix use of fov to match proper perspective projection, as described in
// the doc comment.
// Pointing downhill, forward
// (index--note that (0,0,1) is backward right-handed)
let forward_vec = Vec3::new(
(downhill_wpos.x - wposi.x) as f64,
((downhill_alt - alt) * gain) as f64 * fov,
(downhill_wpos.y - wposi.y) as f64,
);
// Pointing 90 degrees left (in horizontal xy) of downhill, up
// (middle--note that (1,0,0), 90 degrees CCW backward, is right right-handed)
let up_vec = Vec3::new(
(cross_pos.x - wposi.x) as f64,
((cross_alt - alt) * gain) as f64 * fov,
(cross_pos.y - wposi.y) as f64,
);
// let surface_normal = Vec3::new(fov* (f.y * u.z - f.z * u.y), -(f.x * u.z -
// f.z * u.x), fov* (f.x * u.y - f.y * u.x)).normalized();
// Then cross points "to the right" (upwards) on a right-handed coordinate
// system. (right-handed coordinate system means (0, 0, 1.0) is
// "forward" into the screen).
let surface_normal = forward_vec.cross(up_vec).normalized();
// TODO: Figure out if we can reimplement debugging.
/* if is_debug {
let quad =
|x: f32| ((x as f64 * QUADRANTS as f64).floor() as usize).min(QUADRANTS - 1);
if river_kind.is_none() || humidity != 0.0 {
quads[quad(humidity)][quad(temperature)] += 1;
}
match river_kind {
Some(RiverKind::River { .. }) => {
rivers += 1;
},
Some(RiverKind::Lake { .. }) => {
lakes += 1;
},
Some(RiverKind::Ocean { .. }) => {
oceans += 1;
},
None => {},
}
} */
let rgb = if is_shaded {
let shade_frac = horizon_map
.and_then(|(angles, heights)| {
chunk_idx
.and_then(|chunk_idx| angles.get(chunk_idx))
.map(|&e| (e as f64, heights))
})
.and_then(|(e, heights)| {
chunk_idx
.and_then(|chunk_idx| heights.get(chunk_idx))
.map(|&f| (e, f as f64))
})
.map(|(angle, height)| {
let w = 0.1;
let height = (height - f64::from(alt * gain)).max(0.0);
if angle != 0.0 && light_direction.x != 0.0 && height != 0.0 {
let deltax = height / angle;
let lighty = (light_direction.y / light_direction.x * deltax).abs();
let deltay = lighty - height;
let s = (deltay / deltax / w).clamp(0.0, 1.0);
// Smoothstep
s * s * (3.0 - 2.0 * s)
} else {
1.0
}
})
.unwrap_or(1.0);
// Phong reflection model with shadows:
//
// I_p = k_a i_a + shadow * Σ {m ∈ lights} (k_d (L_m ⋅ N) i_m,d + k_s (R_m ⋅
// V)^α i_m,s)
//
// where for the whole scene,
// i_a = (RGB) intensity of ambient lighting component
let i_a = if is_stylized_topo {
Rgb::new(0.4, 0.4, 0.4)
} else {
Rgb::new(0.1, 0.1, 0.1)
};
// V = direction pointing towards the viewer (e.g. virtual camera).
let v = Vec3::new(0.0, 0.0, -1.0).normalized();
// for each light m,
// i_m,d = (RGB) intensity of diffuse component of light source m
let i_m_d = Rgb::new(1.0, 1.0, 1.0);
// i_m,s = (RGB) intensity of specular component of light source m
let i_m_s = Rgb::new(0.45, 0.45, 0.45);
// for each light m and point p,
// L_m = (normalized) direction vector from point on surface to light source m
let l_m = light;
// N = (normalized) normal at this point on the surface,
let n = surface_normal;
// R_m = (normalized) direction a perfectly reflected ray of light from m would
// take from point p = 2(L_m ⋅ N)N - L_m
let r_m = (-l_m).reflected(n); // 2 * (l_m.dot(n)) * n - l_m;
//
// and for each point p in the scene,
// shadow = computed shadow factor at point p
// FIXME: Should really just be shade_frac, but with only ambient light we lose
// all local lighting detail... some sort of global illumination (e.g.
// radiosity) is of course the "right" solution, but maybe we can find
// something cheaper?
let shadow = 0.2 + 0.8 * shade_frac;
let lambertian = l_m.dot(n).max(0.0);
let spec_angle = r_m.dot(v).max(0.0);
let ambient = k_a * i_a;
let diffuse = k_d * lambertian * i_m_d;
let specular = k_s * spec_angle.powf(alpha) * i_m_s;
(ambient + shadow * (diffuse + specular)).map(|e| e.min(1.0))
} else {
rgb
}
.map(|e| (e * 255.0) as u8);
let rgba = (rgb.r, rgb.g, rgb.b, 255);
write_pixel(Vec2::new(i, j), rgba);
});
MapDebug {
quads,
rivers,
lakes,
oceans,
}
}
}