veloren/common/src/path.rs
2023-10-08 11:35:01 +00:00

1073 lines
39 KiB
Rust

use crate::{
astar::{Astar, PathResult},
terrain::Block,
vol::{BaseVol, ReadVol},
};
use common_base::span;
use hashbrown::hash_map::DefaultHashBuilder;
#[cfg(rrt_pathfinding)] use hashbrown::HashMap;
#[cfg(rrt_pathfinding)]
use kiddo::{distance::squared_euclidean, KdTree}; // For RRT paths (disabled for now)
#[cfg(rrt_pathfinding)]
use rand::distributions::Uniform;
use rand::{thread_rng, Rng};
#[cfg(rrt_pathfinding)] use std::f32::consts::PI;
use std::iter::FromIterator;
use vek::*;
// Path
#[derive(Clone, Debug)]
pub struct Path<T> {
pub nodes: Vec<T>,
}
impl<T> Default for Path<T> {
fn default() -> Self {
Self {
nodes: Vec::default(),
}
}
}
impl<T> FromIterator<T> for Path<T> {
fn from_iter<I: IntoIterator<Item = T>>(iter: I) -> Self {
Self {
nodes: iter.into_iter().collect(),
}
}
}
impl<T> IntoIterator for Path<T> {
type IntoIter = std::vec::IntoIter<T>;
type Item = T;
fn into_iter(self) -> Self::IntoIter { self.nodes.into_iter() }
}
impl<T> Path<T> {
pub fn is_empty(&self) -> bool { self.nodes.is_empty() }
pub fn len(&self) -> usize { self.nodes.len() }
pub fn iter(&self) -> impl Iterator<Item = &T> { self.nodes.iter() }
pub fn start(&self) -> Option<&T> { self.nodes.first() }
pub fn end(&self) -> Option<&T> { self.nodes.last() }
pub fn nodes(&self) -> &[T] { &self.nodes }
}
// Route: A path that can be progressed along
#[derive(Default, Clone, Debug)]
pub struct Route {
path: Path<Vec3<i32>>,
next_idx: usize,
}
impl From<Path<Vec3<i32>>> for Route {
fn from(path: Path<Vec3<i32>>) -> Self { Self { path, next_idx: 0 } }
}
pub struct TraversalConfig {
/// The distance to a node at which node is considered visited.
pub node_tolerance: f32,
/// The slowdown factor when following corners.
/// 0.0 = no slowdown on corners, 1.0 = total slowdown on corners.
pub slow_factor: f32,
/// Whether the agent is currently on the ground.
pub on_ground: bool,
/// Whether the agent is currently in water.
pub in_liquid: bool,
/// The distance to the target below which it is considered reached.
pub min_tgt_dist: f32,
/// Whether the agent can climb.
pub can_climb: bool,
/// Whether the agent can fly.
pub can_fly: bool,
}
const DIAGONALS: [Vec2<i32>; 8] = [
Vec2::new(1, 0),
Vec2::new(1, 1),
Vec2::new(0, 1),
Vec2::new(-1, 1),
Vec2::new(-1, 0),
Vec2::new(-1, -1),
Vec2::new(0, -1),
Vec2::new(1, -1),
];
impl Route {
pub fn path(&self) -> &Path<Vec3<i32>> { &self.path }
pub fn next(&self, i: usize) -> Option<Vec3<i32>> {
self.path.nodes.get(self.next_idx + i).copied()
}
pub fn is_finished(&self) -> bool { self.next(0).is_none() }
pub fn traverse<V>(
&mut self,
vol: &V,
pos: Vec3<f32>,
vel: Vec3<f32>,
traversal_cfg: &TraversalConfig,
) -> Option<(Vec3<f32>, f32)>
where
V: BaseVol<Vox = Block> + ReadVol,
{
let (next0, next1, next_tgt, be_precise) = loop {
// If we've reached the end of the path, stop
let next0 = self.next(0)?;
let next1 = self.next(1).unwrap_or(next0);
// Stop using obstructed paths
if !walkable(vol, next1) {
return None;
}
let be_precise = DIAGONALS.iter().any(|pos| {
(-1..2).all(|z| {
vol.get(next0 + Vec3::new(pos.x, pos.y, z))
.map(|b| !b.is_solid())
.unwrap_or(false)
})
});
// Map position of node to middle of block
let next_tgt = next0.map(|e| e as f32) + Vec3::new(0.5, 0.5, 0.0);
let closest_tgt = next_tgt.map2(pos, |tgt, pos| pos.clamped(tgt.floor(), tgt.ceil()));
// Determine whether we're close enough to the next to to consider it completed
let dist_sqrd = pos.xy().distance_squared(closest_tgt.xy());
if dist_sqrd
< traversal_cfg.node_tolerance.powi(2)
* if be_precise {
0.25
} else if traversal_cfg.in_liquid {
2.5
} else {
1.0
}
&& (((pos.z - closest_tgt.z > 1.2 || (pos.z - closest_tgt.z > -0.2 && traversal_cfg.on_ground))
&& (pos.z - closest_tgt.z < 1.2 || (pos.z - closest_tgt.z < 2.9 && vel.z < -0.05))
&& vel.z <= 0.0
// Only consider the node reached if there's nothing solid between us and it
&& (vol
.ray(pos + Vec3::unit_z() * 1.5, closest_tgt + Vec3::unit_z() * 1.5)
.until(Block::is_solid)
.cast()
.0
> pos.distance(closest_tgt) * 0.9 || dist_sqrd < 0.5)
&& self.next_idx < self.path.len())
|| (traversal_cfg.in_liquid
&& pos.z < closest_tgt.z + 0.8
&& pos.z > closest_tgt.z))
{
// Node completed, move on to the next one
self.next_idx += 1;
} else {
// The next node hasn't been reached yet, use it as a target
break (next0, next1, next_tgt, be_precise);
}
};
fn gradient(line: LineSegment2<f32>) -> f32 {
let r = (line.start.y - line.end.y) / (line.start.x - line.end.x);
if r.is_nan() { 100000.0 } else { r }
}
fn intersect(a: LineSegment2<f32>, b: LineSegment2<f32>) -> Option<Vec2<f32>> {
let ma = gradient(a);
let mb = gradient(b);
let ca = a.start.y - ma * a.start.x;
let cb = b.start.y - mb * b.start.x;
if (ma - mb).abs() < 0.0001 || (ca - cb).abs() < 0.0001 {
None
} else {
let x = (cb - ca) / (ma - mb);
let y = ma * x + ca;
Some(Vec2::new(x, y))
}
}
// We don't always want to aim for the centre of block since this can create
// jerky zig-zag movement. This function attempts to find a position
// inside a target block's area that aligned nicely with our velocity.
// This has a twofold benefit:
//
// 1. Entities can move at any angle when
// running on a flat surface
//
// 2. We don't have to search diagonals when
// pathfinding - cartesian positions are enough since this code will
// make the entity move smoothly along them
let corners = [
Vec2::new(0, 0),
Vec2::new(1, 0),
Vec2::new(1, 1),
Vec2::new(0, 1),
Vec2::new(0, 0), // Repeated start
];
let vel_line = LineSegment2 {
start: pos.xy(),
end: pos.xy() + vel.xy() * 100.0,
};
let align = |block_pos: Vec3<i32>, precision: f32| {
let lerp_block =
|x, precision| Lerp::lerp(x, block_pos.xy().map(|e| e as f32), precision);
(0..4)
.filter_map(|i| {
let edge_line = LineSegment2 {
start: lerp_block(
(block_pos.xy() + corners[i]).map(|e| e as f32),
precision,
),
end: lerp_block(
(block_pos.xy() + corners[i + 1]).map(|e| e as f32),
precision,
),
};
intersect(vel_line, edge_line).filter(|intersect| {
intersect
.clamped(
block_pos.xy().map(|e| e as f32),
block_pos.xy().map(|e| e as f32 + 1.0),
)
.distance_squared(*intersect)
< 0.001
})
})
.min_by_key(|intersect: &Vec2<f32>| {
(intersect.distance_squared(vel_line.end) * 1000.0) as i32
})
.unwrap_or_else(|| {
(0..2)
.flat_map(|i| (0..2).map(move |j| Vec2::new(i, j)))
.map(|rpos| block_pos + rpos)
.map(|block_pos| {
let block_posf = block_pos.xy().map(|e| e as f32);
let proj = vel_line.projected_point(block_posf);
let clamped = lerp_block(
proj.clamped(
block_pos.xy().map(|e| e as f32),
block_pos.xy().map(|e| e as f32),
),
precision,
);
(proj.distance_squared(clamped), clamped)
})
.min_by_key(|(d2, _)| (d2 * 1000.0) as i32)
.unwrap()
.1
})
};
let bez = CubicBezier2 {
start: pos.xy(),
ctrl0: pos.xy() + vel.xy().try_normalized().unwrap_or_default() * 1.0,
ctrl1: align(next0, 1.0),
end: align(next1, 1.0),
};
// Use a cubic spline of the next few targets to come up with a sensible target
// position. We want to use a position that gives smooth movement but is
// also accurate enough to avoid the agent getting stuck under ledges or
// falling off walls.
let next_dir = bez
.evaluate_derivative(0.85)
.try_normalized()
.unwrap_or_default();
let straight_factor = next_dir
.dot(vel.xy().try_normalized().unwrap_or(next_dir))
.max(0.0)
.powi(2);
let bez = CubicBezier2 {
start: pos.xy(),
ctrl0: pos.xy() + vel.xy().try_normalized().unwrap_or_default() * 1.0,
ctrl1: align(
next0,
(1.0 - if (next0.z as f32 - pos.z).abs() < 0.25 && !be_precise {
straight_factor
} else {
0.0
})
.max(0.1),
),
end: align(next1, 1.0),
};
let tgt2d = bez.evaluate(if (next0.z as f32 - pos.z).abs() < 0.25 {
0.25
} else {
0.5
});
let tgt = if be_precise {
next_tgt
} else {
Vec3::from(tgt2d) + Vec3::unit_z() * next_tgt.z
};
Some((
tgt - pos,
// Control the entity's speed to hopefully stop us falling off walls on sharp
// corners. This code is very imperfect: it does its best but it
// can still fail for particularly fast entities.
straight_factor * traversal_cfg.slow_factor + (1.0 - traversal_cfg.slow_factor),
))
.filter(|(bearing, _)| bearing.z < 2.1)
}
}
/// A self-contained system that attempts to chase a moving target, only
/// performing pathfinding if necessary
#[derive(Default, Clone, Debug)]
pub struct Chaser {
last_search_tgt: Option<Vec3<f32>>,
/// `bool` indicates whether the Route is a complete route to the target
route: Option<(Route, bool)>,
/// We use this hasher (AAHasher) because:
/// (1) we care about DDOS attacks (ruling out FxHash);
/// (2) we don't care about determinism across computers (we can use
/// AAHash).
astar: Option<Astar<Vec3<i32>, DefaultHashBuilder>>,
}
impl Chaser {
/// Returns bearing and speed
/// Bearing is a Vec3<f32> dictating the direction of movement
/// Speed is an f32 between 0.0 and 1.0
pub fn chase<V>(
&mut self,
vol: &V,
pos: Vec3<f32>,
vel: Vec3<f32>,
tgt: Vec3<f32>,
traversal_cfg: TraversalConfig,
) -> Option<(Vec3<f32>, f32)>
where
V: BaseVol<Vox = Block> + ReadVol,
{
span!(_guard, "chase", "Chaser::chase");
let pos_to_tgt = pos.distance(tgt);
// If we're already close to the target then there's nothing to do
let end = self
.route
.as_ref()
.and_then(|(r, _)| r.path.end().copied())
.map(|e| e.map(|e| e as f32 + 0.5))
.unwrap_or(tgt);
if ((pos - end) * Vec3::new(1.0, 1.0, 2.0)).magnitude_squared()
< traversal_cfg.min_tgt_dist.powi(2)
{
self.route = None;
return None;
}
let bearing = if let Some((end, complete)) = self
.route
.as_ref()
.and_then(|(r, complete)| Some((r.path().end().copied()?, *complete)))
{
let end_to_tgt = end.map(|e| e as f32).distance(tgt);
// If the target has moved significantly since the path was generated then it's
// time to search for a new path. Also, do this randomly from time
// to time to avoid any edge cases that cause us to get stuck. In
// theory this shouldn't happen, but in practice the world is full
// of unpredictable obstacles that are more than willing to mess up
// our day. TODO: Come up with a better heuristic for this
if end_to_tgt > pos_to_tgt * 0.3 + 5.0 && complete {
None
} else if thread_rng().gen::<f32>() < 0.001 {
self.route = None;
None
} else {
self.route
.as_mut()
.and_then(|(r, _)| r.traverse(vol, pos, vel, &traversal_cfg))
}
} else {
// There is no route found yet
None
};
// If a bearing has already been determined, use that
if let Some((bearing, speed)) = bearing {
Some((bearing, speed))
} else {
// Since no bearing has been determined yet, a new route will be
// calculated if the target has moved, pathfinding is not complete,
// or there is no route
let tgt_dir = (tgt - pos).xy().try_normalized().unwrap_or_default();
// Only search for a path if the target has moved from their last position. We
// don't want to be thrashing the pathfinding code for targets that
// we're unable to access!
if self
.last_search_tgt
.map(|last_tgt| last_tgt.distance(tgt) > pos_to_tgt * 0.15 + 5.0)
.unwrap_or(true)
|| self.astar.is_some()
|| self.route.is_none()
{
self.last_search_tgt = Some(tgt);
// NOTE: Enable air paths when air braking has been figured out
let (path, complete) = /*if cfg!(rrt_pathfinding) && traversal_cfg.can_fly {
find_air_path(vol, pos, tgt, &traversal_cfg)
} else */{
find_path(&mut self.astar, vol, pos, tgt, &traversal_cfg)
};
self.route = path.map(|path| {
let start_index = path
.iter()
.enumerate()
.min_by_key(|(_, node)| {
node.map(|e| e as f32).distance_squared(pos + tgt_dir) as i32
})
.map(|(idx, _)| idx);
(
Route {
path,
next_idx: start_index.unwrap_or(0),
},
complete,
)
});
}
// Start traversing the new route if it exists
if let Some(bearing) = self
.route
.as_mut()
.and_then(|(r, _)| r.traverse(vol, pos, vel, &traversal_cfg))
{
Some(bearing)
} else {
// At this point no route is available and no bearing
// has been determined, so we start sampling terrain.
// Check for falling off walls and try moving straight
// towards the target if falling is not a danger
let walking_towards_edge = (-8..2).all(|z| {
vol.get(
(pos + Vec3::<f32>::from(tgt_dir) * 2.5).map(|e| e as i32)
+ Vec3::unit_z() * z,
)
.map(|b| b.is_air())
.unwrap_or(false)
});
// Enable when airbraking/flight is figured out
/*if traversal_cfg.can_fly {
Some(((tgt - pos) , 1.0))
} else */
if traversal_cfg.can_fly {
Some(((tgt - pos) * Vec3::new(1.0, 1.0, 0.5), 1.0))
} else if !walking_towards_edge {
Some(((tgt - pos) * Vec3::new(1.0, 1.0, 0.0), 1.0))
} else {
// This is unfortunately where an NPC will stare blankly
// into space. No route has been found and no temporary
// bearing would suffice. Hopefully a route will be found
// in the coming ticks.
None
}
}
}
}
}
fn walkable<V>(vol: &V, pos: Vec3<i32>) -> bool
where
V: BaseVol<Vox = Block> + ReadVol,
{
let below = vol
.get(pos - Vec3::unit_z())
.ok()
.copied()
.unwrap_or_else(Block::empty);
let a = vol.get(pos).ok().copied().unwrap_or_else(Block::empty);
let b = vol
.get(pos + Vec3::unit_z())
.ok()
.copied()
.unwrap_or_else(Block::empty);
let on_ground = below.is_filled();
let in_liquid = a.is_liquid();
(on_ground || in_liquid) && !a.is_solid() && !b.is_solid()
}
/// Attempt to search for a path to a target, returning the path (if one was
/// found) and whether it is complete (reaches the target)
fn find_path<V>(
astar: &mut Option<Astar<Vec3<i32>, DefaultHashBuilder>>,
vol: &V,
startf: Vec3<f32>,
endf: Vec3<f32>,
traversal_cfg: &TraversalConfig,
) -> (Option<Path<Vec3<i32>>>, bool)
where
V: BaseVol<Vox = Block> + ReadVol,
{
let is_walkable = |pos: &Vec3<i32>| walkable(vol, *pos);
let get_walkable_z = |pos| {
let mut z_incr = 0;
for _ in 0..32 {
let test_pos = pos + Vec3::unit_z() * z_incr;
if is_walkable(&test_pos) {
return Some(test_pos);
}
z_incr = -z_incr + i32::from(z_incr <= 0);
}
None
};
let (start, end) = match (
get_walkable_z(startf.map(|e| e.floor() as i32)),
get_walkable_z(endf.map(|e| e.floor() as i32)),
) {
(Some(start), Some(end)) => (start, end),
_ => return (None, false),
};
let heuristic = |pos: &Vec3<i32>, _: &Vec3<i32>| (pos.distance_squared(end) as f32).sqrt();
let transition = |a: Vec3<i32>, b: Vec3<i32>| {
let crow_line = LineSegment2 {
start: startf.xy(),
end: endf.xy(),
};
// Modify the heuristic a little in order to prefer paths that take us on a
// straight line toward our target. This means we get smoother movement.
1.0 + crow_line.distance_to_point(b.xy().map(|e| e as f32)) * 0.025
+ (b.z - a.z - 1).max(0) as f32 * 10.0
};
let neighbors = |pos: &Vec3<i32>| {
let pos = *pos;
const DIRS: [Vec3<i32>; 17] = [
Vec3::new(0, 1, 0), // Forward
Vec3::new(0, 1, 1), // Forward upward
Vec3::new(0, 1, -1), // Forward downward
Vec3::new(0, 1, -2), // Forward downwardx2
Vec3::new(1, 0, 0), // Right
Vec3::new(1, 0, 1), // Right upward
Vec3::new(1, 0, -1), // Right downward
Vec3::new(1, 0, -2), // Right downwardx2
Vec3::new(0, -1, 0), // Backwards
Vec3::new(0, -1, 1), // Backward Upward
Vec3::new(0, -1, -1), // Backward downward
Vec3::new(0, -1, -2), // Backward downwardx2
Vec3::new(-1, 0, 0), // Left
Vec3::new(-1, 0, 1), // Left upward
Vec3::new(-1, 0, -1), // Left downward
Vec3::new(-1, 0, -2), // Left downwardx2
Vec3::new(0, 0, -1), // Downwards
];
const JUMPS: [Vec3<i32>; 4] = [
Vec3::new(0, 1, 2), // Forward Upwardx2
Vec3::new(1, 0, 2), // Right Upwardx2
Vec3::new(0, -1, 2), // Backward Upwardx2
Vec3::new(-1, 0, 2), // Left Upwardx2
];
// let walkable = [
// is_walkable(&(pos + Vec3::new(1, 0, 0))),
// is_walkable(&(pos + Vec3::new(-1, 0, 0))),
// is_walkable(&(pos + Vec3::new(0, 1, 0))),
// is_walkable(&(pos + Vec3::new(0, -1, 0))),
// ];
// const DIAGONALS: [(Vec3<i32>, [usize; 2]); 8] = [
// (Vec3::new(1, 1, 0), [0, 2]),
// (Vec3::new(-1, 1, 0), [1, 2]),
// (Vec3::new(1, -1, 0), [0, 3]),
// (Vec3::new(-1, -1, 0), [1, 3]),
// (Vec3::new(1, 1, 1), [0, 2]),
// (Vec3::new(-1, 1, 1), [1, 2]),
// (Vec3::new(1, -1, 1), [0, 3]),
// (Vec3::new(-1, -1, 1), [1, 3]),
// ];
DIRS.iter()
.chain(
Some(JUMPS.iter())
.filter(|_| {
vol.get(pos - Vec3::unit_z())
.map(|b| !b.is_liquid())
.unwrap_or(true)
|| traversal_cfg.can_climb
|| traversal_cfg.can_fly
})
.into_iter()
.flatten(),
)
.map(move |dir| (pos, dir))
.filter(move |(pos, dir)| {
(traversal_cfg.can_fly || is_walkable(pos) && is_walkable(&(*pos + **dir)))
&& ((dir.z < 1
|| vol
.get(pos + Vec3::unit_z() * 2)
.map(|b| !b.is_solid())
.unwrap_or(true))
&& (dir.z < 2
|| vol
.get(pos + Vec3::unit_z() * 3)
.map(|b| !b.is_solid())
.unwrap_or(true))
&& (dir.z >= 0
|| vol
.get(pos + *dir + Vec3::unit_z() * 2)
.map(|b| !b.is_solid())
.unwrap_or(true)))
})
.map(|(pos, dir)| {
let destination = pos + dir;
(destination, transition(pos, destination))
})
// .chain(
// DIAGONALS
// .iter()
// .filter(move |(dir, [a, b])| {
// is_walkable(&(pos + *dir)) && walkable[*a] &&
// walkable[*b] })
// .map(move |(dir, _)| pos + *dir),
// )
};
let satisfied = |pos: &Vec3<i32>| pos == &end;
let mut new_astar = match astar.take() {
None => Astar::new(25_000, start, DefaultHashBuilder::default()),
Some(astar) => astar,
};
let path_result = new_astar.poll(100, heuristic, neighbors, satisfied);
*astar = Some(new_astar);
match path_result {
PathResult::Path(path, _cost) => {
*astar = None;
(Some(path), true)
},
PathResult::None(path) => {
*astar = None;
(Some(path), false)
},
PathResult::Exhausted(path) => {
*astar = None;
(Some(path), false)
},
PathResult::Pending => (None, false),
}
}
// Enable when airbraking/sensible flight is a thing
#[cfg(rrt_pathfinding)]
fn find_air_path<V>(
vol: &V,
startf: Vec3<f32>,
endf: Vec3<f32>,
traversal_cfg: &TraversalConfig,
) -> (Option<Path<Vec3<i32>>>, bool)
where
V: BaseVol<Vox = Block> + ReadVol,
{
let radius = traversal_cfg.node_tolerance;
let mut connect = false;
let total_dist_sqrd = startf.distance_squared(endf);
// First check if a straight line path works
if vol
.ray(startf + Vec3::unit_z(), endf + Vec3::unit_z())
.until(Block::is_opaque)
.cast()
.0
.powi(2)
>= total_dist_sqrd
{
let mut path = Vec::new();
path.push(endf.map(|e| e.floor() as i32));
connect = true;
(Some(path.into_iter().collect()), connect)
// Else use RRTs
} else {
let is_traversable = |start: &Vec3<f32>, end: &Vec3<f32>| {
vol.ray(*start, *end)
.until(Block::is_solid)
.cast()
.0
.powi(2)
> (*start).distance_squared(*end)
//vol.get(*pos).ok().copied().unwrap_or_else(Block::empty).
// is_fluid();
};
informed_rrt_connect(start, end, is_traversable)
}
}
/// Attempts to find a path from a start to the end using an informed
/// RRT-Connect algorithm. A point is sampled from a bounding spheroid
/// between the start and end. Two separate rapidly exploring random
/// trees extend toward the sampled point. Nodes are stored in k-d trees
/// for quicker nearest node calculations. Points are sampled until the
/// trees connect. A final path is then reconstructed from the nodes.
/// This pathfinding algorithm is more appropriate for 3D pathfinding
/// with wider gaps, such as flying through a forest than for terrain
/// with narrow gaps, such as navigating a maze.
/// Returns a path and whether that path is complete or not.
#[cfg(rrt_pathfinding)]
fn informed_rrt_connect(
start: Vec3<f32>,
end: Vec3<f32>,
is_valid_edge: impl Fn(&Vec3<f32>, &Vec3<f32>) -> bool,
) -> (Option<Path<Vec3<i32>>>, bool) {
let mut path = Vec::new();
// Each tree has a vector of nodes
let mut node_index1: usize = 0;
let mut node_index2: usize = 0;
let mut nodes1 = Vec::new();
let mut nodes2 = Vec::new();
// The parents hashmap stores nodes and their parent nodes as pairs to
// retrace the complete path once the two RRTs connect
let mut parents1 = HashMap::new();
let mut parents2 = HashMap::new();
// The path vector stores the path from the appropriate terminal to the
// connecting node or vice versa
let mut path1 = Vec::new();
let mut path2 = Vec::new();
// K-d trees are used to find the closest nodes rapidly
let mut kdtree1 = KdTree::new();
let mut kdtree2 = KdTree::new();
// Add the start as the first node of the first k-d tree
kdtree1
.add(&[startf.x, startf.y, startf.z], node_index1)
.unwrap_or_default();
nodes1.push(startf);
node_index1 += 1;
// Add the end as the first node of the second k-d tree
kdtree2
.add(&[endf.x, endf.y, endf.z], node_index2)
.unwrap_or_default();
nodes2.push(endf);
node_index2 += 1;
let mut connection1_idx = 0;
let mut connection2_idx = 0;
let mut connect = false;
// Scalar non-dimensional value that is proportional to the size of the
// sample spheroid volume. This increases in value until a path is found.
let mut search_parameter = 0.01;
// Maximum of 7000 iterations
for _i in 0..7000 {
if connect {
break;
}
// Sample a point on the bounding spheroid
let (sampled_point1, sampled_point2) = {
let point = point_on_prolate_spheroid(startf, endf, search_parameter);
(point, point)
};
// Find the nearest nodes to the the sampled point
let nearest_index1 = kdtree1
.nearest_one(
&[sampled_point1.x, sampled_point1.y, sampled_point1.z],
&squared_euclidean,
)
.map_or(0, |n| *n.1);
let nearest_index2 = kdtree2
.nearest_one(
&[sampled_point2.x, sampled_point2.y, sampled_point2.z],
&squared_euclidean,
)
.map_or(0, |n| *n.1);
let nearest1 = nodes1[nearest_index1];
let nearest2 = nodes2[nearest_index2];
// Extend toward the sampled point from the nearest node of each tree
let new_point1 = nearest1 + (sampled_point1 - nearest1).normalized().map(|a| a * radius);
let new_point2 = nearest2 + (sampled_point2 - nearest2).normalized().map(|a| a * radius);
// Ensure the new nodes are valid/traversable
if is_valid_edge(&nearest1, &new_point1) {
kdtree1
.add(&[new_point1.x, new_point1.y, new_point1.z], node_index1)
.unwrap_or_default();
nodes1.push(new_point1);
parents1.insert(node_index1, nearest_index1);
node_index1 += 1;
// Check if the trees connect
if let Ok((check, index)) = kdtree2.nearest_one(
&[new_point1.x, new_point1.y, new_point1.z],
&squared_euclidean,
) {
if check < radius {
let connection = nodes2[*index];
connection2_idx = *index;
nodes1.push(connection);
connection1_idx = nodes1.len() - 1;
parents1.insert(node_index1, node_index1 - 1);
connect = true;
}
}
}
// Repeat the validity check for the second tree
if is_valid_edge(&nearest2, &new_point2) {
kdtree2
.add(&[new_point2.x, new_point2.y, new_point1.z], node_index2)
.unwrap_or_default();
nodes2.push(new_point2);
parents2.insert(node_index2, nearest_index2);
node_index2 += 1;
// Again check for a connection
if let Ok((check, index)) = kdtree1.nearest_one(
&[new_point2.x, new_point2.y, new_point1.z],
&squared_euclidean,
) {
if check < radius {
let connection = nodes1[*index];
connection1_idx = *index;
nodes2.push(connection);
connection2_idx = nodes2.len() - 1;
parents2.insert(node_index2, node_index2 - 1);
connect = true;
}
}
}
// Increase the search parameter to widen the sample volume
search_parameter += 0.02;
}
if connect {
// Construct paths from the connection node to the start and end
let mut current_node_index1 = connection1_idx;
while current_node_index1 > 0 {
current_node_index1 = *parents1.get(&current_node_index1).unwrap_or(&0);
path1.push(nodes1[current_node_index1].map(|e| e.floor() as i32));
}
let mut current_node_index2 = connection2_idx;
while current_node_index2 > 0 {
current_node_index2 = *parents2.get(&current_node_index2).unwrap_or(&0);
path2.push(nodes2[current_node_index2].map(|e| e.floor() as i32));
}
// Join the two paths together in the proper order and remove duplicates
path1.pop();
path1.reverse();
path.append(&mut path1);
path.append(&mut path2);
path.dedup();
} else {
// If the trees did not connect, construct a path from the start to
// the closest node to the end
let mut current_node_index1 = kdtree1
.nearest_one(&[endf.x, endf.y, endf.z], &squared_euclidean)
.map_or(0, |c| *c.1);
// Attempt to pick a node other than the start node
for _i in 0..3 {
if current_node_index1 == 0
|| nodes1[current_node_index1].distance_squared(startf) < 4.0
{
if let Some(index) = parents1.values().choose(&mut thread_rng()) {
current_node_index1 = *index;
} else {
break;
}
} else {
break;
}
}
path1.push(nodes1[current_node_index1].map(|e| e.floor() as i32));
// Construct the path
while current_node_index1 != 0 && nodes1[current_node_index1].distance_squared(startf) > 4.0
{
current_node_index1 = *parents1.get(&current_node_index1).unwrap_or(&0);
path1.push(nodes1[current_node_index1].map(|e| e.floor() as i32));
}
path1.reverse();
path.append(&mut path1);
}
let mut new_path = Vec::new();
let mut node = path[0];
new_path.push(node);
let mut node_idx = 0;
let num_nodes = path.len();
let end = path[num_nodes - 1];
while node != end {
let next_idx = if node_idx + 4 > num_nodes - 1 {
num_nodes - 1
} else {
node_idx + 4
};
let next_node = path[next_idx];
let start_pos = node.map(|e| e as f32 + 0.5);
let end_pos = next_node.map(|e| e as f32 + 0.5);
if vol
.ray(start_pos, end_pos)
.until(Block::is_solid)
.cast()
.0
.powi(2)
> (start_pos).distance_squared(end_pos)
{
node_idx = next_idx;
new_path.push(next_node);
} else {
node_idx += 1;
}
node = path[node_idx];
}
path = new_path;
}
/// Returns a random point within a radially symmetrical ellipsoid with given
/// foci and a `search parameter` to determine the size of the ellipse beyond
/// the foci. Technically the point is within a prolate spheroid translated and
/// rotated to the proper place in cartesian space.
/// The search_parameter is a float that relates to the length of the string for
/// a two dimensional ellipse or the size of the ellipse beyond the foci. In
/// this case that analogy still holds as the ellipse is radially symmetrical
/// along the axis between the foci. The value of the search parameter must be
/// greater than zero. In order to increase the sample area, the
/// search_parameter should be increased linearly as the search continues.
#[cfg(rrt_pathfinding)]
pub fn point_on_prolate_spheroid(
focus1: Vec3<f32>,
focus2: Vec3<f32>,
search_parameter: f32,
) -> Vec3<f32> {
let mut rng = thread_rng();
// Uniform distribution
let range = Uniform::from(0.0..1.0);
// Midpoint is used as the local origin
let midpoint = 0.5 * (focus1 + focus2);
// Radius between the start and end of the path
let radius: f32 = focus1.distance(focus2);
// The linear eccentricity of an ellipse is the distance from the origin to a
// focus A prolate spheroid is a half-ellipse rotated for a full revolution
// which is why ellipse variables are used frequently in this function
let linear_eccentricity: f32 = 0.5 * radius;
// For an ellipsoid, three variables determine the shape: a, b, and c.
// These are the distance from the center/origin to the surface on the
// x, y, and z axes, respectively.
// For a prolate spheroid a and b are equal.
// c is determined by adding the search parameter to the linear eccentricity.
// As the search parameter increases the size of the spheroid increases
let c: f32 = linear_eccentricity + search_parameter;
// The width is calculated to prioritize increasing width over length of
// the ellipsoid
let a: f32 = (c.powi(2) - linear_eccentricity.powi(2)).powf(0.5);
// The width should be the same in both the x and y directions
let b: f32 = a;
// The parametric spherical equation for an ellipsoid measuring from the
// center point is as follows:
// x = a * cos(theta) * cos(lambda)
// y = b * cos(theta) * sin(lambda)
// z = c * sin(theta)
//
// where -0.5 * PI <= theta <= 0.5 * PI
// and 0.0 <= lambda < 2.0 * PI
//
// Select these two angles using the uniform distribution defined at the
// beginning of the function from 0.0 to 1.0
let rtheta: f32 = PI * range.sample(&mut rng) - 0.5 * PI;
let lambda: f32 = 2.0 * PI * range.sample(&mut rng);
// Select a point on the surface of the ellipsoid
let point = Vec3::new(
a * rtheta.cos() * lambda.cos(),
b * rtheta.cos() * lambda.sin(),
c * rtheta.sin(),
);
// NOTE: Theoretically we should sample a point within the spheroid
// requiring selecting a point along the radius. In my tests selecting
// a point *on the surface* of the spheroid results in sampling that is
// "good enough". The following code is commented out to reduce expense.
//let surface_point = Vec3::new(a * rtheta.cos() * lambda.cos(), b *
// rtheta.cos() * lambda.sin(), c * rtheta.sin()); let magnitude =
// surface_point.magnitude(); let direction = surface_point.normalized();
//// Randomly select a point along the vector to the previously selected surface
//// point using the uniform distribution
//let point = magnitude * range.sample(&mut rng) * direction;
// Now that a point has been selected in local space, it must be rotated and
// translated into global coordinates
// NOTE: Don't rotate about the z axis as the point is already randomly
// selected about the z axis
//let dx = focus2.x - focus1.x;
//let dy = focus2.y - focus1.y;
let dz = focus2.z - focus1.z;
// Phi and theta are the angles from the x axis in the x-y plane and from
// the z axis, respectively. (As found in spherical coordinates)
// These angles are used to rotate the random point in the spheroid about
// the local origin
//
// Rotate about z axis by phi
//let phi: f32 = if dx.abs() > 0.0 {
// (dy / dx).atan()
//} else {
// 0.5 * PI
//};
// This is unnecessary as rtheta is randomly selected between 0.0 and 2.0 * PI
// let rot_z_mat = Mat3::new(phi.cos(), -1.0 * phi.sin(), 0.0, phi.sin(),
// phi.cos(), 0.0, 0.0, 0.0, 1.0);
// Rotate about perpendicular vector in the xy plane by theta
let theta: f32 = if radius > 0.0 {
(dz / radius).acos()
} else {
0.0
};
// Vector from focus1 to focus2
let r_vec = focus2 - focus1;
// Perpendicular vector in xy plane
let perp_vec = Vec3::new(-1.0 * r_vec.y, r_vec.x, 0.0).normalized();
let l = perp_vec.x;
let m = perp_vec.y;
let n = perp_vec.z;
// Rotation matrix for rotation about a vector
let rot_2_mat = Mat3::new(
l * l * (1.0 - theta.cos()),
m * l * (1.0 - theta.cos()) - n * theta.sin(),
n * l * (1.0 - theta.cos()) + m * theta.sin(),
l * m * (1.0 - theta.cos()) + n * theta.sin(),
m * m * (1.0 - theta.cos()) + theta.cos(),
n * m * (1.0 - theta.cos()) - l * theta.sin(),
l * n * (1.0 - theta.cos()) - m * theta.sin(),
m * n * (1.0 - theta.cos()) + l * theta.sin(),
n * n * (1.0 - theta.cos()) + theta.cos(),
);
// Get the global coordinates of the point by rotating and adding the origin
// rot_z_mat is unneeded due to the random rotation defined by lambda
// let global_coords = midpoint + rot_2_mat * (rot_z_mat * point);
midpoint + rot_2_mat * point
}