diff --git a/Cargo.lock b/Cargo.lock index af7f0a0bd0..4bbd825ed2 100644 --- a/Cargo.lock +++ b/Cargo.lock @@ -5873,6 +5873,7 @@ dependencies = [ "fxhash", "hashbrown 0.11.2", "indexmap", + "kiddo", "lazy_static", "num-derive", "num-traits", diff --git a/common/Cargo.toml b/common/Cargo.toml index fed28470a3..2c18050994 100644 --- a/common/Cargo.toml +++ b/common/Cargo.toml @@ -11,6 +11,7 @@ simd = ["vek/platform_intrinsics"] bin_csv = ["ron", "csv", "structopt"] bin_graphviz = ["petgraph"] bin_cmd_doc_gen = [] +rrt_pathfinding = ["kiddo"] default = ["simd"] @@ -63,6 +64,8 @@ csv = { version = "1.1.3", optional = true } structopt = { version = "0.3.13", optional = true } # graphviz exporters petgraph = { version = "0.5.1", optional = true } +# K-d trees used for RRT pathfinding +kiddo = { version = "0.1", optional = true } # Data structures hashbrown = { version = "0.11", features = ["rayon", "serde", "nightly"] } @@ -103,4 +106,4 @@ required-features = ["bin_graphviz"] [[bin]] name = "cmd_doc_gen" -required-features = ["bin_cmd_doc_gen"] \ No newline at end of file +required-features = ["bin_cmd_doc_gen"] diff --git a/common/src/path.rs b/common/src/path.rs index 6c6657cecd..11a367ed0b 100644 --- a/common/src/path.rs +++ b/common/src/path.rs @@ -5,7 +5,13 @@ use crate::{ }; use common_base::span; use hashbrown::hash_map::DefaultHashBuilder; -use rand::prelude::*; +#[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::*; @@ -135,9 +141,9 @@ impl Route { }) }); + // 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 @@ -312,9 +318,9 @@ impl Route { 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. + // 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) @@ -336,6 +342,9 @@ pub struct Chaser { } impl Chaser { + /// Returns bearing and speed + /// Bearing is a Vec3 dictating the direction of movement + /// Speed is an f32 between 0.0 and 1.0 pub fn chase( &mut self, vol: &V, @@ -386,12 +395,17 @@ impl Chaser { .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 @@ -406,7 +420,12 @@ impl Chaser { { self.last_search_tgt = Some(tgt); - let (path, complete) = find_path(&mut self.astar, vol, pos, tgt, &traversal_cfg); + // 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 @@ -429,19 +448,40 @@ impl Chaser { ) }); } - - let walking_towards_edge = (-3..2).all(|z| { - vol.get( - (pos + Vec3::::from(tgt_dir) * 2.5).map(|e| e as i32) + Vec3::unit_z() * z, - ) - .map(|b| b.is_air()) - .unwrap_or(false) - }); - - if !walking_towards_edge || traversal_cfg.can_fly { - Some(((tgt - pos) * Vec3::new(1.0, 1.0, 0.0), 1.0)) + // 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 { - None + // 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 = (-3..2).all(|z| { + vol.get( + (pos + Vec3::::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 !walking_towards_edge || traversal_cfg.can_fly { + 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 + } } } } @@ -631,3 +671,399 @@ where PathResult::Pending => (None, false), } } + +// Enable when airbraking/sensible flight is a thing +#[cfg(rrt_pathfinding)] +fn find_air_path( + vol: &V, + startf: Vec3, + endf: Vec3, + traversal_cfg: &TraversalConfig, +) -> (Option>>, bool) +where + V: BaseVol + 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, end: &Vec3| { + 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, + end: Vec3, + is_valid_edge: impl Fn(&Vec3, &Vec3) -> bool, +) -> (Option>>, 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(¤t_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(¤t_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(¤t_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. +#[allow(clippy::many_single_char_names)] +#[cfg(rrt_pathfinding)] +pub fn point_on_prolate_spheroid( + focus1: Vec3, + focus2: Vec3, + search_parameter: f32, +) -> Vec3 { + 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 +}