Merge branch 'james/rrt-pathfinding' into 'master'

Initial RRT flight pathfinding

See merge request veloren/veloren!2773

Cargo.lock

@@ -5873,6 +5873,7 @@ dependencies = [
  "fxhash",
  "hashbrown 0.11.2",
  "indexmap",
+ "kiddo",
  "lazy_static",
  "num-derive",
  "num-traits",

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"]
+required-features = ["bin_cmd_doc_gen"]

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.
+            // Control the entity's speed to hopefully stop us falling off walls on sharp
-            // This code is very imperfect: it does its best but it can still fail for particularly
+            // corners. This code is very imperfect: it does its best but it
-            // fast entities.
+            // 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<f32> dictating the direction of movement
+    /// Speed is an f32 between 0.0 and 1.0
     pub fn chase<V>(
         &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 {
                     )
                 });
             }
-
+            // Start traversing the new route if it exists
-            let walking_towards_edge = (-3..2).all(|z| {
+            if let Some(bearing) = self
-                vol.get(
+                .route
-                    (pos + Vec3::<f32>::from(tgt_dir) * 2.5).map(|e| e as i32) + Vec3::unit_z() * z,
+                .as_mut()
-                )
+                .and_then(|(r, _)| r.traverse(vol, pos, vel, &traversal_cfg))
-                .map(|b| b.is_air())
+            {
-                .unwrap_or(false)
+                Some(bearing)
-            });
-
-            if !walking_towards_edge || traversal_cfg.can_fly {
-                Some(((tgt - pos) * Vec3::new(1.0, 1.0, 0.0), 1.0))
             } 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::<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 !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<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.
+#[allow(clippy::many_single_char_names)]
+#[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
+}