1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293
//! A [dynamic bounding volume tree implementation](struct.DynamicBoundingVolumeTree.html), //! index based (not pointer based). //! //! The following invariants are true: //! //! * A branch node must have exactly two children. //! * Only leaf nodes contain user data. //! //! Internal nodes may have incorrect bounding volumes and height after insertion, removal and //! updates to values in the tree. These will be fixed during refitting, which is done by calling //! [`do_refit`](struct.DynamicBoundingVolumeTree.html#method.do_refit). //! //! The main heuristic used for insertion and tree rotation, is surface area of the bounding volume. //! //! Updating of values in the tree, can either be performed by using the //! [`values`](struct.DynamicBoundingVolumeTree.html#method.values) function to get a mutable //! iterator over the values in the tree, or by using //! [`update_node`](struct.DynamicBoundingVolumeTree.html#method.update_node). //! It is recommended to use the latter when possible. If the former is used, //! [`reindex_values`](struct.DynamicBoundingVolumeTree.html#method.reindex_values) //! must be called if the order of the values is changed in any way. //! //! The trait [`TreeValue`](trait.TreeValue.html) needs to be implemented for a type to be usable //! in the tree. //! //! # Examples //! //! ``` //! # extern crate cgmath; //! # extern crate collision; //! //! use cgmath::{Point2, Vector2, InnerSpace}; //! use collision::{Aabb, Aabb2, Ray2}; //! //! use collision::dbvt::{DynamicBoundingVolumeTree, TreeValue, ContinuousVisitor}; //! //! #[derive(Debug, Clone)] //! struct Value { //! pub id: u32, //! pub aabb: Aabb2<f32>, //! fat_aabb: Aabb2<f32>, //! } //! //! impl Value { //! pub fn new(id: u32, aabb: Aabb2<f32>) -> Self { //! Self { //! id, //! fat_aabb : aabb.add_margin(Vector2::new(3., 3.)), //! aabb, //! } //! } //! } //! //! impl TreeValue for Value { //! type Bound = Aabb2<f32>; //! //! fn bound(&self) -> &Aabb2<f32> { //! &self.aabb //! } //! //! fn get_bound_with_margin(&self) -> Aabb2<f32> { //! self.fat_aabb.clone() //! } //! } //! //! fn aabb2(minx: f32, miny: f32, maxx: f32, maxy: f32) -> Aabb2<f32> { //! Aabb2::new(Point2::new(minx, miny), Point2::new(maxx, maxy)) //! } //! //! fn main() { //! let mut tree = DynamicBoundingVolumeTree::<Value>::new(); //! tree.insert(Value::new(10, aabb2(5., 5., 10., 10.))); //! tree.insert(Value::new(11, aabb2(21., 14., 23., 16.))); //! tree.do_refit(); //! //! let ray = Ray2::new(Point2::new(0., 0.), Vector2::new(-1., -1.).normalize()); //! let mut visitor = ContinuousVisitor::<Ray2<f32>, Value>::new(&ray); //! assert_eq!(0, tree.query(&mut visitor).len()); //! //! let ray = Ray2::new(Point2::new(6., 0.), Vector2::new(0., 1.).normalize()); //! let mut visitor = ContinuousVisitor::<Ray2<f32>, Value>::new(&ray); //! let results = tree.query(&mut visitor); //! assert_eq!(1, results.len()); //! assert_eq!(10, results[0].0.id); //! assert_eq!(Point2::new(6., 5.), results[0].1); //! } //! ``` //! pub use self::util::*; pub use self::visitor::*; pub use self::wrapped::TreeValueWrapped; use std::cmp::max; use std::fmt; use cgmath::num_traits::NumCast; use rand; use rand::Rng; use crate::prelude::*; mod wrapped; mod visitor; mod util; const SURFACE_AREA_IMPROVEMENT_FOR_ROTATION: f32 = 0.3; const PERFORM_ROTATION_PERCENTAGE: u32 = 10; /// Trait that needs to be implemented for any value that is to be used in the /// [`DynamicBoundingVolumeTree`](struct.DynamicBoundingVolumeTree.html). /// pub trait TreeValue: Clone { /// Bounding volume type type Bound; /// Return the bounding volume of the value fn bound(&self) -> &Self::Bound; /// Return a fattened bounding volume. For shapes that do not move, this can be the same as the /// base bounding volume. It is recommended for moving shapes to have a larger fat bound, so /// tree rotations don't have to be performed every frame. fn get_bound_with_margin(&self) -> Self::Bound; } /// Make it possible to run broad phase algorithms directly on the value storage in DBVT impl<T> HasBound for (usize, T) where T: TreeValue, T::Bound: Bound, { type Bound = T::Bound; fn bound(&self) -> &Self::Bound { self.1.bound() } } /// Visitor trait used for [querying](struct.DynamicBoundingVolumeTree.html#method.query) the tree. pub trait Visitor { /// Bounding volume accepted by the visitor type Bound; /// Result returned by the acceptance test type Result; /// Acceptance test function fn accept(&mut self, bound: &Self::Bound, is_leaf: bool) -> Option<Self::Result>; } /// A dynamic bounding volume tree, index based (not pointer based). /// /// The following invariants are true: /// /// * A branch node must have exactly two children. /// * Only leaf nodes contain user data. /// /// Internal nodes may have incorrect bounding volumes and height after insertion, removal and /// updates to values in the tree. These will be fixed during refitting, which is done by calling /// [`do_refit`](struct.DynamicBoundingVolumeTree.html#method.do_refit). This function should /// ideally not be called more than once per frame. /// /// The main heuristic used for insertion and tree rotation, is surface area of the bounding volume. /// /// Updating of values in the tree, can either be performed by using the /// [`values`](struct.DynamicBoundingVolumeTree.html#method.values) function to get a mutable /// iterator over the values in the tree, or by using /// [`update_node`](struct.DynamicBoundingVolumeTree.html#method.update_node). /// It is recommended to use the latter when possible. If the former is used, /// [`reindex_values`](struct.DynamicBoundingVolumeTree.html#method.reindex_values) /// must be called if the order of the values is changed in any way. /// /// # Type parameters: /// /// - `T`: A type that implements [`TreeValue`](trait.TreeValue.html), and is usable in the tree. /// Needs to be able to store the node index of itself, and handle its own bound and /// fattened bound. /// /// # Examples /// /// ``` /// # extern crate cgmath; /// # extern crate collision; /// /// use cgmath::{Point2, Vector2, InnerSpace}; /// use collision::{Aabb, Aabb2, Ray2}; /// use collision::dbvt::{DynamicBoundingVolumeTree, TreeValue, ContinuousVisitor}; /// /// #[derive(Debug, Clone)] /// struct Value { /// pub id: u32, /// pub aabb: Aabb2<f32>, /// fat_aabb: Aabb2<f32>, /// } /// /// impl Value { /// pub fn new(id: u32, aabb: Aabb2<f32>) -> Self { /// Self { /// id, /// fat_aabb : aabb.add_margin(Vector2::new(3., 3.)), /// aabb, /// } /// } /// } /// /// impl TreeValue for Value { /// type Bound = Aabb2<f32>; /// /// fn bound(&self) -> &Aabb2<f32> { /// &self.aabb /// } /// /// fn get_bound_with_margin(&self) -> Aabb2<f32> { /// self.fat_aabb.clone() /// } /// } /// /// fn aabb2(minx: f32, miny: f32, maxx: f32, maxy: f32) -> Aabb2<f32> { /// Aabb2::new(Point2::new(minx, miny), Point2::new(maxx, maxy)) /// } /// /// fn main() { /// let mut tree = DynamicBoundingVolumeTree::<Value>::new(); /// tree.insert(Value::new(10, aabb2(5., 5., 10., 10.))); /// tree.insert(Value::new(11, aabb2(21., 14., 23., 16.))); /// tree.do_refit(); /// /// let ray = Ray2::new(Point2::new(0., 0.), Vector2::new(-1., -1.).normalize()); /// let mut visitor = ContinuousVisitor::<Ray2<f32>, Value>::new(&ray); /// assert_eq!(0, tree.query(&mut visitor).len()); /// /// let ray = Ray2::new(Point2::new(6., 0.), Vector2::new(0., 1.).normalize()); /// let mut visitor = ContinuousVisitor::<Ray2<f32>, Value>::new(&ray); /// let results = tree.query(&mut visitor); /// assert_eq!(1, results.len()); /// assert_eq!(10, results[0].0.id); /// assert_eq!(Point2::new(6., 5.), results[0].1); /// } /// ``` /// pub struct DynamicBoundingVolumeTree<T> where T: TreeValue, { nodes: Vec<Node<T::Bound>>, values: Vec<(usize, T)>, free_list: Vec<usize>, updated_list: Vec<usize>, root_index: usize, refit_nodes: Vec<(u32, usize)>, } impl<T> Default for DynamicBoundingVolumeTree<T> where T: TreeValue, { fn default() -> Self { DynamicBoundingVolumeTree { // we add Nil to first position so only the root node can have parent = 0 nodes: vec![Node::Nil], values: Vec::default(), free_list: Vec::default(), updated_list: Vec::default(), root_index: 0, refit_nodes: Vec::default(), } } } impl<T> fmt::Debug for DynamicBoundingVolumeTree<T> where T: TreeValue, T::Bound: fmt::Debug, { fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { write!(f, "graph tree {{")?; for n_index in 1..self.nodes.len() { match self.nodes[n_index] { Node::Branch(ref b) => { write!(f, " n_{} [label=\"{:?}\"];", n_index, b.bound)?; write!(f, " n_{} -- n_{};", n_index, b.left)?; write!(f, " n_{} -- n_{};", n_index, b.right)?; } Node::Leaf(ref l) => { write!(f, " n_{} [label=\"{:?}\"];", n_index, l.bound)?; } Node::Nil => (), } } write!(f, "}}") } } /// Branch node #[derive(Debug)] struct Branch<B> { parent: usize, left: usize, right: usize, height: u32, bound: B, } /// Leaf node #[derive(Debug)] struct Leaf<B> { parent: usize, value: usize, bound: B, } /// Nodes #[derive(Debug)] enum Node<B> { Branch(Branch<B>), Leaf(Leaf<B>), Nil, } impl<T> DynamicBoundingVolumeTree<T> where T: TreeValue, T::Bound: Clone + Contains<T::Bound> + Union<T::Bound, Output = T::Bound> + SurfaceArea, { /// Create a new tree. /// /// ### Type parameters: /// /// - `T`: A type that implements [`TreeValue`](trait.TreeValue.html), and is usable in the /// tree. Needs to be able to store the node index of itself, and handle its own bound /// and fattened bound. /// - `T::Bound`: Bounding volume type that implements the following collision-rs traits: /// [`Contains`][1] on itself, [`Union`][2] on itself, and [`SurfaceArea`][3]. /// /// [1]: ../trait.Contains.html /// [2]: ../trait.Union.html /// [3]: ../trait.SurfaceArea.html /// pub fn new() -> Self { Default::default() } /// Return the number of nodes in the tree. /// pub fn size(&self) -> usize { // -1 because the first slot in the nodes vec is never used self.nodes.len() - self.free_list.len() - 1 } /// Return the height of the root node. Leafs are considered to have height 1. /// pub fn height(&self) -> u32 { if self.values.is_empty() { 0 } else { match self.nodes[self.root_index] { Node::Branch(ref b) => b.height, Node::Leaf(_) => 1, Node::Nil => 0, } } } /// Get an immutable list of all values in the tree. /// /// ### Returns /// /// A immutable reference to the [`Vec`](https://doc.rust-lang.org/std/vec/struct.Vec.html) /// of values in the tree. /// pub fn values(&self) -> &Vec<(usize, T)> { &self.values } /// Get a mutable list of all values in the tree. /// /// Do not insert or remove values directly in this list, instead use /// [`insert`](struct.DynamicBoundingVolumeTree.html#method.insert) and /// [`remove`](struct.DynamicBoundingVolumeTree.html#method.remove) /// on the tree. It is allowed to change the order of the values, but when doing so it is /// required to use /// [`reindex_values`](struct.DynamicBoundingVolumeTree.html#method.reindex_values) /// after changing the order, and before any other operation /// is performed on the tree. Otherwise the internal consistency of the tree will be broken. /// /// Do not change the first value in the tuple, this is the node index of the value, and without /// that the tree will not function. /// /// ### Returns /// /// A mutable reference to the [`Vec`](https://doc.rust-lang.org/std/vec/struct.Vec.html) /// of values in the tree. /// pub fn values_mut(&mut self) -> &mut Vec<(usize, T)> { &mut self.values } /// Reindex the values list, making sure that nodes in the tree point to the correct entry in /// the values list. /// /// Complexity is O(n). /// pub fn reindex_values(&mut self) { for i in 0..self.values.len() { if let Node::Leaf(ref mut leaf) = self.nodes[self.values[i].0] { leaf.value = i; } } } /// Clear the tree. /// /// Will remove all nodes and their values. /// pub fn clear(&mut self) { self.root_index = 0; self.nodes = vec![Node::Nil]; self.free_list.clear(); self.refit_nodes.clear(); self.values.clear(); } /// Return the value index for the given node index. pub fn value_index(&self, node_index: usize) -> Option<usize> { match self.nodes[node_index] { Node::Leaf(ref leaf) => Some(leaf.value), _ => None, } } /// Query the tree for all leafs that the given visitor accepts. /// /// Will do a depth first search of the tree and pass all bounding volumes on the way to the /// visitor. /// /// This function have approximate complexity O(log^2 n). /// /// ### Parameters: /// /// - `visitor`: The visitor to check for bounding volume tests. /// /// ### Type parameters: /// /// - `V`: Type that implements of [`Visitor`](trait.Visitor.html) /// /// ### Returns /// /// Will return a list of tuples of values accepted and the result returned by the visitor for /// the acceptance test. /// pub fn query<V>(&self, visitor: &mut V) -> Vec<(&T, V::Result)> where V: Visitor<Bound = T::Bound>, { self.query_for_indices(visitor) .into_iter() .map(|(value_index, result)| (&self.values[value_index].1, result)) .collect() } /// Query the tree for all leafs that the given visitor accepts. /// /// Will do a depth first search of the tree and pass all bounding volumes on the way to the /// visitor. /// /// This function have approximate complexity O(log^2 n). /// /// ### Parameters: /// /// - `visitor`: The visitor to check for bounding volume tests. /// /// ### Type parameters: /// /// - `V`: Type that implements of [`Visitor`](trait.Visitor.html) /// /// ### Returns /// /// Will return a list of tuples of value indices accepted and the result returned by the /// visitor for the acceptance test. /// pub fn query_for_indices<V>(&self, visitor: &mut V) -> Vec<(usize, V::Result)> where V: Visitor<Bound = T::Bound>, { let mut stack = [0; 256]; stack[0] = self.root_index; let mut stack_pointer = 1; let mut values = Vec::default(); while stack_pointer > 0 { // depth search, use last added as next test subject stack_pointer -= 1; let node_index = stack[stack_pointer]; let node = &self.nodes[node_index]; match *node { Node::Leaf(ref leaf) => { // if we encounter a leaf, do a real bound intersection test, and add to return // values if there's an intersection if let Some(result) = visitor.accept(self.values[leaf.value].1.bound(), true) { values.push((leaf.value, result)); } } // if we encounter a branch, do intersection test, and push the children if the // branch intersected Node::Branch(ref branch) => if visitor.accept(&branch.bound, false).is_some() { stack[stack_pointer] = branch.left; stack[stack_pointer + 1] = branch.right; stack_pointer += 2; }, Node::Nil => (), } } values } /// Update a node in the tree with a new value. /// /// The node will be fed its node_index after updating in the tree, so there is no need to /// add that manually in the value. /// /// Will cause the node to be updated and be flagged as updated, which will cause /// [`update`](struct.DynamicBoundingVolumeTree.html#method.update) to process the node the next /// time it is called. /// /// ### Parameters /// /// - `node_index`: index of the node to update /// - `new_value`: the new value to write in that node /// pub fn update_node(&mut self, node_index: usize, new_value: T) { if let Node::Leaf(ref mut leaf) = self.nodes[node_index] { self.values[leaf.value].1 = new_value; } self.flag_updated(node_index); } /// Flag a node as having been updated (moved/rotated). /// /// Will cause [`update`](struct.DynamicBoundingVolumeTree.html#method.update) to process the /// node the next time it is called. /// /// ### Parameters /// /// - `node_index`: the node index of the updated node /// pub fn flag_updated(&mut self, node_index: usize) { self.updated_list.push(node_index); } /// Go through the updated list and check the fat bounds in the tree. /// /// After updating values in the values list, it is possible that some of the leafs values have /// outgrown their fat bounds. If so, they may need to be moved in the tree. This is done during /// refitting. /// /// Note that no parents have their bounds/height updated directly by this function, instead /// [`do_refit`](struct.DynamicBoundingVolumeTree.html#method.do_refit) should be called after /// all insert/remove/updates have been performed this frame. /// pub fn update(&mut self) { let nodes = self.updated_list .iter() .filter_map(|&index| { if let Node::Leaf(ref l) = self.nodes[index] { if !l.bound.contains(self.values[l.value].1.bound()) { Some(( index, l.parent, self.values[l.value].1.get_bound_with_margin(), )) } else { None } } else { None } }) .collect::<Vec<(usize, usize, T::Bound)>>(); for (node_index, parent_index, fat_bound) in nodes { if let Node::Leaf(ref mut leaf) = self.nodes[node_index] { leaf.bound = fat_bound; } self.mark_for_refit(parent_index, 2); } self.updated_list.clear(); } /// Utility method to perform updates and refitting. Should be called once per frame. /// /// Will in turn call [`update`](struct.DynamicBoundingVolumeTree.html#method.update), followed /// by [`do_refit`](struct.DynamicBoundingVolumeTree.html#method.do_refit). /// pub fn tick(&mut self) { self.update(); self.do_refit(); } /// Insert a value into the tree. /// /// This will search the tree for the best leaf to pair the value up with, using the surface /// area of the value's bounding volume as the main heuristic. Will always cause a new branch /// node and a new leaf node (containing the given value) to be added to the tree. /// This is to keep the invariant of branches always having 2 children true. /// /// This function should have approximate complexity O(log^2 n). /// /// Note that no parents have their bounds/height updated directly by this function, instead /// [`do_refit`](struct.DynamicBoundingVolumeTree.html#method.do_refit) should be called after /// all insert/remove/updates have been performed this frame. /// /// ### Parameters /// /// - `value`: The value to insert into the tree. /// /// ### Returns /// /// The node index of the inserted value. This value should never change after insertion. /// pub fn insert(&mut self, value: T) -> usize { let fat_bound = value.get_bound_with_margin(); let value_index = self.values.len(); self.values.push((0, value)); // Create a new leaf node for the given value let mut new_leaf = Leaf { parent: 0, value: value_index, bound: fat_bound, }; // If the root index is 0, this is the first node inserted, and we can circumvent a lot of // checks. if self.root_index == 0 { self.root_index = self.nodes.len(); self.nodes.push(Node::Leaf(new_leaf)); self.values[value_index].0 = self.root_index; self.root_index } else { // Start searching from the root node let mut node_index = self.root_index; // We will always insert a branch node and the new leaf node, so get 2 new indices // into the node list let (new_branch_index, new_leaf_index) = self.next_free(); // We need to tell the value what it's node index is self.values[value_index].0 = new_leaf_index; // The new leaf will always be a child of the new branch node. new_leaf.parent = new_branch_index; let mut branch_parent_index = 0; loop { // If we encounter a leaf node, we've found the place where we want to add the new // nodes. The branch node will be inserted into the tree here, and this node will be // moved down as the left child of the new branch node, and the new leaf will be the // right child. let add_branch = match self.nodes[node_index] { Node::Leaf(ref leaf) => { let new_branch = Branch { left: node_index, // old leaf at the current position is left child right: new_leaf_index, // new leaf node is the right child parent: leaf.parent, // parent of the branch is the old leaf parent height: 2, // leafs have height 1, so new branch have height 2 bound: leaf.bound.union(&new_leaf.bound), }; Some((node_index, new_branch)) } // If we hit a branch, we compute the surface area of the bounding volumes for // if the new leaf was added to the right or left. Whichever surface area is // lowest will decide which child to go to next. Node::Branch(ref branch) => { let left_bound = get_bound(&self.nodes[branch.left]); let right_bound = get_bound(&self.nodes[branch.right]); let left_area = left_bound.union(&new_leaf.bound).surface_area(); let right_area = right_bound.union(&new_leaf.bound).surface_area(); if left_area < right_area { node_index = branch.left; } else { node_index = branch.right; } None } Node::Nil => break, }; // time to actually update the tree if let Some((leaf_index, branch)) = add_branch { // the old leaf node needs to point to the new branch node as its parent if let Node::Leaf(ref mut n) = self.nodes[leaf_index] { n.parent = new_branch_index; }; // if the old leaf node wasn't the root of tree, we update it's parent to point // to the new branch node insteaf of the old leaf node branch_parent_index = branch.parent; if branch.parent != 0 { if let Node::Branch(ref mut n) = self.nodes[branch.parent] { if n.left == leaf_index { n.left = new_branch_index; } else { n.right = new_branch_index; } } } // insert to new branch and leaf nodes self.nodes[new_branch_index] = Node::Branch(branch); self.nodes[new_leaf_index] = Node::Leaf(new_leaf); // if the leaf node was the root of the tree, // the new root is the new branch node if leaf_index == self.root_index { self.root_index = new_branch_index; } break; } } // mark the new branch nodes parent for bounds/height updating and possible rotation if branch_parent_index != 0 { self.mark_for_refit(branch_parent_index, 3); } new_leaf_index } } /// Remove the node with the given node index. /// /// The reason this function takes the node index and not a reference to the value, is because /// the only way to get at the values in the tree is by doing a mutable borrow, making this /// function unusable. /// /// If the given node index points to a non-leaf, this function is effectively a nop. /// Else the leaf node and it's parent branch node will be removed, and the leaf nodes sibling /// will take the place of the parent branch node in the tree. /// /// Note that no parents have their bounds/height updated directly by this function, instead /// [`do_refit`](struct.DynamicBoundingVolumeTree.html#method.do_refit) should be called after /// all insert/remove/updates have been performed this frame. /// /// This function should have approximate complexity O(log^2 n). /// /// ### Parameters /// /// - `node_index`: index of the leaf to remove /// /// ### Returns /// /// If a value was removed, the value is returned, otherwise None. /// pub fn remove(&mut self, node_index: usize) -> Option<T> { let (value_index, parent_index) = if let Node::Leaf(ref leaf) = self.nodes[node_index] { (leaf.value, leaf.parent) } else { // If a value points to a non-leaf something has gone wrong, // ignore remove and continue with life return None; }; // remove from values list and update node list with new value indices let (_, value) = self.values.swap_remove(value_index); // we only need to update the node for the value that we swapped into the old values place if value_index < self.values.len() { // should only fail if we just removed the last value if let Node::Leaf(ref mut leaf) = self.nodes[self.values[value_index].0] { leaf.value = value_index; } } // remove from node list and add index to free list self.nodes[node_index] = Node::Nil; self.free_list.push(node_index); if parent_index != 0 { // remove parent branch from node list and add index to free list let (parent_parent_index, sibling_index) = if let Node::Branch(ref branch) = self.nodes[parent_index] { ( branch.parent, if branch.left == node_index { branch.right } else { branch.left }, ) } else { return Some(value); }; self.nodes[parent_index] = Node::Nil; self.free_list.push(parent_index); // set sibling parent to parent.parent match self.nodes[sibling_index] { Node::Branch(ref mut branch) => branch.parent = parent_parent_index, Node::Leaf(ref mut leaf) => leaf.parent = parent_parent_index, Node::Nil => (), } // if parents parent is 0, the sibling is the last node in the tree and becomes the new // root node if parent_parent_index == 0 { self.root_index = sibling_index; } else { // else we have a remaining branch, and need to update either left or right to point // to the sibling, based on where the old branch node was if let Node::Branch(ref mut b) = self.nodes[parent_parent_index] { if b.left == parent_index { b.left = sibling_index; } else { b.right = sibling_index; } } // mark parents parent for recalculation self.mark_for_refit(parent_parent_index, 0); } } else { // if parent was 0, this was the last node in the tree, and the tree is now empty. // reset all values. self.clear(); } Some(value) } /// Go through the list of nodes marked for refitting, update their bounds/heights and check if /// any of them need to be rotated to new locations. /// /// This method have worst case complexity O(m * log^2 n), where m is the number of nodes in the /// refit list. /// pub fn do_refit(&mut self) { while !self.refit_nodes.is_empty() { let (_, node_index) = self.refit_nodes.remove(0); self.refit_node(node_index); } } /// Get two new node indices, where nodes can be inserted in the tree. /// fn next_free(&mut self) -> (usize, usize) { (self.take_free(), self.take_free()) } /// Get a new node index, where a node can be inserted in the tree. /// fn take_free(&mut self) -> usize { if self.free_list.is_empty() { let index = self.nodes.len(); self.nodes.push(Node::Nil); index } else { self.free_list.remove(0) } } /// Add the given node to the refitting list. /// /// The refit list is sorted by the height of the node, and only have the same value /// once, any duplicates are rejected. This because we don't want to refit the same node /// twice. /// /// ### Parameters /// /// - `node_index`: index of the node to do refitting on. /// - `min_height`: the minimum height the node has. Used primarily by insertion where we can't /// be sure that the node has been refitted yet and might have an incorrect /// height /// fn mark_for_refit(&mut self, node_index: usize, min_height: u32) { let node_height = match self.nodes[node_index] { Node::Branch(ref b) => b.height, _ => 0, }; let height = max(node_height, min_height); let value = (height, node_index); match self.refit_nodes.binary_search(&value) { Ok(_) => (), Err(i) => self.refit_nodes.insert(i, value), } } /// Actually refit a node in the tree. This will check the node for rotation, and if rotated, /// will update the bound/height of itself and any other rotated nodes, and also mark its parent /// for refitting. /// fn refit_node(&mut self, node_index: usize) { if let Some((parent_index, height)) = self.recalculate_node(node_index) { if parent_index != 0 { self.mark_for_refit(parent_index, height + 1); } } // Only do rotations occasionally, as they are fairly expensive, and shouldn't be overused. // For most scenarios, the majority of shapes will not have moved, so this is fine. if rand::thread_rng().gen_range(0, 100) < PERFORM_ROTATION_PERCENTAGE { self.rotate(node_index); } } /// Recalculate the bound and height of the node. /// fn recalculate_node(&mut self, node_index: usize) -> Option<(usize, u32)> { let (height, bound, parent_index) = { let (left_height, left_bound, right_height, right_bound, parent_index) = if let Node::Branch(ref branch) = self.nodes[node_index] { ( get_height(&self.nodes[branch.left]), get_bound(&self.nodes[branch.left]), get_height(&self.nodes[branch.right]), get_bound(&self.nodes[branch.right]), branch.parent, ) } else { return None; }; ( 1 + max(left_height, right_height), left_bound.union(right_bound), parent_index, ) }; if let Node::Branch(ref mut branch) = self.nodes[node_index] { branch.height = height; branch.bound = bound; } Some((parent_index, height)) } /// Check if the node needs to be rotated, and perform the rotation if that is the case. /// /// ### Parameters: /// /// - `node_index`: index of the node to check for rotation /// /// ### Returns /// /// The parent index of the given node /// fn rotate(&mut self, node_index: usize) -> Option<usize> { let improvement_percentage: <T::Bound as SurfaceArea>::Scalar = NumCast::from(SURFACE_AREA_IMPROVEMENT_FOR_ROTATION).unwrap(); let (left_index, right_index, my_surface_area, parent_index) = if let Node::Branch(ref branch) = self.nodes[node_index] { ( branch.left, branch.right, branch.bound.surface_area(), branch.parent, ) } else { return None; }; let left_is_leaf = is_leaf(&self.nodes[left_index]); let right_is_leaf = is_leaf(&self.nodes[right_index]); // if the node is a grandparent, we can do rotation checks if !left_is_leaf || !right_is_leaf { let (rot, min_sa) = get_best_rotation( &self.nodes, left_index, right_index, my_surface_area, left_is_leaf, right_is_leaf, ); // we now know which rotation will give us the best surface area // only do actual rotation if the surface area is reduced by atleast 25% if (my_surface_area - min_sa) / my_surface_area > improvement_percentage { match rot { // do nothing Rotation::None => (), // swap left child with right left grandchild // right child and node needs to be recalculated Rotation::LeftRightLeft => { let right_left_index = get_left_index(&self.nodes[right_index]); swap( &mut self.nodes, left_index, right_left_index, node_index, right_index, ); self.recalculate_node(right_index); self.recalculate_node(node_index); } // swap left child with right right grandchild // right child and node needs to be recalculated Rotation::LeftRightRight => { let right_right_index = get_right_index(&self.nodes[right_index]); swap( &mut self.nodes, left_index, right_right_index, node_index, right_index, ); self.recalculate_node(right_index); self.recalculate_node(node_index); } // swap right child with left left grandchild // left child and node needs to be recalculated Rotation::RightLeftLeft => { let left_left_index = get_left_index(&self.nodes[left_index]); swap( &mut self.nodes, left_left_index, right_index, left_index, node_index, ); self.recalculate_node(left_index); self.recalculate_node(node_index); } // swap right child with left right grandchild // left child and node needs to be recalculated Rotation::RightLeftRight => { let left_right_index = get_right_index(&self.nodes[left_index]); swap( &mut self.nodes, left_right_index, right_index, left_index, node_index, ); self.recalculate_node(left_index); self.recalculate_node(node_index); } // swap left left grandchild with right left grandchild // left child, right child and node needs to be recalculated Rotation::LeftLeftRightLeft => { let left_left_index = get_left_index(&self.nodes[left_index]); let right_left_index = get_left_index(&self.nodes[right_index]); swap( &mut self.nodes, left_left_index, right_left_index, left_index, right_index, ); self.recalculate_node(left_index); self.recalculate_node(right_index); self.recalculate_node(node_index); } // swap left left grandchild with right right grandchild // left child, right child and node needs to be recalculated Rotation::LeftLeftRightRight => { let left_left_index = get_left_index(&self.nodes[left_index]); let right_right_index = get_right_index(&self.nodes[right_index]); swap( &mut self.nodes, left_left_index, right_right_index, left_index, right_index, ); self.recalculate_node(left_index); self.recalculate_node(right_index); self.recalculate_node(node_index); } } } } Some(parent_index) } } enum Rotation { None, LeftRightLeft, LeftRightRight, RightLeftLeft, RightLeftRight, LeftLeftRightLeft, LeftLeftRightRight, } /// Swap two nodes in the tree. /// /// left_parent.`[left,right]` = right_swap /// right_parent.`[left,right]` = left_swap /// left_swap.parent = right_parent /// right_swap.parent = left_parent /// #[inline] fn swap<B>( nodes: &mut Vec<Node<B>>, left_swap_index: usize, right_swap_index: usize, left_parent_index: usize, right_parent_index: usize, ) { if let Node::Branch(ref mut left_parent) = nodes[left_parent_index] { if left_parent.left == left_swap_index { left_parent.left = right_swap_index; } else { left_parent.right = right_swap_index; } } if let Node::Branch(ref mut right_parent) = nodes[right_parent_index] { if right_parent.left == right_swap_index { right_parent.left = left_swap_index; } else { right_parent.right = left_swap_index; } } match nodes[left_swap_index] { Node::Branch(ref mut left) => left.parent = right_parent_index, Node::Leaf(ref mut left) => left.parent = right_parent_index, _ => (), } match nodes[right_swap_index] { Node::Branch(ref mut rl) => rl.parent = left_parent_index, Node::Leaf(ref mut rl) => rl.parent = left_parent_index, _ => (), } } /// Calculate the best rotation for a given grandparent node in the tree #[inline] fn get_best_rotation<B>( nodes: &[Node<B>], left_index: usize, right_index: usize, node_surface_area: <B as SurfaceArea>::Scalar, left_is_leaf: bool, right_is_leaf: bool, ) -> (Rotation, <B as SurfaceArea>::Scalar) where B: Union<B, Output = B> + SurfaceArea, { let mut rot = Rotation::None; let mut min_sa = node_surface_area; // we need the left and right child bounds for 4 tests let l_bound = get_bound(&nodes[left_index]); let r_bound = get_bound(&nodes[right_index]); // if the right child is not a leaf, we want to consider swapping its children with // either the left child or the left left grandchild if !right_is_leaf { let (rl_bound, rr_bound) = match nodes[right_index] { Node::Branch(ref right) => ( get_bound(&nodes[right.left]), get_bound(&nodes[right.right]), ), _ => panic!(), }; // check for left child swapped with right left grandchild let l_rl_sa = sa(rl_bound, l_bound, rr_bound); if l_rl_sa < min_sa { rot = Rotation::LeftRightLeft; min_sa = l_rl_sa; } // check for left child swapped with right right grandchild let l_rr_sa = sa(rr_bound, l_bound, rl_bound); if l_rr_sa < min_sa { rot = Rotation::LeftRightRight; min_sa = l_rr_sa; } // check for left left grandchild swapped with either of the right grandchildren if !left_is_leaf { let (ll_bound, lr_bound) = match nodes[left_index] { Node::Branch(ref left) => { (get_bound(&nodes[left.left]), get_bound(&nodes[left.right])) } _ => panic!(), }; // check for left left grandchild swapped with right left grandchild let ll_rl_sa = sa(&rl_bound.union(lr_bound), ll_bound, rr_bound); if ll_rl_sa < min_sa { rot = Rotation::LeftLeftRightLeft; min_sa = ll_rl_sa; } // check for left left grandchild swapped with right right grandchild let ll_rr_sa = sa(&rr_bound.union(lr_bound), rl_bound, ll_bound); if ll_rr_sa < min_sa { rot = Rotation::LeftLeftRightRight; min_sa = ll_rr_sa; } // we don't need to check for left right grandchild swapped with any of the right // grandchildren. this would only result in mirrored trees and have the same cost // as other cases, making it redundant work } } // if the left child is not a leaf, we want to consider swapping its children with the // right child if !left_is_leaf { let (ll_bound, lr_bound) = match nodes[left_index] { Node::Branch(ref left) => (get_bound(&nodes[left.left]), get_bound(&nodes[left.right])), _ => panic!(), }; // check for right child swapped with left left grandchild let r_ll_sa = sa(ll_bound, r_bound, lr_bound); if r_ll_sa < min_sa { rot = Rotation::RightLeftLeft; min_sa = r_ll_sa; } // check for right child swapped with left right grandchild let r_lr_sa = sa(lr_bound, r_bound, ll_bound); if r_lr_sa < min_sa { rot = Rotation::RightLeftRight; min_sa = r_lr_sa; } } (rot, min_sa) } /// Calculate the surface area of 3 combined bounding volumes, a.union(b.union(c)). #[inline] fn sa<B>(a: &B, b: &B, c: &B) -> <B as SurfaceArea>::Scalar where B: Union<B, Output = B> + SurfaceArea, { a.union(&b.union(c)).surface_area() } #[inline] fn get_left_index<B>(node: &Node<B>) -> usize { match *node { Node::Branch(ref b) => b.left, _ => panic!(), } } #[inline] fn get_right_index<B>(node: &Node<B>) -> usize { match *node { Node::Branch(ref b) => b.right, _ => panic!(), } } #[inline] fn is_leaf<B>(node: &Node<B>) -> bool { match *node { Node::Leaf(_) => true, _ => false, } } /// Get the height of the node, regardless of node type. Leafs have height 1, nil height 0. /// #[inline] fn get_height<B>(node: &Node<B>) -> u32 { match *node { Node::Branch(ref branch) => branch.height, Node::Leaf(_) => 1, Node::Nil => 0, } } /// Get the bound of the node. Will panic if node is nil. /// #[inline] fn get_bound<B>(node: &Node<B>) -> &B { match *node { Node::Branch(ref branch) => &branch.bound, Node::Leaf(ref leaf) => &leaf.bound, Node::Nil => panic!(), } }