Revamped A* algorithm

with extended test suite
This commit is contained in:
tamasmeszaros 2022-06-02 17:44:51 +02:00
parent df552a9226
commit f9fb7f947d
2 changed files with 450 additions and 71 deletions

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@ -1,11 +1,11 @@
#ifndef ASTAR_HPP #ifndef ASTAR_HPP
#define ASTAR_HPP #define ASTAR_HPP
#include <unordered_map>
#include "libslic3r/Point.hpp" #include "libslic3r/Point.hpp"
#include "libslic3r/MutablePriorityQueue.hpp" #include "libslic3r/MutablePriorityQueue.hpp"
#include <unordered_map>
namespace Slic3r { namespace astar { namespace Slic3r { namespace astar {
// Input interface for the Astar algorithm. Specialize this struct for a // Input interface for the Astar algorithm. Specialize this struct for a
@ -34,6 +34,8 @@ template<class T> struct TracerTraits_
// Get the estimated distance heuristic from node 'n' to the destination. // Get the estimated distance heuristic from node 'n' to the destination.
// This is referred to as the h value in AStar context. // This is referred to as the h value in AStar context.
// If node 'n' is the goal, this function should return a negative value. // If node 'n' is the goal, this function should return a negative value.
// Note that this heuristic should be admissible (never bigger than the real
// cost) in order for Astar to work.
static float goal_heuristic(const T &tracer, const Node &n) static float goal_heuristic(const T &tracer, const Node &n)
{ {
return tracer.goal_heuristic(n); return tracer.goal_heuristic(n);
@ -81,100 +83,133 @@ size_t unique_id(const T &tracer, const TracerNodeT<T> &n)
} // namespace astar_detail } // namespace astar_detail
constexpr size_t UNASSIGNED = size_t(-1);
template<class Tracer>
struct QNode // Queue node. Keeps track of scores g, and h
{
TracerNodeT<Tracer> node; // The actual node itself
size_t queue_id; // Position in the open queue or UNASSIGNED if closed
size_t parent; // unique id of the parent or UNASSIGNED
float g, h;
float f() const { return g + h; }
QNode(TracerNodeT<Tracer> n = {},
size_t p = UNASSIGNED,
float gval = std::numeric_limits<float>::infinity(),
float hval = 0.f)
: node{std::move(n)}, parent{p}, queue_id{UNASSIGNED}, g{gval}, h{hval}
{}
};
// Run the AStar algorithm on a tracer implementation. // Run the AStar algorithm on a tracer implementation.
// The 'tracer' argument encapsulates the domain (grid, point cloud, etc...) // The 'tracer' argument encapsulates the domain (grid, point cloud, etc...)
// The 'source' argument is the starting node. // The 'source' argument is the starting node.
// The 'out' argument is the output iterator into which the output nodes are // The 'out' argument is the output iterator into which the output nodes are
// written. // written. For performance reasons, the order is reverse, from the destination
// Note that no destination node is given. The tracer's goal_heuristic() method // to the source -- (destination included, source is not).
// should return a negative value if a node is a destination node. // The 'cached_nodes' argument is an optional associative container to hold a
template<class Tracer, class It> // QNode entry for each visited node. Any compatible container can be used
bool search_route(const Tracer &tracer, const TracerNodeT<Tracer> &source, It out) // (like std::map or maps with different allocators, even a sufficiently large
// std::vector).
//
// Note that no destination node is given in the signature. The tracer's
// goal_heuristic() method should return a negative value if a node is a
// destination node.
template<class Tracer,
class It,
class NodeMap = std::unordered_map<size_t, QNode<Tracer>>>
bool search_route(const Tracer &tracer,
const TracerNodeT<Tracer> &source,
It out,
NodeMap &&cached_nodes = {})
{ {
using namespace detail; using namespace detail;
using Node = TracerNodeT<Tracer>; using Node = TracerNodeT<Tracer>;
enum class QueueType { Open, Closed, None }; using QNode = QNode<Tracer>;
struct QNode // Queue node. Keeps track of scores g, and h struct LessPred { // Comparison functor needed by the priority queue
{ NodeMap &m;
Node node; // The actual node itself
QueueType qtype = QueueType::None; // Which queue holds this node
float g = 0.f, h = 0.f;
float f() const { return g + h; }
};
// TODO: apply a linear memory allocator
using QMap = std::unordered_map<size_t, QNode>;
// The traversed nodes are stored here encapsulated in QNodes
QMap cached_nodes;
struct LessPred { // Comparison functor needed by MutablePriorityQueue
QMap &m;
bool operator ()(size_t node_a, size_t node_b) { bool operator ()(size_t node_a, size_t node_b) {
auto ait = m.find(node_a); return m[node_a].f() < m[node_b].f();
auto bit = m.find(node_b);
assert (ait != m.end() && bit != m.end());
return ait->second.f() < bit->second.f();
} }
}; };
auto qopen = auto qopen = make_mutable_priority_queue<size_t, true>(
make_mutable_priority_queue<size_t, false>([](size_t, size_t){}, [&cached_nodes](size_t el, size_t qidx) {
cached_nodes[el].queue_id = qidx;
},
LessPred{cached_nodes}); LessPred{cached_nodes});
auto qclosed = QNode initial{source, /*parent = */ UNASSIGNED, /*g = */0.f};
make_mutable_priority_queue<size_t, false>([](size_t, size_t){}, size_t source_id = unique_id(tracer, source);
LessPred{cached_nodes}); cached_nodes[source_id] = initial;
qopen.push(source_id);
QNode initial{source, QueueType::Open}; size_t goal_id = goal_heuristic(tracer, source) < 0.f ? source_id :
cached_nodes.insert({unique_id(tracer, source), initial}); UNASSIGNED;
qopen.push(unique_id(tracer, source));
bool goal_reached = false; while (goal_id == UNASSIGNED && !qopen.empty()) {
while (!goal_reached && !qopen.empty()) {
size_t q_id = qopen.top(); size_t q_id = qopen.top();
qopen.pop(); qopen.pop();
QNode q = cached_nodes.at(q_id); QNode &q = cached_nodes[q_id];
foreach_reachable(tracer, q.node, [&](const Node &nd) { // This should absolutely be initialized in the cache already
if (goal_reached) return goal_reached; assert(!std::isinf(q.g));
foreach_reachable(tracer, q.node, [&](const Node &succ_nd) {
if (goal_id != UNASSIGNED)
return true;
float h = goal_heuristic(tracer, succ_nd);
float dst = trace_distance(tracer, q.node, succ_nd);
size_t succ_id = unique_id(tracer, succ_nd);
QNode qsucc_nd{succ_nd, q_id, q.g + dst, h};
float h = goal_heuristic(tracer, nd);
if (h < 0.f) { if (h < 0.f) {
goal_reached = true; goal_id = succ_id;
cached_nodes[succ_id] = qsucc_nd;
} else { } else {
float dst = trace_distance(tracer, q.node, nd); // If succ_id is not in cache, it gets created with g = infinity
QNode qnd{nd, QueueType::None, q.g + dst, h}; QNode &prev_nd = cached_nodes[succ_id];
size_t qnd_id = unique_id(tracer, nd);
auto it = cached_nodes.find(qnd_id); if (qsucc_nd.g < prev_nd.g) {
// new route is better, apply it:
if (it == cached_nodes.end() || // Save the old queue id, it would be lost after the next line
(it->second.qtype != QueueType::None && qnd.f() < it->second.f())) { size_t queue_id = prev_nd.queue_id;
qnd.qtype = QueueType::Open;
cached_nodes.insert_or_assign(qnd_id, qnd); // The cache needs to be updated either way
qopen.push(qnd_id); prev_nd = qsucc_nd;
if (queue_id == UNASSIGNED)
// was in closed or unqueued, rescheduling
qopen.push(succ_id);
else // was in open, updating
qopen.update(queue_id);
} }
} }
return goal_reached; return goal_id != UNASSIGNED;
}); });
q.qtype = QueueType::Closed;
cached_nodes.insert_or_assign(q_id, q);
qclosed.push(q_id);
// write the output
*out = q.node;
++out;
} }
return goal_reached; // Write the output, do not reverse. Clients can do so if they need to.
if (goal_id != UNASSIGNED) {
const QNode *q = &cached_nodes[goal_id];
while (!std::isinf(q->g) && q->parent != UNASSIGNED) {
*out = q->node;
++out;
q = &cached_nodes[q->parent];
}
if (std::isinf(q->g)) // Something went wrong
goal_id = UNASSIGNED;
}
return goal_id != UNASSIGNED;
} }
}} // namespace Slic3r::astar }} // namespace Slic3r::astar

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@ -7,12 +7,42 @@
using namespace Slic3r; using namespace Slic3r;
struct PointGridTracer { TEST_CASE("Testing basic invariants of AStar", "[AStar]") {
struct DummyTracer {
using Node = int;
int goal = 0;
float distance(int a, int b) const { return a - b; }
float goal_heuristic(int n) const { return n == goal ? -1.f : 0.f; }
size_t unique_id(int n) const { return n; }
void foreach_reachable(int, std::function<bool(int)>) const {}
};
std::vector<int> out;
SECTION("Output is empty when source is also the destination") {
bool found = astar::search_route(DummyTracer{}, 0, std::back_inserter(out));
REQUIRE(out.empty());
REQUIRE(found);
}
SECTION("Return false when there is no route to destination") {
bool found = astar::search_route(DummyTracer{}, 1, std::back_inserter(out));
REQUIRE(!found);
REQUIRE(out.empty());
}
}
struct PointGridTracer3D {
using Node = size_t; using Node = size_t;
const PointGrid<float> &grid; const PointGrid<float> &grid;
size_t final; size_t final;
PointGridTracer(const PointGrid<float> &g, size_t goal) : PointGridTracer3D(const PointGrid<float> &g, size_t goal) :
grid{g}, final{goal} {} grid{g}, final{goal} {}
template<class Fn> template<class Fn>
@ -49,14 +79,328 @@ struct PointGridTracer {
size_t unique_id(size_t n) const { return n; } size_t unique_id(size_t n) const { return n; }
}; };
template<class Node, class Cmp = std::less<Node>>
bool has_duplicates(const std::vector<Node> &res, Cmp cmp = {})
{
auto cpy = res;
std::sort(cpy.begin(), cpy.end(), cmp);
auto it = std::unique(cpy.begin(), cpy.end());
return it != cpy.end();
}
TEST_CASE("astar algorithm test over 3D point grid", "[AStar]") { TEST_CASE("astar algorithm test over 3D point grid", "[AStar]") {
auto vol = BoundingBox3Base<Vec3f>{{0.f, 0.f, 0.f}, {1.f, 1.f, 1.f}}; auto vol = BoundingBox3Base<Vec3f>{{0.f, 0.f, 0.f}, {1.f, 1.f, 1.f}};
auto pgrid = point_grid(ex_seq, vol, {0.1f, 0.1f, 0.1f}); auto pgrid = point_grid(ex_seq, vol, {0.1f, 0.1f, 0.1f});
PointGridTracer pgt{pgrid, pgrid.point_count() - 1}; size_t target = pgrid.point_count() - 1;
PointGridTracer3D pgt{pgrid, target};
std::vector<size_t> out; std::vector<size_t> out;
bool found = astar::search_route(pgt, size_t(0), std::back_inserter(out)); bool found = astar::search_route(pgt, 0, std::back_inserter(out));
REQUIRE(found); REQUIRE(found);
REQUIRE(!out.empty());
REQUIRE(out.front() == target);
#ifndef NDEBUG
std::cout << "Route taken: ";
for (auto it = out.rbegin(); it != out.rend(); ++it) {
std::cout << "(" << pgrid.get_coord(*it).transpose() << ") ";
}
std::cout << std::endl;
#endif
REQUIRE(!has_duplicates(out)); // No duplicates in output
}
enum CellValue {ON, OFF};
struct CellGridTracer2D_AllDirs {
using Node = Vec2i;
static constexpr auto Cols = size_t(5);
static constexpr auto Rows = size_t(8);
static constexpr size_t GridSize = Cols * Rows;
const std::array<std::array<CellValue, Cols>, Rows> &grid;
Vec2i goal;
CellGridTracer2D_AllDirs(const std::array<std::array<CellValue, Cols>, Rows> &g,
const Vec2i &goal_)
: grid{g}, goal{goal_}
{}
template<class Fn>
void foreach_reachable(const Vec2i &src, Fn &&fn) const
{
auto is_inside = [](const Vec2i& v) { return v.x() >= 0 && v.x() < Cols && v.y() >= 0 && v.y() < Rows; };
if (Vec2i crd = src + Vec2i{0, 1}; is_inside(crd) && grid[crd.y()] [crd.x()] == ON) fn(crd);
if (Vec2i crd = src + Vec2i{1, 0}; is_inside(crd) && grid[crd.y()] [crd.x()] == ON) fn(crd);
if (Vec2i crd = src + Vec2i{1, 1}; is_inside(crd) && grid[crd.y()] [crd.x()] == ON) fn(crd);
if (Vec2i crd = src + Vec2i{0, -1}; is_inside(crd) && grid[crd.y()] [crd.x()] == ON) fn(crd);
if (Vec2i crd = src + Vec2i{-1, 0}; is_inside(crd) && grid[crd.y()] [crd.x()] == ON) fn(crd);
if (Vec2i crd = src + Vec2i{-1, -1}; is_inside(crd) && grid[crd.y()] [crd.x()] == ON) fn(crd);
if (Vec2i crd = src + Vec2i{1, -1}; is_inside(crd) && grid[crd.y()] [crd.x()] == ON) fn(crd);
if (Vec2i crd = src + Vec2i{-1, 1}; is_inside(crd) && grid[crd.y()] [crd.x()] == ON) fn(crd);
}
float distance(const Vec2i & a, const Vec2i & b) const { return (a - b).squaredNorm(); }
float goal_heuristic(const Vec2i & n) const { return n == goal ? -1.f : (n - goal).squaredNorm(); }
size_t unique_id(const Vec2i & n) const { return n.y() * Cols + n.x(); }
};
struct CellGridTracer2D_Axis {
using Node = Vec2i;
static constexpr auto Cols = size_t(5);
static constexpr auto Rows = size_t(8);
static constexpr size_t GridSize = Cols * Rows;
const std::array<std::array<CellValue, Cols>, Rows> &grid;
Vec2i goal;
CellGridTracer2D_Axis(
const std::array<std::array<CellValue, Cols>, Rows> &g,
const Vec2i &goal_)
: grid{g}, goal{goal_}
{}
template<class Fn>
void foreach_reachable(const Vec2i &src, Fn &&fn) const
{
auto is_inside = [](const Vec2i& v) { return v.x() >= 0 && v.x() < Cols && v.y() >= 0 && v.y() < Rows; };
if (Vec2i crd = src + Vec2i{0, 1}; is_inside(crd) && grid[crd.y()] [crd.x()] == ON) fn(crd);
if (Vec2i crd = src + Vec2i{0, -1}; is_inside(crd) && grid[crd.y()] [crd.x()] == ON) fn(crd);
if (Vec2i crd = src + Vec2i{1, 0}; is_inside(crd) && grid[crd.y()] [crd.x()] == ON) fn(crd);
if (Vec2i crd = src + Vec2i{-1, 0}; is_inside(crd) && grid[crd.y()] [crd.x()] == ON) fn(crd);
}
float distance(const Vec2i & a, const Vec2i & b) const { return (a - b).squaredNorm(); }
float goal_heuristic(const Vec2i &n) const
{
int manhattan_dst = std::abs(n.x() - goal.x()) +
std::abs(n.y() - goal.y());
return n == goal ? -1.f : manhattan_dst;
}
size_t unique_id(const Vec2i & n) const { return n.y() * Cols + n.x(); }
};
using TestClasses = std::tuple< CellGridTracer2D_AllDirs, CellGridTracer2D_Axis >;
TEMPLATE_LIST_TEST_CASE("Astar should avoid simple barrier", "[AStar]", TestClasses) {
std::array<std::array<CellValue, 5>, 8> grid = {{
{ON , ON , ON , ON , ON},
{ON , ON , ON , ON , ON},
{ON , ON , ON , ON , ON},
{ON , ON , ON , ON , ON},
{ON , ON , ON , ON , ON},
{ON , OFF, OFF, OFF, ON},
{ON , ON , ON , ON , ON},
{ON , ON , ON , ON , ON}
}};
Vec2i dst = {2, 0};
TestType cgt{grid, dst};
std::vector<Vec2i> out;
bool found = astar::search_route(cgt, {2, 7}, std::back_inserter(out));
REQUIRE(found);
REQUIRE(!out.empty());
REQUIRE(out.front() == dst);
REQUIRE(!has_duplicates(out, [](const Vec2i &a, const Vec2i &b) {
return a.x() == b.x() ? a.y() < b.y() : a.x() < b.x();
}));
#ifndef NDEBUG
std::cout << "Route taken: ";
for (auto it = out.rbegin(); it != out.rend(); ++it) {
std::cout << "(" << it->transpose() << ") ";
}
std::cout << std::endl;
#endif
}
TEMPLATE_LIST_TEST_CASE("Astar should manage to avoid arbitrary barriers", "[AStar]", TestClasses) {
std::array<std::array<CellValue, 5>, 8> grid = {{
{ON , ON , ON , ON , ON},
{ON , ON , ON , OFF, ON},
{OFF, OFF, ON , OFF, ON},
{ON , ON , ON , OFF, ON},
{ON , OFF, ON , OFF, ON},
{ON , OFF, ON , ON , ON},
{ON , OFF, ON , OFF, ON},
{ON , ON , ON , ON , ON}
}};
Vec2i dst = {0, 0};
TestType cgt{grid, dst};
std::vector<Vec2i> out;
bool found = astar::search_route(cgt, {0, 7}, std::back_inserter(out));
REQUIRE(found);
REQUIRE(!out.empty());
REQUIRE(out.front() == dst);
REQUIRE(!has_duplicates(out, [](const Vec2i &a, const Vec2i &b) {
return a.x() == b.x() ? a.y() < b.y() : a.x() < b.x();
}));
#ifndef NDEBUG
std::cout << "Route taken: ";
for (auto it = out.rbegin(); it != out.rend(); ++it) {
std::cout << "(" << it->transpose() << ") ";
}
std::cout << std::endl;
#endif
}
TEMPLATE_LIST_TEST_CASE("Astar should find the way out of a labyrinth", "[AStar]", TestClasses) {
std::array<std::array<CellValue, 5>, 8> grid = {{
{ON , ON , ON , ON , ON },
{ON , OFF, OFF, OFF, OFF},
{ON , ON , ON , ON , ON },
{OFF, OFF, OFF, OFF, ON },
{ON , ON , ON , ON , ON },
{ON , OFF, OFF, OFF, OFF},
{ON , ON , ON , ON , ON },
{OFF, OFF, OFF, OFF, ON }
}};
Vec2i dst = {4, 0};
TestType cgt{grid, dst};
std::vector<Vec2i> out;
bool found = astar::search_route(cgt, {4, 7}, std::back_inserter(out));
REQUIRE(found);
REQUIRE(!out.empty());
REQUIRE(out.front() == dst);
REQUIRE(!has_duplicates(out, [](const Vec2i &a, const Vec2i &b) {
return a.x() == b.x() ? a.y() < b.y() : a.x() < b.x();
}));
#ifndef NDEBUG
std::cout << "Route taken: ";
for (auto it = out.rbegin(); it != out.rend(); ++it) {
std::cout << "(" << it->transpose() << ") ";
}
std::cout << std::endl;
#endif
}
TEST_CASE("Zero heuristic function should result in dijsktra's algo", "[AStar]")
{
struct GraphTracer {
using Node = size_t;
using QNode = astar::QNode<GraphTracer>;
struct Edge
{
size_t to_id = size_t(-1);
float cost = 0.f;
bool operator <(const Edge &e) const { return to_id < e.to_id; }
};
struct ENode: public QNode {
std::vector<Edge> edges;
ENode(size_t node_id, std::initializer_list<Edge> edgelist)
: QNode{node_id}, edges(edgelist)
{}
ENode &operator=(const QNode &q)
{
assert(node == q.node);
g = q.g;
h = q.h;
parent = q.parent;
queue_id = q.queue_id;
return *this;
}
};
// Example graph from
// https://www.geeksforgeeks.org/dijkstras-shortest-path-algorithm-greedy-algo-7/?ref=lbp
std::vector<ENode> nodes = {
{0, {{1, 4.f}, {7, 8.f}}},
{1, {{0, 4.f}, {2, 8.f}, {7, 11.f}}},
{2, {{1, 8.f}, {3, 7.f}, {5, 4.f}, {8, 2.f}}},
{3, {{2, 7.f}, {4, 9.f}, {5, 14.f}}},
{4, {{3, 9.f}, {5, 10.f}}},
{5, {{2, 4.f}, {3, 14.f}, {4, 10.f}, {6, 2.f}}},
{6, {{5, 2.f}, {7, 1.f}, {8, 6.f}}},
{7, {{0, 8.f}, {1, 11.f}, {6, 1.f}, {8, 7.f}}},
{8, {{2, 2.f}, {6, 6.f}, {7, 7.f}}}
};
float distance(size_t a, size_t b) const {
float ret = std::numeric_limits<float>::infinity();
if (a < nodes.size()) {
auto it = std::lower_bound(nodes[a].edges.begin(),
nodes[a].edges.end(),
Edge{b, 0.f});
if (it != nodes[a].edges.end()) {
ret = it->cost;
}
}
return ret;
}
float goal_heuristic(size_t) const { return 0.f; }
size_t unique_id(size_t n) const { return n; }
void foreach_reachable(size_t n, std::function<bool(int)> fn) const
{
if (n < nodes.size()) {
for (const Edge &e : nodes[n].edges)
fn(e.to_id);
}
}
} graph;
std::vector<size_t> out;
// 'graph.nodes' is able to be a node cache (it simulates an associative container)
bool found = astar::search_route(graph, size_t(0), std::back_inserter(out), graph.nodes);
// But should not crash or loop infinitely.
REQUIRE(!found);
// Without a destination, there is no output. But the algorithm should halt.
REQUIRE(out.empty());
// Source node should have it's parent unset
REQUIRE(graph.nodes[0].parent == astar::UNASSIGNED);
// All other nodes should have their parents set
for (size_t i = 1; i < graph.nodes.size(); ++i)
REQUIRE(graph.nodes[i].parent != astar::UNASSIGNED);
std::array<float, 9> ref_distances = {0.f, 4.f, 12.f, 19.f, 21.f,
11.f, 9.f, 8.f, 14.f};
// Try to trace each node back to the source node. Each of them should
// arrive to the source within less hops than the full number of nodes.
for (size_t i = 0, k = 0; i < graph.nodes.size(); ++i, k = 0) {
GraphTracer::QNode *q = &graph.nodes[i];
REQUIRE(q->g == Approx(ref_distances[i]));
while (k++ < graph.nodes.size() && q->parent != astar::UNASSIGNED)
q = &graph.nodes[q->parent];
REQUIRE(q->parent == astar::UNASSIGNED);
}
} }