Add basic pathfinding API

This should cover all requirements from the assignment, but a more specific use case will be added later.

include/Gedeng/NavMesh.h

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+#pragma once
+#include "Node.h"
+#include "Path.h"
+
+namespace Gedeng {
+
+class NavMesh {
+    // Build the NavMesh from all collider geometry in the given node and all
+    // its children.
+    void create_from_nodes(const Node &root);
+
+    // Return true if the NavMesh has succesfully been created from nodes (by a
+    // former `create_from_nodes` call) and its geometry is valid.
+    bool is_valid() const;
+
+    // Return a valid path from a given Vector3 to a given Vector3.
+    // If no valid path can be constructed, the returned path will be of size 1
+    // and contain only the `from` vector.
+    // The returned path may not be optimal -- if that is undesired, call
+    // `optimize_path` on the result.
+    Path get_path(const Vector3 &from, const Vector3 &to) const;
+
+    // Optimize the given path to traverse the NavMesh as efficiently as
+    // possible. This can be slow!
+    void optimize_path(Path &path) const;
+};
+
+} // namespace Gedeng

include/Gedeng/Node.h

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+#pragma once
+#include "Gedeng/String.h"
+#include "Gedeng/Vector.h"
+
+namespace Gedeng {
+
+class Node {
+    // Add the given node as a child of this node.
+    void add_child(const Node &node);
+
+    // Return a vector with all child nodes of this node.
+    Vector<Node &> get_children() const;
+};
+
+} // namespace Gedeng

include/Gedeng/NodeSystem.h

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+#pragma once
+#include "Gedeng/Node.h"
+#include "Gedeng/String.h"
+
+namespace Gedeng {
+
+class NodeSystem {
+    // Load a node with all its children from a node definition file (`.gnd`) on
+    // disk.
+    static Node load_nodes_from_disk(const String &path);
+
+    // Save a node and all its children to disk, at the given path. It is
+    // recommended to end the path with `.gnd`.
+    static void save_nodes_to_disk(const Node &node, const String &path);
+};
+
+} // namespace Gedeng

include/Gedeng/Path.h

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+#pragma once
+#include "Vector3.h"
+
+namespace Gedeng {
+
+class Path {
+    // Return a Vector3 on the path. `t` should be between 0 (path begin) and 1
+    // (path end).
+    Vector3 get_interpolated_position(float t) const;
+
+    // Return the number of Vector3's which make up the path.
+    unsigned int get_size() const;
+};
+
+} // namespace Gedeng

include/Gedeng/Vector3.h

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+#pragma once
+
+namespace Gedeng {
+
+class Vector3 {};
+
+} // namespace Gedeng