Published Jul 21, 2020
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The axis-aligned bounding box (AABB) is one of the most common bounding volumes. It is a rectangular six-sided box (in 3D, four-sided in 2D) categorized by having its faces oriented in such a way that its face normals are at all times parallel with the axes of the given coordinate system. The best feature of the AABB is its fast overlap check, which simply involves direct comparison of individual coordinate values.
There are three common representations of AABBs. One is by the minimum and maximum coordinate values along each axis
// region R = { (x, y, z) | min.x<=x<=max.x, min.y<=y<=max.y, min.z<=z<=max.z }
struct AABB {
Point min;
Point max;
};
#ifndef BOUNDINGBOX_H
#define BOUNDINGBOX_H
#include <glm/vec3.hpp>
#include <glm/mat4x4.hpp>
namespace fly
{
inline glm::vec3 component_wise_apply(const glm::vec3& a, const glm::vec3& b,
const float& (*f)(const float&, const float&))
{
return {f(a.x, b.x), f(a.y, b.y), f(a.z, b.z)};
}
struct AABB
{
glm::vec3 position;
glm::vec3 dimensions;
};
struct OBB
{
OBB(const glm::vec3& dimensions, const glm::mat4& transformation);
AABB getAABB() const;
glm::vec3 points[8];
};
}
#endif //BOUNDINGBOX_H
#include <glm/vec4.hpp>
#include "BoundingBox.h"
#include <algorithm>
#include <numeric>
namespace fly
{
OBB::OBB(const glm::vec3& dimensions, const glm::mat4& transformation)
{
glm::vec4 half_extent {dimensions / 2.0f, 1.f};
for (auto i = 0u; i < 8; ++i)
{
// get (x, y, z, w) here where
// x = 1/-1
// y = 1/-1
// z = 1/-1
// so in total 8 points
glm::vec4 local_point {((i & 4) >> 1) - 1.f,
(i & 2) - 1.f,
((i & 1) << 1) - 1.f,
1.f};
// to get the bounding box
local_point = local_point * half_extent;
// do the transformation
points[i] = transformation * local_point;
}
}
AABB OBB::getAABB() const
{
// get min (x, y, z)
auto min = std::accumulate(std::begin(points), std::end(points), points[0],
[](const glm::vec3& a, const glm::vec3& b){ return component_wise_apply(a, b, std::min); });
// get max (x, y z)
auto max = std::accumulate(std::begin(points), std::end(points), points[0],
[](const glm::vec3& a, const glm::vec3& b){ return component_wise_apply(a, b, std::max); });
// get middle point (position)
// get dimension
return {(min + max) / 2.f, max - min};
}
}