Simple Oriented Bounding Box OBB collision detection explaining
I can implement the AABB method to detect collisions it is easy and cheap but I want to implement OBB for more accuracy so I create the bounding box with the model initialization it is consists of 8 bounding vertices and center, each frame I transform all the vertices with the transformation matrix to fit the Oriented Bounding Box but I can't understand the method for detecting the collision between two OBBs and I can't find a simplified and clear tutorial which explain the algorithm with the code view point not the math because I am not a mathematician.
if I have
struct Box {
glm::vec3 vertices[8];
Box() {
for (int i = 0; i < 8; i++) {
vertices[i] = glm::vec3(0);
}
}
glm::vec3 max;
glm::vec3 min;
glm::vec3 origin;
void reCompute() {
max = vertices[0];
min = vertices[0];
for (int i = 1; i < 8; i++) {
max.x = max.x > vertices[i].x ? max.x : vertices[i].x;
max.y = max.y > vertices[i].y ? max.y : vertices[i].y;
max.z = max.z > vertices[i].z ? max.z : vertices[i].z;
min.x = min.x < vertices[i].x ? min.x : vertices[i].x;
min.y = min.y < vertices[i].y ? min.y : vertices[i].y;
min.z = min.z < vertices[i].z ? min.z : vertices[i].z;
}
origin = glm::vec3((max.x + min.x) / 2.0f, (max.y + min.y) / 2.0f, (max.z + min.z) / 2.0f);
}
//AABB intersection
bool intersects(const Box &b) const {
return (min.x < b.max.x) && (max.x > b.min.x) && (min.y < b.max.y) && (max.y > b.min.y) && (min.z < b.max.z) && (max.z > b.min.z) && *this != b;
}
bool operator==(const Box& b) const {
return (max.x == b.max.x && max.y == b.max.y && max.z == b.max.z && min.x == b.min.x && min.y == b.min.y && min.z == b.min.z);
}
bool operator!=(const Box& b) const {
return (max.x != b.max.x) || (max.y != b.max.y) || (max.z != b.max.z) || (min.x != b.min.x) || (min.y != b.min.y) || (min.z != b.min.z);
}
};
on model initialization I create the box
box.vertices[0] = glm::vec3(meshMinX, meshMinY, meshMinZ);
box.vertices[1] = glm::vec3(meshMaxX, meshMinY, meshMinZ);
box.vertices[2] = glm::vec3(meshMinX, meshMaxY, meshMinZ);
box.vertices[3] = glm::vec3(meshMaxX, meshMaxY, meshMinZ);
box.vertices[4] = glm::vec3(meshMinX, meshMinY, meshMaxZ);
box.vertices[5] = glm::vec3(meshMaxX, meshMinY, meshMaxZ);
box.vertices[6] = glm::vec3(meshMinX, meshMaxY, meshMaxZ);
box.vertices[7] = glm::vec3(meshMaxX, meshMaxY, meshMaxZ);
and each frame I recompute the box with the transformation matrix of the model
for (int n = 0; n < 8; n++) {
boxs[j].vertices[n] = glm::vec3(matrix * glm::vec4(box.vertices[n], 1));
}
boxs[j].reCompute();
Answer
A C++ code implementation of the separating axis theorem for simple collision detection between two 3D OBB would be this:
#include <iostream>
// define the operations to be used in our 3D vertices
struct vec3
{
float x, y, z;
vec3 operator- (const vec3 & rhs) const { return{ x - rhs.x, y - rhs.y, z - rhs.z }; }
float operator* (const vec3 & rhs) const { return{ x * rhs.x + y * rhs.y + z * rhs.z }; } // DOT PRODUCT
vec3 operator^ (const vec3 & rhs) const { return{ y * rhs.z - z * rhs.y, z * rhs.x - x * rhs.z, x * rhs.y - y * rhs.x }; } // CROSS PRODUCT
vec3 operator* (const float& rhs)const { return vec3{ x * rhs, y * rhs, z * rhs }; }
};
// set the relevant elements of our oriented bounding box
struct OBB
{
vec3 Pos, AxisX, AxisY, AxisZ, Half_size;
};
// check if there's a separating plane in between the selected axes
bool getSeparatingPlane(const vec3& RPos, const vec3& Plane, const OBB& box1, const OBB&box2)
{
return (fabs(RPos*Plane) >
(fabs((box1.AxisX*box1.Half_size.x)*Plane) +
fabs((box1.AxisY*box1.Half_size.y)*Plane) +
fabs((box1.AxisZ*box1.Half_size.z)*Plane) +
fabs((box2.AxisX*box2.Half_size.x)*Plane) +
fabs((box2.AxisY*box2.Half_size.y)*Plane) +
fabs((box2.AxisZ*box2.Half_size.z)*Plane)));
}
// test for separating planes in all 15 axes
bool getCollision(const OBB& box1, const OBB&box2)
{
static vec3 RPos;
RPos = box2.Pos - box1.Pos;
return !(getSeparatingPlane(RPos, box1.AxisX, box1, box2) ||
getSeparatingPlane(RPos, box1.AxisY, box1, box2) ||
getSeparatingPlane(RPos, box1.AxisZ, box1, box2) ||
getSeparatingPlane(RPos, box2.AxisX, box1, box2) ||
getSeparatingPlane(RPos, box2.AxisY, box1, box2) ||
getSeparatingPlane(RPos, box2.AxisZ, box1, box2) ||
getSeparatingPlane(RPos, box1.AxisX^box2.AxisX, box1, box2) ||
getSeparatingPlane(RPos, box1.AxisX^box2.AxisY, box1, box2) ||
getSeparatingPlane(RPos, box1.AxisX^box2.AxisZ, box1, box2) ||
getSeparatingPlane(RPos, box1.AxisY^box2.AxisX, box1, box2) ||
getSeparatingPlane(RPos, box1.AxisY^box2.AxisY, box1, box2) ||
getSeparatingPlane(RPos, box1.AxisY^box2.AxisZ, box1, box2) ||
getSeparatingPlane(RPos, box1.AxisZ^box2.AxisX, box1, box2) ||
getSeparatingPlane(RPos, box1.AxisZ^box2.AxisY, box1, box2) ||
getSeparatingPlane(RPos, box1.AxisZ^box2.AxisZ, box1, box2));
}
// a quick test to see the code working
int _tmain(int argc, _TCHAR* argv[])
{
// create two obbs
OBB A, B;
// set the first obb's properties
A.Pos = { 0.f, 0.f, 0.f }; // set its center position
// set the half size
A.Half_size.x = 10.f;
A.Half_size.y = 1.f;
A.Half_size.z = 1.f;
// set the axes orientation
A.AxisX = { 1.f, 0.f, 0.f };
A.AxisY = { 0.f, 1.f, 0.f };
A.AxisZ = { 0.f, 0.f, 1.f };
// set the second obb's properties
B.Pos = { 20.f, 0.f, 0.f }; // set its center position
// set the half size
B.Half_size.x = 10.f;
B.Half_size.y = 1.f;
B.Half_size.z = 1.f;
// set the axes orientation
B.AxisX = { 1.f, 0.f, 0.f };
B.AxisY = { 0.f, 1.f, 0.f };
B.AxisZ = { 0.f, 0.f, 1.f };
// run the code and get the result as a message
if (getCollision(A, B)) std::cout << "Collision!!!" << std::endl;
else std::cout << "No collision." << std::endl;
// pause and quit
std::cout << std::endl;
system("pause");
return 0;
}