How do I generate a vector/array of random cuboids without them intersecting? - math

Question

Suppose I have constraints like the minimum and maximum dimensions of a random cuboid as well as constraints on its center's position. How would I generate a vector/array of cuboids in 3d space where they don't intersect with each other, without relying on checking every cuboid with each other and leave it to a random cuboid to be valid before pushing to the vector/array.
I've tried brute-forcing it by generating random cuboids and checking it against each of the other cuboids and only adding if it doesn't intersect, but I don't want to rely on just using random and hoping that it is valid.
Here are my implementations of a point intersecting with a cuboid, cuboid-cuboid intersection, and cuboid-cuboid[] intersection:
bool cuboid::point_intersects(Vec3 a, Cuboid b) {
Vec3 dimensions = {b.width, b.height, b.depth};
for (unsigned int i = 0; i < 3; i++) { // x,y,z
if (!(a[i] <= b.center[i] + dimensions[i] &&
a[i] >= b.center[i] - dimensions[i])) {
return false;
}
}
return true;
}
bool cuboid::intersects(Cuboid a, Cuboid b) {
Vec3 a_points[8];
Vec3 b_points[8];
cuboid::assign_vertices(a, a_points);
cuboid::assign_vertices(b, b_points);
for (unsigned int i = 0; i < 8; i++) {
if (cuboid::point_intersects(a_points[i], b)) {
return true;
}
if (cuboid::point_intersects(b_points[i], a)) {
return true;
}
}
return false;
}
bool cuboid::intersects_with_vector(std::vector<Cuboid> cuboids, Cuboid a) {
for (Cuboid c : cuboids) {
if (cuboid::intersects(a, c))
return true;
}
return false;
}
Here's how it is used:
#include "cuboid.h"
#include "vector3.h"
// #include <cstdlib>
#include <ctime>
#include <iostream>
#include <random>
#include <vector>
#define MIN_WIDTH 0.01
#define MAX_WIDTH 0.2
#define MIN_HEIGHT 0.01
#define MAX_HEIGHT 0.2
#define MIN_DEPTH 0.01
#define MAX_DEPTH 0.2
#define NUM_ROOMS 12
int main() {
std::mt19937 mt(time(nullptr));
std::vector<Cuboid> rooms = {};
rooms.push_back(cuboid::random_cuboid(MIN_WIDTH, MAX_WIDTH, MIN_HEIGHT,
MAX_HEIGHT, MIN_DEPTH, MAX_DEPTH, &mt));
for (unsigned int i = 0; i < NUM_ROOMS - 1; i++) {
Cuboid c = cuboid::random_cuboid(MIN_WIDTH, MAX_WIDTH, MIN_HEIGHT,
MAX_HEIGHT, MIN_DEPTH, MAX_DEPTH, &mt);
while (cuboid::intersects_with_vector(rooms, c)) {
c = cuboid::random_cuboid(MIN_WIDTH, MAX_WIDTH, MIN_HEIGHT, MAX_HEIGHT,
MIN_DEPTH, MAX_DEPTH, &mt);
}
rooms.push_back(c);
}
for (Cuboid c : rooms) {
std::cout << c << std::endl;
}
return 0;
}
In the following I attempt to generate cuboids whose center's lies in (0,1), with minimum and maximum height, width, and depth.