C++ - 如何通过将 x/y/z 增加给定值 x 来生成 n 个 3D 坐标的每个可能组合

Question

As part of a larger program I need to generate every possible set of 3D coordinate points contained within the rectangular prism formed by the origin and point (Y1, Y2, Y3), given the number of points, n, that will be in the set, and the value by which the x/y/z values are to be incremented by.

This was what I initially wrote, which does the job of cycling through all possible coordinates correctly for an individual point, but does not correctly generate all the overall combinations of points needed.

In the program I created a point object, and created a vector of point objects with default x/y/z values of zero.

void allPoints(double Y1, double Y2, double Y3, double increment, vector<Point> pointset)
{
int count = pointset.size()-1;

while (count>=0)
{
    while (pointset.at(count).getX()<Y1) 
    {
        while (pointset.at(count).getY()<Y2)
        {
            while (pointset.at(count).getZ()<Y3)
            {
                //insert intended statistical test to be run on each possible set here 
            }
            pointset.at(count).setZ(0);
            pointset.at(count).incY(increment);
        }
        pointset.at(count).setY(0);
        pointset.at(count).incX(increment);

    }
    count--;
}

}

I am new to coding and may be approaching this entirely wrong, and am just looking for help getting in the right direction. If using a point object isn't the way to go, it's not needed in the rest of the program - I could use 3d arrays instead.

Thanks!

Answer 1

The chief problem appears to be that your textual description is about creating a pointset. The count isn't known up front. The example code takes an already created pointset. That just doesn't work.

That's also why you end up with the // insert test here - that's not the location for a test, that's where you would add a new point to the pointset you have to create.

Answer 2

Lets assume you have class Point3d which represents a point, Vec3d which represents a vector which can translate points (proper operators are defined). In such case this should go like this:

std::vector<Point3d> CrystalNet(
    size_t size,
    const Point3d& origin,
    const Vec3d& a = { 1, 0, 0 },
    const Vec3d& b = { 0, 1, 0 },
    const Vec3d& c = { 0, 0, 1 })
{
    std::vector<Point3d> result;
    result.reserve(size * size * size);

    for (int i = 0; i < size; ++i)
    for (int j = 0; j < size; ++j)
    for (int k = 0; k < size; ++k) {
         result.empalce_back(origin + a * i + b * j + c * k);
    }
    return result;
}

Defining Point3d and Vec3d is quite standard and I'm sure there is ready library which can do it.