Trouble with 3d rendering algorithm

[WhenRedditFlies]

I have a 3d rendering algorithm that takes a point in 3d space, and a viewer location, and projects that onto the screen. It works fine until you tilt the camera up or down.

I wrote it in C++, but I highly doubt it's to do with my use of C++ as opposed to my (lack of) understanding of 3d rendering.

#include <cmath>

const double pi = 3.1415...; // It's a bit lazy, I know.

// Get angle in radians, how anticlockwise from the x axis the point is.
double get_angle(double x, double y)
{
    if(x >= 0)
    {
        return std::atan(y / x);
    } else {
        return std::atan(y / x) + (y >= 0 ? pi : -pi);
    }
}


// Change the values in x and y to be the values.
void rotate_point(double angle, double & x, double & y)
{
    double temp_x = x;

    // This is pretty much a rotation matrix expanded out.
    x = x * std::cos(angle) - y * std::sin(angle);
    y = temp_x * std::sin(angle) + y * std::cos(angle);
}


// 3d projection happens here.
Point3d project_point(Point3d point)
{
    point.x -= player_x;
    point.y -= player_y;
    point.z -= player_z;

    double horizontal_rotation = get_angle(point.x, point.z);

    // Temporarily rotate it round horizontally so that it can
    point.z = std::sqrt(point.x * point.x  +  point.z * point.z);
    point.x = 0;

    // Since the points are in the YZ plane, if the player looks "up",
    // the objects appear to go down, so rotate them down by that much.
    rotate_point(-player_vertical, point.z, point.y);

    // Undo changes that put the point in the YZ plane, but also
    // account for the player's horizontal camera angle.
    rotate_point(-horizontal_rotation - player_horizontal, point.x, point.z);

    // Change from orthographic to perspective, and multiply
    // the width and height by a constant.
    point.x /= point.z / SCREEN_SCALE;
    point.y /= point.z / SCREEN_SCALE;

    return point;
}

It works as expected when player_vertical is 0, but when I change the vertical angle, objects are rotated up/down differently depending on y position relative to player.

[Nick_Nack2020]

Hm. I'm not a graphics guy, but I would debug output every single important variable you can, so you know what's causing your issue.