JShell script that loads a method for finding intersections between a ray and a sphere given the origin of the sphere, the origin of the ray, the direction vector of the ray, and the radius of the sphere.

intersections.jsh

import static java.lang.Math.*;

double[][] intersections(double[] p, double[] o, double[] d, double r) {
    double[] ip = inverse(p);

    double a = dot(d, d);
    double b = 2 * dot(o, d) + 2 * dot(ip, d);
    double c = dot(o, o) + 2 * dot(ip, o) + dot(ip, ip) - pow(r, 2);

    double dct = pow(b, 2) - 4 * a * c;

    double[] t = new double[]{
        (-b - sqrt(dct)) / (2 * a),
        (-b + sqrt(dct)) / (2 * a)
    };

    return new double[][]{
        add(o, mult(d, t[0])),
        add(o, mult(d, t[1]))
    };
}

double[] inverse(double[] input) {
    return mult(input, -1);
}

double sum(double[] input) {
    double sum = 0;
    for (int i = 0; i < input.length; i++) {
        sum += input[i];
    }
    return sum;
}

double[] mult(double[] input, double scalar) {
    double[] clone = new double[input.length];
    for (int i = 0; i < input.length; i++) {
        clone[i] = scalar * input[i];
    }
    return clone;
}

double[] add(double[] a, double[] b) {
    double[] result = new double[a.length];
    for (int i = 0; i < a.length; i++) {
        result[i] = a[i] + b[i];
    }
    return result;
}

double dot(double[] a, double[] b) {
    assert a.length == b.length: "Dot product inputs must be of equal dimension";

    double sum = 0;
    for (int i = 0; i < a.length; i++) {
        sum += a[i] * b[i];
    }
    return sum;
}

Java 17 comes with a binary, jshell, which can execute this script — simply run the binary with the path to this script as the argument, and it'll load each method and throw you into a read-eval-print loop in which you can run intersections with your desired inputs.

input	description
p	the centre of the sphere
o	the origin of the ray
d	the direction vector of the ray
r	the radius of the sphere