function findLineIntersection (line1, line2) {
    let formula1 = getLineFormula(line1);
    let formula2 = getLineFormula(line2);

    let x = (formula2.c - formula1.c)/(formula1.m - formula2.m);
    let y = formula1.m*x + formula1.c;

    return {'x': x, 'y': y};
}

function findCircleIntersection(line, circle) {
    let lineFormula = getLineFormula(line);

    // 1 + m^2
    let a = 1 + Math.pow(lineFormula.m, 2);
    // 2mc - 2mk - 2h -> 2mc since k & h are 0
    let b = 2*lineFormula.m*lineFormula.c;
    // h^2 + c^2 + k^2 - r^2 - 2ck -> c^2 - r^2 since k & h are 0
    let c = Math.pow(lineFormula.c, 2) - Math.pow(circle.r, 2);

    let discriminant = Math.pow(b, 2) - 4*a*c;

    let x1 = (-b + Math.sqrt(discriminant))/(2*a);
    let x2 = (-b - Math.sqrt(discriminant))/(2*a);

    let x = checkIfInBound(x1, x2, line);
    let y = lineFormula.m*x + lineFormula.c;
    return {'x': x, 'y': y};
}

function extendLineToCircle(line, circle) {
    let lineFormula = getLineFormula(line);

    // 1 + m^2
    let a = 1 + Math.pow(lineFormula.m, 2);
    // 2mc - 2mk - 2h -> 2mc since k & h are 0
    let b = 2*lineFormula.m*lineFormula.c;
    // h^2 + c^2 + k^2 - r^2 - 2ck -> c^2 - r^2 since k & h are 0
    let c = Math.pow(lineFormula.c, 2) - Math.pow(circle.r, 2);

    let discriminant = Math.pow(b, 2) - 4*a*c;

    let x1 = (-b + Math.sqrt(discriminant))/(2*a);
    let x2 = (-b - Math.sqrt(discriminant))/(2*a);

    return {x1: x1, y1: lineFormula.m*x1 + lineFormula.c, x2: x2, y2: lineFormula.m*x2 + lineFormula.c};
}

function getLineFormula (line) {
    let rise = line.y2-line.y1;
    let run = line.x2-line.x1;
    run = run ? run : -0.000001;
    let m = Math.round(rise*1000/run)/1000;

    let c = Math.round((line.y1 - m*line.x1)*1000)/1000;
    return {'m': m, 'c': c};
}

function checkIfInBound(x1, x2, line) {
    if (Math.min(line.x1, line.x2) <= x1 && Math.max(line.x1, line.x2) >= x1) {
        return x1;
    }
    return x2;
}