function vec2(x = 0, y = 0) {
    return { x: x, y: y};
}

function addVec2(v1, v2) {
    return {
        x: v1.x + v2.x,
        y: v1.y + v2.y
    };
}

function subVec2(v1, v2) {
    return {
        x: v1.x - v2.x,
        y: v1.y - v2.y
    };
}

function scaleVec2(v, s) {
    return {
        x: v.x * s,
        y: v.y * s
    };
}

function dot2(v1, v2) {
    return v1.x * v2.x + v1.y * v2.y;
}

function length2(v) {
    return Math.sqrt(v.x * v.x + v.y * v.y);
}

function normalize2(v) {
    const lLength = length2(v);
    const lInverseLength = lLength === 0 ? 1.0 : 1.0 / length2(v);
    return { x: v.x * lInverseLength, y: v.y * lInverseLength };
}

function vec2str(v) {
    return `(${v.x.toFixed(2)}, ${v.y.toFixed(2)})`;
}

function getPerp2(v) {
    return {
        x: -v.y,
        y: v.x
    };
}

function negate2(v) {
    return {
        x: -v.x,
        y: -v.y
    };
}

// Algorithm plucked from: https://matthew-brett.github.io/teaching/rotation_2d.html
function rotateAboutOrigin2(v, angle) {
    return {
        x: v.x * Math.cos(angle) - v.y * Math.sin(angle),
        y: v.x * Math.sin(angle) + v.y * Math.cos(angle),
    };
}