OuterTangents vex

outerTangents.vfl

function vector[] outerTangents(vector circle1Pos, circle2Pos;
                                    float circle1Radius, circle2Radius) {
    float hypotenuse = distance(circle1Pos, circle2Pos);
    float shortEdgeLen = circle1Radius - circle2Radius;
    
    // xz
    float rad = atan2(circle2Pos.z - circle1Pos.z, circle2Pos.x - circle1Pos.x)
                    + acos(shortEdgeLen/hypotenuse);
    vector circle1OuterTangent1 = set(
        circle1Pos.x + circle1Radius * cos(rad),
        circle1Pos.y,
        circle1Pos.z + circle1Radius * sin(rad)
    );

    vector circle2OuterTangent1 = set(
        circle2Pos.x + circle2Radius * cos(rad),
        circle2Pos.y,
        circle2Pos.z + circle2Radius * sin(rad)
    );

    float oppositeRad = atan2(circle2Pos.z - circle1Pos.z, circle2Pos.x - circle1Pos.x)
                    - acos(shortEdgeLen/hypotenuse);
    vector circle1OuterTangent2 = set(
        circle1Pos.x + circle1Radius * cos(oppositeRad),
        circle1Pos.y,
        circle1Pos.z + circle1Radius * sin(oppositeRad)
    );
    
    vector circle2OuterTangent2 = set(
        circle2Pos.x + circle2Radius * cos(oppositeRad),
        circle2Pos.y,
        circle2Pos.z + circle2Radius * sin(oppositeRad)
    );
    
    return array(circle1OuterTangent1, circle1OuterTangent2, circle2OuterTangent1, circle2OuterTangent2);
}