const tan = (curvature: number) => (x: number) => {
    if (curvature < 0) {
        return (
            (1 / Math.sqrt(-curvature)) * Math.tanh(Math.sqrt(-curvature) * x)
        );
    } else if (curvature === 0) {
        return x;
    } else {
        return (1 / Math.sqrt(curvature)) * Math.tan(Math.sqrt(curvature) * x);
    }
};

const atan = (curvature: number) => (x: number) => {
    if (curvature < 0) {
        return (
            (1 / Math.sqrt(-curvature)) * Math.atanh(Math.sqrt(-curvature) * x)
        );
    } else if (curvature === 0) {
        return x;
    } else {
        return (1 / Math.sqrt(curvature)) * Math.atan(Math.sqrt(curvature) * x);
    }
};

export type Curvature = {
    value: number;
    tan: (x: number) => number;
    atan: (x: number) => number;
};

export const createCurvature = (curvature: number): Readonly<Curvature> => {
    return { value: curvature, tan: tan(curvature), atan: atan(curvature) };
};