5-ary Base Code

// Parametric Recursive 5-Ary Base Algorithm

ct_complex
ct_map_x(
    ct_complex const& z,
    ct_float sign = 1
) {
    ct_complex I = { 0, sign };

    ct_complex m = (I + z) / (I - z);

    //{Re[(I+z)/(I-z)),Im[(I+z)/(I-z))
    return m;
}


void ct_draw_line(
    ct::plot2d& plot,
    ct_complex p0,
    ct_complex p1,
    unsigned int n
) {
    ct_complex dif = p1 - p0;

    double base = 1.0 / n;

    for (unsigned int i = 0; i < n; ++i)
    {
        double ratio = base * i;

        ct_complex p = p0 + dif * ratio;

        ct_complex p_proj = p;
        //ct_complex p_proj = ct_map_x(p, -1);



        plot.set_pixelf(p_proj, CT_RGBF(1, 1, 0));
        //plot.set_pixelf(-p_proj, CT_RGBF(1, 0, 1));
    }
}


void ct_draw_poly(
    ct::plot2d& plot,
    ct_complex origin,
    double radius,
    double start_angle,
    unsigned int n
) {
    double abase = CT_PI2 / n;

    //plot.circle(origin, radius, CT_RGBF(0, 1, 0));

    for (unsigned int i = 0; i < n; ++i)
    {
        double angle_0 = abase * i + start_angle;
        double angle_1 = angle_0 + abase;

        ct_complex p0_raw = {
            cos(angle_0) * radius,
            sin(angle_0) * radius
        };

        ct_complex p1_raw = {
            cos(angle_1) * radius,
            sin(angle_1) * radius
        };

        ct_complex p0_proj = origin + p0_raw;
        ct_complex p1_proj = origin + p1_raw;

        //plot.line(p0_proj, p1_proj, CT_RGBF(1, 0, 0));

        ct_draw_line(plot, p0_proj, p1_proj, 256);
    }
}


void ct_bearing(
    ct::plot2d& plot,
    unsigned int r_i,
    unsigned int r_max,
    ct_complex origin,
    double origin_radius,
    double start_angle,
    unsigned int n
) {
    if (r_i >= r_max) return;

    // BASE ANGLE
    double ball_abase = CT_PI2 / n;

    // BALL SCALE
    ct_complex d0 = {
        origin.real() + origin_radius,
        origin.imag()
    };

    ct_complex d1 = {
        origin.real() + cos(ball_abase) * origin_radius,
        origin.imag() + sin(ball_abase) * origin_radius
    };

    double ball_diameter = abs(d1 - d0);
    double ball_radius = ball_diameter / 2;
    double ball_scale = origin_radius / (origin_radius + ball_radius);

    double ball_inner_radius = origin_radius - ball_diameter * ball_scale;


    double scale_ball_inner_radius = ball_inner_radius * 1.479;

    //plot.circle_filled(origin, scale_ball_inner_radius, CT_RGBF(1, 1, 1));
    ct_bearing(plot, r_i + 1, r_max, origin, scale_ball_inner_radius, start_angle + ball_abase / 2, n);


    for (unsigned int i = 0; i < n; ++i)
    {
        double ball_angle_0 = ball_abase * i + start_angle;

        ct_complex p0 = {
            cos(ball_angle_0) * origin_radius,
            sin(ball_angle_0) * origin_radius
        };

        ct_complex ball_proj_p0 = origin + p0 * ball_scale;
        double ball_proj_radius = ball_radius * ball_scale;

        double scale_ball_radius = ball_proj_radius * 1.03;

        //plot.circle(ball_proj_p0, scale_ball_radius, CT_RGBF(1, 0, 0));

        if (r_i == r_max - 1)
        {
            //plot.circle_filled(ball_proj_p0, scale_ball_radius * .75, CT_RGBF(0, 1, 1));
            //plot.line(origin, -ball_proj_p0 * scale_ball_radius, CT_RGBF(1, 1, 1));
            ct_draw_poly(plot, ball_proj_p0, scale_ball_radius, ball_angle_0 + ball_abase, n);
        }


        ct_bearing(plot, r_i + 1, r_max, ball_proj_p0, scale_ball_radius, ball_angle_0, n);
    }


}