The Bresenham line algorithm avoids trigonometry and uses integer math to calculate the points of a line, circle or ellipse.

Here is a small example (implemented in C++ / SFML):

#include <SFML/Graphics.hpp>

void drawEllipse(sf::RenderWindow &w, int cx, int cy, int r1, int r2) {
    sf::Shape point = sf::Shape::Circle(0, 0, 1, sf::Color::White);

    int x = -r1, y = 0;
    int err = r1 * r1 - (2 * r1 - 1) * r2 * r2, e2;

    do {
        point.SetPosition(cx - x, cy + y) ; w.Draw(point);
        point.SetPosition(cx + x, cy + y) ; w.Draw(point);
        point.SetPosition(cx + x, cy - y) ; w.Draw(point);
        point.SetPosition(cx - x, cy - y) ; w.Draw(point);

        e2 = 2 * err;

        if (e2 >= (x * 2 + 1) * r2 * r2)
            err += (++x * 2 + 1) * r2 * r2;

        if (e2 

To learn more about the theory behind the algorithm, please have a look at the Midpoint Circle Algorithm at Wikipedia.