A smiling face is drawn as an orange circle with a green outline, two black eyes, and a green arc for the mouth, all centered on an SVG canvas. The visualization is built with React and D3.js, where the mouth path is generated using `d3.arc()` with specified inner and outer radii and angle parameters, while the eyes and face are rendered as SVG circles. The code defines reusable components for the face and eyeballs, and positions the elements relative to the canvas center using a translation transform.