A smiley face is drawn with a grey blurred circle for the head, two white circles for the sclera, black circles for the irises, and a dark mouth path. The visualization uses React with SVG elements for rendering, and the mouth is generated via the `d3.arc` API, which produces a path with inner and outer radii and specified start and end angles. A `feGaussianBlur` filter is applied to the head circle for a soft shadow effect.