roundtooval

Roundtooval is a term that appears in niche discussions of computational geometry and computer graphics. It is not a standard mathematical function with a single universal definition, but rather a label used for related operations that transform data into an oval or elliptical form. In practice, roundtooval can refer to at least two closely related ideas: projecting points onto an oval boundary and shaping a rectangle into an oval silhouette.

One common interpretation is an ellipse projection transform. Given a point p = (x, y) and an axis-aligned ellipse with semi-axes a and b, the roundtooval transform maps p to a point on the ellipse boundary along the radial line from the origin. If x^2/a^2 + y^2/b^2 <= 1, the point remains unchanged. Otherwise, a scaling factor s = 1 / sqrt(x^2/a^2 + y^2/b^2) is computed, and the result is (s·x, s·y). This maps any point to the ellipse boundary and is useful in graphics for snapping coordinates to an oval outline or for collision detection within elliptical regions.

A second usage concerns rounding a rectangular shape toward an oval silhouette in user interface design. Here, dimensions and corner radii are adjusted so the overall shape approaches an ellipse, producing pill-like or circular forms depending on the width-to-height ratio. This is commonly implemented via vector paths or shape tools in graphics software.

See also: ellipse, rounding, rounded rectangle, vector graphics.