quarterelliptic

A quarterellipse is a geometric shape representing one-fourth of an ellipse. An ellipse is a closed curve formed by the intersection of a cone and a plane that is not parallel to the cone's axis or base. The shape of an ellipse is defined by two focal points, and the sum of the distances from any point on the ellipse to these two foci is constant.

A quarterellipse is typically formed by considering an ellipse centered at the origin of a Cartesian coordinate system with its axes aligned with the x and y axes. If the equation of the ellipse is given by (x²/a²) + (y²/b²) = 1, where 'a' is the semi-major axis and 'b' is the semi-minor axis, then a quarterellipse can be one of the four segments defined by the intersection of the ellipse with the x and y axes. For instance, the quarterellipse in the first quadrant would be the portion of the ellipse where x ≥ 0 and y ≥ 0.

These shapes find applications in various fields, including computer graphics for drawing curved lines, engineering for designing components with specific curvature profiles, and in physics for describing certain types of motion or trajectories that are constrained to a portion of an elliptical path. The mathematical definition of a quarterellipse utilizes the same parameters as a full ellipse, namely the lengths of its semi-major and semi-minor axes, and its orientation.