The 3D graphic on the right shows an office chair with a support cushion attached - Leaving Cert DCG - Question C-2 - 2011

Using the semi-ellipse equation, determine key points on the contour, including:

1. The endpoints of the major axis: (360, 0) and (-360, 0)
2. The endpoints of the minor axis: (0, 128) and (0, -128)

Calculate additional points on the ellipse for accuracy.

Using the identified points, sketch the semi-ellipse ensuring smooth curvature, keeping the ellipse's properties in mind.

From point A, draw a horizontal line extending towards both sides, indicating the top limit of the cushion.

Connect points A, B, C, and D based on calculated coordinates to form quadrilateral ABCD, marking each corner visibly in the elevation drawing.

Draw and label two sets of construction lines in elevation, ensuring they both reflect the semi-ellipse accurately.

Project the previously established points and construction lines to extend to the overall outline of the elevation profile.

Illustrate quadrilateral ABCD in the end view, ensuring appropriate perspective and scale is maintained.

From the end view, draw the curve AC. Ensure all construction lines leading into AC are properly established.

Identify five significant points along the left hand curve, including the lowest point. These points should assist in accurately defining the curve.

Develop lines of intersection to find point P within the defined plane of the end view.

Using the established points, sketch the left-hand curve maintaining smooth arcs that reflect realistic curvature.

To calculate curvature along section S-S, use the formula for curvature $K = \frac{d^2y}{dx^2}$ at the relevant points of the surface to establish the necessary curvature values.