Euclidean geometry | Descriptive geometry

Rytz's construction

The Rytz’s axis construction is a basic method of descriptive geometry to find the axes, the semi-major axis and semi-minor axis and the vertices of an ellipse, starting from two conjugated half-diameters. If the center and the semi axis of an ellipse are determined the ellipse can be drawn using an ellipsograph or by hand (see ellipse). Rytz’s construction is a classical construction of Euclidean geometry, in which only compass and ruler are allowed as aids. The design is named after its inventor David Rytz of Brugg (1801–1868). Conjugate diameters appear always if a circle or an ellipse is projected parallelly (the rays are parallel) as images of orthogonal diameters of a circle (see second diagram) or as images of the axes of an ellipse. An essential property of two conjugate diameters is: The tangents at the ellipse points of one diameter are parallel to the second diameter (see second diagram). (Wikipedia).

Rytz's construction
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Related pages

Descriptive geometry | Euclidean geometry | Ellipse | Axonometric projection | Conjugate diameters