Drawing a circle in perspective
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In the following picture, the red circle is inscribed inside the square \(W'X'Y'Z'\) which lies on the plane \(QRS\). The points \(W', X', Y', Z'\) project to the points \(W, X, Y, Z\) respectively on the \(xy\) plane, using \(P\) as a point of perspective. The red circle projects to the orange conic section.
In these pages we will explore the question of how to construct the conic section, i.e. how to construct the major/minor axes and the focal points.
You can click and drag the point \(P\) to move the point of perspective. The circle lies on the plane through \(Q\), \(R\) and \(S\), and you can change this plane by moving these points. The circle has centre \(O\) and radius \(OF\), and you can move these points to change the circle. The points \(W', X', Y', Z'\) and \(W, X, Y, Z\) will automatically be redrawn. You can rotate the 3D figure to change your viewpoint by clicking and dragging the box.
In the case where the projection of the circle is an ellipse, the next four pages show how to carry out the following steps to construct the orange ellipse.
