I have been wanting to do a perspective drawing of ripples on a lake.
To help me, I imagine a pin hole camera projecting an image of the ripples on a film plane.
The pin hole is the origin: (0, 0, 0) Camera face plane is y = 0 Film plane is z = -1 The lake surface lies in the plane z = -1 The ripples are concentric circles lieing in the lake plane, each circle having the center (0, 1, -1)
I believe these things to be true:
The image of the circles' center is (0, -1, 1).
The image of each circle is a conic section. Each conic section has (0, -1, 1) as a focus. And the horizon line is the directrix.
A circle having radius r maps into a conic section of eccentricity r. For example, a circle of radius .5 maps into an ellipse with eccentricity .5. The circle of radius 1 maps into a parabola.