The uploaded worksheet contains the general definition of a pedal curve related to the curve [f(t),g(t)], and includes several example pedal curves.

Is there a comparable general definition of a pedal surface? If so, in your answer please include the Maple code for one or two simple examples e.g. relating to a sphere, to an ellipsoid.

To everyone in the Maple Forum community, Happy Holidays and a fulfilling New Year!

Pedal_curves.mw 

Please see the question posed in the opening text of the uploaded worksheet.

Oloid.mw

What type of mathematics can perform the type of transformation seen in the uploaded worksheet?

Could it be done with the Maple plottools transform command?

Could it be a projective transformation using homogeneous coordinates?

Could it be a complex conformal transformation?

Transformation.mw

The worksheet below mimics some of the construction in the web site https://www.geogebra.org/m/d4k6SjFX.

This seems a crude and limiting way to display a pencil of ellipses tangent in a quadrilateral.

Please provide references (textbooks, articles, etc.) to the mathematics which produces this kind of display.

Pencil_in_quad.mw

Sorry, I was not able to change the displays to inline.

The worksheet below is a failed attempt to produce the display of a pencil of conics tangent to four lines. The worksheet contains an image of the display.

Comments within the worksheet describe the details of the attempt and the solve command which fails.

dhaar provided an answer to a similar question which I posed on November 12 (its web address is in the worksheet) and I hope s(he) will reply to this one as well.

ConicsTangent.mw