@Rouben Rostamian  I greatly appreciate the educational aspect of this and many of your previous replies. In future, I will look for alternate and simpler parametrizations of surfaces. Thank you.

@acer I tried the option grid = [100,100] but it didn't affect the plot's smoothness. It seems I used the wrong grid values.

@vv I thank you for your  excellent reply.

Is there any way in which the "distorted" grid indicates the complex expression in F(x,y) or can this only be found by trial and error?

@vv Thank you for your reference. I will pursue it and its sub-references and hope to expand my knowledge.

@dharr I hope in future to have additional questions sufficiently intriguing to draw your interest.

@vv I have tried to "parse" your reply but I do not have the background knowledge of transformations to understand how f(x,y) maps the unit square to a quadrilateral.

Can you refer me to a source which explains transformations such as this at an undergrad level, which is where my math education stopped many years ago?

@dharr Your reply produces the full pencil of conics within and bordering the quadrilateral. I am deeply grateful for your insights into this problem's logic and Maple coding techniques.

@vv Your reply reveals a new approach of mapping a simple shape to a more complex one. Thank you for this food for thought.

@dharr Unfortunately your tips do not stop solve from running endlessly. I hope you will be able to return to this question with more time available.

In the meantime I am working on implementing in Maple the GeoGebra picture of an ellipse in a quadrilateral at https://www.geogebra.org/m/d4k6SjFX

@dharr Your reply is wonderful and gives me a base for attempting to display the other pencils in the book

@dharr Thanks for your correction.

What I really want is Maple code which produces a display that duplicates figure 3.20 in my worksheet. My own effort is quite wide of the mark.

The book referred to in my worksheet contains several more intriguing pencil figures. I would also like to reproduce these if someone can show me a general technique for doing so.

@acer Although Rouben Rostamian has shown that there is no need to refer to plot3d's output, it was interesting to work with MESH.

@Rouben Rostamian  Your method is both simpler and more beautiful!

@ Thank you.

@nm I appreciate your help