How to Plot Intersection of Two Cylinders in Maple

A tricky but reasonable affair!

Two cylinders passing through each other.

I’d like to show you basic usage of two plotting commands in Maple by solving a relatively difficult problem to reason about and visualize (at least for some of us!). The commands are implicitplot and plot3d.

Each of these Maple commands (ie functions) has multiple possible calling sequences. By “calling sequence” I mean a specific order and number of arguments that you can pass to one of these functions.

In other words, you can call these functions in different ways. The walkthrough below will use only some of such calling sequences, and I refer you to the docs if you are interested in all the other ways these commands can be used.

Here is a github repo with a Maple file containing all the calculations and plots below (plus a version in spherical coordinates). The relevant file is called 14.8-Ex 15-Two Cylinders.mw.

Problem Description

Consider the cylinders

and

The first is a cylinder with the z axis running down through the middle, and the second has the y axis running down through the middle.

Our ultimate goal is to plot the intersection of the two cylinders (can you guess what it looks like?), but we will…