Introduction: Type III Panoramas
A fun and educational form of visual art combines Type I and Type II panoramas. In this example the portion on the left side of the image is a Type I panorama and the portion on the right side of the image is a Type II panorama. When combined together in the same picture, I, II, we call this a Type III panorama.
Step 1: First, Become Familiar With Constructing Ordinary (Type I) Panoramas
Hold the camera at a fixed location and turn it around 360 degrees while keeping the center of the camera lens at exactly one place. Here I did a selfie during one of our cold water swims. I moved a bit during the selfie so my facial expression is a little different at 0 degrees than it is at 360 degrees. You can "stitch" the images together using VideoOrbits, e.g. the original open-source code I developed in the 1980s and 1990s, or by now there's quite a few other people writing code to stitch images together, and many cameras even have this built-in.
Step 2: Learn How to Do Type II Panoramas
Type II panoramas are for capturing flat objects like this row of storefronts. Pick subject matter that has a dominant planar surface, and move your camera parallel to the planar surface. You can use a track, rail, slider, wagon, roll-cart, or simply be a passenger in a car and do a "drive-by shooting". Railways also work nicely for Type II panoramas.
You can get some crazy fun results. Objects outside the dominant plane will look strange and wonderful.
Step 3: Now Combine the Type I and Type II Together. That's Called Type III.
Here you can see that I moved my camera along parallel to the drugstore shelves. I picked this as a flat almost perfectly planar subject matter. Then when I got to a certain point, I stopped moving and began rotating the camera clockwise while remaining perfectly still. With practice you'll learn how to transition from Type I to Type II or vice-versa without any seams or jumps, so you have a nice smooth transition from I to II to make a Type III like the one pictured above. We might call this drugstore pano a Type II-I because it transitions from Type II to Type I.
Step 4: Type I-II-I
Here's a Type III panorama that starts as Type I, then transitions to Type II, and then transitions back to Type I. Sometimes we call this a Type I-II-I or simply Type IIII or Type IV. Practice transitioning between Type I and Type II and back again, and see how smooth you can make the transition.
Step 5: Become a Master of Prograde and Retrograde Motion
In the above example, the camera is panning from right to left (West to East), from the roof of a building on Dundas Street West, facing the AGO (Art Gallery of Ontario). The Eastbound streetcar exhibits prograde ("forward" with respect to the camera) motion, moving with the camera, and thus appears dilated (stretched). The Westbound streetcar exhibits retrograde motion, moving against the direction of the camera, and thus appears contracted (squashed). While in reality both these streetcars are the same length, Westbound occupies greater imagespace and Eastbound occupies lesser imagespace then they are in reality.
Step 6: Be Creative
One thing we all like to do is run around and get in the picture more than once. You can make multiple copies of yourself or others in a variety of different poses.
Step 7: Study and Learn Something While Having Fun
Computational panoramic imaging is my own invention from the 1980s for wearable computing XR (eXtended Reality) which I brought to MIT in 1991. You can learn more about it by reading my textbook or early papers.
Here's a partial bibliography from my own perspective, and by now many others have written on this topic too.
For more information see my website on the topic:
 Mann was the first to propose and implement an algorithm to estimate a camera's response function from a plurality of differently exposed images of the same subject matter. He was also the first to propose and implement an algorithm to automatically extend dynamic range in an image by combining multiple differently exposed pictures of the same subject matter. High-dynamic-range imaging (HDR): "The first report of digitally combining multiple pictures of the same scene to improve dynamic range appears to be Mann." (Robertson et al.)
 1993: Mann was the first to produce an algorithm for automatically combining multiple pictures of the same subject matter, using algebraic projective geometry, to "stitch together" images using automatically estimated perspective correction. This is called the "Video Orbits" algorithm. 
 Video orbits, http://wearcam.org/orbits/
 Intelligent Image Processing, Wiley, 2001.
author = "Steve Mann",
title = "Intelligent Image Processing",
publisher = "John Wiley and Sons",
pages = "384",
month = "November 2",
year = "2001",
note = "ISBN: 0-471-40637-6",