Written just a decade ago Plus.Maths.org provides a good trigonometric explanation of how to construct an Analemmatic Sundial. In their introduction, "An analemmatic sundial is a particular kind of horizontal sundial in which the shadow-casting object is vertical, and is moved depending on the date, or to be more precise, depending on the declination of the sun on a given day. The time is read from the dial by noting where the shadow cast by the vertical pin crosses hour points laid out on an ellipse. If we make the dial on the ground and large enough, we can use the shadow cast by a person. This makes it very different from the traditional sundial we see often in parks and gardens where the shadow is cast by a triangular shaped wedge. The analemmatic sundial is perfect as a piece of large mathematical sculpture."

Read more and make your own sundial: https://plus.maths.org/content/analemmatic-sundials-how-build-one-and-why-they-work