Tom Egan of Costa Mesa California invented an indoor sundial, which works by redirecting the sunlight. The photo, diagram, and result-trace below show how it works. Egan published a detailed description in The Compendium [the journal of the North American Sundial Society], vol. 19, no, 3, September 2012. The synopsis version of that says the device is:
a novel indoor sundial using an externally mounted convex mirror to compress the entire visual arc of the sky down to the size of the mirror. A pinhole in a mask on the window acts as a camera obscura, projecting the image of the sun onto an indoor dial face that can be as small as a letter-size piece of paper. The system has four parts: A convex mirror mounted just above the roof line; a pinhole lens affixed to the window; and two paired flat mirrors to relay the sun beam from the convex mirror through the pinhole and onto the dial face inside the building.
BONUS: Others have invented, as jokes, reverse indoor sundials, which work by providing their own light source which rotates around a fixed dial. One is the Saddletrout Studio indoor sundial, pictured here:
Another is the Noddystuff Secondlife indoor sundial, pictured here:
Another, not at all for purists, is the three-light-source Bulbdial clock, pictured here:
BONUS: Tom Egan says that Isaac Newton, too, experimented with an indoor sundial:
“The earliest mention of Newton’s dial that I know of is on page 490, fifth paragraph of M. A. Gatty’s The Book of Sun-dials, 1900″:
“A further variety of sun-dials are those called reflective. In the numbers of “Aunt Judy’s Magazine” for March and April, 1878, there is a charming account of how Sir Isaac Newton placed a mirror on the floor of his room which reflected the sun’s rays on to the ceiling, upon which the hour lines were traced.”
Wikipedia has this, based on Waugh (Waugh AE (1973). Sundials: Their Theory and Construction. New York: Dover Publications. ISBN 0-486-22947-5.):
Isaac Newton developed a convenient and inexpensive sundial, in which a small mirror is placed on the sill of a south-facing window. The mirror acts like a nodus, casting a single spot of light on the ceiling. Depending on the geographical latitude and time of year, the light-spot follows a conic section, such as the hyperbolae of the pelikonon. If the mirror is parallel to the Earth’s equator, and the ceiling is horizontal, then the resulting angles are those of a conventional horizontal sundial. Using the ceiling as a sundial surface exploits unused space, and the dial may be large enough to be very accurate.