In The Solar House I discuss how modern architects developed a new understanding of the science of solar geometry through drawings. Studies including solar angles, to determine the spacing of buildings for heliotherapeutic considerations, came out of the Bauhaus in c.1930. I conclude that the first solar geometry studies made specifically for solar heating (and shading to prevent overheating) were made in late 1937, probably independently, by Keck & Keck and Henry N. Wright. In addition to those examples, Le Corbusier made such a drawing 1938, as I discuss and show in Le Corbusier and the Sun.
It's possible that Alvar Aalto should be included in that short list. In a 2012 lecture, British historian Dean Hawkes mentions that he found section drawings of the Villa Mairea with a critical sun angle of 52˚ shown. This indeed corresponds to noon at the summer solstice in Noormarkku, Finland. Aalto designed the Villa Mairea in 1938. (Video here; the pertinent bit starts about 18:42.) Hawkes is one of my favorite historians, and the full video is well worth the time.
We may never know definitively who drew the first 2D shading diagram, but clearly the convention came of age in 1937-38.
[Added July 2015] Aalto used solar geometry diagrams in the design of the Paimio Sanatorium. The drawing below is undated but made in the 1929-33 period.
To be clear, this is not a shading diagram, as the purpose is to show winter sunlight penetrating deep into the patient rooms for therapeutic purposes, and no shading devices are shown. In this case Aalto used a sun angle of 34˚.
This drawing was included in the terrific exhibit Alvar Aalto 1898-1976. Organic Architecture, Art and Design, which I saw at the Caixa Forum in Barcelona. It is also published in the exhibition catalog Alvar Aalto: Second Nature.
For more on the Paimio Sanatorium, see Tuberculosis and Solar Architecture (part 2).