Street networks can be visualized in various ways depending on the purpose. Here we introduce (in the present context) a new technique for visualizing the orientation of street networks in relation to complex topography. The technique is tested on the city of Sheffield, England, with a current population of about 555,500 (in 2010) and a total street number of 23,500. Using digital elevation maps and unique historical datasets, we show how the street network of Sheffield has expanded in a complex topographical environment for close to three centuries, that is, since 1736. The results demonstrate how the topography has affected the spatial orientation of the evolving network. We quantify the network geometry through entropy analysis; entropy is a measure of dispersion or spreading. The results show that the orientation entropy of the network has gradually increased with time. In 1736 the network was primarily composed of orthogonal streets, and had comparatively low entropy. As the network expanded the topographical constraints have contributed to the street orientation becoming more uniform on the rose, resulting in increasing entropy. The analysis also shows that the entropy of the central part of the present network is lower than that of the outer and younger parts. The potential solar radiation for Sheffield is also calculated, visualized, and compared with the topography model and the street network density. The results show that the network density (number of streets per unit area) correlates solar radiation; high-density parts of the network tend to coincide with high-intensity solar radiation.