Distance constancy was clearly defined with Thouless and Brunswik indexes by examining its previous definitions. The typical functions expressing the relationships between apparent distance and physical distance were derived from; 1. much available data obtained by many researchers, 2. Thouless and Brunswik indexes (formulas), 3. Luneburg's theory. These derived functions were classified into type I, II and III according to their psychological significance. The validity of the classification was verified by experiments showing that the functions of type III were available in poorly articulated spaces with a long viewing distance, that is, on a housetop and a road, with the method of equal appearing intervals. Moreover, the relationships between distance constancy and personal constants in Luneburg's theory were clarified.