We report camera-free three-dimensional (3D) dual photography. Inspired by the linkage between fringe projection profilometry (FPP) and dual photography, we propose to implement coordinate mapping to simultaneously sense the direct component of the light transport matrix and the surface profiles of 3D objects. By exploiting Helmholtz reciprocity, dual photography and scene relighting can thus be performed on 3D images. To verify the proposed imaging method, we have developed a single-pixel imaging system based on two digital micromirror devices (DMDs). Binary cyclic S-matrix patterns and binary sinusoidal fringe patterns are loaded on each DMD for scene encoding and virtual fringe projection, respectively. Using this system, we have demonstrated viewing and relighting 3D images at user-selectable perspectives. Our work extends the conceptual scope and the imaging capability of dual photography.