Neural networks that map 3D coordinates to signed distance function (SDF) or\noccupancy values have enabled high-fidelity implicit representations of object\nshape. This paper develops a new shape model that allows synthesizing novel\ndistance views by optimizing a continuous signed directional distance function\n(SDDF). Similar to deep SDF models, our SDDF formulation can represent whole\ncategories of shapes and complete or interpolate across shapes from partial\ninput data. Unlike an SDF, which measures distance to the nearest surface in\nany direction, an SDDF measures distance in a given direction. This allows\ntraining an SDDF model without 3D shape supervision, using only distance\nmeasurements, readily available from depth camera or Lidar sensors. Our model\nalso removes post-processing steps like surface extraction or rendering by\ndirectly predicting distance at arbitrary locations and viewing directions.\nUnlike deep view-synthesis techniques, such as Neural Radiance Fields, which\ntrain high-capacity black-box models, our model encodes by construction the\nproperty that SDDF values decrease linearly along the viewing direction. This\nstructure constraint not only results in dimensionality reduction but also\nprovides analytical confidence about the accuracy of SDDF predictions,\nregardless of the distance to the object surface.\n