Laser-inscribing arbitrary patterns with a sub-wavelength resolution in the bulk of transparent materials is of great importance for enabling reliable and versatile nano-manufacturing. Here, we propose a seeding-writing near-field enhancement based method for creating nanoplanes at arbitrary location with programmable length and curvature in a fused silica substrate. These nanoplanes, characterised by an etching contrast, present a thickness of the order of tens of nanometers and have a different refractive index from the surrounding material. Seed-less side planes are also produced under certain writing conditions. While defining ideal writing conditions for the single nanoplane inscription, we propose a model for the formation of the lateral ones. Lastly, a tomography inspired method is developed to reveal their geometry. Precisely defining the nanoplane location and its curvature make this technology of great interest for applications requiring nano-manufacturing in transparent materials.