It is becoming increasingly easy to bring the body directly to digital form via stereoscopic immmersive displays and tracked input devices. Is this space a viable one in which to construct 3d objects? Interfaces built upon two-dimensional displays and 2d input devices are the current standard for spatial construction, yet 3d interfaces, where the dimensionality of the interactive space matches that of the design space, have something unique to offer.This work increases the richness of 3d interfaces by bringing several new tools into the picture: the hand is used directly to trace surfaces; tangible tongs grab, stretch, and rotate shapes; a handle becomes a lightsaber and a tool for dropping simple objects; and a raygun, analagous to the mouse, is used to select distant things. With these tools, a richer 3d interface is constructed in which a variety of objects are created by novice users with relative ease. What we see is a space, not exactly like the traditional 2d computer, but rather one in which a distinct and different set of operations is easy and natural.Design studies, complemented by user studies, explore the larger space of three-dimensional input possibilities. The target applications are spatial arrangment, freeform shape construction, and molecular design. New possibilities for spatial construction develop alongside particular nuances of input devices and the interactions they support. Task-specific tangible controllers provide a cultural affordance which links input devices to deep histories of tool use, enhancing intuition and affective connection within an interface. On a more practical, but still emotional level, these input devices frame kinesthetic space, resulting in high-bandwidth interactions where large amounts of data can be comfortably and quickly communicated.A crucial issue with this interface approach is the tension between specific and generic input devices. Generic devices are the tradition in computing -- versatile, remappable, frequently bereft of culture or relevance to the task at hand. Specific interfaces are an emerging trend -- customized, culturally rich, to date these systems have been tightly linked to a single application, limiting their widespread use. The theoretical heart of this thesis, and its chief contribution to interface research at large is an approach to customization. Instead of matching an application domain's data, each new input device supports a functional class. The spatial construction task is split into four types of manipulation: grabbing, pointing, holding, and rubbing. Each of these action classes spans the space of spatial construction, allowing a single tool to be used in many settings without losing the unique strengths of its specific form. Outside of 3d interface, outside of spatial construction, this approach strikes a balance between generic and specific suitable for many interface scenarios.In practice, these specific function groups are given versatility via a quick remapping technique which allows one physical tool to perform many digital tasks. For example, the handle can be quickly remapped from a lightsaber that cuts shapes to tools that place simple platonic solids, erase portions of objects, and draw double-helices in space.The contributions of this work lie both in a theoretical model of spatial interaction, and input devices (combined with new interactions) which illustrate the efficacy of this philosophy. This research brings the new results of Tangible User Interface to the field of Virtual Reality. We find a space, in and around the hand, where full-fledged haptics are not necessary for users physically connect with digital form.