Exploring Freehand Selection Techniques of Polyhedron Faces in VR Environments

Virtual reality (VR) allows users to observe and manipulate 3D geometry from multiple viewpoints. Most VR selection work, however, optimizes techniques for selecting entire objects. Selecting a single face on a polyhedron remains underexplored and is more challenging because the interaction must act on a local component while preserving the object's global structure. We introduce a design space tailored to this task with three dimensions: viewing strategy, disambiguation consistency, and interaction metaphor. Guided by this space, we design eight freehand techniques for polyhedral face selection. A within-subjects study with 16 participants evaluates these techniques across polyhedral complexity (two radii; face counts 4, 6, and 12). The results identify three complementary top techniques, reveal tradeoffs between viewing choices and geometric preservation, and yield concrete guidelines for matching techniques to target geometry and task demands. A follow-up study with complex, realistic models confirms the robust ness and practical usability of the three techniques. Together, these contributions shift attention from whole object selection to precise component selection in VR and provide actionable methods for 3D modeling, assembly, and texturing.