Deformable component models. (a) Example surgical tools (K-wire, flexible screwdriver, drill, and spinal fixation rod) presenting a cylindrical profile. (b) Parametric B-spline component model showing control points , attached discs , and tangent lines at clamped endpoints. (c) Tessellated 3D model with computed surface normals. (d) Non-convex polygon projection with multiple red line segments indicating line integrals through the mesh.