Tendon-driven continuum robots (TDCRs) are increasingly used in minimally invasive settings due to their compliance and dexterity, yet quantifying their effective workspace remains challenging because inverse kinematics is computationally expensive and sensitive to pose constraints. This paper presents a voxel-based capability mapping framework for a custom-built, two-segment TDCR with antagonistic tendon actuation and a non-interference routing sleeve around the pulley region. The method samples task-space targets within a discretized volume and enforces a downward tip-orientation constraint to reflect surgical operation requirements. For each sampled target pose, a particle swarm optimization (PSO) based inverse kinematics solver estimates a feasible configuration, and the resulting position and orientation errors are evaluated against predefined tolerances. Capability is then summarized per voxel as a success ratio over multiple randomized trials, producing a compact map that highlights regions with higher reliability for task execution. The resulting capability map provides practical insight for target selection and procedure planning while avoiding repeated online inverse-kinematics calls.