Many automated manufacturing processes rely on industrial robot arms to move process-specific tools along workpiece surfaces. In applications like grinding, sanding, spray painting, or inspection, they need to cover a workpiece fully while keeping their tools perpendicular to its surface. While there are approaches to generate trajectories for these applications, there are no sufficient methods for analyzing the feasibility of full surface coverage. This work proposes a sampling-based approach for continuous coverage estimation that explores reachable surface regions in the configuration space. We define an extended ambient configuration space that allows for the representation of tool position and orientation constraints. A continuation-based approach is used to explore it using two different sampling strategies. A thorough evaluation across different kinematics and environments analyzes their runtime and efficiency. This validates our ability to accurately and efficiently calculate surface coverage for complex surfaces in complicated environments.