Semi-automatic Navigation on 3D Triangle Meshes Using BVP Based Path-Planning

Efficient path-planning methods are being explored along the years to allow the movement of robots or virtual agents in planar environments. However, there is a lot of space to improve the quality of paths restricted to 3D surfaces, with holes and bends for instance. This work presents a new technique for path-planning on 3D surfaces called 3DS-BVP. This path planner is based on Boundary Value Problem (BVP), which generates potential fields whose gradient descent represents navigation routes from any point on the surface to a goal position. Resulting paths are smooth and free from local minima. The 3DS-BVP works on complex surfaces of arbitrary genus or curvature, represented by a triangle mesh, without the need of 2D parametrizations. Our results demonstrate that our technique can generate paths in arbitrary surfaces with similar quality as those generated by BVP-based methods in planar environments. Our approach can be applied in the development of new tools to automate the navigation on 3D surfaces, like the camera control in the exploratory visualization of 3D models.