Surface registration is a fundamental problem in Computer Graphics and Computer Aided Design. In the industrial context, machining programs for aircraft fuselage panels are defined on the theoretical pieces only. However, they can not be directly applied to real panels due to high deformability of these pieces. Thus, real pieces must be registered to the theoretical ones to adapt the machining programs. In our registration pipeline, theoretical pieces are surface meshes and real pieces are point clouds from laser system measures. To satisfy the quality and precision standards of the industry, the machining programs before and after adaptation must not be distorted. The registration must therefore be isometric. It must be scalable to support potentially very large meshes and point clouds. It must also support the usual points clouds defects, eg. noise, partial data and non-uniform sampling. Naturally, simultaneously satisfying all these constraints is challenging.

In this thesis work, we are first interested in the complete setting with very dense objects, and propose a mesh to point clouds As-Rigid-As-Possible registration algorithm. The alignment between the surfaces is solved by using orientation constraints instead of positional ones to better support the isometry constraint. We also propose a hierarchical optimization to make the registration scalable. Our experiments show that we obtain a fast and efficient algorithm compared to the state-of-the art methods, while keeping its numerical accuracy. Then we are interested in partial-to-partial setting with potentially low sampling. To support this new context, we propose an As-Rigid-As-Possible energy with sparse orientation constraints and a
second registration algorithm based on this new term. To efficiently minimize this energy and solve the registration, we also propose a global-local-global minimization method based on rotation interpolation on curved surfaces. Our experiments show that our partial-to-partial registration algorithm supports the partial setting while satisfying the isometry and alignment constraints. Moreover, we show that the registration can be solved on point clouds with very low sampling with the addition of only one or two landmarks between the real and the
theoretical surfaces. Our contributions improve the quality and the accuracy of the isometric registration and are now implemented and used in real life industrial applications.