  A two step mesh deformation approach for large nodal deformations, typically
arising from non-parametric shape optimization, fluid-structure interaction or
computer graphics, is considered. Two major difficulties, collapsed cells and
an undesirable parameterization, are overcome by considering a special form of
ray tracing paired with a centroid Voronoi reparameterization. The ray
direction is computed by solving an Eikonal equation. With respect to the
Hadamard form of the shape derivative, both steps are within the kernel of the
objective and have no negative impact on the minimizer. The paper concludes
with applications in 2D and 3D fluid dynamics and automatic code generation and
manages to solve these problems without any remeshing. The methodology is
available as a FEniCS shape optimization add-on at
http://www.mathematik.uni-wuerzburg.de/~schmidt/femorph.
