  Neural implicit fields have emerged as a powerful 3D representation for
reconstructing and rendering photo-realistic views, yet they possess limited
editability. Conversely, explicit 3D representations, such as polygonal meshes,
offer ease of editing but may not be as suitable for rendering high-quality
novel views. To harness the strengths of both representations, we propose a new
approach that employs a mesh as a guiding mechanism in editing the neural
radiance field. We first introduce a differentiable method using marching
tetrahedra for polygonal mesh extraction from the neural implicit field and
then design a differentiable color extractor to assign colors obtained from the
volume renderings to this extracted mesh. This differentiable colored mesh
allows gradient back-propagation from the explicit mesh to the implicit fields,
empowering users to easily manipulate the geometry and color of neural implicit
fields. To enhance user control from coarse-grained to fine-grained levels, we
introduce an octree-based structure into its optimization. This structure
prioritizes the edited regions and the surface part, making our method achieve
fine-grained edits to the neural implicit field and accommodate various user
modifications, including object additions, component removals, specific area
deformations, and adjustments to local and global colors. Through extensive
experiments involving diverse scenes and editing operations, we have
demonstrated the capabilities and effectiveness of our method. Our project page
is: \url{https://cassiepython.github.io/MNeuEdit/}
