Constructive solid geometry (CSG) is a classical CAD representation; it models a 3D shape as a recursive assembly of solid primitives, e.g., cuboids, cylinders, etc., through Boolean operations

CSG and CAPRI-Net mentioned in Section 3 of the main paper. To prove Proposition 1, we provide an example that CAPRI-Net's sequence fails to support. CSG is able to support any CSG sequence. Each sub-figure represents a 2D implicit filed defined by the notation below. Specifically, we obtain the mesh for each primitive by performing Marching-Cube on the signed distance field produced by the quadric equation of that primitive.

Signed distance field (SDF) is a prominent implicit representation of 3D meshes.

We thank the reviewers for their insightful comments. In this rebuttal, we respond to remarks from reviews. Remark 1 The work lacks discussion about the comparison of interpretability with BSP-Net. Moreover, their CSG structure is fixed by definition. CSG trees for different instances (see Figure on the right). Remark 2 Only a single instance of CSG visualization for each class is shown.

Additional Feedback: I tend to accept this paper because it demonstrates a very promising probability - that it is now possible to learn a relatively complex shape representation (CSG) that are often used in actual production settings. Granted, the novelty is slightly limited (the training protocol is similar to earlier works in implicit shape generation/reconstruction and the representation (CSG) is also widely used), and the results are not super convincing (will explain below); however, I still feel the idea is interesting enough and will easily sparkle future works in similar directions. I am not completely positive because I am uncertain if the method leads to a dead end - as there are infinitely many possible CSG trees for a given shape, an unsupervised method might never be able to learn something that is truly usable, even after many improvements over the current method. Additional comments: -Could the authors explain the motivation of adopting a bottom-up process that groups primitive to form final outputs? It seems to me that it would be much harder for the network to understand shape decomposition in this way, since it is trying to select form a large set of primitives and find which ones can be grouped to form something that look similar to the input, rather than directly thinking about how to decompose the input shape (in a top-down way).

This paper presents a unified differentiable boolean operator for implicit solid shape modeling using Constructive Solid Geometry (CSG). Traditional CSG relies on min, max operators to perform boolean operations on implicit shapes. But because these boolean operators are discontinuous and discrete in the choice of operations, this makes optimization over the CSG representation challenging. Drawing inspiration from fuzzy logic, we present a unified boolean operator that outputs a continuous function and is differentiable with respect to operator types. This enables optimization of both the primitives and the boolean operations employed in CSG with continuous optimization techniques, such as gradient descent. We further demonstrate that such a continuous boolean operator allows modeling of both sharp mechanical objects and smooth organic shapes with the same framework. Our proposed boolean operator opens up new possibilities for future research toward fully continuous CSG optimization.