Computer Graphics · Geometric Computing

CSG SweepsFeature-aware sweep surfacing of deformable CSGs

Jianjun Xia,Qingnan Zhou,Yiwen Ju,Xingyi Du,Nathan Carr,Tao Ju

Washington University in St. Louis  ·  Adobe Research

ACM Transactions on Graphics (Proc. SIGGRAPH Asia 2026)

PaperSupplementaryCode
Feature-aware sweep surfacing of a deforming CSG shape.

Abstract

Computing the sweep surface of a moving 3D solid is fundamental to geometric modeling, manufacturing, and robotics. We present the first feature-aware method for surfacing the sweep of a deforming piecewise-smooth shape. Our method accepts a 4D time-varying Constructive Solid Geometry (CSG) representation, allowing geometry and topology to change during a sweep. It generalizes lifted sweeping from smooth functions to CSG functions and introduces robust algorithms for discretizing multiple intersecting implicit surfaces in arbitrary dimensions. The resulting watertight meshes preserve the sharp features induced by shape corners, sweep endpoints, and self-intersections under both rigid and non-rigid motion.

What makes CSG sweeps difficult?

01

Piecewise-smooth input

Sharp edges and corners on a CSG shape generate a rich network of features on the sweep surface.

02

Deformation over time

The method supports non-rigid motion, including geometry and topology changes throughout the sweep.

03

Feature-preserving output

It produces a watertight mesh while retaining sweep-end features, swept-corner creases, and self-intersections.

Method overview

1

Time-varying CSG

Represent the sweep as a 4D implicit CSG.

2

Lifted envelope

Construct smooth and sharp contour components in space-time.

3

Implicit arrangement

Discretize the intersecting surfaces robustly in 4D.

4

Trimmed sweep surface

Project, trim, and label the final watertight mesh.

Overview of the lifted-envelope construction
Our lifted construction discretizes a CSG sweep in space-time, then projects and trims its envelope to obtain the sweep boundary.

Method comparison

Comparison of sweep surfacing methods on a rolling tetrahedron
Method comparison. Our surface preserves sharp sweep features that prior methods either smooth away or only partially retain.

Results gallery

Results rotate automatically. Use the controls to browse manually, or click any figure to open it at its original resolution.

Sweep-end featuresIn-sweep featuresEnvelope self-intersections
Sweep of a deforming CAD-like CSG shape

Deforming CAD-like shape. A piecewise-smooth solid undergoes non-rigid motion while its feature curves are recovered.

Feature-aware sweep surface of a deforming cube

Twisting cube. Sharp features on the resulting sweep surface are explicitly retained and labeled.

Topology-changing CSG sweep examples

Topology changes. The CSG representation supports sweeps with changing genus and connected components.

Feature-aware sweep example with a complex CSG input

Complex CSG example. Feature curves reveal sweep endpoints, swept corners, and self-intersections.

Sweep surface with sharp feature curves

Sharp-feature sweep. The final watertight mesh retains the underlying piecewise-smooth structure.

Deforming sweep with feature curves

Deforming sweep. The method is applicable to non-rigid CSG motions as well as rigid ones.

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BibTeX

@article{xia2026csg,
  author    = {Xia, J. and Zhou, Q. and Ju, Y. and Du, X.-Y. and Carr, N. and Ju, T.},
  title     = {CSG Sweeps: Feature-aware sweep surfacing of deformable CSGs},
  journal   = {ACM Transactions on Graphics (TOG)},
  year      = {2026},
  publisher = {ACM Digital Library},
  url       = {https://par.nsf.gov/biblio/10708992}
}