Our paper, “Lightweight Implicit Approximation of the Minkowski Sum of an N-Dimensional Ellipsoid and Hyperrectangle”, has been accepted as a feature paper in MDPI Mathematics.
In this paper, we present a non-iterative and GPU-friendly method to approximate the Minkowski sum of an N-dimensional ellipsoid and a hyperrectangle. This operation is increasingly relevant in modern computer graphics, particularly with the rise of ellipsoid-based techniques such as Gaussian splatting. Our approach is particularly well-suited for performance-critical applications, e.g., during rasterization of 3D Gaussian Splats.
The proposed method:
- Constructs two oriented bounding boxes: one aligned with the standard coordinate axes, and another aligned with the principal axes of the ellipsoid.
- Defines the approximation as the intersection of these two boxes, guaranteeing full coverage of the true Minkowski sum.
- Is represented implicitly via 2N linear inequalities, enabling extremely fast inclusion tests.
- Outperforms traditional outer ellipsoid approximations in terms of tightness.
Read the full paper: Lightweight Implicit Approximation of the Minkowski Sum of an N-Dimensional Ellipsoid and Hyperrectangle
