D Gaussian Splatting (3DGS) algorithms have gained increasing attention due to their ability to enable realistic 3D scene reconstruction with faster runtime. However, training these models on graphical processing units (GPU) faces unique challenges during the backpropagation stage, primarily due to memory barriers in the execution model, where every pixel within a tile computes the gradient for a single Gaussian per thread. In this paper, we propose the Backward-Striding Optimized Accelerator for 3D Gaussian Splatting (BOA-3DGS), a hardware-software co-optimized accelerator designed to optimize backward rasterization of 3D Gaussian Splatting by enabling pixels to stride through and select only relevant Gaussians for computing. However, such processing styles lead to a large number of memory stalls due to conflicting gradient storage and Gaussian parameter fetches. By introducing a pixel-independent, funnel-like multi-Gaussian alpha computation and a majoritybased gradient accumulation method, we avoid such memory stalls to efficiently accelerate backpropagation of 3DGS. Together, these enhancements improve gradient calculation efficiency and accelerate the backpropagation stage of 3DGS rasterization. Experimental results demonstrate that BOA-3DGS achieves up to $1.58 \times$ speedup during backpropagation compared to prior work, while utilizing only $0.86 \times$ the area and consuming $0.99 \times$ power.

Let $P$ be a convex polyhedron and $Q$ be a convex polygon with $n$ vertices in total in three-dimensional space. We present a deterministic algorithm that finds a translation vector $v \in \mathbb{R}^3$ maximizing the overlap area $|P \cap (Q + v)|$ in $O(n \log^2 n)$ time. We then apply our algorithm to solve two related problems. We give an $O(n \log^3 n)$ time algorithm that finds the maximum overlap area of three convex polygons with $n$ vertices in total. We also give an $O(n \log^2 n)$ time algorithm that minimizes the symmetric difference of two convex polygons under scaling and translation.

We present an algorithm to compute an approximate overlap of two convex polytopes P_1 and P_2 in R^3 under rigid motion. Given any epsilon in (0,1/2], our algorithm runs in O(epsilon^{-3}n log^{3.5}n) time with probability 1 - n^{-O(1)} and returns a (1-epsilon)-approximate maximum overlap, provided that the maximum overlap is at least lambda max(|P_1|,|P_2|) for some given constant lambda in (0,1].