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The boundary representation (B-rep) models a 3D solid as its explicit boundaries: trimmed corners, edges, and faces. Recovering B-rep representation from unstructured data is a challenging and valuable task of computer vision and graphics. Recent advances in deep learning have greatly improved the recovery of 3D shape geometry, but still depend on dense and clean point clouds and struggle to generalize to novel shapes. We propose B-rep Gaussian Splatting (BrepGaussian), a novel framework that learns 3D parametric representations from 2D images. We employ a Gaussian Splatting renderer with learnable features, followed by a specific fitting strategy. To disentangle geometry reconstruction and feature learning, we introduce a two-stage learning framework that first captures geometry and edges and then refines patch features to achieve clean geometry and coherent instance representations. Extensive experiments demonstrate the superior performance of our approach to state-of-the-art methods. We will release our code and datasets upon acceptance.