Faithfully capturing diverse real-world objects with fuzzy, anisotropic structures—such as hair, fur, fibers, and textiles—for efficient real-time visualization remains challenging. Recent radiance field reconstruction methods capture these structures from multi-view images using translucent volumetric primitives such as 3D Gaussians rather than opaque low-dimensional primitives (e.g., triangles, line segments, and polylines), thereby limiting compatibility with standard depth-tested rasterization, reflection modeling, and physical simulation. We present an inverse rendering method for reconstructing fuzzy geometry using explicit line segments, which are rasterized on a subpixel grid for anti-aliasing to reproduce a semi-transparent appearance. While straightforward to render, optimizing numerous line primitives to match target images poses a significant challenge. We address this by introducing a stochastic differentiable rasterizer for line segments that produces informative gradients with respect to vertex positions, attributes, and discrete connectivity. Experiments on synthetic and real-world datasets show that our method outperforms surface-based approaches in capturing fuzzy boundaries and achieves quality comparable to volumetric representations while relying entirely on explicit geometry. The resulting representation integrates seamlessly with standard graphics pipelines, enabling cross-platform rendering, various shading models, and physical simulation.