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This paper presents a new interactive rendering and display technique for complex scenes with expensive shading, such as global illumination. Our approach combines sparsely sampled shading (points) and analytically computed discontinuities (edges) to interactively generate high-quality images. The edge-and-point image is a new compact representation that combines edges and points such that fast, table-driven interpolation of pixel shading from nearby point samples is possible, while respecting discontinuities.The edge-and-point renderer is extensible, permitting the use of arbitrary shaders to collect shading samples. Shading discontinuities, such as silhouettes and shadow edges, are found at interactive rates. Our software implementation supports interactive navigation and object manipulation in scenes that include expensive lighting effects (such as global illumination) and geometrically complex objects. For interactive rendering we show that high-quality images of these scenes can be rendered at 8--14 frames per second on a desktop PC: a speedup of 20--60 over a ray tracer computing a single sample per pixel.