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We present Confetti, a novel point-based rendering approach based on object-space point interpolation of densely sampled surfaces. We introduce the concept of a transformation-invariant covariance matrix of a set of points which can efficiently be used to determine splat sizes in a multiresolution point hierarchy. We also analyze continuous point interpolation in object-space and we define a new class of parameterized blending kernels as well as a normalization procedure to achieve smooth blending. Furthermore, we present a hardware accelerated rendering algorithm based on texture mapping and α-blending as well as programmable vertex and pixel-shaders.