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In this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape. We call the representation the Curvature Primal Sketch because of the close analogy to the primal sketch representation advocated by Marr for describing significant intensity changes. We define a set of primitive parameterized curvature discontinuities, and derive expressions for their convolutions with the first and second derivatives of a Gaussian. We describe an implemented algorithm that computes the Curvature Primal Sketch by matching the multiscale convolutions of a shape, and illustrate its performance on a set of tool shapes. Several applications of the representation are sketched.