Parallel coordinates have been widely applied to visualize high-dimensional and multivariate data, discerning patterns within the data through visual clustering. However, the effectiveness of this technique on large data is reduced by edge clutter. In this paper, we present a novel framework to reduce edge clutter, consequently improving the effectiveness of visual clustering. We exploit curved edges and optimize the arrangement of these curved edges by minimizing their curvature and maximizing the parallelism of adjacent edges. The overall visual clustering is improved by adjusting the shape of the edges while keeping their relative order. The experiments on several representative datasets demonstrate the effectiveness of our approach.