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Abstract: Current curve smoothing technologies provide a smoothed curve by joining together separate curves that have certain degrees of continuity at junctions. These technologies have found many applications in science and engineering. However, none of them can provide a smoothed curve using a single continuous function for arbitrary segmental curves. This paper reports a new approach that can be used to construct a single continuous function that joins an arbitrary number of different segmental curves, with the required degree of continuity at all junctions. The smoothness of transition at different junctions can be controlled by separate parameters to suit different needs. The combined continuous function can approach the original segmental functions asymptotically or match the original segmental functions “exactly” inside each segment by adjusting the smoothness parameter. This new approach may also find application outside the scope of curve smoothing/curving fitting in the future.

This work developed a new curve smoothing technology using a single continuous function for arbitrary segmental curves. The single continuous function has required degree of continuity at all junctions, which can be controlled by separate parameters for different demands. This new approach is significantly important in the field of the constitutive relations of materials in civil engineering, since the constitutive relations of materials always consist of segmental curves. The smoothness of the single continuous function at all junctions for the constitutive relation is also significant for numerical application.

连续函数式曲线光滑法

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