دانلود رایگان مقاله بازسازی مارپیچها از طرح متعامد آنها

Abstract

We describe a method for modeling helices from planar curves. Given a polygonal curve in the (x,y) plane, the method computes a helix such that its orthogonal projection onto the (x,y) plane fits the polygonal curve. The helix curve is first sampled and the transformation matrix that best aligns points of the sampled helix to those of the polygonal curve is calculated. This transformation matrix is then used to estimate the parameters of the helix whose projection fits the polygonal curve.

7.4. Robustness with respect to coarse sampling

In this section, we analyze the performances of our algorithm for input curves with different levels of sampling and different level of noises. The input curve C is generated by orthogonally projecting a helix curve whose radius r, pitch p, endpoint parameter α (i.e. length of the curve) and rotation angle with respect to the x-axis θx are 2, 1, π and 0.8 respectively. The number of points has been set to 80, 40, 20, 10 and 5 for C1, C2, C3, C4 and C5 respectively. The helix fitting has been computed twice for each of these curves, the first time without noise (first row of Fig. 12) and the second time with uniform noises (second row of Fig. 12). As one may observe, our algorithm successfully computes the fitting of the helix; the fitting error remains small even for the curve C5 which has 5 points only. On the other hand, our algorithm fails to compute the rotation angle θx of C5; its value is 0.006 and it should be 0.8. This is because C5 has so few points that some of the curve details are missing. In particular, C5 does not show the curve loop which is visible in other curves C1 to C4.