Since the horizontal axis of the residual graph (bar {Q}_{alpha }= alpha, e_{alpha })^{top }) is an index of the input point sequence, the computed error curvature depends on the scale of the horizontal axis of the residual graph.
As shown in the simulation, the contour error, curvature of tool path, feedrate fluctuation and machining time are reduced compared with G2 transition scheme.
For this reason, in the first iteration of our algorithm, we select among the arcs that are sufficiently long the one whose error curvature ϕ at its peak point is the smallest.
(b) Select the arcs whose error curvature ϕs are smaller than a threshold (hat {phi }) 3 and fit an ellipse to them. 5.
We compute the variation of the tangent angle to the graph of the fitting residual, which we simply call "error curvature" in this paper, and judge if each arc is an inlier or an outlier based on this "error curvature".
Therefore, we normalize the scale of the horizontal axis of the residual graph in the form boldsymbol{Q}_{alpha} = left(frac{lambda e_{text{max}}alpha}{N}, e_{alpha}right)^{top}, (11) Fig. 3 Error curvature ϕ of the peak point α ∗ for a partial arc.
For each segmented arc, detect the point where the residual value takes a maximum and compute its error curvature ϕ at this point.
After segmenting the point sequence, we detect the point α ∗ where the fitting residual takes its maximum and compute its error curvature at this point by using its neighboring points β and γ (Fig. 3).
After the first iteration, we select all arcs whose error curvature ϕs are smaller than a threshold (hat {phi }).
From these results, we could confirm that our method could select inlier arcs by repeating inlier selection based on an error curvature and ellipse fitting.
