| Summary: | A curve with single-signed, monotonically increasing or decreasing curvatures is referred to as a planar spiral. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>G</mi><mn>2</mn></msup></semantics></math></inline-formula> Hermite data are spiral <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>G</mi><mn>2</mn></msup></semantics></math></inline-formula> Hermite data for which only interpolation by a spiral is possible. In this study, we design segmented spirals to geometrically interpolate arbitrary C-shaped <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>G</mi><mn>2</mn></msup></semantics></math></inline-formula> Hermite data. To separate the data into two or three spiral data sets, we add one or two new points, related tangent vectors and curvatures. We provide different approaches in accordance with the various locations of the external homothetic centers of two end-curvature circles. We then match new data by constructing two or three segmented spirals. We generate at most three piecewise spirals for arbitrary C-shaped data. Furthermore, we illustrate the suggested techniques with several examples.
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