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Full-Text Articles in Physical Sciences and Mathematics
Calculating Ellipse Overlap Areas, Gary Hughes, Mohcine Chraibi
Calculating Ellipse Overlap Areas, Gary Hughes, Mohcine Chraibi
Gary B. Hughes
We present an approach for finding the overlap area between two ellipses that does not rely on proxy curves. The Gauss-Green formula is used to determine a segment area between two points on an ellipse. Overlap between two ellipses is calculated by combining the areas of appropriate segments and polygons in each ellipse. For four of the ten possible orientations of two ellipses, the method requires numerical determination of transverse intersection points. Approximate intersection points can be determined by solving the two implicit ellipse equations simultaneously. Alternative approaches for finding transverse intersection points are available using tools from algebraic geometry, …
Modern Spectral Climate Patterns In Rhythmically Deposited Argillites Of The Gowganda Formation (Early Proterozoic), Southern Ontario, Canada, Gary B. Hughes, Robert Giegengack, Haralambos N. Kritikos
Modern Spectral Climate Patterns In Rhythmically Deposited Argillites Of The Gowganda Formation (Early Proterozoic), Southern Ontario, Canada, Gary B. Hughes, Robert Giegengack, Haralambos N. Kritikos
Gary B. Hughes
Rhythmically deposited argillites of the Gowganda Formation (ca. 2.0–2.5 Ga) probably formed in a glacial setting. Drop stones and layered sedimentary couplets in the rock presumably indicate formation in a lacustrine environment with repeating freeze–thaw cycles. It is plausible that temporal variations in the thickness of sedimentary layers are related to interannual climatic variability, e.g. average seasonal temperature could have influenced melting and the amount of sediment source material carried to the lake. A sequence of layer couplet thickness measurements was made from high-resolution digitized photographs taken at an outcrop in southern Ontario, Canada. The frequency spectrum of thickness measurements …