Distance from a Point to an Ellipse, an Ellipsoid, or a Hyperellipsoid
نویسنده
چکیده
2 Distance from a Point to an Ellipse 3 2.1 The Closest Point’s Normal is Directed Toward the Query Point . . . . . . . . . . . . . . . . 3 2.2 The Case of a Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 The Query Point is the Origin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 The Query Point is on the Vertical Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.5 The Query Point is on the Horizontal Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.6 The Query Point is Strictly in the First Quadrant . . . . . . . . . . . . . . . . . . . . . . . . 5 2.7 A Summary of the Mathematical Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.8 Robust Root Finders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.8.1 Bisection Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.8.2 Newton’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.8.3 Conversion to a Polynomial Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.9 A Robust Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
منابع مشابه
Approximate formulas for the Point-to-Ellipse and for the Point-to-Ellipsoid Distance Problem
We deduce some approximate formulas for the distance evaluation problem between a point and an ellipse in IR2 and a point and an ellipsoid in IR3. The proposed approach is based on the analytical representation of the distance function as a zero of an appropriate univariate algebraic equation. Key–Words: Distance, point-to-ellipse, point-to-ellipsoid
متن کاملList of Files Ellipsoid-cal- Apr22-apr29.tex 2 a Note on Flows of a Second Order Fluid around an Ellipsoid /13pages
No. title/pages date update file name 1 A note on the elliptic integrals and elliptic functions ellipsoid-may04.tex 3 A note on " Potential flow of a second order fluid over a sphere or an ellipse " ellipse-wang-joseph-apr27.tex 4 A note on flows of a second order fluid around an ellipsoid ellipse-may31a.tex 5 A note on flows of a second order fluid around an ellipsoid of revolution/11pages
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