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Methods of Spatial Visualisation
Published in Ken Morling, Stéphane Danjou, Geometric and Engineering Drawing, 2022
An ellipse is the locus of a point that moves so that its distance from a fixed point (called the focus) bears a constant ratio, always less than 1, to its perpendicular distance from a straight line (called the directrix). An ellipse has two foci and two directrices.
In-Process Measurement in Manufacturing Processes
Published in Wasim Ahmed Khan, Ghulam Abbas, Khalid Rahman, Ghulam Hussain, Cedric Aimal Edwin, Functional Reverse Engineering of Machine Tools, 2019
Ahmad Junaid, Muftooh Ur Rehman Siddiqi, Riaz Mohammad, Muhammad Usman Abbasi
Specifies the eccentricity of the ellipse. The eccentricity is the ratio of the distance between the foci of the ellipse and its major axis length. The value is between 0 and 1. An ellipse with 0 eccentricity is a circle, while an ellipse whose eccentricity is 1 is a line segment.
Geometric Shape Features
Published in Jyotismita Chaki, Nilanjan Dey, A Beginner’s Guide to Image Shape Feature Extraction Techniques, 2019
Jyotismita Chaki, Nilanjan Dey
Eccentricity is the calculation of aspect ratio. It is basically the major axis length to the minor axis length ratio, thus, though the image is rotated, scaled, or translated, eccentricity remains identical [5]. Eccentricity returns a scalar that denotes the eccentricity of the ellipse that has the same second-moments as the region. The eccentricity is the ratio of the distance among the foci of the ellipse and its major axis length. The value is between 0 and 1. (0 and 1 are degenerate cases. An ellipse whose eccentricity is 0 is actually a circle, while an ellipse whose eccentricity is 1 is a line segment.) It can be computed by minimum bounding rectangle or principal axes technique.
Camera calibration method based on circular array calibration board
Published in Systems Science & Control Engineering, 2023
Haifeng Chen, Jinlei Zhuang, Bingyou Liu, Lichao Wang, Luxian Zhang
Eccentricity is the degree to which a conic deviate from an ideal circle. The eccentricity of an ideal circle is 0, so the eccentricity represents how different the curve is from the circle. The greater the eccentricity, the less camber of the curve. Among them, an ellipse with an eccentricity between 0 and 1 is an ellipse, and an eccentricity equal to 1 is a parabola. Given that directly calculating the eccentricity of a graphic is complicated, the concept of image moment can be used to calculate the inertial rate of the graphic, and then the eccentricity can be calculated from the inertial rate. The relationship between the eccentricity and the inertia rate is: In the formula, the eccentricity of the circle is equal to 0, and the inertia rate is equal to 1. The closer the inertia rate is to 1, the higher the degree of the circle. Convexity
Non-equivalent notions of the eccentricity of the conics: an exploratory study with high school teachers
Published in International Journal of Mathematical Education in Science and Technology, 2023
Antonio Rivera-Figueroa, Ernesto Bravo-Díaz
The BA is one where the circle is the locus in the plane of the points whose distance from a fixed point F is a constant. The point F is called the centre of the circle, and the distance from either point of the circle to the centre is called the circle's radius. The parabola is the locus of points in the plane whose distance from a fixed point F equals their distance from a fixed line l. Point F is called the parabola's focus, and line l is called the directrix of the parabola. The ellipse and the hyperbola are defined by two foci. The ellipse is the locus of points such that the sum of their distances from two fixed points is a constant, and the hyperbola is the locus of points such that the positive difference between their distances from two fixed points is a constant. In both cases, the fixed points, and , are called foci of the curves (Figure 1), and the respective constant is called the constant of the curve. The eccentricity of the ellipse is the quotient where c is the semi-distance between the foci, and a is the length of the semi-major axis (see, e.g. Larson & Edwards, 2010, p. 701; Lehmann, 1964, p. 176; Rider, 1947, p. 120; Simmons, 1996, p. 536). Some authors allow the equality , in which case c has the value zero and, consequently, e is also zero, and the locus is a circle. In this regard, Rider (1947) comments, ‘the circle can be considered an ellipse whose eccentricity is zero’ (p. 121), while Apostol (1966, p. 498), without alluding to eccentricity, points out that ‘if the foci coincide, the ellipse is reduced to a circle’. Other authors (e.g. Hahn, 1998) allow the equality , so we have e = 1, and ‘the ellipse consists of points on the segment ’ (p. 91). The eccentricity e of the hyperbola is the same quotient , where now c is the semi-distance between the foci and a is the length of the transverse semiaxis of the hyperbola (Larson & Edwards, 2010, p. 704; Lehmann, 1964, p. 176; Rider, 1947, p. 132; Simmons, 1996, p. 545). Since , we have . In the bifocal approach, the authors generally do not assign the value to any curve; in particular, it is not assigned to the parabola.