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 requ...

let e be the ellipse with major and minor radii a and b respectively, and pbe its perimeter, then p = lim 4 tan(p/n)(a + b + 2) σ a2 cos2 (2k-2)pi/n+ sin2 (2k-2)pi/n; where n = 2m. so without considering the limit, it gives a reasonable approxi-mation for p, it means that we can choose n large enough such that the amountof error be less than any given small number. on the other hand, the formul...

We describe invariants of centers ellipse-inscribed triangle families with two vertices fixed to the ellipse boundary and a third one which sweeps it. prove that: (i) if center is affine combination barycenter orthocenter, its locus an ellipse; (ii) that over family said combinations, loci sweep line; (iii) parallel vertices, rigidly translate along second line. Additionally, we study envelope ...

1. INTRODUCTION. STANDARD TRAMMEL. Figure 1a shows a line segment of fixed length whose ends slide along two perpendicular axes. It can be realized physically as a sliding ladder or as a sliding door moving with its ends on two perpendicular tracks. During the motion, a fixed point on the segment traces an ellipse with one quarter of the ellipse in each quadrant (Figure 1b), so this device is c...

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

The Löwner-John ellipse of a full-dimensional bounded convex set is a circumscribed ellipse with the property that if we shrink it by a factor n (where n is dimension), we obtain an inscribed ellipse. Goffin’s algorithm constructs, in polynomial time, a tight approximation of the Löwner-John ellipse of a polyhedron given by facet description. In this text we adapt the algorithm for zonotopes gi...

The least squares fitting minimizes the squares sum of error-ofifit in predefined measures. By the geometric fitting, the error distances are defined with the shortest distances from the given points to the geometric feature to be fitted. For the geometric fitting of ellipse, a robust algorithm is proposed. This is based on the coordinate description of the corresponding point on the ellipse fo...

In this paper we present a vision system that performs tracking a human face in 3D. To achieve this we combine color and stereo cues to find likely image regions where face may exist. A greedy search algorithm examines for a face candidate focusing the action around the position of the face which was detected in the previous time step. The aim of the search is to find the best-fit head ellipse....

Although local interactions involving orientation and spatial frequency are well understood, less is known about spatial interactions involving higher level pattern features. We examined interactive coding of aspect ratio, a prevalent two-dimensional feature. We measured perception of two simultaneously flashed ellipses by randomly post-cueing one of them and having observers indicate its aspec...

A novel ellipse fitting method which is selective for digital and noisy elliptic curves is proposed in this paper. The method aims at fitting an ellipse only when the data points are highly likely belong to an ellipse. This is achieved using the geometric distances of the ellipse from the data points. The proposed method models the non-linear problem of ellipse fitting as a combination of two o...