Lines Matching refs:ellipse
38 #include <2geom/ellipse.h>
56 * Elliptical arc is a curve taking the shape of a section of an ellipse.
61 * determines which part of the ellipse forms the arc. The arc is said to contain an angle
64 * The angular domain considers each ellipse to be
73 * where \f$r_X, r_Y\f$ are the X and Y rays of the ellipse, \f$\theta\f$ is its angle of rotation,
74 * and \f$c_X, c_Y\f$ the coordinates of the ellipse's center - thus mapping the angle
75 * to some point on the ellipse. Note that for example the point at angluar coordinate 0,
77 * create an angle of \f$\pi/4\f$ radians; it is only the case if both axes of the ellipse
80 * @image html ellipse-angular-coordinates.png "An illustration of the angular domain"
82 * Each arc is defined by five variables: The initial and final point, the ellipse's rays,
83 * and the ellipse's rotation. Each set of those parameters corresponds to four different arcs,
84 * with two of them larger than half an ellipse and two of them turning clockwise while traveling
98 * are either the endpoints or local minima / maxima of the ellipse.
110 * and if they do, we evaluate the ellipse at these angles.
234 // D(E(t,C),t) = E(t+PI/2,O), where C is the ellipse center
235 // the derivative doesn't rotate the ellipse but there is a translation
236 // of the parameter t by an angle of PI/2 so the ellipse points are shifted
415 // on the ellipse E wrt the point p
684 // If the ellipse was enlarged, c will be zero - this is correct.
726 // without passing through the implicit form of the ellipse,
775 // ellipse transformation does not preserve its functional form,
788 // TODO: all arcs with ellipse rays which are too small