Interface Conic

  • All Superinterfaces:
    CurveSegment, GenericCurve

    public interface Conic
    extends CurveSegment
    Any general conic curve. Any of the conic section curves can be canonically represented in polar co-ordinates (ρ, φ) as:
    Conic curve

    where "P" is semi-latus rectum and "e" is the eccentricity. This gives a conic with focus at the pole (origin), and the vertex on the conic nearest this focus in the direction of the polar axis, φ=0.

    For e=0, this is a circle. For 0 < e < 1, this is an ellipse. For e=1, this is a parabola. For e>1, this is one branch of a hyperbola.

    These generic conics can be viewed in a two-dimensional Cartesian parameter space (uv) given by the usual coordinate conversions u=ρcos(φ) and v=ρsin(φ). We can then convert this to a 3D coordinate reference system by using an affine transformation, (uv) → (xyz) which is defined by:

    (TODO: paste the matrix here, same as AffinePlacement)

    This gives us φ as the constructive parameter. The direct position given by (x₀, y₀, z₀) is the image of the origin in the local coordinate space (u, v) Alternatively, the origin may be shifted to the vertex of the conic as

    u' = ρcos(φ) - P/(1 + e)   and   v' = ρsin(φ)

    and v can be used as the constructive parameter. In general, conics with small eccentricity and small P, use the first or "central" representation. Those with large eccentricity or large P tend to use the second or "linear" representation.

    GeoAPI 1.0
    • Method Detail

      • getPosition

        AffinePlacement getPosition()
        Returns an affine transformation object that maps the conic from parameter space into the coordinate space of the target coordinate reference system of the conic corresponding to the coordinate reference system of the Geometry. This affine transformation is given by the formulae in the class description.
      • isShifted

        boolean isShifted()
        Returns false if the affine transformation is used on the unshifted (u, v) and true if the affine transformation is applied to the shifted parameters (u', v'). This controls whether the focus or the vertex of the conic is at the origin in parameter space.
      • getEccentricity

        double getEccentricity()
        Returns the value of the eccentricity parameter "e" used in the defining equation above. It controls the general shape of the curve, determining whether the curve is a circle, ellipse, parabola, or hyperbola.
      • getSemiLatusRectum

        double getSemiLatusRectum()
        Returns the value of the parameter "P" used in the defining equation above. It controls how broad the conic is at each of its foci.