Interface Curve

  • All Superinterfaces:
    GenericCurve, Geometry, OrientableCurve, OrientablePrimitive, Primitive, TransfiniteSet

    public interface Curve
    extends OrientableCurve, GenericCurve
    Curve with a positive orientation. Curve is a descendent subtype of Primitive through OrientablePrimitive. It is the basis for 1-dimensional geometry. A curve is a continuous image of an open interval and so could be written as a parameterized function such as c(t):(a, b) → Eⁿ where "t" is a real parameter and Eⁿ is Euclidean space of dimension n (usually 2 or 3, as determined by the coordinate reference system). Any other parameterization that results in the same image curve, traced in the same direction, such as any linear shifts and positive scales such as e(t) = c(a + t(b-a)):(0,1) → Eⁿ, is an equivalent representation of the same curve. For the sake of simplicity, Curves should be parameterized by arc length, so that the parameterization operation inherited from GenericCurve will be valid for parameters between 0 and the length of the curve.

    Curves are continuous, connected, and have a measurable length in terms of the coordinate system. The orientation of the curve is determined by this parameterization, and is consistent with the tangent function, which approximates the derivative function of the parameterization and shall always point in the "forward" direction. The parameterization of the reversal of the curve defined by c(t):(a, b) → Eⁿ would be defined by a function of the form s(t) = c(a + b - t):(a, b) → Eⁿ.

    A curve is composed of one or more curve segments. Each curve segment within a curve may be defined using a different interpolation method. The curve segments are connected to one another, with the end point of each segment except the last being the start point of the next segment in the segment list.

    GeoAPI 1.0
    See Also: