org.opengis.geometry.coordinate

Interface Conic

All Superinterfaces:

CurveSegment, GenericCurve

@UML(identifier="GM_Conic",
     specification=ISO_19107)
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:

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 (u, v) 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, (u, v) → (x, y, z) 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.

Since:

GeoAPI 1.0

Author:

Martin Desruisseaux (IRD)

Method Summary

Modifier and Type	Method and Description
double	getEccentricity() Returns the value of the eccentricity parameter "e" used in the defining equation above.
double	getEndConstructiveParam() Return the end point parameter used in the constructive paramerization.
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.
double	getSemiLatusRectum() Returns the value of the parameter "P" used in the defining equation above.
double	getStartConstructiveParam() Return the start point parameter used in the constructive paramerization.
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').

Methods inherited from interface CurveSegment

getBoundary, getCurve, getInterpolation, getNumDerivativesAtEnd, getNumDerivativesAtStart, getNumDerivativesInterior, getSamplePoints, reverse

Methods inherited from interface GenericCurve

asLineString, forConstructiveParam, forParam, getEndParam, getEndPoint, getParamForPoint, getStartParam, getStartPoint, getTangent, length, length

Method Detail

getPosition

@UML(identifier="position",
     obligation=MANDATORY,
     specification=ISO_19107)
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

@UML(identifier="shifted",
     obligation=MANDATORY,
     specification=ISO_19107)
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

@UML(identifier="eccentricity",
     obligation=MANDATORY,
     specification=ISO_19107)
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

@UML(identifier="semiLatusRectum",
     obligation=MANDATORY,
     specification=ISO_19107)
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.

getStartConstructiveParam

@UML(identifier="startConstrParam",
     obligation=MANDATORY,
     specification=ISO_19107)
double getStartConstructiveParam()

Return the start point parameter used in the constructive paramerization. The following relation must be hold:

forConstructiveParam(getStartConstructiveParam()) .equals( getStartPoint() )

There is no assumption that the start constructive parameter is less than the end constructive parameter, but the parameterization must be strictly monotonic (strictly increasing, or strictly decreasing).

Specified by:

getStartConstructiveParam in interface GenericCurve

Returns:

The parameter used in the constructive paramerization for the start point.

See Also:

GenericCurve.getStartParam(), GenericCurve.getEndConstructiveParam(), GenericCurve.forConstructiveParam(double)

getEndConstructiveParam

@UML(identifier="endConstrParam",
     obligation=MANDATORY,
     specification=ISO_19107)
double getEndConstructiveParam()

Return the end point parameter used in the constructive paramerization. The following relation must be hold:

forConstructiveParam(getEndConstructiveParam()) .equals( getEndPoint() )

There is no assumption that the start constructive parameter is less than the end constructive parameter, but the parameterization must be strictly monotonic (strictly increasing, or strictly decreasing).

Specified by:

getEndConstructiveParam in interface GenericCurve

Returns:

The parameter used in the constructive paramerization for the end point.

See Also:

GenericCurve.getEndParam(), GenericCurve.getStartConstructiveParam(), GenericCurve.forConstructiveParam(double)