# Package org.opengis.geometry.coordinate

Core package needed to investigate coordinate-defined geometry. The following is adapted from OpenGIS® Feature Geometry (Topic 1) specification.

A large number of the geometric types in the ISO 19107 standard are defined parametrically, that is they are represented by functions from a set of parameters (in a parametric space, usually a subset of some Euclidean n-dimensional coordinate space) into a coordinate space of some larger dimension. The first few dimensions (up to 3) representing geographic space, the next possibly time, and any remainder representing whatever the application needs, such as distributed attributes or some other measures. The type of geometry is usually determined by the dimension of the parameter space, which will normally be equal to the topological dimension of the resulting geometry. So a 0- parameter geometric object is a point, 1-parameter geometric object is a curve, a 2-parameter geometric object is a surface, a 3-parameter geometric object is a solid.

An n-dimensional coordinate space consists of all n-long arrays of numbers; each array represents a point in the space. In particular situations, this may be restricted to a subset of such points, called the extent of validity, usually based on a set of constraints on values of the various offsets within the array. Each point is associated to a spatial or spatial-temporal location, but a single location may be the target of multiple coordinate space points. Locations given by such structures are called direct positions.

All locations in a list or array shall use the same coordinate system and shall reference reality in a manner representable by continuous functions from the coordinate tuples (`DirectPosition`s) to reality in such a manner that “nearby” coordinates in the `DirectPosition`s map to “nearby” positions in reality. The ISO 19107 standard does not assume that these functions maintain topological dimension. See for example homogeneous direct position.

Since:
1.0
• Interface Summary
Interface Description
AffinePlacement
A placement defined by linear transformation from the parameter space to the target coordinate space.
Arc
Arc of the circle determined by 3 points, starting at the first, passing through the second and terminating at the third.
ArcByBulge
Equivalents to the `Arc`, except the bulge representation is maintained.
ArcString
Similar to a line string except that the interpolation is by circular arcs.
ArcStringByBulge
A variant of the arc that stores the parameters of the second constructor of the component arcs and recalculates the other attributes of the standard arc.
Bezier
Polynomial splines that use Bezier or Bernstein polynomials for interpolation purposes.
BicubicGrid
A gridded surface that uses cubic polynomial splines as the horizontal and vertical curves.
BilinearGrid
A gridded surface that uses line strings as the horizontal and vertical curves.
BSplineCurve
A piecewise parametric polynomial or rational curve described in terms of control points and basis functions.
BSplineSurface
A rational or polynomial parametric surface that is represented by control points, basis functions and possibly weights.
Circle
Same as an arc, but closed to form a full circle.
Clothoid
The clothoid (or Cornu's spiral), a plane curve whose curvature is a fixed function of its length.
Cone
A gridded surface given as a family of conic sections whose control points vary linearly.
Conic
Any general conic curve.
CoordinateSystem
Organizes the manner in which the direct positions are described.
CubicSpline
Cubic splines.
Cylinder
A gridded surface given as a family of circles whose positions vary along a set of parallel lines, keeping the cross sectional horizontal curves of a constant shape.
GenericCurve
Common interface for curve and curve segment.
GenericSurface
Common interface for surface and surface patch.
Geodesic
Two distinct positions joined by a geodesic curve.
GeodesicString
Sequence of geodesic segments.
GeometryFactory
A factory of geometries.
GriddedSurface
A parametric curve surface defined from a rectangular grid in the parameter space.
HomogeneousDirectPosition
A direct position adding another element to the coordinate array which carries a non-zero “weight”, and multiplies all other columns in the coordinate array by that weight.
Knot
Controls the constructive parameter space for spline curves and surfaces.
LineSegment
Two distinct direct positions (the start point and end point) joined by a straight line.
LineString
A sequence of line segments, each having a parameterization like the one `LineSegment`.
OffsetCurve
A curve at a constant distance from the basis curve.
Parameterization
A locally bi-continuous mapping from a domain coordinate system to a range coordinate system.
ParametricCurveSurface
The surface patches that make up the parametric curve surfaces.
ParamForPoint
The curve parameter for a point.
Permutation
Represents the rearrangement of a list, or a projection.
Placement
Takes a standard geometric construction and places it in geographic space.
PointArray
A sequence of points.
PointGrid
A grid of points.
Polygon
A surface patch that is defined by a set of boundary curves and an underlying surface to which these curves adhere.
PolyhedralSurface
A surface composed of polygon surfaces connected along their common boundary curves.
PolynomialSpline
A polynimal spline.
Sphere
A gridded surface given as a family of circles whose positions vary linearly along the axis of the sphere, and whose radius varies in proportion to the cosine function of the central angle.
SplineCurve
Root for subtypes of curve segment using some version of spline, either polynomial or rational functions.
Tin
A triangulated surface that uses the Delaunay algorithm or a similar algorithm complemented with consideration for breaklines, stoplines and maximum length of triangle sides.
Triangle
A planar polygon defined by 3 corners.
TriangulatedSurface
A polyhedral surface that is composed only of triangles.
• Class Summary
Class Description
BSplineSurfaceForm
Indicates a particular geometric form represented by a `BSplineSurface`.
Handed
Labels coordinate systems as being right or left handed as commonly defined in Mathematics.
KnotType
The type of a B-spline.
SplineCurveForm
Indicates which sort of curve may be approximated by a particular B-spline.