org.tinfour.interpolation

Class NaturalNeighborInterpolator

java.lang.Object

org.tinfour.interpolation.NaturalNeighborInterpolator

All Implemented Interfaces:

IProcessUsingTin, IInterpolatorOverTin

public class NaturalNeighborInterpolator
extends Object
implements IInterpolatorOverTin

Provides interpolations based on Sibson's Natural Neighbor Interpolation method. See Sibson, Robin, "A Brief Description of Natural Neighbor Interpolation". Interpreting Multivariate Data. Ed. Barnett, Vic. England. John Wiley & Sons (1981).

Constructor Summary

Constructors

Constructor and Description
NaturalNeighborInterpolator(IIncrementalTin tin) Construct an interpolator that operates on the specified TIN.

Method Summary

Modifier and Type	Method and Description
double	getBarycentricCoordinateDeviation() Gets the deviation of the computed equivalent of the input query (x,y) coordinates based on barycentric coordinates.
double[]	getBarycentricCoordinates(List<IQuadEdge> polygon, double x, double y) Given a reference point inside a simple, but potentially non-convex polygon, creates an array of barycentric coordinates for the point.
List<IQuadEdge>	getBowyerWatsonPolygon(double x, double y) Gets a list of edges for the polygonal cavity that would be created as part of the Bowyer-Watson insertion algorithm.
List<IQuadEdge>	getConnectedPolygon(IQuadEdge e) Gets a polygon consisting of edges connected to the specified edge (in effect providing the set of vertices connected to the starting vertex of the specified edge).
String	getMethod() Gets a string describing the interpolation method that can be used for labeling graphs and printouts.
double[]	getSurfaceNormal() Gets the unit normal to the surface at the position of the most recent interpolation.
double	interpolate(double x, double y, IVertexValuator valuator) Perform interpolation using Sibson's C0 method.
double	interpolateUsingTestMethod(double x, double y, IVertexValuator valuator) Perform interpolation using Sibson's C0 method and a test algorithm based on computing the barycentric coordinates rather than through the circumcenter approach used for the original interpolation method.
boolean	isSurfaceNormalSupported() Indicates whether the interpolation class supports the computation of surface normals through the getUnitNormal() method.
void	resetForChangeToTin() Used by an application to reset the state data within the interpolator when the content of the TIN may have changed.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

NaturalNeighborInterpolator

public NaturalNeighborInterpolator(IIncrementalTin tin)

Construct an interpolator that operates on the specified TIN. Because the interpolator will access the TIN on a read-only basis, it is possible to construct multiple instances of this class and allow them to operate in parallel threads.

Important Synchronization Issue

To improve performance, the classes in this package frequently maintain state-data about the TIN that can be reused for query to query. They also avoid run-time overhead by not implementing any kind of Java synchronization or or even the concurrent-modification testing provided by the Java collection classes. If an application modifies the TIN, instances of this class will not be aware of the change. In such cases, interpolation methods may fail by either throwing an exception or, worse, returning an incorrect value. The onus is on the calling application to manage the use of this class and to ensure that no modifications are made to the TIN between interpolation operations. If the TIN is modified, the internal state data for this class must be reset using a call to resetForChangeToTIN().

Parameters:

tin - a valid instance of an incremental TIN.

Method Detail

resetForChangeToTin

public void resetForChangeToTin()

Used by an application to reset the state data within the interpolator when the content of the TIN may have changed. Reseting the state data unnecessarily may result in a minor performance reduction when processing a large number of interpolations, but is otherwise harmless.

Specified by:

resetForChangeToTin in interface IProcessUsingTin

interpolate

public double interpolate(double x,
                          double y,
                          IVertexValuator valuator)

Perform interpolation using Sibson's C0 method. This interpolation develops a continuous surface, and provides first derivative continuity at all except the input vertex points.

The domain of the interpolator is limited to the interior of the convex hull. Methods for extending to the edge of the TIN or beyond are being investigated.

The interpolation is treated as undefined at points that lie directly on a constrained edge.

Specified by:

interpolate in interface IInterpolatorOverTin

Parameters:

x - the x coordinate for the interpolation point

y - the y coordinate for the interpolation point

valuator - a valid valuator for interpreting the z value of each vertex or a null value to use the default.

Returns:

if the interpolation is successful, a valid floating point value; otherwise, a Double.NaN.

interpolateUsingTestMethod

public double interpolateUsingTestMethod(double x,
                                         double y,
                                         IVertexValuator valuator)

Perform interpolation using Sibson's C0 method and a test algorithm based on computing the barycentric coordinates rather than through the circumcenter approach used for the original interpolation method. This method was developed to test the getBarycentricCoordinates method and investigate replacing the circumcenter method with simpler code. However, the results appear to be slightly less accurate than the original, so further investigation is required.

The domain of the interpolator is limited to the interior of the convex hull. Methods for extending to the edge of the TIN or beyond are being investigated.

Parameters:

x - the x coordinate for the interpolation point

y - the y coordinate for the interpolation point

valuator - a valid valuator for interpreting the z value of each vertex or a null value to use the default.

Returns:

if the interpolation is successful, a valid floating point value; otherwise, a NaN.

getBarycentricCoordinateDeviation

public double getBarycentricCoordinateDeviation()

Gets the deviation of the computed equivalent of the input query (x,y) coordinates based on barycentric coordinates. As a byproduct, Sibson's method can be used to compute the coordinates of the query point by combining the normalized interpolating weights with the coordinates of the vertices. The normalized weights are, in fact, Barycentric Coordinates for the query point. While the computed equivalent should be an exact match for the query point, errors in implementation or numeric errors due to float-point precision limitations would result in a deviation. Thus, this method provides a diagnostic on the most recent interpolation. A large non-zero value indicates a potential implementation problem. A small non-zero value indicates an error due to numeric issues.

Returns:

a positive value, ideally zero but usually a small number slightly larger than that.

getBowyerWatsonPolygon

public List<IQuadEdge> getBowyerWatsonPolygon(double x,
                                              double y)

Gets a list of edges for the polygonal cavity that would be created as part of the Bowyer-Watson insertion algorithm. If the list is empty, it indicates that TIN was not bootstrapped or the query was to the exterior of the TIN.

Parameters:

x - A Cartesian coordinate in the coordinate system used for the TIN

y - A Cartesian coordinate in the coordinate system used for the TIN

Returns:

a valid, potentially empty, list.

getMethod

public String getMethod()

Description copied from interface: IInterpolatorOverTin

Gets a string describing the interpolation method that can be used for labeling graphs and printouts. Because this string may be used as a column header in a table, its length should be kept short.

Specified by:

getMethod in interface IInterpolatorOverTin

Returns:

A valid string

isSurfaceNormalSupported

public boolean isSurfaceNormalSupported()

Description copied from interface: IInterpolatorOverTin

Indicates whether the interpolation class supports the computation of surface normals through the getUnitNormal() method.

Specified by:

isSurfaceNormalSupported in interface IInterpolatorOverTin

Returns:

true if the class implements the ability to compute surface normals; otherwise, false.

getSurfaceNormal

public double[] getSurfaceNormal()

Gets the unit normal to the surface at the position of the most recent interpolation. The unit normal is computed based on the partial derivatives of the surface polynomial evaluated at the coordinates of the query point. Note that this method assumes that the vertical and horizontal coordinates of the input sample points are isotropic.

NOT COMPLETELY TESTED AND VERIFIED YET. WHen I visually inspect the results, the surface appears to be unexpectedly blurred and flattened. At the very least, I think a code review is required to determine whether the implementation is correct or if the behavior I am seeing is just the way the algorithm works.

Specified by:

getSurfaceNormal in interface IInterpolatorOverTin

Returns:

if defined, a valid array of dimension 3 giving the x, y, and z components of the unit normal, respectively; otherwise, a zero-sized array.

getConnectedPolygon

public List<IQuadEdge> getConnectedPolygon(IQuadEdge e)

Gets a polygon consisting of edges connected to the specified edge (in effect providing the set of vertices connected to the starting vertex of the specified edge). The polygon is ordered in counterclockwise order.

Parameters:

e - the starting edge

Returns:

a valid list of edges (some of which may be perimeter or ghost edges).

getBarycentricCoordinates

public double[] getBarycentricCoordinates(List<IQuadEdge> polygon,
                                          double x,
                                          double y)

Given a reference point inside a simple, but potentially non-convex polygon, creates an array of barycentric coordinates for the point. The coordinates are normalized, so that their sum is 1.0. This method populates the barycentric deviation member element which may be used as a figure of merit for evaluating the success of the coordinate computation. If the point is not inside the polygon or if the polygon is self-intersecting, the results are undefined and the method may return a null array or a meaningless result. If the point is on the perimeter of the TIN, this method will return a null array.

Parameters:

polygon - list of edges defining a non-self-intersecting, potentially non-convex polygon.

x - the x coordinate of the reference point

y - the y coordinate of the reference point

Returns:

if successful, a valid array; otherwise a null.