jwo.landserf.structure
Class Quadratic

java.lang.Object
  |
  +--jwo.landserf.structure.Quadratic

public class Quadratic

extends Object

Class for fitting a Quadratic surface through a local window of values. Uses least squares found through LU decomposition to calculate the 6 coefficients that represent the surface.

Version:

1.8.0, 6th June, 2000.

Author:

Jo Wood

Field Summary

static int	CIRCULAR Circular elliptic section.
static int	ELLIPTIC Elliptic conic section.
static int	HORIZONTAL Horizontal, planar conic section.
static int	HYPERBOLIC Hyperbolic conic section.
static int	PARABOLIC Parabolic conic section.
static int	PLANAR Sloping planar conic section.

Constructor Summary

Quadratic(float[] x, float[] y, float cx, float cy, float radius, double decayExp)
Solves the best-fit quadratic surface for a given set of coordinates.

Quadratic(int wSize, double gSize)
Creates the normal equations used to calculate the quadratic coefficients.

Quadratic(int wSize, double gSize, double decayExp)
Creates the normal equations used to calculate the quadratic coefficients.

Method Summary

float[]	getCoeff(float[] zCoords) Returns the 6 quadratic coefficients for a given set of irregular points.
float[]	getCoeff(float[][] window) Returns the 6 quadratic coefficients.
FeatureAxis[]	getIntersections() Returns an array of axis objects containing the principal axes of any surface feature and the region of interest.
float	getMeanResidual(float[] coeff, float[][] window) Returns weighted Root Mean Squared residuals for a given set of quadratic coefficients and local window.
double	getPointConfidence() Reports the confidence of point classification (pits, peaks, passes).
int	getType(float[] coeff) Returns the type of conic section represented by the quadratic.
double	getXCentre() Returns the x coordinate of the point of inflection of the quadratic.
double	getYCentre() Returns the y coordinate of the point of inflection of the quadratic.
float	getZ(float[][] window, float xOffset, float yOffset) Reports the height at a given offset from the centre of the quadratic surface.

Methods inherited from class java.lang.Object

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

Field Detail

HORIZONTAL

public static final int HORIZONTAL

Horizontal, planar conic section.

See Also:

Constant Field Values

PLANAR

public static final int PLANAR

Sloping planar conic section.

See Also:

Constant Field Values

PARABOLIC

public static final int PARABOLIC

Parabolic conic section.

See Also:

Constant Field Values

ELLIPTIC

public static final int ELLIPTIC

Elliptic conic section.

See Also:

Constant Field Values

CIRCULAR

public static final int CIRCULAR

Circular elliptic section.

See Also:

Constant Field Values

HYPERBOLIC

public static final int HYPERBOLIC

Hyperbolic conic section.

See Also:

Constant Field Values

Constructor Detail

Quadratic

public Quadratic(int wSize,
                 double gSize)

Creates the normal equations used to calculate the quadratic coefficients. These values remain constant for any single window size and distance decay function. Assumes no distance decay away from central cell.

Parameters:

wSize - Size of local window (odd only).

gSize - Size of 1 grid cell (resolution).

Quadratic

public Quadratic(int wSize,
                 double gSize,
                 double decayExp)

Creates the normal equations used to calculate the quadratic coefficients.

Parameters:

wSize - Size of local window (odd only).

gSize - Size of 1 grid cell (resolution).

decayExp - Distance decay exponent (0 no decay, 1 linear distance decay, 2 distance squared decay etc.)

Quadratic

public Quadratic(float[] x,
                 float[] y,
                 float cx,
                 float cy,
                 float radius,
                 double decayExp)

Solves the best-fit quadratic surface for a given set of coordinates. Must supply at least 6 coordinate triplets for the surface to be solved.

Parameters:

x - Array of at least 6 x coordinates.

y - Array of at least 6 y coordinates.

cx - x coordinate of centre point of function.

cy - y coordinate of centre point of function.

radius - Radius of interest for feature classification (equivalent to grid size for raster processing).

decayExp - Distance decay exponent(0 no decay, 1 linear distance decay, 2 distance squared decay etc.)

Method Detail

getCoeff

public float[] getCoeff(float[][] window)

Returns the 6 quadratic coefficients.

Parameters:

window - Array holding local window values.

Returns:

Vector containting the 6 quadratic coefficients.

getCoeff

public float[] getCoeff(float[] zCoords)

Returns the 6 quadratic coefficients for a given set of irregular points. The list of z coordinates must match the x and y coordinates supplied when constructing this object and must contain at least 6 values.

Parameters:

zCoords - list of z coordinates defining surface heights.

Returns:

Vector containting the 6 quadratic coefficients.

getZ

public float getZ(float[][] window,
                  float xOffset,
                  float yOffset)

Reports the height at a given offset from the centre of the quadratic surface. Note that the coordinate system relative to the centre of the window and is dependent on the grid resolution.

Parameters:

window - Array holding the local window values.

xOffset - Offset from the centre in the x direction.

yOffset - Offset from the centre in the y direction (positive values below the centre, negative values above.

Returns:

Height at given offset.

getMeanResidual

public float getMeanResidual(float[] coeff,
                             float[][] window)

Returns weighted Root Mean Squared residuals for a given set of quadratic coefficients and local window.

Parameters:

coeff - Array holding the 6 quadratic coefficients.

window - Array holding local window values.

Returns:

Weighted RMS quadratic residuals.

getType

public int getType(float[] coeff)

Returns the type of conic section represented by the quadratic. This will be one of PARABOLIC, ELLIPTIC, or HYPERBOLIC, or one of the special cases, HORIZONTAL, PLANAR or CIRCULAR.

Parameters:

coeff - Array holding the 6 quadratic coefficients.

Returns:

Type of conic section represented by the quadratic.

getIntersections

public FeatureAxis[] getIntersections()

Returns an array of axis objects containing the principal axes of any surface feature and the region of interest. Contains between 0 and 2 axes depending on the surface feature. HORIZONTAL and CIRCULAR surfaces contain no intersections; PLANAR surfaces contain one (in the aspect direction); PARABOLIC surfaces contain one (along the channel/ridge axis); ELLIPTIC and HYPERBOLIC surfaces contain two (along the ridge and channel axes).

Returns:

Array of axis objects containing the principle object axes.

See Also:

FeatureAxis

getXCentre

public double getXCentre()

Returns the x coordinate of the point of inflection of the quadratic. Useful for identifying highest point of peaks, lowest of pits and centres of passes.

Returns:

x coordinate of the point of inflection.

getYCentre

public double getYCentre()

Returns the y coordinate of the point of inflection of the quadratic. Useful for identifying highest point of peaks, lowest of pits and centres of passes.

Returns:

y coordinate of the point of inflection.

getPointConfidence

public double getPointConfidence()

Reports the confidence of point classification (pits, peaks, passes). Confidence is based on the lowest intersection of the most ridge-like feature with the region of interest, and the similarly hights channel-like intersection. The greater these values the 'stronger' the feature is.

Returns:

Point classification confidence. Value is in elevation units or -Double.MAX_VALUE if not a point feature.