Module imagingbook.common

Package imagingbook.common.geometry.ellipse.project

Class OrthogonalEllipseProjectorNewton

java.lang.Object

imagingbook.common.geometry.ellipse.project.EllipseProjector

imagingbook.common.geometry.ellipse.project.OrthogonalEllipseProjectorNewton

public class OrthogonalEllipseProjectorNewton
extends EllipseProjector

Calculates the closest point on the ellipse for a given 2D point inside or outside the ellipse, using orthogonal projection of points onto the ellipse. This is a robust algorithm based on [1]. See Sec.11.2.2 (Alg. 11.9) of [2] for details. This version uses the Newton-method for root finding, which is quick but may fail to return a valid result if the target point is close to the x- or y-axis. See OrthogonalEllipseProjector for a robust solution or ConfocalConicEllipseProjector for an approximate but non-iterative (i.e., fast) alternative.

[1] D. Eberly: "Distance from a point to an ellipse, an ellipsoid, or a hyperellipsoid", Technical Report, Geometric Tools, www.geometrictools.com, Redmont, WA (June 2013).
[2] W. Burger, M.J. Burge, Digital Image Processing – An Algorithmic Introduction, 3rd ed, Springer (2022).

Version:

2022/04/09

See Also:

• OrthogonalEllipseProjector
• ConfocalConicEllipseProjector

Constructor Summary

Constructors

Constructor	Description
OrthogonalEllipseProjectorNewton(GeometricEllipse ellipse)

Method Summary

Modifier and Type	Method	Description
int	getLastIterationCount()
protected double[]	projectCanonical(double[] u1)	Calculates the projection point in canonical coordinates.

Methods inherited from class imagingbook.common.geometry.ellipse.project.EllipseProjector

fromCanonicalFrame, fromFirstQuadrant, getDistance, getDistanceSq, project, project, toCanonicalFrame, toFirstQuadrant

Methods inherited from class java.lang.Object

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

Constructor Details

OrthogonalEllipseProjectorNewton

public OrthogonalEllipseProjectorNewton(GeometricEllipse ellipse)

Method Details

projectCanonical

protected double[] projectCanonical(double[] u1)

Description copied from class: EllipseProjector

Calculates the projection point in canonical coordinates.

Specified by:

projectCanonical in class EllipseProjector

Parameters:

u1 - target point in canonical coordinates.

Returns:

the associated "contact" point on the ellipse

getLastIterationCount

public int getLastIterationCount()