org.jhotdraw.geom
Class Bezier

java.lang.Object
  org.jhotdraw.geom.Bezier

public class Bezier
extends java.lang.Object

Provides algorithms for fitting Bezier curves to a set of digitized points.

Source:
Phoenix: An Interactive Curve Design System Based on the Automatic Fitting of Hand-Sketched Curves.
© Copyright by Philip J. Schneider 1988.
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science, University of Washington.

http://autotrace.sourceforge.net/Interactive_Curve_Design.ps.gz

Version:

$Id: Bezier.java 660 2010-07-08 20:52:06Z rawcoder $

Author:

Werner Randelshofer

Method Summary

static java.util.ArrayList<java.lang.Integer>	findCorners(java.util.List<java.awt.geom.Point2D.Double> digitizedPoints, double minAngle, double minDistance) Finds corners in the provided point list, and returns their indices.
static BezierPath	fitBezierPath(BezierPath digitizedPoints, double error) Fits a bezier path to the specified list of digitized points.
static BezierPath	fitBezierPath(java.util.List<java.awt.geom.Point2D.Double> digitizedPoints, double error) Fits a bezier path to the specified list of digitized points.
static BezierPath	fitBezierPath(java.awt.geom.Point2D.Double[] digitizedPoints, double error) Fits a bezier path to the specified list of digitized points.
static void	main(java.lang.String[] args)
static java.util.ArrayList<java.awt.geom.Point2D.Double>	reduceNoise(java.util.List<java.awt.geom.Point2D.Double> digitizedPoints, double weight) Reduces noise from the digitized points, by applying an approximation of a gaussian filter to the data.
static java.util.ArrayList<java.awt.geom.Point2D.Double>	removeClosePoints(java.util.List<java.awt.geom.Point2D.Double> digitizedPoints, double minDistance) Removes points which are closer together than the specified minimal distance.
static java.util.ArrayList<java.util.ArrayList<java.awt.geom.Point2D.Double>>	splitAtCorners(java.util.List<java.awt.geom.Point2D.Double> digitizedPoints, double maxAngle, double minDistance) Splits the digitized points into multiple segments at each corner point.

Methods inherited from class java.lang.Object

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

Method Detail

main

public static void main(java.lang.String[] args)

fitBezierPath

public static BezierPath fitBezierPath(java.awt.geom.Point2D.Double[] digitizedPoints,
                                       double error)

Fits a bezier path to the specified list of digitized points.

This is a convenience method for calling fitCubicSegments(List, double);

Parameters:

digitizedPoints - digited points.

error - the maximal allowed error between the bezier path and the digitized points.

fitBezierPath

public static BezierPath fitBezierPath(java.util.List<java.awt.geom.Point2D.Double> digitizedPoints,
                                       double error)

Fits a bezier path to the specified list of digitized points.

Parameters:

digitizedPoints - digited points.

error - the maximal allowed error between the bezier path and the digitized points.

fitBezierPath

public static BezierPath fitBezierPath(BezierPath digitizedPoints,
                                       double error)

Fits a bezier path to the specified list of digitized points.

This is a convenience method for calling fitCubicSegments(List, double);

Parameters:

digitizedPoints - digited points.

error - the maximal allowed error between the bezier path and the digitized points.

removeClosePoints

public static java.util.ArrayList<java.awt.geom.Point2D.Double> removeClosePoints(java.util.List<java.awt.geom.Point2D.Double> digitizedPoints,
                                                                                  double minDistance)

Removes points which are closer together than the specified minimal distance.

The minimal distance should be chosen dependent on the size and resolution of the display device, and on the sampling rate. A good value for mouse input on a display with 100% Zoom factor is 2.

The purpose of this method, is to remove points, which add no additional information about the shape of the curve from the list of digitized points.

The cleaned up set of digitized points gives better results, when used as input for method splitAtCorners(java.util.List, double, double).

Parameters:

digitizedPoints - Digitized points

minDistance - minimal distance between two points. If minDistance is 0, this method only removes sequences of coincident points.

Returns:

Digitized points with a minimal distance.

splitAtCorners

public static java.util.ArrayList<java.util.ArrayList<java.awt.geom.Point2D.Double>> splitAtCorners(java.util.List<java.awt.geom.Point2D.Double> digitizedPoints,
                                                                                                    double maxAngle,
                                                                                                    double minDistance)

Splits the digitized points into multiple segments at each corner point.

Corner points are both contained as the last point of a segment and the first point of a subsequent segment.

Parameters:

digitizedPoints - Digitized points

maxAngle - maximal angle in radians between the current point and its predecessor and successor up to which the point does not break the digitized list into segments. Recommended value 44° = 44 * 180d / Math.PI

Returns:

Segments of digitized points, each segment having less than maximal angle between points.

findCorners

public static java.util.ArrayList<java.lang.Integer> findCorners(java.util.List<java.awt.geom.Point2D.Double> digitizedPoints,
                                                                 double minAngle,
                                                                 double minDistance)

Finds corners in the provided point list, and returns their indices.

Parameters:

digitizedPoints - List of digitized points.

minAngle - Minimal angle for corner points

minDistance - Minimal distance between a point and adjacent points for corner detection

Returns:

list of corner indices.

reduceNoise

public static java.util.ArrayList<java.awt.geom.Point2D.Double> reduceNoise(java.util.List<java.awt.geom.Point2D.Double> digitizedPoints,
                                                                            double weight)

Reduces noise from the digitized points, by applying an approximation of a gaussian filter to the data.

The filter does the following for each point P, with weight 0.5:

x[i] = 0.5*x[i] + 0.25*x[i-1] + 0.25*x[i+1]; y[i] = 0.5*y[i] + 0.25*y[i-1] + 0.25*y[i+1];

Parameters:

digitizedPoints - Digitized points

weight - Weight of the current point

Returns:

Digitized points with reduced noise.