Module org.jhotdraw8.geom

Package org.jhotdraw8.geom

Class CubicCurveCharacteristics

java.lang.Object

org.jhotdraw8.geom.CubicCurveCharacteristics

public class CubicCurveCharacteristics
extends Object

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static enum	CubicCurveCharacteristics.Characteristics

Method Summary

Modifier and Type	Method	Description
static double[]	align(double x0, double y0, double x1, double y1, double x2, double y2, double x3, double y3)	Rotates and translates the provided bezier curve so that 3 coordinates are approximately zero: x0, y0 and y3.
static @Nullable Point2D.Double	canonicalForm(double x0, double y0, double x1, double y1, double x2, double y2, double x3, double y3)	Transforms the given cubic curve into canonical form.
static CubicCurveCharacteristics.Characteristics	characteristics(double[] b, int o)
static CubicCurveCharacteristics.Characteristics	characteristics(double x0, double y0, double x1, double y1, double x2, double y2, double x3, double y3)
static DoubleArrayList	extremePoints(double x0, double y0, double x1, double y1, double x2, double y2, double x3, double y3)	Computes the extreme points of the given cubic curve.
static DoubleArrayList	extremePoints(CubicCurve2D.Double c)	Computes the extreme points of the given cubic curve.
static DoubleArrayList	inflectionPoints(double[] b, int o)
static DoubleArrayList	inflectionPoints(double x0, double y0, double x1, double y1, double x2, double y2, double x3, double y3)	Computes the inflection points of the given cubic curve.
static DoubleArrayList	inflectionPoints(CubicCurve2D.Double c)	Computes the inflection points of the given cubic curve.
static @Nullable Double	singularPoint(double[] b, int o)
static @Nullable Double	singularPoint(double x0, double y0, double x1, double y1, double x2, double y2, double x3, double y3)

Methods inherited from class java.lang.Object

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

Method Details

characteristics

public static CubicCurveCharacteristics.Characteristics characteristics(double[] b,
 int o)

characteristics

public static CubicCurveCharacteristics.Characteristics characteristics(double x0,
 double y0,
 double x1,
 double y1,
 double x2,
 double y2,
 double x3,
 double y3)

canonicalForm

public static @Nullable Point2D.Double canonicalForm(double x0,
 double y0,
 double x1,
 double y1,
 double x2,
 double y2,
 double x3,
 double y3)

Transforms the given cubic curve into canonical form.

Where:

   B0: x0 = 0, y0 = 0
   B1: x1 = 0, y1 = 1
   B2: x2 = 1, y2 = 1
   B3: x3 = ..., y3 = ...
 

References:

Calculating the Extremal Points of a Cubic Bezier Curve

pomax.github.io

Pomax. A Primer on Bézier Curves. The canonical form (for cubic curves).

pomax.github.io

Returns:

returns the coordinates of x3,y3 or null if the mapping failed

align

public static double[] align(double x0,
 double y0,
 double x1,
 double y1,
 double x2,
 double y2,
 double x3,
 double y3)

Rotates and translates the provided bezier curve so that 3 coordinates are approximately zero: x0, y0 and y3.

inflectionPoints

public static DoubleArrayList inflectionPoints(CubicCurve2D.Double c)

Computes the inflection points of the given cubic curve.

inflectionPoints

public static DoubleArrayList inflectionPoints(double[] b,
 int o)

singularPoint

public static @Nullable Double singularPoint(double[] b,
 int o)

inflectionPoints

public static DoubleArrayList inflectionPoints(double x0,
 double y0,
 double x1,
 double y1,
 double x2,
 double y2,
 double x3,
 double y3)

Computes the inflection points of the given cubic curve.

If the curve has two inflection points:

• The point in the middle of the two inflection points (t₀+t₁)/2 has maximal curvature. This point is called a 'singular point' by Zhiyi Zhang et al.
• If the inflection points are the same almostEqual(t₀,t₁) value, we have a cusp.

References:

Stackoverflow, Calculating the Inflection Point of a Cubic Bezier Curve, Copyright MBo, CC BY-SA 4.0 license

stackoverflow.com

Zhiyi Zhang, Min Chen , Xian Zhang, Zepeng Wang. Analysis of Inflection Points for Planar Cubic Bé́zier Curve

cie.nwsuaf.edu.cn

singularPoint

public static @Nullable Double singularPoint(double x0,
 double y0,
 double x1,
 double y1,
 double x2,
 double y2,
 double x3,
 double y3)

extremePoints

public static DoubleArrayList extremePoints(CubicCurve2D.Double c)

Computes the extreme points of the given cubic curve.

extremePoints

public static DoubleArrayList extremePoints(double x0,
 double y0,
 double x1,
 double y1,
 double x2,
 double y2,
 double x3,
 double y3)

Computes the extreme points of the given cubic curve.

References:

Extremes for Bézier curves

github.polettix.it