## org.jscience.mathematics.geometry Class Point3D

```java.lang.Object
org.jscience.mathematics.geometry.GeometryElement
org.jscience.mathematics.geometry.AbstractPoint
org.jscience.mathematics.geometry.Point3D
```
All Implemented Interfaces:
java.io.Serializable
Direct Known Subclasses:
CartesianPoint3D, HomogeneousPoint3D, IntersectionPoint3D, PointOnGeometry3D

`public abstract class Point3Dextends AbstractPoint`

�R�����̓_��\����?ۃN���X?B

`Vector3D`, Serialized Form

Field Summary
`static Point3D` `origin`
�R�����̌��_ (0, 0, 0)?

Constructor Summary
`protected ` `Point3D()`
�I�u�W�F�N�g��?

Method Summary
` Point3D` `add(Vector3D vector)`
���̓_�ɗ^����ꂽ�x�N�g���𑫂����_��Ԃ�?
` int` `dimension()`
������Ԃ�?
` double` `distance(Point3D mate)`
���̓_�Ɨ^����ꂽ�_�Ƃ̊Ԃ̋�����Ԃ�?
` double` `distance2(Point3D mate)`
���̓_�Ɨ^����ꂽ�_�Ƃ̊Ԃ̋����̎�?
` Point3D` `divide(double scale)`
���̓_��^����ꂽ�X�P?
`protected abstract  Point3D` ```doTransformBy(boolean reverseTransform, CartesianTransformationOperator3D transformationOperator, java.util.Hashtable transformedGeometries)```
���̓_��?
` boolean` `identical(Point3D mate)`
�Q�_�̓���?
` boolean` `is3D()`
�R�������ۂ���Ԃ�

?

` boolean` `isOn(ParametricCurve3D mate)`
���̓_���^����ꂽ��?
` boolean` `isOn(ParametricSurface3D mate)`
���̓_���^����ꂽ�Ȗʂ�?
` Point3D` ```linearInterpolate(Point3D mate, double weightForThis)```
���̓_�Ɨ^����ꂽ�_��?
` Point3D` `longestPoint(Point3D[] pnts)`
�^����ꂽ�_��̒���?
` Point3D` ```longestPoint(Point3D[] pnts, int start, int end)```
�^����ꂽ�_��̎w��͈̔͂̒���?
` Point3D` `midPoint(Point3D mate)`
���̓_�Ɨ^����ꂽ�_�̒��_��Ԃ�?
` Point3D` `multiply(double scale)`
���̓_�ɗ^����ꂽ�X�P?
`static CartesianPoint3D` `of(double[] components)`
CartesianPoint3D �̃C���X�^���X��?
`static CartesianPoint3D` ```of(double x, double y, double z)```
CartesianPoint3D �̃C���X�^���X��?
` PointOnCurve3D[]` `project(ParametricCurve3D mate)`
���̓_����^����ꂽ��?
`static Point3D[]` ```reverseTransform(Point3D[] points, CartesianTransformationOperator3D transformationOperator, java.util.Hashtable transformedGeometries)```
�_���?
` Point3D` ```reverseTransformBy(CartesianTransformationOperator3D transformationOperator, java.util.Hashtable transformedGeometries)```
���̓_��?
` Vector3D` `subtract(Point3D mate)`
���̓_�Ɨ^����ꂽ�_�Ƃ�?
` Point3D` `subtract(Vector3D vector)`
���̓_����^����ꂽ�x�N�g����򢂽�_��Ԃ�?
` Vector3D` `toVector3D()`
���̓_��R�����̃x�N�g�� (Vector3D) �ɕϊ�����?
`static Vector3D[]` `toVector3D(Point3D[] pnts)`
�_�̔z���x�N�g�� (Vector3D) �̔z��ɕϊ�����?
`static Point3D[]` ```transform(Point3D[] points, boolean reverseTransform, CartesianTransformationOperator3D transformationOperator, java.util.Hashtable transformedGeometries)```
�_���?
`static Point3D[]` ```transform(Point3D[] points, CartesianTransformationOperator3D transformationOperator, java.util.Hashtable transformedGeometries)```
�_���?
` Point3D` ```transformBy(boolean reverseTransform, CartesianTransformationOperator3D transformationOperator, java.util.Hashtable transformedGeometries)```
���̓_��?
` Point3D` ```transformBy(CartesianTransformationOperator3D transformationOperator, java.util.Hashtable transformedGeometries)```
���̓_��?
`abstract  double` `x()`
�_�� X ?
`abstract  double` `y()`
�_�� Y ?
`abstract  double` `z()`
�_�� Z ?

Methods inherited from class org.jscience.mathematics.geometry.AbstractPoint
`isPoint`

Methods inherited from class org.jscience.mathematics.geometry.GeometryElement
`getClassName, getToleranceForAngle, getToleranceForAngleAsObject, getToleranceForDistance, getToleranceForDistance2, getToleranceForDistanceAsObject, getToleranceForParameter, getToleranceForParameterAsObject, getToleranceForRealNumber, getToleranceForRealNumberAsObject, is1D, is2D, isCurve, isFreeform, isParametric, isPlacement, isSurface, isTransformationOperator, isVector, makeIndent, output, output`

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Field Detail

### origin

`public static final Point3D origin`
�R�����̌��_ (0, 0, 0)?B

Constructor Detail

### Point3D

`protected Point3D()`
�I�u�W�F�N�g��?\�z����?B

`ConditionOfOperation`
Method Detail

### dimension

`public int dimension()`
������Ԃ�?B

?�� 3 ��Ԃ�?B

Specified by:
`dimension` in class `GeometryElement`
Returns:
�R�����Ȃ̂�?A?�� 3

### is3D

`public boolean is3D()`
�R�������ۂ���Ԃ�

?�� true ��Ԃ�?B

Overrides:
`is3D` in class `GeometryElement`
Returns:
�R�����Ȃ̂�?A?�� `true`

### x

`public abstract double x()`
�_�� X ?W�l��Ԃ���?ۃ?�\�b�h?B

Returns:
�_�� X ?W�l

### y

`public abstract double y()`
�_�� Y ?W�l��Ԃ���?ۃ?�\�b�h?B

Returns:
�_�� Y ?W�l

### z

`public abstract double z()`
�_�� Z ?W�l��Ԃ���?ۃ?�\�b�h?B

Returns:
�_�� Z ?W�l

`public Point3D add(Vector3D vector)`
���̓_�ɗ^����ꂽ�x�N�g���𑫂����_��Ԃ�?B

Parameters:
`vector` - �_�ɑ����x�N�g��
Returns:
�^����ꂽ�x�N�g���𑫂����_ (this + vector)

### subtract

`public Point3D subtract(Vector3D vector)`
���̓_����^����ꂽ�x�N�g����򢂽�_��Ԃ�?B

Parameters:
`vector` - �_�����x�N�g��
Returns:
�^����ꂽ�x�N�g����򢂽�_ (this - vector)

### subtract

`public Vector3D subtract(Point3D mate)`
���̓_�Ɨ^����ꂽ�_�Ƃ�?���Ԃ�?B

Parameters:
`mate` - ?����鑊��̓_
Returns:
��_��?� (this - mate)

### multiply

`public Point3D multiply(double scale)`
���̓_�ɗ^����ꂽ�X�P?[����?悶���_��Ԃ�?B

Parameters:
`scale` - �X�P?[��
Returns:
(this * scale)

### divide

`public Point3D divide(double scale)`
���̓_��^����ꂽ�X�P?[���Ŋ��B��_��Ԃ�?B

Parameters:
`scale` - �X�P?[��
Returns:
(this / scale)

### linearInterpolate

```public Point3D linearInterpolate(Point3D mate,
double weightForThis)```
���̓_�Ɨ^����ꂽ�_��?�^��Ԃ������ʂ�Ԃ�?B

Parameters:
`mate` - ?�`��Ԃ̑���ƂȂ�_
`weightForThis` - ��?g�ɑ΂���?d�� (����ɑ΂���?d�݂� 1 - weightForThis)
Returns:
?�`��Ԃ������ʂ̓_ (weightForThis * this + (1 - weightForThis) * mate)

### midPoint

`public Point3D midPoint(Point3D mate)`
���̓_�Ɨ^����ꂽ�_�̒��_��Ԃ�?B

Parameters:
`mate` - ���_��?�߂鑊��ƂȂ�_
Returns:
���_ (0.5 * this + 0.5 * mate)

### identical

`public boolean identical(Point3D mate)`
�Q�_�̓���?��𔻒肷��?B

Parameters:
`mate` - ����̑�?ۂƂȂ�_
Returns:
this �� mate ��?u�����̋��e��?�?v�ȓ�� ����̓_�ł���Ƃ݂Ȃ���� true?A����Ȃ��� false
`ConditionOfOperation`

### toVector3D

`public Vector3D toVector3D()`
���̓_��R�����̃x�N�g�� (Vector3D) �ɕϊ�����?B

Returns:
���_����̃x�N�g���Ƃ݂Ȃ����x�N�g��

### toVector3D

`public static Vector3D[] toVector3D(Point3D[] pnts)`
�_�̔z���x�N�g�� (Vector3D) �̔z��ɕϊ�����?B

Returns:
���_����̃x�N�g���Ƃ݂Ȃ����x�N�g���̔z��

### project

```public PointOnCurve3D[] project(ParametricCurve3D mate)
throws IndefiniteSolutionException```
���̓_����^����ꂽ��?�ւ̓��e�_��?�߂�?B

Parameters:
`mate` - ���e��?ۂ̋�?�
Returns:
�w�肳�ꂽ��?�ւ̓��e�_ (��?݂��Ȃ��Ƃ��͒���0�̔z���Ԃ�)
Throws:
`IndefiniteSolutionException` - �⪕s��ł���

### isOn

`public boolean isOn(ParametricCurve3D mate)`
���̓_���^����ꂽ��?��?��?�BĂ��邩�ǂ�����Ԃ�?B

Parameters:
`mate` - �����?ۂ̋�?�
Returns:
��?��?��?�BĂ���� true?A�����łȂ���� false

### isOn

`public boolean isOn(ParametricSurface3D mate)`
���̓_���^����ꂽ�Ȗʂ�?��?�BĂ��邩�ǂ�����Ԃ�?B

Parameters:
`mate` - �����?ۂ̋Ȗ�
Returns:
�Ȗʂ�?��?�BĂ���� true?A�����łȂ���� false

### distance

`public double distance(Point3D mate)`
���̓_�Ɨ^����ꂽ�_�Ƃ̊Ԃ̋�����Ԃ�?B

Parameters:
`mate` - ������?�߂�_
Returns:
this - mate �Ԃ̋���

### distance2

`public double distance2(Point3D mate)`
���̓_�Ɨ^����ꂽ�_�Ƃ̊Ԃ̋����̎�?��Ԃ�?B

Parameters:
`mate` - �����̎�?��?�߂�_
Returns:
this - mate �Ԃ̋����̎�?�

### longestPoint

`public Point3D longestPoint(Point3D[] pnts)`
�^����ꂽ�_��̒���?A���̓_����?łɓ���_��Ԃ�?B

Parameters:
`pnts` - �_��
Returns:
?łɓ���_

### longestPoint

```public Point3D longestPoint(Point3D[] pnts,
int start,
int end)```
�^����ꂽ�_��̎w��͈̔͂̒���?A���̓_����?łɓ���_��Ԃ�?B

Parameters:
`pnts` - �_��
`start` - �J�n�_�̃C���f�b�N�X (0 ~ pnts.length - 1)
`end` - ?I���_�̃C���f�b�N�X (0 ~ pnts.length - 1, start <= end)
Returns:
?łɓ���_

### doTransformBy

```protected abstract Point3D doTransformBy(boolean reverseTransform,
CartesianTransformationOperator3D transformationOperator,
java.util.Hashtable transformedGeometries)```
���̓_��?A�^����ꂽ�􉽓I�ϊ����Z�q�ŕϊ�����?B

transformedGeometries ��?A �ϊ��O�̊􉽗v�f��L?[�Ƃ�?A �ϊ���̊􉽗v�f��l�Ƃ���n�b�V���e?[�u���ł���?B

this �� transformedGeometries ��ɃL?[�Ƃ��đ�?݂��Ȃ�?�?��ɂ�?A this �� transformationOperator �ŕϊ�������̂�Ԃ�?B ����?ۂɃ?�\�b�h�Ք�ł� this ��L?[?A �ϊ����ʂ�l�Ƃ��� transformedGeometries �ɒǉB���?B

this �� transformedGeometries ��Ɋ�ɃL?[�Ƃ��đ�?݂���?�?��ɂ�?A ��?ۂ̕ϊ���?s�Ȃ킸?A���̃L?[�ɑΉ�����l��Ԃ�?B ����?��?��?ċA�I��?s�Ȃ���?B

transformedGeometries �� null �ł�?\��Ȃ�?B transformedGeometries �� null ��?�?��ɂ�?A ?�� this �� transformationOperator �ŕϊ�������̂�Ԃ�?B

Parameters:
`reverseTransform` - �t�ϊ�����̂ł���� true?A�����łȂ���� false
`transformationOperator` - �􉽓I�ϊ����Z�q
`transformedGeometries` - ��ɓ��l�̕ϊ���{�����􉽗v�f��܂ރn�b�V���e?[�u��
Returns:
�ϊ���̊􉽗v�f

### transformBy

```public Point3D transformBy(boolean reverseTransform,
CartesianTransformationOperator3D transformationOperator,
java.util.Hashtable transformedGeometries)```
���̓_��?A�^����ꂽ�􉽓I�ϊ����Z�q�ŕϊ�����?B

transformedGeometries ��?A �ϊ��O�̊􉽗v�f��L?[�Ƃ�?A �ϊ���̊􉽗v�f��l�Ƃ���n�b�V���e?[�u���ł���?B

this �� transformedGeometries ��ɃL?[�Ƃ��đ�?݂��Ȃ�?�?��ɂ�?A this �� transformationOperator �ŕϊ�������̂�Ԃ�?B ����?ۂɃ?�\�b�h�Ք�ł� this ��L?[?A �ϊ����ʂ�l�Ƃ��� transformedGeometries �ɒǉB���?B

this �� transformedGeometries ��Ɋ�ɃL?[�Ƃ��đ�?݂���?�?��ɂ�?A ��?ۂ̕ϊ���?s�Ȃ킸?A���̃L?[�ɑΉ�����l��Ԃ�?B ����?��?��?ċA�I��?s�Ȃ���?B

transformedGeometries �� null �ł�?\��Ȃ�?B transformedGeometries �� null ��?�?��ɂ�?A ?�� this �� transformationOperator �ŕϊ�������̂�Ԃ�?B

Parameters:
`reverseTransform` - �t�ϊ�����̂ł���� true?A�����łȂ���� false
`transformationOperator` - �􉽓I�ϊ����Z�q
`transformedGeometries` - ��ɓ��l�̕ϊ���{�����􉽗v�f��܂ރn�b�V���e?[�u��
Returns:
�ϊ���̊􉽗v�f

### transformBy

```public Point3D transformBy(CartesianTransformationOperator3D transformationOperator,
java.util.Hashtable transformedGeometries)```
���̓_��?A�^����ꂽ�􉽓I�ϊ����Z�q�ŕϊ�����?B

transformedGeometries ��?A �ϊ��O�̊􉽗v�f��L?[�Ƃ�?A �ϊ���̊􉽗v�f��l�Ƃ���n�b�V���e?[�u���ł���?B

this �� transformedGeometries ��ɃL?[�Ƃ��đ�?݂��Ȃ�?�?��ɂ�?A this �� transformationOperator �ŕϊ�������̂�Ԃ�?B ����?ۂɃ?�\�b�h�Ք�ł� this ��L?[?A �ϊ����ʂ�l�Ƃ��� transformedGeometries �ɒǉB���?B

this �� transformedGeometries ��Ɋ�ɃL?[�Ƃ��đ�?݂���?�?��ɂ�?A ��?ۂ̕ϊ���?s�Ȃ킸?A���̃L?[�ɑΉ�����l��Ԃ�?B ����?��?��?ċA�I��?s�Ȃ���?B

transformedGeometries �� null �ł�?\��Ȃ�?B transformedGeometries �� null ��?�?��ɂ�?A ?�� this �� transformationOperator �ŕϊ�������̂�Ԃ�?B

Parameters:
`transformationOperator` - �􉽓I�ϊ����Z�q
`transformedGeometries` - ��ɓ��l�̕ϊ���{�����􉽗v�f��܂ރn�b�V���e?[�u��
Returns:
�ϊ���̊􉽗v�f

### reverseTransformBy

```public Point3D reverseTransformBy(CartesianTransformationOperator3D transformationOperator,
java.util.Hashtable transformedGeometries)```
���̓_��?A�^����ꂽ�􉽓I�ϊ����Z�q�ŋt�ϊ�����?B

transformedGeometries ��?A �ϊ��O�̊􉽗v�f��L?[�Ƃ�?A �ϊ���̊􉽗v�f��l�Ƃ���n�b�V���e?[�u���ł���?B

this �� transformedGeometries ��ɃL?[�Ƃ��đ�?݂��Ȃ�?�?��ɂ�?A this �� transformationOperator �ŋt�ϊ�������̂�Ԃ�?B ����?ۂɃ?�\�b�h�Ք�ł� this ��L?[?A �ϊ����ʂ�l�Ƃ��� transformedGeometries �ɒǉB���?B

this �� transformedGeometries ��Ɋ�ɃL?[�Ƃ��đ�?݂���?�?��ɂ�?A ��?ۂ̕ϊ���?s�Ȃ킸?A���̃L?[�ɑΉ�����l��Ԃ�?B ����?��?��?ċA�I��?s�Ȃ���?B

transformedGeometries �� null �ł�?\��Ȃ�?B transformedGeometries �� null ��?�?��ɂ�?A ?�� this �� transformationOperator �ŋt�ϊ�������̂�Ԃ�?B

Parameters:
`transformationOperator` - �􉽓I�ϊ����Z�q
`transformedGeometries` - ��ɓ��l�̕ϊ���{�����􉽗v�f��܂ރn�b�V���e?[�u��
Returns:
�t�ϊ���̊􉽗v�f

### transform

```public static Point3D[] transform(Point3D[] points,
boolean reverseTransform,
CartesianTransformationOperator3D transformationOperator,
java.util.Hashtable transformedGeometries)```
�_���?A�^����ꂽ�􉽓I�ϊ����Z�q�ŕϊ�����?B

transformedGeometries ��?A �ϊ��O�̊􉽗v�f��L?[�Ƃ�?A �ϊ���̊􉽗v�f��l�Ƃ���n�b�V���e?[�u���ł���?B

��?ۂƂȂ�_�� transformedGeometries ��ɃL?[�Ƃ��đ�?݂��Ȃ�?�?��ɂ�?A ����� transformationOperator �ŕϊ�������̂�Ԃ�?B ����?ۂɃ?�\�b�h�Ք�ł͑�?ۂƂȂ��L?[?A ���̕ϊ����ʂ�l�Ƃ��� transformedGeometries �ɒǉB���?B

��?ۂƂȂ邪 transformedGeometries ��Ɋ�ɃL?[�Ƃ��đ�?݂���?�?��ɂ�?A ��?ۂ̕ϊ���?s�Ȃ킸?A���̃L?[�ɑΉ�����l��Ԃ�?B ����?��?��?ċA�I��?s�Ȃ���?B

transformedGeometries �� null �ł�?\��Ȃ�?B transformedGeometries �� null ��?�?��ɂ�?A ?�ɑ�?ۂƂȂ�_�� transformationOperator �ŕϊ�������̂�Ԃ�?B

Parameters:
`points` - �_��
`reverseTransform` - �t�ϊ�����̂ł���� true?A�����łȂ���� false
`transformationOperator` - �􉽓I�ϊ����Z�q
`transformedGeometries` - ��ɓ��l�̕ϊ���{�����􉽗v�f��܂ރn�b�V���e?[�u��

### transform

```public static Point3D[] transform(Point3D[] points,
CartesianTransformationOperator3D transformationOperator,
java.util.Hashtable transformedGeometries)```
�_���?A�^����ꂽ�􉽓I�ϊ����Z�q�ŕϊ�����?B

transformedGeometries ��?A �ϊ��O�̊􉽗v�f��L?[�Ƃ�?A �ϊ���̊􉽗v�f��l�Ƃ���n�b�V���e?[�u���ł���?B

��?ۂƂȂ�_�� transformedGeometries ��ɃL?[�Ƃ��đ�?݂��Ȃ�?�?��ɂ�?A ����� transformationOperator �ŕϊ�������̂�Ԃ�?B ����?ۂɃ?�\�b�h�Ք�ł͑�?ۂƂȂ�_��L?[?A ���̕ϊ����ʂ�l�Ƃ��� transformedGeometries �ɒǉB���?B

��?ۂƂȂ邪 transformedGeometries ��Ɋ�ɃL?[�Ƃ��đ�?݂���?�?��ɂ�?A ��?ۂ̕ϊ���?s�Ȃ킸?A���̃L?[�ɑΉ�����l��Ԃ�?B ����?��?��?ċA�I��?s�Ȃ���?B

transformedGeometries �� null �ł�?\��Ȃ�?B transformedGeometries �� null ��?�?��ɂ�?A ?�ɑ�?ۂƂȂ�_�� transformationOperator �ŕϊ�������̂�Ԃ�?B

Parameters:
`points` - �_��
`transformationOperator` - �􉽓I�ϊ����Z�q
`transformedGeometries` - ��ɓ��l�̕ϊ���{�����􉽗v�f��܂ރn�b�V���e?[�u��

### reverseTransform

```public static Point3D[] reverseTransform(Point3D[] points,
CartesianTransformationOperator3D transformationOperator,
java.util.Hashtable transformedGeometries)```
�_���?A�^����ꂽ�􉽓I�ϊ����Z�q�ŋt�ϊ�����?B

transformedGeometries ��?A �ϊ��O�̊􉽗v�f��L?[�Ƃ�?A �ϊ���̊􉽗v�f��l�Ƃ���n�b�V���e?[�u���ł���?B

��?ۂƂȂ�_�� transformedGeometries ��ɃL?[�Ƃ��đ�?݂��Ȃ�?�?��ɂ�?A ����� transformationOperator �ŋt�ϊ�������̂�Ԃ�?B ����?ۂɃ?�\�b�h�Ք�ł͑�?ۂƂȂ�_��L?[?A ���̕ϊ����ʂ�l�Ƃ��� transformedGeometries �ɒǉB���?B

��?ۂƂȂ邪 transformedGeometries ��Ɋ�ɃL?[�Ƃ��đ�?݂���?�?��ɂ�?A ��?ۂ̕ϊ���?s�Ȃ킸?A���̃L?[�ɑΉ�����l��Ԃ�?B ����?��?��?ċA�I��?s�Ȃ���?B

transformedGeometries �� null �ł�?\��Ȃ�?B transformedGeometries �� null ��?�?��ɂ�?A ?�ɑ�?ۂƂȂ�_�� transformationOperator �ŋt�ϊ�������̂�Ԃ�?B

Parameters:
`points` - �_��
`transformationOperator` - �􉽓I�ϊ����Z�q
`transformedGeometries` - ��ɓ��l�̕ϊ���{�����􉽗v�f��܂ރn�b�V���e?[�u��

### of

```public static CartesianPoint3D of(double x,
double y,
double z)```
CartesianPoint3D �̃C���X�^���X��?�?�����?B

Parameters:
`x` - X ?���
`y` - Y ?���
`z` - Z ?���
Returns:
CartesianPoint3D �̃C���X�^���X

### of

`public static CartesianPoint3D of(double[] components)`
CartesianPoint3D �̃C���X�^���X��?�?�����?B

Parameters:
`components` - X, Y?����̔z�� (�v�f?� 3)
Returns:
CartesianPoint3D �̃C���X�^���X