Point3Vector (CML Euclid 2.9 API)

java.lang.Object
- org.xmlcml.euclid.Point3Vector

All Implemented Interfaces:

EuclidConstants
```
public class Point3Vector
extends Object
implements EuclidConstants
```
a (Java) Vector of Point3s (Note that 'Vector' is used by Java to describe an array of objects - there is no relationship to geometrical vectors in this package.)
There are a large number of routines for manipulating 3-D coordinates. Examples are distance, torsion, angle, planes, fitting, etc. The routines have NOT been optimised. In the previous incarnation (C++) all coordinates were handled by Point3s, etc because pointers are fragile. In Java, however, a lot more intermediate information could be passed through double[] arrays and this will be gradually converted.
All the routines compile and give answers. The answers were right in the C++ version. Most seem to be right here, but the FITTING ROUTINES ARE CURRENTLY NOT WORKING PROPERLY. This will be fixed...
Default is an empty (Java) Vector;

Author:

(C) P. Murray-Rust, 1996

Field Summary

Fields
Modifier and Type Field and Description

protected List<Point3> vector
- Fields inherited from interface org.xmlcml.euclid.EuclidConstants
  C_AMP, C_APOS, C_ATSIGN, C_BACKSLASH, C_BACKSPACE, C_CARET, C_COLON, C_COMMA, C_DEL, C_DOLLAR, C_EQUALS, C_FORMFEED, C_HASH, C_LANGLE, C_LBRAK, C_LCURLY, C_LSQUARE, C_MINUS, C_NBSP, C_NEWLINE, C_NL, C_PERCENT, C_PERIOD, C_PIPE, C_PLUS, C_POUND, C_QUERY, C_QUOT, C_RANGLE, C_RBRAK, C_RCURLY, C_RETURN, C_RSQUARE, C_SEMICOLON, C_SHRIEK, C_SLASH, C_SPACE, C_STAR, C_TAB, C_TILDE, C_UNDER, EPS, F_S, NONWHITEPUNC, NONWHITEPUNC0, NONWHITEPUNC0REGEX, ONE_THIRD, PUNC, S_AMP, S_APOS, S_ATSIGN, S_BACKSLASH, S_CARET, S_COLON, S_COMMA, S_DOLLAR, S_EMPTY, S_EQUALS, S_FORMFEED, S_HASH, S_LANGLE, S_LBRAK, S_LCURLY, S_LSQUARE, S_MINUS, S_NEWLINE, S_NL, S_PERCENT, S_PERIOD, S_PIPE, S_PLUS, S_POUND, S_QUERY, S_QUOT, S_RANGLE, S_RBRAK, S_RCURLY, S_RETURN, S_RSQUARE, S_SEMICOLON, S_SHRIEK, S_SLASH, S_SPACE, S_STAR, S_TAB, S_TILDE, S_UNDER, S_WHITEREGEX, TWO_THIRDS, U_S, WHITESPACE

Fields
Modifier and Type	Field and Description
`protected List<Point3>`	`vector`

Constructor Summary

Constructors
Constructor and Description
`Point3Vector()` constructor.
`Point3Vector(double[] flarray)` constructor.
`Point3Vector(int n, double[] x, double[] y, double[] z)` from three parallel arrays of x, y and z - by REFERENCE
`Point3Vector(Point3Vector pv)` copy constructor from Point3Vector COPIES pv
`Point3Vector(RealArray m)` constructor from RealArray - by REFERENCE

Method Summary

All Methods Static Methods Instance Methods Concrete Methods Deprecated Methods
Modifier and Type	Method and Description
`void`	`add(Point3 p)` add point.
`void`	`addElement(Point3 p)` add point.
`Transform3`	`align3PointVectors(Point3Vector ref)` fit two sets of three points.
`Transform3`	`alignUsing3Points(Point3Vector ref)` fit two coordinates of same length and alignment.
`Angle`	`angle(int i1, int i2, int i3)` get angle between 3 points.
`Angle`	`angle(IntSet is)` get angle between 3 points
`Plane3`	`bestPlane()` Deprecated. doesn't work
`RealSquareMatrix`	`calculateNonMassWeightedInertialTensor()`
`RealSquareMatrix`	`calculateNonMassWeightedInertialTensorOld()` get inertial tensor.
`RealSquareMatrix`	`calculateRotationToInertialAxes()`
`RealArray`	`deviationsFromPlane(Plane3 p)` get deviations of coordinates from plane
`double`	`distance(int i1, int i2)` get distance between 2 points.
`double`	`distance(IntSet is)` get distance between 2 points.
`Point3`	`elementAt(int i)` get Point3 element.
`RealArray`	`extractRealArray()`
`Transform3`	`fitTo(Point3Vector ref)` fit two coordinates of same length and alignment CURRENTLY NOT VALIDATED
`Point3`	`get(int i)` get Point3 element.
`int[]`	`get3SeparatedPoints()` get three widely separated points.
`double[]`	`getArray()` get array.
`Point3`	`getCentroid()` get centroid of all points
`double`	`getCoordinate(int i, Axis.Axis3 j)` get a single coordinate value
`RealSquareMatrix`	`getDistanceMatrix()` distance matrix
`int`	`getFurthestPointFrom(Point3 p)` get point furthest from another.
`Line3`	`getLine(int i1, int i2)` get the line between two points
`Point3`	`getPoint3(int i)` get a single point by REFERENCE
`List<Point3>`	`getPoint3List()` get points as list.
`int`	`getPointMakingSmallestAngle(Point3 p1, Point3 p2)` get point making smallest angle with two others.
`RealRange`	`getRange(Axis.Axis3 ax)` get range of one coordinate
`Real3Range`	`getRange3()` get range of all 3 coordinates
`double`	`getSigmaDeltaSquared(Point3Vector v)` gets sums of squared distances between points.
`RealArray`	`getXYZ()` get the coordinate coordinate array as doubles x,y,z,x,y,z,
`RealArray`	`getXYZ(Axis.Axis3 axis)` get a single coordinate array for example all x-coordinates
`void`	`inertialAxes(RealArray eigval, RealSquareMatrix eigvect, EuclidRuntimeException illCond)` Deprecated. (doesn't work)
`Double`	`innerProduct()`
`boolean`	`isEqualTo(Point3Vector p)` is equal.
`void`	`moveToCentroid()` centre molecule on origin.
`Point3Vector`	`multiplyBy(double scale)` multiply all coords.
`void`	`multiplyByEquals(double scale)` multiply all coords - alters this.
`Point3Vector`	`plus(Point3Vector pv2)` form the point+point sum for two vectors of points
`Point3Vector`	`plus(Vector3 v)` translate by a vector - do NOT modify `this`
`void`	`plusEquals(Vector3 v)` translate by a vector - modify `this`
`static void`	`removeNullValues(Point3Vector a, Point3Vector b)` removes null values if both vectors have them at same position.
`double`	`rms(Point3Vector c)` rms between two molecules - per atom
`Transform3`	`roughAlign(Point3Vector ref)` fit two coordinates of same length and alignment.
`void`	`setElementAt(Point3 p, int i)` insert point.
`void`	`setElementAt(Vector3 v, int i)` sets a given coordinate (i) to vector
`int`	`size()` size of vector.
`Point3Vector`	`subArray(IntSet is)` create a NEW subset of the points; points are COPIED
`Point3Vector`	`subtract(Point3Vector pv2)` form the point+point difference for two vectors of points
`Point3Vector`	`subtract(Vector3 v)` translate negatively.
`Angle`	`torsion(int i1, int i2, int i3, int i4)` get torsion angle between 4 points.
`Angle`	`torsion(IntSet is)` get torsion angle between 4 points.
`String`	`toString()` to string.
`void`	`transform(Transform3 t)` transform all coordinates.
`void`	`transform(Transform3 t, IntSet is)` transform subset of coordinates - MODIFIES Vector

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

- Field Detail
  - vector
```
protected List<Point3> vector
```
- Constructor Detail
  - Point3Vector
```
public Point3Vector()
```
    constructor.
  - Point3Vector
```
public Point3Vector(double[] flarray)
             throws EuclidRuntimeException
```
    constructor.
    
    Parameters:
    
    flarray -
    
    Throws:
    
    EuclidRuntimeException
  - Point3Vector
```
public Point3Vector(int n,
                    double[] x,
                    double[] y,
                    double[] z)
             throws EuclidRuntimeException
```
    from three parallel arrays of x, y and z - by REFERENCE
    
    Parameters:
    
    n -
    
    x -
    
    y -
    
    z -
    
    Throws:
    
    EuclidRuntimeException
  - Point3Vector
```
public Point3Vector(RealArray m)
             throws EuclidRuntimeException
```
    constructor from RealArray - by REFERENCE
    
    Parameters:
    
    m -
    
    Throws:
    
    EuclidRuntimeException - size of flarray must be multiple of 3
  - Point3Vector
```
public Point3Vector(Point3Vector pv)
```
    copy constructor from Point3Vector COPIES pv
    
    Parameters:
    
    pv -
- Method Detail
  - size
```
public int size()
```
    size of vector.
    
    Returns:
    
    the size
  - getPoint3List
```
public List<Point3> getPoint3List()
```
    get points as list.
    
    Returns:
    
    list
  - isEqualTo
```
public boolean isEqualTo(Point3Vector p)
```
    is equal.
    
    Parameters:
    
    p -
    
    Returns:
    
    true if equals
  - getArray
```
public double[] getArray()
```
    get array.
    
    Returns:
    
    array
  - add
```
public void add(Point3 p)
```
    add point.
    
    Parameters:
    
    p - the point
  - setElementAt
```
public void setElementAt(Point3 p,
                         int i)
```
    insert point.
    
    Parameters:
    
    p - point to insert
    
    i - position to insert at
  - elementAt
```
public Point3 elementAt(int i)
```
    get Point3 element.
    
    Parameters:
    
    i - serial of the element to get
    
    Returns:
    
    the element
  - get
```
public Point3 get(int i)
```
    get Point3 element.
    
    Parameters:
    
    i - serial of the element to get
    
    Returns:
    
    the element
  - addElement
```
public void addElement(Point3 p)
```
    add point.
    
    Parameters:
    
    p -
  - setElementAt
```
public void setElementAt(Vector3 v,
                         int i)
                  throws EuclidRuntimeException
```
    sets a given coordinate (i) to vector
    
    Parameters:
    
    v -
    
    i -
    
    Throws:
    
    EuclidRuntimeException - i is >= number of current points (cann use this to increase size of Point3Vector)
  - getRange
```
public RealRange getRange(Axis.Axis3 ax)
```
    get range of one coordinate
    
    Parameters:
    
    ax -
    
    Returns:
    
    range
  - getRange3
```
public Real3Range getRange3()
```
    get range of all 3 coordinates
    
    Returns:
    
    range
  - getSigmaDeltaSquared
```
public double getSigmaDeltaSquared(Point3Vector v)
                            throws EuclidRuntimeException
```
    gets sums of squared distances between points. result = sigma[i = 1, npoints] (this.point(i)getDistanceFrom(vector.point(i)) ** 2
    
    Parameters:
    
    v - the other vector
    
    Returns:
    
    the sums of squared distances
    
    Throws:
    
    EuclidRuntimeException - vectors not of same length
  - subArray
```
public Point3Vector subArray(IntSet is)
                      throws EuclidRuntimeException
```
    create a NEW subset of the points; points are COPIED
    
    Parameters:
    
    is -
    
    Returns:
    
    vector
    
    Throws:
    
    EuclidRuntimeException - an element of is is outside range of this
  - multiplyBy
```
public Point3Vector multiplyBy(double scale)
```
    multiply all coords. does not alter this.
    
    Parameters:
    
    scale -
    
    Returns:
    
    the scaled vector
  - multiplyByEquals
```
public void multiplyByEquals(double scale)
```
    multiply all coords - alters this.
    
    Parameters:
    
    scale -
  - plus
```
public Point3Vector plus(Point3Vector pv2)
                  throws EuclidRuntimeException
```
    form the point+point sum for two vectors of points
    
    Parameters:
    
    pv2 -
    
    Returns:
    
    vector
    
    Throws:
    
    EuclidRuntimeException - pv2 is different size from this
  - subtract
```
public Point3Vector subtract(Point3Vector pv2)
                      throws EuclidRuntimeException
```
    form the point+point difference for two vectors of points
    
    Parameters:
    
    pv2 -
    
    Returns:
    
    vector
    
    Throws:
    
    EuclidRuntimeException - pv2 is different size from this
  - getLine
```
public Line3 getLine(int i1,
                     int i2)
```
    get the line between two points
    
    Parameters:
    
    i1 -
    
    i2 -
    
    Returns:
    
    line
  - getCentroid
```
public Point3 getCentroid()
```
    get centroid of all points
    
    Returns:
    
    point
  - plus
```
public Point3Vector plus(Vector3 v)
```
    translate by a vector - do NOT modify this
    
    Parameters:
    
    v -
    
    Returns:
    
    vector
  - plusEquals
```
public void plusEquals(Vector3 v)
```
    translate by a vector - modify this
    
    Parameters:
    
    v -
  - subtract
```
public Point3Vector subtract(Vector3 v)
```
    translate negatively. does NOT modify this
    
    Parameters:
    
    v - vector to subtract
    
    Returns:
    
    the NEW translated p3v
  - moveToCentroid
```
public void moveToCentroid()
```
    centre molecule on origin. translate to centroid MODIFIES PV
  - removeNullValues
```
public static void removeNullValues(Point3Vector a,
                                    Point3Vector b)
```
    removes null values if both vectors have them at same position. else throws exception
    
    Parameters:
    
    a -
    
    b -
  - calculateNonMassWeightedInertialTensorOld
```
public RealSquareMatrix calculateNonMassWeightedInertialTensorOld()
```
    get inertial tensor. (second moments)
    
    Returns:
    
    the inertial tensor
  - calculateRotationToInertialAxes
```
public RealSquareMatrix calculateRotationToInertialAxes()
```
  - transform
```
public void transform(Transform3 t)
```
    transform all coordinates. MODIFIES p3Vector
    
    Parameters:
    
    t -
  - transform
```
public void transform(Transform3 t,
                      IntSet is)
```
    transform subset of coordinates - MODIFIES Vector
    
    Parameters:
    
    t -
    
    is -
  - distance
```
public double distance(int i1,
                       int i2)
```
    get distance between 2 points.
    
    Parameters:
    
    i1 - index of first point
    
    i2 - index of second point
    
    Returns:
    
    distance
  - distance
```
public double distance(IntSet is)
                throws EuclidRuntimeException
```
    get distance between 2 points.
    
    Parameters:
    
    is - of exactly 2 integers
    
    Returns:
    
    distance
    
    Throws:
    
    EuclidRuntimeException - is must have exactly 2 points
  - angle
```
public Angle angle(int i1,
                   int i2,
                   int i3)
            throws EuclidRuntimeException
```
    get angle between 3 points.
    
    Parameters:
    
    i1 - serial of first point
    
    i2 - serial of second point
    
    i3 - serial of third point
    
    Returns:
    
    the angle
    
    Throws:
    
    EuclidRuntimeException - two points are coincident or identical
  - angle
```
public Angle angle(IntSet is)
            throws EuclidRuntimeException
```
    get angle between 3 points
    
    Parameters:
    
    is - of exactly 3 integers
    
    Returns:
    
    the angle
    
    Throws:
    
    EuclidRuntimeException - is must have exactly 3 points
    
    EuclidRuntimeException - two points are coincident or identical
  - torsion
```
public Angle torsion(int i1,
                     int i2,
                     int i3,
                     int i4)
              throws EuclidRuntimeException
```
    get torsion angle between 4 points.
    
    Parameters:
    
    i1 - serial of first point
    
    i2 - serial of second point
    
    i3 - serial of third point
    
    i4 - serial of fourth point
    
    Returns:
    
    the angle
    
    Throws:
    
    EuclidRuntimeException - either 2 points are identical or coincident or 3 successive points are colinear
  - torsion
```
public Angle torsion(IntSet is)
              throws EuclidRuntimeException
```
    get torsion angle between 4 points.
    
    Parameters:
    
    is - of exactly 3 integers
    
    Returns:
    
    the angle
    
    Throws:
    
    EuclidRuntimeException - is must have exactly 4 points
    
    EuclidRuntimeException - either 2 points are identical or coincident or 3 successive points are colinear
  - getDistanceMatrix
```
public RealSquareMatrix getDistanceMatrix()
```
    distance matrix
    
    Returns:
    
    matrix
  - calculateNonMassWeightedInertialTensor
```
public RealSquareMatrix calculateNonMassWeightedInertialTensor()
```
  - inertialAxes
```
public void inertialAxes(RealArray eigval,
                         RealSquareMatrix eigvect,
                         EuclidRuntimeException illCond)
                  throws EuclidRuntimeException
```
    Deprecated. (doesn't work)
    
    get Inertial axes; do not throw exception for pathological cases, but return it. Axes (lengths and unit vectors) are returned through the arguments eigval and eigvect. OBSOLETE NYI
    
    Parameters:
    
    eigval -
    
    eigvect -
    
    illCond -
    
    Throws:
    
    EuclidRuntimeException - must have at least 3 points
  - bestPlane
```
public Plane3 bestPlane()
                 throws EuclidRuntimeException
```
    Deprecated. doesn't work
    
    get best plane
    
    Returns:
    
    plane
    
    Throws:
    
    EuclidRuntimeException - must have at least 3 points
  - deviationsFromPlane
```
public RealArray deviationsFromPlane(Plane3 p)
```
    get deviations of coordinates from plane
    
    Parameters:
    
    p -
    
    Returns:
    
    deviations
  - getPoint3
```
public Point3 getPoint3(int i)
```
    get a single point by REFERENCE
    
    Parameters:
    
    i -
    
    Returns:
    
    point
  - getXYZ
```
public RealArray getXYZ()
```
    get the coordinate coordinate array as doubles x,y,z,x,y,z,
    
    Returns:
    
    array
  - getCoordinate
```
public double getCoordinate(int i,
                            Axis.Axis3 j)
```
    get a single coordinate value
    
    Parameters:
    
    i -
    
    j -
    
    Returns:
    
    coordinate
  - getXYZ
```
public RealArray getXYZ(Axis.Axis3 axis)
```
    get a single coordinate array for example all x-coordinates
    
    Parameters:
    
    axis -
    
    Returns:
    
    array
  - rms
```
public double rms(Point3Vector c)
```
    rms between two molecules - per atom
    
    Parameters:
    
    c -
    
    Returns:
    
    rms
  - getFurthestPointFrom
```
public int getFurthestPointFrom(Point3 p)
```
    get point furthest from another. useful for alignments
    
    Parameters:
    
    p - point to avoid (need not be in this)
    
    Returns:
    
    the serial of the furthest point
  - getPointMakingSmallestAngle
```
public int getPointMakingSmallestAngle(Point3 p1,
                                       Point3 p2)
```
    get point making smallest angle with two others. useful for alignments
    
    Parameters:
    
    p1 - point to avoid (need not be in this)
    
    p2 - point to avoid (need not be in this)
    
    Returns:
    
    the serial of the point making smallest angle
  - alignUsing3Points
```
public Transform3 alignUsing3Points(Point3Vector ref)
                             throws EuclidRuntimeException
```
    fit two coordinates of same length and alignment. very approximate uses get3SeparatedPoints() and then three find point1 furthest from centroid find point2 furthest from point1 find point3 making smallest angle with point1 and point2 m1 is moving molecule, m2 is fixed translate centroids to match then rotate so that m1-point1 coincides with m2-point1 then rotate so that m1-point2 coincides with m2-point2 This is rough, but will be a good starting point for most molecules.
    
    Parameters:
    
    ref -
    
    Returns:
    
    transformation
    
    Throws:
    
    EuclidRuntimeException - some unusual geometry (for example one coordinate set is linear, has coincident points, etc.)
  - get3SeparatedPoints
```
public int[] get3SeparatedPoints()
                          throws EuclidRuntimeException
```
    get three widely separated points. useful for initial alignments p1 is furthest from centroid p2 is furthest from p1 p3 is the point making smallest value of p1-p3-p2
    
    Returns:
    
    array with serial numbers of points
    
    Throws:
    
    EuclidRuntimeException - this or ref do not have 3 points or one has colinear or coincident points
  - align3PointVectors
```
public Transform3 align3PointVectors(Point3Vector ref)
                              throws EuclidRuntimeException
```
    fit two sets of three points. simple method. this and ref must each have 3 points rotates p1-p2 vector in each to be parallel then rotates p1-p2-p3 plane to be parallel This is rough, but will be a good starting point for many systems, especially if get3SeparatedPoints is used no translation this is not changed
    
    Parameters:
    
    ref - reference points
    
    Returns:
    
    transform such that ttansform * this = ref
    
    Throws:
    
    EuclidRuntimeException - this or ref do not have 3 points or one has colinear or coincident points
  - roughAlign
```
public Transform3 roughAlign(Point3Vector ref)
                      throws EuclidRuntimeException
```
    fit two coordinates of same length and alignment. rough method . fit 'this' to ref ('this' is moving molecule, ref is fixed) take copies and refer each to their centroid as origin. pick three points in ref which are well separated Find the plane of these three and use the normal, together with the vector to one of the points, to define two coordinate axes. Calculate the third axis as right-handed orthogonal (check). This gives a pure rotation matrix (Tref) using the corresponding points in 'this' repeat to give Tthis Tranformation matrix is then Tthis(T). Tref. Defining the intercentroid vector as Tthis2ref = centRef - centThis we have Tfinal = Tthis2Ref . Tthis(T) . Tref . (-Tthis2Ref) This is rough, but will be a good starting point for many systems.
    
    Parameters:
    
    ref -
    
    Returns:
    
    transformation
    
    Throws:
    
    EuclidRuntimeException - some unusual geometry (for example one coordinate set is linear, has coincident points, etc.)
  - fitTo
```
public Transform3 fitTo(Point3Vector ref)
                 throws EuclidRuntimeException
```
    fit two coordinates of same length and alignment CURRENTLY NOT VALIDATED
    
    Parameters:
    
    ref -
    
    Returns:
    
    transformation
    
    Throws:
    
    EuclidRuntimeException - some unusual geometry (for example one coordinate set is linear, has coincident points, etc.)
  - toString
```
public String toString()
```
    to string.
    
    Overrides:
    
    toString in class Object
    
    Returns:
    
    string
  - extractRealArray
```
public RealArray extractRealArray()
```
  - innerProduct
```
public Double innerProduct()
```

Class Point3Vector

Field Summary

Fields inherited from interface org.xmlcml.euclid.EuclidConstants

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

vector

Constructor Detail

Point3Vector

Point3Vector

Point3Vector

Point3Vector

Point3Vector

Method Detail

size

getPoint3List

isEqualTo

getArray

add

setElementAt

elementAt

get

addElement

setElementAt

getRange

getRange3

getSigmaDeltaSquared

subArray

multiplyBy

multiplyByEquals

plus

subtract

getLine

getCentroid

plus

plusEquals

subtract

moveToCentroid

removeNullValues

calculateNonMassWeightedInertialTensorOld

calculateRotationToInertialAxes

transform

transform

distance

distance

angle

angle

torsion

torsion

getDistanceMatrix

calculateNonMassWeightedInertialTensor

inertialAxes

bestPlane

deviationsFromPlane

getPoint3

getXYZ

getCoordinate

getXYZ

rms

getFurthestPointFrom

getPointMakingSmallestAngle

alignUsing3Points

get3SeparatedPoints

align3PointVectors

roughAlign

fitTo

toString

extractRealArray

innerProduct