Point

java.lang.Object
- ProGAL.geomNd.Point
- - ProGAL.geom3d.Point

All Implemented Interfaces:

java.io.Serializable, Shape, Simplex

Direct Known Subclasses:

CVertex, PointWeighted, Vertex
```
public class Point
extends Point
implements Simplex
```
A point in (x,y,z)-space represented with double precision.

See Also:

Serialized Form

Field Summary
- Fields inherited from class ProGAL.geomNd.Point
  coords, dim

Constructor Summary

Constructors
Constructor and Description
`Point(double[] coords)` Construct a point with the specified coordinates.
`Point(double x, double y, double z)` Construct a point with the specified coordinates.
`Point(Point p)` Construct a point that is a clone of p.
`Point(Vector v)` Construct a point at the coordinates of v.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`Point`	`add(double x, double y, double z)` Returns a point translated from this one by (x,y,z)
`Point`	`add(Point p)`
`Point`	`add(Vector p)` Returns a point translated from this one by p (without changing this object).
`Point`	`addThis(Point p)`
`Point`	`addThis(Vector p)` Returns p added to this (changing this object).
`Point`	`clone()` Return a new object that equals this object.
`static boolean`	`collinear(Point p0, Point p1, Point p2)` Returns true if three points are on the same line.
`static boolean`	`coplanar(Point p0, Point p1, Point p2, Point p3)` Returns true if four specified points are in the same plane
`double`	`distance(Point q)` Get the distance from this point to point q
`double`	`distanceSquared(Point q)` Get the squared distance from this point to point q.
`boolean`	`dominates(Point q)` Returns true if this point dominates point q.
`boolean`	`dominates(Point q, int i, int j, int k)` Returns true if this point dominates point q (i=0,1,2 is the most important coordinate, j=0,1,2 is the second most important coordinate and k=0,1,2 is the least important coordinate).
`double`	`dot(Point p)`
`double`	`dot(Vector v)`
`boolean`	`equals(java.lang.Object o)` Returns true iff o is a point that equals this point.
`boolean`	`equals(Point p)` Returns true iff this point and point p are overlapping.
`static double`	`getAngle(Point p1, Point p2, Point p3)` Get the angle between the line segments p2->p1 and p2->p3.
`static Plane`	`getBisector(Point p, Point q)` Creates a bisector between points p and q
`Point`	`getCenter()` Returns a clone of this point.
`static Point`	`getCircumCenter(Point a, Point b, Point c)`
`static double`	`getCosDihedralAngle(Point p1, Point p2, Point p3, Point p4)`
`static double`	`getDihedralAngle(Point p1, Point p2, Point p3, Point p4)` Get the dihedral angle defined by the 4 non-collinear points p1, p2, p3, p4.
`int`	`getDimension()` Return the 'dimension' of this object.
`static Circle`	`getEquilateralCircle(Point a, Point b, Point c)`
`static Point`	`getEquilateralPoint(Point a, Point b, Point c)`
`static Circle`	`getEquilateralPoints(Point a, Point b)`
`static Point`	`getMidpoint(Point p, Point q)` Creates the midpoint of two points.
`Point`	`getPoint(int i)` TODO: Comment
`static Point`	`getSteinerPoint(Point a, Point b, Point c)`
`static double`	`inSphere(Point p, Point q, Point r, Point s, Point t)` Returns a positive double if point t is inside the sphere through points p, q, r, s.
`static double`	`orientation(Point p, Point q, Point r, Point s)`
`static double`	`orientation(Point p, Point q, Point r, Point s, Point t)`
`double`	`polarAngleCosZ()` Returns the cosinus of the polar angle of this point with the z-axis
`double`	`polarAngleSinZ()` Returns the sinus of the polar angle of this point with the z-axis
`Point`	`reflectThroughOrigoThis()` Reflects this point through origo.
`void`	`rotation(Vector v, double alpha, Point p)` rotates (clockwise) the point around the line through the point p with the direction unit vector v.
`void`	`rotationCCW(Vector v, double alpha)`
`void`	`rotationCW(Vector v, double alpha)` rotates (clockwise) the point around the line through the origo with the direction unit vector v.
`void`	`scaleThis(double s)` Scale this point by a factor s
`void`	`setX(double x)` Set the first coordinate
`void`	`setY(double y)` Set the second coordinate
`void`	`setZ(double z)` Set the third coordinate
`Point`	`subtract(Point p)`
`Point`	`subtract(Vector p)` Returns p subtracted from this (without changing this object).
`Point`	`subtractThis(Point p)`
`Point`	`subtractThis(Vector p)` Returns p subtracted from this (changing this object).
`static void`	`swap(Point a, Point b)` Swaps points a and b
`void`	`toConsole()` Writes this point to `System.out`.
`void`	`toConsole(int dec)` Writes this point to `System.out` with `dec` decimals precision.
`java.lang.String`	`toString()` Returns a string-representation of this point formatted with two decimals precision.
`java.lang.String`	`toString(int dec)` Returns a string-representation of this point formatted with `dec` decimals precision.
`Vector`	`toVector()` Returns the vector from origo to this point.
`void`	`translateThis(double dx, double dy, double dz)` Translates this point by (x,y,z).
`void`	`translateThis(Point p)` Translates this point by p.
`Vector`	`vectorTo(Point p)` Get the vector that points from this point to p
`double`	`x()` Get the first coordinate.
`double`	`y()` Get the second coordinate.
`double`	`z()` Get the third coordinate.

Methods inherited from class ProGAL.geomNd.Point
add, addThis, distance, distance, distanceSquared, distanceSquared, distanceSquaredXY, distanceXY, dot, fill, get, getCoord, getCoords, getDimensions, getRandomPoint, multiplyThis, polarAngleCosXY, polarAngleSinXY, polarAngleXY, set, set, setCoord, setCoord, vectorTo

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

Constructor Detail
- Point
```
public Point(double x,
             double y,
             double z)
```
  Construct a point with the specified coordinates.
- Point
```
public Point(double[] coords)
```
  Construct a point with the specified coordinates.
- Point
```
public Point(Point p)
```
  Construct a point that is a clone of p.
- Point
```
public Point(Vector v)
```
  Construct a point at the coordinates of v.

Method Detail

x
```
public final double x()
```
Get the first coordinate.

y
```
public final double y()
```
Get the second coordinate.

z
```
public final double z()
```
Get the third coordinate.

setX
```
public final void setX(double x)
```
Set the first coordinate

setY
```
public final void setY(double y)
```
Set the second coordinate

setZ
```
public final void setZ(double z)
```
Set the third coordinate

getDimension
```
public final int getDimension()
```
Return the 'dimension' of this object. Required by the interface Simplex. Beware not to confuse this method with getDimensions from geomNd.Point.

Specified by:

getDimension in interface Simplex

vectorTo
```
public Vector vectorTo(Point p)
```
Get the vector that points from this point to p

collinear

public static boolean collinear(Point p0,
                                Point p1,
                                Point p2)

Returns true if three points are on the same line. This implies that overlapping points are considered collinear.

coplanar

public static boolean coplanar(Point p0,
                               Point p1,
                               Point p2,
                               Point p3)

Returns true if four specified points are in the same plane

orientation

public static double orientation(Point p,
                                 Point q,
                                 Point r,
                                 Point s)

orientation

public static double orientation(Point p,
                                 Point q,
                                 Point r,
                                 Point s,
                                 Point t)

inSphere

public static double inSphere(Point p,
                              Point q,
                              Point r,
                              Point s,
                              Point t)

Returns a positive double if point t is inside the sphere through points p, q, r, s.

translateThis

public void translateThis(double dx,
                          double dy,
                          double dz)

Translates this point by (x,y,z).

translateThis
```
public void translateThis(Point p)
```
Translates this point by p.

scaleThis
```
public void scaleThis(double s)
```
Scale this point by a factor s

addThis
```
public Point addThis(Vector p)
```
Returns p added to this (changing this object).

addThis
```
public Point addThis(Point p)
```

add
```
public Point add(Vector p)
```
Returns a point translated from this one by p (without changing this object).

add

public Point add(double x,
                 double y,
                 double z)

Returns a point translated from this one by (x,y,z)

add
```
public Point add(Point p)
```

subtractThis
```
public Point subtractThis(Vector p)
```
Returns p subtracted from this (changing this object).

subtractThis
```
public Point subtractThis(Point p)
```

subtract
```
public Point subtract(Vector p)
```
Returns p subtracted from this (without changing this object).

subtract
```
public Point subtract(Point p)
```

reflectThroughOrigoThis
```
public Point reflectThroughOrigoThis()
```
Reflects this point through origo.

rotationCW
```
public void rotationCW(Vector v,
                       double alpha)
```
rotates (clockwise) the point around the line through the origo with the direction unit vector v. For counterclockwise rotation change signs within parentheses in non-diagonal terms.

rotationCCW

public void rotationCCW(Vector v,
                        double alpha)

rotation
```
public void rotation(Vector v,
                     double alpha,
                     Point p)
```
rotates (clockwise) the point around the line through the point p with the direction unit vector v. For counterclockwise rotation change signs within parentheses in non-diagonal terms.

polarAngleSinZ
```
public double polarAngleSinZ()
```
Returns the sinus of the polar angle of this point with the z-axis

polarAngleCosZ
```
public double polarAngleCosZ()
```
Returns the cosinus of the polar angle of this point with the z-axis

distanceSquared
```
public double distanceSquared(Point q)
```
Get the squared distance from this point to point q.

distance
```
public double distance(Point q)
```
Get the distance from this point to point q

dot
```
public double dot(Point p)
```

dot
```
public double dot(Vector v)
```

getBisector

public static Plane getBisector(Point p,
                                Point q)

Creates a bisector between points p and q

getMidpoint

public static Point getMidpoint(Point p,
                                Point q)

Creates the midpoint of two points.

getAngle

public static double getAngle(Point p1,
                              Point p2,
                              Point p3)

Get the angle between the line segments p2->p1 and p2->p3.

getDihedralAngle

public static double getDihedralAngle(Point p1,
                                      Point p2,
                                      Point p3,
                                      Point p4)

Get the dihedral angle defined by the 4 non-collinear points p1, p2, p3, p4.

getCosDihedralAngle

public static double getCosDihedralAngle(Point p1,
                                         Point p2,
                                         Point p3,
                                         Point p4)

dominates
```
public boolean dominates(Point q)
```
Returns true if this point dominates point q. One point is said to dominate another if it has a higher x-coordinate. If two points have identical x-coordinates, the y-coordinate is considered and so forth.

dominates
```
public boolean dominates(Point q,
                         int i,
                         int j,
                         int k)
```
Returns true if this point dominates point q (i=0,1,2 is the most important coordinate, j=0,1,2 is the second most important coordinate and k=0,1,2 is the least important coordinate).

getCenter
```
public Point getCenter()
```
Returns a clone of this point. Since a point can be interpreted as a geometric shape (a 0-simplex) the Shape interface requires the getCenter method to be implemented. TODO: Test

Specified by:

getCenter in interface Shape

getPoint
```
public Point getPoint(int i)
```
Description copied from interface: Simplex

TODO: Comment

Specified by:

getPoint in interface Simplex

equals
```
public boolean equals(java.lang.Object o)
```
Returns true iff o is a point that equals this point.

Overrides:

equals in class java.lang.Object

equals
```
public boolean equals(Point p)
```
Returns true iff this point and point p are overlapping.

getCircumCenter

public static Point getCircumCenter(Point a,
                                    Point b,
                                    Point c)

getEquilateralPoint

public static Point getEquilateralPoint(Point a,
                                        Point b,
                                        Point c)

getEquilateralCircle

public static Circle getEquilateralCircle(Point a,
                                          Point b,
                                          Point c)

getEquilateralPoints

public static Circle getEquilateralPoints(Point a,
                                          Point b)

getSteinerPoint

public static Point getSteinerPoint(Point a,
                                    Point b,
                                    Point c)

clone
```
public Point clone()
```
Return a new object that equals this object.

Overrides:

clone in class Point

swap

public static void swap(Point a,
                        Point b)

Swaps points a and b

toVector
```
public Vector toVector()
```
Returns the vector from origo to this point. Converts this point to a vector.

Overrides:

toVector in class Point

toString
```
public java.lang.String toString()
```
Returns a string-representation of this point formatted with two decimals precision.

Overrides:

toString in class Point

toString
```
public java.lang.String toString(int dec)
```
Returns a string-representation of this point formatted with dec decimals precision.

Overrides:

toString in class Point

toConsole
```
public void toConsole()
```
Writes this point to System.out.

Overrides:

toConsole in class Point

toConsole
```
public void toConsole(int dec)
```
Writes this point to System.out with dec decimals precision.

Overrides:

toConsole in class Point

Class Point

Field Summary

Fields inherited from class ProGAL.geomNd.Point

Constructor Summary

Method Summary

Methods inherited from class ProGAL.geomNd.Point

Methods inherited from class java.lang.Object

Constructor Detail

Point

Point

Point

Point

Method Detail

x

y

z

setX

setY

setZ

getDimension

vectorTo

collinear

coplanar

orientation

orientation

inSphere

translateThis

translateThis

scaleThis

addThis

addThis

add

add

add

subtractThis

subtractThis

subtract

subtract

reflectThroughOrigoThis

rotationCW

rotationCCW

rotation

polarAngleSinZ

polarAngleCosZ

distanceSquared

distance

dot

dot

getBisector

getMidpoint

getAngle

getDihedralAngle

getCosDihedralAngle

dominates

dominates

getCenter

getPoint

equals

equals

getCircumCenter

getEquilateralPoint

getEquilateralCircle

getEquilateralPoints

getSteinerPoint

clone

swap

toVector

toString

toString

toConsole

toConsole