frink.graphics

Class Point3DFloat

java.lang.Object

frink.graphics.Point3DFloat

public class Point3DFloat
extends java.lang.Object

This is a simple data structure that represents a 3-D point or vector with the coordinates represented as float.

When discussing spherical coordinate systems, this uses the physics conventions (ISO 80000-2:2019) discussed in the Wikipedia article for Spherical Coordinate System.

A spherical coordinate is represented as (r, theta, phi) where r is the distance to the origin, theta is the angle down from the z axis (in radians), and phi is the angle starting from the x axis and rotating toward the y axis (in radians.) When these are mapped to a Point3DDouble, x is r, y is theta, and z is phi.

An altitude-azimuth (altAz) coordinate is represented as (r, alt, az) where r is the distance to the origin, alt is the angle "up" from the horizon, and az is the azimuth angle in radians with 0 being north (y axis) and increasing toward the east (x axis). When these are mapped to a Point3DDouble, x is r, y is alt, and z is az.

A cylindrical coordinate is similar to altitude-azimuth and represented as (r, az, h) where r is the distance in the x-y plane to the z axis, az is the azimuth angle in radians with 0 being north (y axis) and increasing toward the east (x axis), and h is the height (equal to the z axis.) When these are mapped to a Point3DDouble, x is r, y is az, and z is h.

Author:

Alan Eliasen, eliasen@mindspring.com

Field Summary

Fields

Modifier and Type	Field and Description
float	x The x coordinate.
float	y The y coordinate.
float	z The z coordinate.

Constructor Summary

Constructors

Constructor and Description
Point3DFloat(float x, float y, float z) Construct a Point3DFloat with the specified coordinates.
Point3DFloat(Point3DInt orig) Construct a Point3DFloat from a Point3DInt

Method Summary

Modifier and Type	Method and Description
static Point3DFloat	altAzToXYZ(double r, double alt, double az, double cx, double cy, double cz, Point3DFloat out) Transforms altAz coordinates r, alt, az into cartesian coordinates x, y, z.
static Point3DFloat	altAzToXYZ(Point3DDouble altAz, Point3DFloat out) Transforms this point which represents its elements as altAz coordinates r, alt, az, into cartesian coordinates x, y, z.
Point3DFloat	crossProduct(Point3DFloat b) Calculates the cross product of this vector and another vector, each represented as a Point3DFloat, in 3D space and returns the vector cross product.
static Point3DFloat	crossProduct(Point3DFloat V, Point3DFloat W) Calculates the cross product of two vectors in 3D space, each represented as a Point3DFloat, and returns the vector cross product.
static Point3DFloat	crossProduct(Point3DFloat p1, Point3DFloat p2, Point3DFloat p3) Returns the cross prduct of three points in 3D space (as listed in counterclockwise order as seen from the "outside") and returns the vector cross product.
static float	crossProductLength(float vx, float vy, float vz, float wx, float wy, float wz) Calculates the LENGTH of the cross product of two vectors in 3D space and returns the length.
float	crossProductLength(Point3DFloat v) Calculates the LENGTH of the cross product of two vectors in 3D space and returns the length.
static float	crossProductLength(Point3DFloat V, Point3DFloat W) Calculates the LENGTH of the cross product of this vector and another vector in 3D space and returns the length.
static Point3DFloat	cylindricalToXYZ(double r, double az, double h, double cx, double cy, double cz, Point3DFloat out) Transforms cylindrical coordinates r, az, h into cartesian coordinates x, y, z.
static Point3DFloat	cylindricalToXYZ(Point3DDouble cyl, Point3DFloat out) Transforms this point which represents its elements as cylindrical coordinates r, az, h into cartesian coordinates x, y, z.
float	distance(float x2, float y2, float z2) Calculates the distance between this point and some 3-D coordinates.
static float	distance(float x1, float y1, float z1, float x2, float y2, float z2) Returns the distance between two points specified by their coordinates.
float	distance(Point3DFloat p2) Calculates the distance between this point and another point.
static float	distance(Point3DFloat p1, Point3DFloat p2) Calculates the distance between two points.
float	distanceSquared(Point3DFloat p2) Returns the squared distance between this point and another point.
static float	distanceSquared(Point3DFloat p1, Point3DFloat p2) Returns the squared distance between two points.
float	dotProduct(Point3DFloat v2) Returns the dot product of this vector and another vector, each represented as a Point3DFloat.
static float	dotProduct(Point3DFloat v1, Point3DFloat v2) Returns the dot product of two vectors, each represented as a Point3DFloat.
float	length() Treats this point as a vector and returns its length from the origin.
static float	length(float x1, float y1, float z1) Treat the coordinates as a vector and return its length from the origin.
static Point3DFloat	makeNormal(float x, float y, float z) Constructs a Point3DFloat that is normalized to have length 1.
Point3DFloat	normalize() Treats this point as a vector and normalizes it to have length 1, returning a new vector that is the normalized vector.
static double	signum(double a) Java didn't have java.lang.math.Signum until Java 1.5.
static Point3DFloat	sphericalToXYZ(double r, double theta, double phi, double cx, double cy, double cz, Point3DFloat out) Transforms spherical coordinates r, theta, phi into cartesian coordinates x, y, z.
static Point3DFloat	sphericalToXYZ(Point3DDouble spher, Point3DFloat out) Transforms this point which represents its elements as spherical coordinates r, theta, phi into cartesian coordinates x, y, z.
Point3DFloat	subtract(Point3DFloat p2) Constructs a new Point3DFloat where the components of p2 are subtracted from this point.
static Point3DFloat	subtract(Point3DFloat p1, Point3DFloat p2) Constructs a new Point3DFloat where the components are subtracted from each other.
static float	subtractLength(Point3DFloat p1, Point3DFloat p2) Returns the length of p1 - p2.
Point3DDouble	toAltAz() Converts this point represented as an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, alt, az).
static Point3DDouble	toAltAz(double x, double y, double z) Converts an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, alt, az).
static Point3DDouble	toAltAz(double x, double y, double z, double cx, double cy, double cz, Point3DDouble out) Converts an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, alt, az).
Point3DDouble	toAltAz(Point3DDouble out) Converts this point represented as an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, alt, az).
Point3DDouble	toCylindrical() Converts this point represented as an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, az, h).
static Point3DDouble	toCylindrical(double x, double y, double z) Converts an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, az, h).
static Point3DDouble	toCylindrical(double x, double y, double z, double cx, double cy, double cz, Point3DDouble out) Converts an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, az, h).
Point3DDouble	toCylindrical(Point3DDouble out) Converts this point represented as an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, az, h).
Point3DDouble	toSpherical() Converts this point represented as an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, theta, phi).
static Point3DDouble	toSpherical(double x, double y, double z) Converts an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, theta, phi).
static Point3DDouble	toSpherical(double x, double y, double z, double cx, double cy, double cz, Point3DDouble out) Converts an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, theta, phi).
Point3DDouble	toSpherical(Point3DDouble out) Converts this point represented as an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, theta, phi).
java.lang.String	toString() Returns a String representation of this point.

Methods inherited from class java.lang.Object

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

Field Detail

x

public float x

The x coordinate.

y

public float y

The y coordinate.

z

public float z

The z coordinate.

Constructor Detail

Point3DFloat

public Point3DFloat(float x,
                    float y,
                    float z)

Construct a Point3DFloat with the specified coordinates.

Point3DFloat

public Point3DFloat(Point3DInt orig)

Construct a Point3DFloat from a Point3DInt

Method Detail

makeNormal

public static Point3DFloat makeNormal(float x,
                                      float y,
                                      float z)

Constructs a Point3DFloat that is normalized to have length 1.

length

public float length()

Treats this point as a vector and returns its length from the origin.

length

public static float length(float x1,
                           float y1,
                           float z1)

Treat the coordinates as a vector and return its length from the origin.

normalize

public Point3DFloat normalize()

Treats this point as a vector and normalizes it to have length 1, returning a new vector that is the normalized vector.

subtract

public Point3DFloat subtract(Point3DFloat p2)

Constructs a new Point3DFloat where the components of p2 are subtracted from this point.

subtract

public static Point3DFloat subtract(Point3DFloat p1,
                                    Point3DFloat p2)

Constructs a new Point3DFloat where the components are subtracted from each other.

subtractLength

public static float subtractLength(Point3DFloat p1,
                                   Point3DFloat p2)

Returns the length of p1 - p2. This avoids an allocation if only the length is needed.

distance

public static float distance(Point3DFloat p1,
                             Point3DFloat p2)

Calculates the distance between two points.

distance

public float distance(Point3DFloat p2)

Calculates the distance between this point and another point.

distance

public float distance(float x2,
                      float y2,
                      float z2)

Calculates the distance between this point and some 3-D coordinates.

distanceSquared

public static float distanceSquared(Point3DFloat p1,
                                    Point3DFloat p2)

Returns the squared distance between two points.

distanceSquared

public float distanceSquared(Point3DFloat p2)

Returns the squared distance between this point and another point.

distance

public static float distance(float x1,
                             float y1,
                             float z1,
                             float x2,
                             float y2,
                             float z2)

Returns the distance between two points specified by their coordinates.

crossProduct

public static Point3DFloat crossProduct(Point3DFloat V,
                                        Point3DFloat W)

Calculates the cross product of two vectors in 3D space, each represented as a Point3DFloat, and returns the vector cross product. This does *NOT* normalize the resultant vector. The physical meaning of the cross product is to find a third vector which is perpendicular to both of the other two vectors. args: V and W are 3-d vectors represented by Point3DFloat returns: A Point3DFloat representing the cross product.

crossProduct

public Point3DFloat crossProduct(Point3DFloat b)

Calculates the cross product of this vector and another vector, each represented as a Point3DFloat, in 3D space and returns the vector cross product. This does *NOT* normalize the resultant vector. The physical meaning of the cross product is to find a third vector which is perpendicular to both of the other two vectors. args: this and b are 3-d vectors represented by Point3DFloat. returns: A Point3DFloat representing the cross product.

crossProduct

public static Point3DFloat crossProduct(Point3DFloat p1,
                                        Point3DFloat p2,
                                        Point3DFloat p3)

Returns the cross prduct of three points in 3D space (as listed in counterclockwise order as seen from the "outside") and returns the vector cross product. The resulting vector points to the "outside" of the object. This does *NOT* normalize the resultant vector. The physical meaning of the cross product is to find a vector which is perpendicular to the plane defined by the three points. returns: A non-normalized Point3D representing the cross product as a vector.

crossProductLength

public float crossProductLength(Point3DFloat v)

Calculates the LENGTH of the cross product of two vectors in 3D space and returns the length. This is intended to eliminate an allocation of a Point3DFloat. args: this and v are 3-d vectors represented by Point3DFloat returns: A Point3DFloat representing the cross product.

crossProductLength

public static float crossProductLength(Point3DFloat V,
                                       Point3DFloat W)

Calculates the LENGTH of the cross product of this vector and another vector in 3D space and returns the length. This is intended to eliminate an allocation of a Point3DFloat. args: this and v2 are 3-d vectors represented by Point3DFloat returns: A Point3DFloat representing the cross product.

crossProductLength

public static float crossProductLength(float vx,
                                       float vy,
                                       float vz,
                                       float wx,
                                       float wy,
                                       float wz)

Calculates the LENGTH of the cross product of two vectors in 3D space and returns the length. This is intended to eliminate an allocation of a Point3DFloat. returns: A Point3DFloat representing the cross product.

dotProduct

public static float dotProduct(Point3DFloat v1,
                               Point3DFloat v2)

Returns the dot product of two vectors, each represented as a Point3DFloat. The physical meaning of the dot product is to measure how closely the two vectors point in the same direction. For this, the vectors should first be normalized to have length 1. The dot product will range from 1 for two vectors which point in the same direction to 0 for two perpendicular vectors to -1 for vectors which point in opposite directions. To obtain the angle between two normalized vectors, use: angle = Math.acos(dotProduct(v1, v2));

dotProduct

public float dotProduct(Point3DFloat v2)

Returns the dot product of this vector and another vector, each represented as a Point3DFloat. The physical meaning of the dot product is to measure how closely the two vectors point in the same direction. For this, the vectors should first be normalized to have length 1. The dot product will range from 1 for two vectors which point in the same direction to 0 for two perpendicular vectors to -1 for vectors which point in opposite directions. To obtain the angle between two normalized vectors, use: angle = Math.acos(dotProduct(v1, v2));

sphericalToXYZ

public static Point3DFloat sphericalToXYZ(double r,
                                          double theta,
                                          double phi,
                                          double cx,
                                          double cy,
                                          double cz,
                                          Point3DFloat out)

Transforms spherical coordinates r, theta, phi into cartesian coordinates x, y, z. See above for definitions of the coordinate systems.

Parameters:

r - The radial distance

theta - The angle "down" from the z axis

phi - The angle starting from the x axis and rotating toward the y axis.

out - An optional (may be null) Point3DFloat that receives the results to avoid allocations. If this is null, a new object will be allocated. If out is an object, it will be modified in place with the results and also returned.

Returns:

a 3-D point containing the resulting coordinate.

sphericalToXYZ

public static Point3DFloat sphericalToXYZ(Point3DDouble spher,
                                          Point3DFloat out)

Transforms this point which represents its elements as spherical coordinates r, theta, phi into cartesian coordinates x, y, z. See above for definitions of the coordinate systems.

Parameters:

spher - A Point3DDouble which contains its coordinates as (r, theta, phi)

out - An optional (may be null) Point3DFloat that receives the results to avoid allocations. If out is null, a new object will be allocated. If out is an object, it will be modified in place with the results and also returned.

Returns:

a 3-D point containing the resulting coordinate.

toSpherical

public Point3DDouble toSpherical()

Converts this point represented as an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, theta, phi). See the top of this file for a description of coordinate conventions. If x and y are zero, this returns 0 for theta and phi.

Returns:

a new Point3DDouble containing the (r, theta, phi) coordinates. To avoid memory allocations, use the toSpherical(Point3DDouble) method.

toSpherical

public Point3DDouble toSpherical(Point3DDouble out)

Converts this point represented as an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, theta, phi). See the top of this file for a description of coordinate conventions. If x and y are zero, this returns 0 for theta and phi.

Parameters:

out - An optional (may be null) Point3DDouble that receives the results to avoid allocations. If out is null, a new object will be allocated. If out is an object, it will be modified in place with the results and also returned.

Returns:

a Point3DDouble containing the (r, theta, phi) coordinates.

toSpherical

public static Point3DDouble toSpherical(double x,
                                        double y,
                                        double z)

Converts an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, theta, phi). See the top of this file for a description of coordinate conventions. If x and y are zero, this returns 0 for theta and phi.

Returns:

a new Point3DDouble containing the (r,theta,phi) coordinates. To avoid memory allocations, use the toSpherical(double,double,double,double,double,double,Point3DDouble) method.

toSpherical

public static Point3DDouble toSpherical(double x,
                                        double y,
                                        double z,
                                        double cx,
                                        double cy,
                                        double cz,
                                        Point3DDouble out)

Converts an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, theta, phi). See the top of this file for a description of coordinate conventions. If x and y are zero, this returns 0 for theta and phi.

Parameters:

out - An optional (may be null) Point3DDouble that receives the results to avoid allocations. If out is null, a new object will be allocated. If out is an object, it will be modified in place with the results and also returned.

Returns:

a Point3DDouble containing the (r, theta, phi) coordinates.

altAzToXYZ

public static Point3DFloat altAzToXYZ(double r,
                                      double alt,
                                      double az,
                                      double cx,
                                      double cy,
                                      double cz,
                                      Point3DFloat out)

Transforms altAz coordinates r, alt, az into cartesian coordinates x, y, z. See above for definitions of the coordinate systems.

Parameters:

r - The radial distance

alt - The altitude angle "up" from the horizon in radians.

az - The azimuth angle east of north in radians.

out - An optional (may be null) Point3DFloat that receives the results to avoid allocations. If this is null, a new object will be allocated. If out is an object, it will be modified in place with the results and also returned.

Returns:

a 3-D point containing the resulting xyz coordinate.

altAzToXYZ

public static Point3DFloat altAzToXYZ(Point3DDouble altAz,
                                      Point3DFloat out)

Transforms this point which represents its elements as altAz coordinates r, alt, az, into cartesian coordinates x, y, z. See above for definitions of the coordinate systems.

Parameters:

altAz - A Point3DDouble which contains its coordinates as (r, alt, az)

out - An optional (may be null) Point3DFloat that receives the results to avoid allocations. If out is null, a new object will be allocated. If out is an object, it will be modified in place with the results and also returned.

Returns:

a 3-D point containing the resulting coordinate.

toAltAz

public Point3DDouble toAltAz()

Converts this point represented as an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, alt, az). See the top of this file for a description of coordinate conventions. If x and y are zero, this returns 0 for alt and az.

Returns:

a new Point3DDouble containing the (r, alt, az) coordinates. To avoid memory allocations, use the toAltAz(Point3DDouble) method.

toAltAz

public Point3DDouble toAltAz(Point3DDouble out)

Converts this point represented as an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, alt, az). See the top of this file for a description of coordinate conventions. If x and y are zero, this returns 0 for alt and az.

Parameters:

out - An optional (may be null) Point3DDouble that receives the results to avoid allocations. If out is null, a new object will be allocated. If out is an object, it will be modified in place with the results and also returned.

Returns:

a Point3DDouble containing the (r, alt, az) coordinates.

toAltAz

public static Point3DDouble toAltAz(double x,
                                    double y,
                                    double z)

Converts an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, alt, az). See the top of this file for a description of coordinate conventions. If x and y are zero, this returns 0 for alt and az.

Returns:

a new Point3DDouble containing the (r, alt, az) coordinates. To avoid memory allocations, use the toAltAz(double,double,double,double,double,double,Point3DDouble) method.

toAltAz

public static Point3DDouble toAltAz(double x,
                                    double y,
                                    double z,
                                    double cx,
                                    double cy,
                                    double cz,
                                    Point3DDouble out)

Converts an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, alt, az). See the top of this file for a description of coordinate conventions. If x and y are zero, this returns 0 for alt and az.

Parameters:

out - An optional (may be null) Point3DDouble that receives the results to avoid allocations. If out is null, a new object will be allocated. If out is an object, it will be modified in place with the results and also returned.

Returns:

a new Point3DDouble containing the (r, alt, az) coordinates.

cylindricalToXYZ

public static Point3DFloat cylindricalToXYZ(double r,
                                            double az,
                                            double h,
                                            double cx,
                                            double cy,
                                            double cz,
                                            Point3DFloat out)

Transforms cylindrical coordinates r, az, h into cartesian coordinates x, y, z. See above for definitions of the coordinate systems.

Parameters:

r - The radial distance in the x-y plane from the z axis

az - The angle from the y axis (north) and increasing toward the x axis (east.)

h - The height along the z axis.

out - An optional (may be null) Point3DFloat that receives the results to avoid allocations. If this is null, a new object will be allocated. If out is an object, it will be modified in place with the results and also returned.

Returns:

a 3-D point containing the resulting coordinate.

cylindricalToXYZ

public static Point3DFloat cylindricalToXYZ(Point3DDouble cyl,
                                            Point3DFloat out)

Transforms this point which represents its elements as cylindrical coordinates r, az, h into cartesian coordinates x, y, z. See above for definitions of the coordinate systems.

Parameters:

cyl - A Point3DDouble which contains its coordinates as (r, az, h)

out - An optional (may be null) Point3DFloat that receives the results to avoid allocations. If out is null, a new object will be allocated. If out is an object, it will be modified in place with the results and also returned.

Returns:

a 3-D point containing the resulting coordinate.

toCylindrical

public Point3DDouble toCylindrical()

Converts this point represented as an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, az, h). See the top of this file for a description of coordinate conventions. If x and y are zero, this returns 0 for az.

Returns:

a new Point3DDouble containing the (r, az, h) coordinates. To avoid memory allocations, use the toCylindrical(Point3DDouble) method.

toCylindrical

public Point3DDouble toCylindrical(Point3DDouble out)

Converts this point represented as an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, az, h). See the top of this file for a description of coordinate conventions. If x and y are zero, this returns 0 for az.

Parameters:

out - An optional (may be null) Point3DDouble that receives the results to avoid allocations. If out is null, a new object will be allocated. If out is an object, it will be modified in place with the results and also returned.

Returns:

a Point3DDouble containing the (r, az, h) coordinates.

toCylindrical

public static Point3DDouble toCylindrical(double x,
                                          double y,
                                          double z)

Converts an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, az, h). See the top of this file for a description of coordinate conventions. If x and y are zero, this returns 0 for az.

Returns:

a new Point3DDouble containing the (r,az,h) coordinates. To avoid memory allocations, use the toCylindrical(double,double,double,double,double,double,Point3DDouble) method.

toCylindrical

public static Point3DDouble toCylindrical(double x,
                                          double y,
                                          double z,
                                          double cx,
                                          double cy,
                                          double cz,
                                          Point3DDouble out)

Converts an X,Y,Z coordinate to a Point3DDouble indicating the coordinates in (r, az, h). See the top of this file for a description of coordinate conventions. If x and y are zero, this returns 0 for az.

Parameters:

out - An optional (may be null) Point3DDouble that receives the results to avoid allocations. If out is null, a new object will be allocated. If out is an object, it will be modified in place with the results and also returned.

Returns:

a Point3DDouble containing the (r, az, h) coordinates.

toString

public java.lang.String toString()

Returns a String representation of this point.

Overrides:

toString in class java.lang.Object

signum

public static double signum(double a)

Java didn't have java.lang.math.Signum until Java 1.5. Remove this then.