Orientation3D

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net.algart.drawing3d
Class Orientation3D

java.lang.Object
  net.algart.drawing3d.Orientation3D

public final class Orientation3D
extends java.lang.Object

Orthonormal basis in 3D space: 3 orthogonal unit vectors i, j, k (usually describing the orientation of some 3D configuration in the space). Each vector is represented by 3 double values: its components (x,y,z).

This class is immutable and thread-safe: there are no ways to modify settings of the created instance.

AlgART Laboratory 2010

Since:: JDK 1.5
Version:: 1.0
Author:: Daniel Alievsky

Field Summary
Modifier and Type	Field and Description
`static Orientation3D`	`DEFAULT` Standard orientation: i vector is (1,0,0), j vector is (0,1,0), k vector is (0,0,1).

Method Summary
Modifier and Type	Method and Description
`boolean`	`equals(java.lang.Object obj)` Indicates whether some other basis is equal to this instance, that is all corresponding components are absolutely identical.
`static Orientation3D`	`getInstance(double ix, double iy, double iz, double jx, double jy, double jz)` Creates new instance of this class, where the components of i and j vector are specified in the arguments and k vector is chosen automatically as the vector product [i,j] = (i_yj_z−i_zj_y, i_zj_x−i_xj_z, i_xj_y−i_yj_x)
`double`	`getIx()` Returns x-component i_x of i vector in this basis.
`double`	`getIy()` Returns y-component i_y of i vector in this basis.
`double`	`getIz()` Returns z-component i_z of i vector in this basis.
`double`	`getJx()` Returns x-component j_x of j vector in this basis.
`double`	`getJy()` Returns y-component j_y of j vector in this basis.
`double`	`getJz()` Returns z-component j_z of j vector in this basis.
`double`	`getKx()` Returns x-component k_x of k vector in this basis.
`double`	`getKy()` Returns y-component k_y of k vector in this basis.
`double`	`getKz()` Returns z-component k_z of k vector in this basis.
`static Orientation3D`	`getSomeInstance(double ix, double iy, double iz)` Creates new instance of this class, where the components of i vector are specified in the arguments, j and k vectors are chosen automatically by some (undocumented) way, so that the resulting basis i, j, k is orthonormal.
`int`	`hashCode()` Returns the hash code of this object.
`double`	`inverseTransformX(double x, double y, double z)` Returns the projection of the given vector (x,y,z) to the vector i.
`double`	`inverseTransformY(double x, double y, double z)` Returns the projection of the given vector (x,y,z) to the vector j.
`double`	`inverseTransformZ(double x, double y, double z)` Returns the projection of the given vector (x,y,z) to the vector k.
`Orientation3D`	`rotate(double xAngle, double yAngle, double zAngle)` Rotates this basis anticlockwise by the angle `xAngle` (in radians) around x-axis, then by angle `yAngle` (in radians) around y-axis, then by angle `zAngle` (in radians) around z-axis, and returns the result.
`Orientation3D`	`rotate(double vX, double vY, double vZ, double angle)` Rotates this basis by the specified angle (in radians) around the specified vector v=(v_x,v_yv_z) anticlockwise and returns the result.
`Orientation3D`	`rotateI(double angle)` Rotates this basis by the specified angle (in radians) around i vector anticlockwise and returns the result.
`Orientation3D`	`rotateJ(double angle)` Rotates this basis by the specified angle (in radians) around j vector anticlockwise and returns the result.
`Orientation3D`	`rotateK(double angle)` Rotates this basis by the specified angle (in radians) around k vector anticlockwise and returns the result.
`Orientation3D`	`superposition(Orientation3D basis)` Returns new basis, consisting of 3 vectors i''=i_xi'+i_yj'+i_zk', j''=j_xi'+j_yj'+j_zk', k''=k_xi'+k_yj'+k_zk', where i=(i_x,i_y,i_z), j=(j_x,j_y,j_z) and k=(k_x,k_y,k_z) is this basis and i', j', k' is a basis, specified in the argument.
`java.lang.String`	`toString()` Returns a brief string description of this object.
`double`	`transformX(double x, double y, double z)` Returns x-component of the vector xi+yj+zk.
`double`	`transformY(double x, double y, double z)` Returns y-component of the vector xi+yj+zk.
`double`	`transformZ(double x, double y, double z)` Returns z-component of the vector xi+yj+zk.

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

Field Detail

DEFAULT

public static final Orientation3D DEFAULT

Standard orientation: i vector is (1,0,0), j vector is (0,1,0), k vector is (0,0,1).

Method Detail

getSomeInstance

public static Orientation3D getSomeInstance(double ix,
                                            double iy,
                                            double iz)

Creates new instance of this class, where the components of i vector are specified in the arguments, j and k vectors are chosen automatically by some (undocumented) way, so that the resulting basis i, j, k is orthonormal.

If the passed vector i=(i_x,i_y,i_z) is not unit, it is automatically normalized: these 3 numbers are divided by Math.sqrt(i_x²+i_y²+i_z²).

Parameters:: ix - x-component i_x of i vector in the created basis.; iy - y-component i_y of i vector in the created basis.; iz - z-component i_z of i vector in the created basis.
Returns:: new orthonormal basis in 3D space with the given i vector.

getInstance

public static Orientation3D getInstance(double ix,
                                        double iy,
                                        double iz,
                                        double jx,
                                        double jy,
                                        double jz)

Creates new instance of this class, where the components of i and j vector are specified in the arguments and k vector is chosen automatically as the vector product [i,j] = (i_yj_z−i_zj_y, i_zj_x−i_xj_z, i_xj_y−i_yj_x)

If the passed vector i=(i_x,i_y,i_z) is not unit, it is automatically normalized: these 3 numbers are divided by Math.sqrt(i_x²+i_y²+i_z²). If the passed vector j=(j_x,j_y,j_z) is not unit, it is automatically normalized: these 3 numbers are divided by Math.sqrt(j_x²+j_y²+j_z²). If the passed i and j vectors are not orthogonal, j vector is automatically corrected to become orthogonal to i.

Parameters:: ix - x-component i_x of i vector in the created basis.; iy - y-component i_y of i vector in the created basis.; iz - z-component i_z of i vector in the created basis.; jx - x-component j_x of j vector in the created basis.; jy - y-component j_y of j vector in the created basis.; jz - z-component j_z of j vector in the created basis.
Returns:: new orthonormal basis in 3D space with the given i and j vectors.

getIx

public double getIx()

Returns x-component i_x of i vector in this basis.

Returns:: x-component i_x of i vector in this basis.

getIy

public double getIy()

Returns y-component i_y of i vector in this basis.

Returns:: y-component i_y of i vector in this basis.

getIz

public double getIz()

Returns z-component i_z of i vector in this basis.

Returns:: z-component i_z of i vector in this basis.

getJx

public double getJx()

Returns x-component j_x of j vector in this basis.

Returns:: x-component j_x of j vector in this basis.

getJy

public double getJy()

Returns y-component j_y of j vector in this basis.

Returns:: y-component j_y of j vector in this basis.

getJz

public double getJz()

Returns z-component j_z of j vector in this basis.

Returns:: z-component j_z of j vector in this basis.

getKx

public double getKx()

Returns x-component k_x of k vector in this basis.

Returns:: x-component k_x of k vector in this basis.

getKy

public double getKy()

Returns y-component k_y of k vector in this basis.

Returns:: y-component k_y of k vector in this basis.

getKz

public double getKz()

Returns z-component k_z of k vector in this basis.

Returns:: z-component k_z of k vector in this basis.

transformX

public double transformX(double x,
                         double y,
                         double z)

Returns x-component of the vector xi+yj+zk. In other words, returns xi_x+yj_x+zk_x.

Parameters:: x - x-component of some vector, specified in the given basis.; y - y-component of some vector, specified in the given basis.; z - z-component of some vector, specified in the given basis.
Returns:: x-component of the vector xi+yj+zk.

transformY

public double transformY(double x,
                         double y,
                         double z)

Returns y-component of the vector xi+yj+zk. In other words, returns xi_y+yj_y+zk_y.

Parameters:: x - x-component of some vector, specified in the given basis.; y - y-component of some vector, specified in the given basis.; z - z-component of some vector, specified in the given basis.
Returns:: y-component of the vector xi+yj+zk.

transformZ

public double transformZ(double x,
                         double y,
                         double z)

Returns z-component of the vector xi+yj+zk. In other words, returns xi_z+yj_z+zk_z.

Parameters:: x - x-component of some vector, specified in the given basis.; y - y-component of some vector, specified in the given basis.; z - z-component of some vector, specified in the given basis.
Returns:: z-component of the vector xi+yj+zk.

inverseTransformX

public double inverseTransformX(double x,
                                double y,
                                double z)

Returns the projection of the given vector (x,y,z) to the vector i. In other words, returns xi_x+yi_y+zi_z: the x-components of the given vector in terms of this basis.

Parameters:: x - x-component of some vector.; y - y-component of some vector.; z - z-component of some vector.
Returns:: the x-components of the given vector in terms of this basis.

inverseTransformY

public double inverseTransformY(double x,
                                double y,
                                double z)

Returns the projection of the given vector (x,y,z) to the vector j. In other words, returns xj_x+yj_y+zj_z: the y-components of the given vector in terms of this basis.

Parameters:: x - x-component of some vector.; y - y-component of some vector.; z - z-component of some vector.
Returns:: the y-components of the given vector in terms of this basis.

inverseTransformZ

public double inverseTransformZ(double x,
                                double y,
                                double z)

Returns the projection of the given vector (x,y,z) to the vector k. In other words, returns xk_x+yk_y+zk_z: the z-components of the given vector in terms of this basis.

Parameters:: x - x-component of some vector.; y - y-component of some vector.; z - z-component of some vector.
Returns:: the z-components of the given vector in terms of this basis.

superposition

public Orientation3D superposition(Orientation3D basis)

Returns new basis, consisting of 3 vectors i''=i_xi'+i_yj'+i_zk', j''=j_xi'+j_yj'+j_zk', k''=k_xi'+k_yj'+k_zk', where i=(i_x,i_y,i_z), j=(j_x,j_y,j_z) and k=(k_x,k_y,k_z) is this basis and i', j', k' is a basis, specified in the argument. If we'll interpret this and passed bases as rotations of the coordinate system from default basis to i, j, k triplet, then this method describes the composition of the passed and this rotations.

Parameters:: basis - some other basis.
Returns:: this basis, transformed according the passed one.
Throws:: java.lang.NullPointerException - if the argument is null.

rotateI

public Orientation3D rotateI(double angle)

Rotates this basis by the specified angle (in radians) around i vector anticlockwise and returns the result. The returned basis has the same i vector. "Anticlockwise" means, that if, for example, angle=Math.PI/2, then j of the result will be equal to k vector of this basis.

Parameters:: angle - angle for rotation around i vector, in radians.
Returns:: the rotated basis.

rotateJ

public Orientation3D rotateJ(double angle)

Rotates this basis by the specified angle (in radians) around j vector anticlockwise and returns the result. The returned basis has the same j vector. "Anticlockwise" means, that if, for example, angle=Math.PI/2, then k of the result will be equal to i vector of this basis.

Parameters:: angle - angle for rotation around j vector, in radians.
Returns:: the rotated basis.

rotateK

public Orientation3D rotateK(double angle)

Rotates this basis by the specified angle (in radians) around k vector anticlockwise and returns the result. The returned basis has the same k vector. "Anticlockwise" means, that if, for example, angle=Math.PI/2, then i of the result will be equal to j vector of this basis.

Parameters:: angle - angle for rotation around k vector, in radians.
Returns:: the rotated basis.

rotate

public Orientation3D rotate(double xAngle,
                            double yAngle,
                            double zAngle)

Rotates this basis anticlockwise by the angle xAngle (in radians) around x-axis, then by angle yAngle (in radians) around y-axis, then by angle zAngle (in radians) around z-axis, and returns the result. "Anticlockwise" rotation around x axis means, that if, for example, xAngle=Math.PI/2, then (0,1,0) vector is transformed to (0,0,1). Analogously, "anticlockwise" rotation around y axis means, that if yAngle=Math.PI/2, then (0,0,1) vector is transformed to (1,0,0), and "anticlockwise" rotation around z axis means, that if zAngle=Math.PI/2, then (1,0,0) vector is transformed to (0,1,0).

Parameters:: xAngle - angle for rotation around x-axis, in radians.; yAngle - angle for rotation around y-axis, in radians.; zAngle - angle for rotation around z-axis, in radians.
Returns:: the rotated basis.

rotate

public Orientation3D rotate(double vX,
                            double vY,
                            double vZ,
                            double angle)

Rotates this basis by the specified angle (in radians) around the specified vector v=(v_x,v_yv_z) anticlockwise and returns the result. "Anticlockwise" means, that if (vX,vY,vZ) is i, then this method is equivalent to rotateI(angle).

Parameters:: vX - x-component of v vector.; vY - y-component of v vector.; vZ - z-component of v vector.; angle - angle for rotation around v vector, in radians.
Returns:: the rotated basis.

toString

public java.lang.String toString()

Returns a brief string description of this object.

The result of this method may depend on implementation.

Overrides:: toString in class java.lang.Object

Returns:: a brief string description of this object.

hashCode

public int hashCode()

Returns the hash code of this object. The result depends on all components of the basis vectors i, j, k.

Overrides:: hashCode in class java.lang.Object

Returns:: the hash code of this object.

equals

public boolean equals(java.lang.Object obj)

Indicates whether some other basis is equal to this instance, that is all corresponding components are absolutely identical.

Overrides:: equals in class java.lang.Object

Parameters:: obj - the object to be compared for equality with this instance.
Returns:: true if the specified object is a basis equal to this one.

Overview

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SUMMARY: NESTED | FIELD | CONSTR | METHOD

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net.algart.drawing3d Class Orientation3D

DEFAULT

getSomeInstance

getInstance

getIx

getIy

getIz

getJx

getJy

getJz

getKx

getKy

getKz

transformX

transformY

transformZ

inverseTransformX

inverseTransformY

inverseTransformZ

superposition

rotateI

rotateJ

rotateK

rotate

rotate

toString

hashCode

equals

net.algart.drawing3d
Class Orientation3D