spim.vecmath

## Class Transform3D

• ```public class Transform3D
extends Object```
A generalized transform object represented internally as a 4x4 double-precision floating point matrix. The mathematical representation is row major, as in traditional matrix mathematics. A Transform3D is used to perform translations, rotations, and scaling and shear effects.

A transform has an associated type, and all type classification is left to the Transform3D object. A transform will typically have multiple types, unless it is a general, unclassifiable matrix, in which case it won't be assigned a type.

The Transform3D type is internally computed when the transform object is constructed and updated any time it is modified. A matrix will typically have multiple types. For example, the type associated with an identity matrix is the result of ORing all of the types, except for ZERO and NEGATIVE_DETERMINANT, together. There are public methods available to get the ORed type of the transformation, the sign of the determinant, and the least general matrix type. The matrix type flags are defined as follows:

• ZERO - zero matrix. All of the elements in the matrix have the value 0.
• IDENTITY - identity matrix. A matrix with ones on its main diagonal and zeros every where else.
• SCALE - the matrix is a uniform scale matrix - there are no rotational or translation components.
• ORTHOGONAL - the four row vectors that make up an orthogonal matrix form a basis, meaning that they are mutually orthogonal. The scale is unity and there are no translation components.
• RIGID - the upper 3 X 3 of the matrix is orthogonal, and there is a translation component-the scale is unity.
• CONGRUENT - this is an angle- and length-preserving matrix, meaning that it can translate, rotate, and reflect about an axis, and scale by an amount that is uniform in all directions. These operations preserve the distance between any two points, and the angle between any two intersecting lines.
• AFFINE - an affine matrix can translate, rotate, reflect, scale anisotropically, and shear. Lines remain straight, and parallel lines remain parallel, but the angle between intersecting lines can change.
A matrix is also classified by the sign of its determinant:

• NEGATIVE_DETERMINANT - this matrix has a negative determinant. An orthogonal matrix with a positive determinant is a rotation matrix. An orthogonal matrix with a negative determinant is a reflection and rotation matrix.
The Java 3D model for 4 X 4 transformations is:
• ``` [ m00 m01 m02 m03 ]   [ x ]   [ x' ]
[ m10 m11 m12 m13 ] . [ y ] = [ y' ]
[ m20 m21 m22 m23 ]   [ z ]   [ z' ]
[ m30 m31 m32 m33 ]   [ w ]   [ w' ]

x' = m00 . x+m01 . y+m02 . z+m03 . w
y' = m10 . x+m11 . y+m12 . z+m13 . w
z' = m20 . x+m21 . y+m22 . z+m23 . w
w' = m30 . x+m31 . y+m32 . z+m33 . w
```

Note: When transforming a Point3f or a Point3d, the input w is set to 1. When transforming a Vector3f or Vector3d, the input w is set to 0.

• ### Field Summary

Fields
Modifier and Type Field and Description
`static int` `AFFINE`
An affine matrix can translate, rotate, reflect, scale anisotropically, and shear.
`static int` `CONGRUENT`
This is an angle and length preserving matrix, meaning that it can translate, rotate, and reflect about an axis, and scale by an amount that is uniform in all directions.
`static int` `IDENTITY`
An identity matrix.
`static int` `NEGATIVE_DETERMINANT`
This matrix has a negative determinant; an orthogonal matrix with a positive determinant is a rotation matrix; an orthogonal matrix with a negative determinant is a reflection and rotation matrix.
`static int` `ORTHOGONAL`
The four row vectors that make up an orthogonal matrix form a basis, meaning that they are mutually orthogonal; an orthogonal matrix with positive determinant is a pure rotation matrix; a negative determinant indicates a rotation and a reflection.
`static int` `RIGID`
This matrix is a rotation and a translation with unity scale; The upper 3x3 of the matrix is orthogonal, and there is a translation component.
`static int` `SCALE`
A Uniform scale matrix with no translation or other off-diagonal components.
`static int` `TRANSLATION`
A translation-only matrix with ones on the diagonal.
`static int` `ZERO`
A zero matrix.
• ### Constructor Summary

Constructors
Constructor and Description
`Transform3D()`
Constructs and initializes a transform to the identity matrix.
`Transform3D(double[] matrix)`
Constructs and initializes a transform from the double precision array of length 16; the top row of the matrix is initialized to the first four elements of the array, and so on.
`Transform3D(float[] matrix)`
Constructs and initializes a transform from the float array of length 16; the top row of the matrix is initialized to the first four elements of the array, and so on.
```Transform3D(Matrix3d m1, Vector3d t1, double s)```
Constructs and initializes a transform from the rotation matrix, translation, and scale values.
```Transform3D(Matrix3f m1, Vector3d t1, double s)```
Constructs and initializes a transform from the rotation matrix, translation, and scale values.
```Transform3D(Matrix3f m1, Vector3f t1, float s)```
Constructs and initializes a transform from the rotation matrix, translation, and scale values.
`Transform3D(Matrix4d m1)`
Constructs and initializes a transform from the 4 x 4 matrix.
`Transform3D(Matrix4f m1)`
Constructs and initializes a transform from the 4 x 4 matrix.
```Transform3D(Quat4d q1, Vector3d t1, double s)```
Constructs and initializes a transform from the quaternion, translation, and scale values.
```Transform3D(Quat4f q1, Vector3d t1, double s)```
Constructs and initializes a transform from the quaternion, translation, and scale values.
```Transform3D(Quat4f q1, Vector3f t1, float s)```
Constructs and initializes a transform from the quaternion, translation, and scale values.
`Transform3D(Transform3D t1)`
Constructs and initializes a transform from the Transform3D object.
• ### Method Summary

All Methods
Modifier and Type Method and Description
`void` `add(Transform3D t1)`
Adds this transform to transform t1 and places the result into this: this = this + t1.
`void` ```add(Transform3D t1, Transform3D t2)```
Adds transforms t1 and t2 and places the result into this transform.
`double` `determinant()`
Calculates and returns the determinant of this transform.
`boolean` ```epsilonEquals(Transform3D t1, double epsilon)```
Returns true if the L-infinite distance between this matrix and matrix m1 is less than or equal to the epsilon parameter, otherwise returns false.
`boolean` `equals(Object o1)`
Returns true if the Object o1 is of type Transform3D and all of the data members of o1 are equal to the corresponding data members in this Transform3D.
`boolean` `equals(Transform3D t1)`
Returns true if all of the data members of transform t1 are equal to the corresponding data members in this Transform3D.
`void` ```frustum(double left, double right, double bottom, double top, double near, double far)```
Creates a perspective projection transform that mimics a standard, camera-based, view-model.
`void` `get(double[] matrix)`
Places the values of this transform into the double precision array of length 16.
`void` `get(float[] matrix)`
Places the values of this transform into the single precision array of length 16.
`void` `get(Matrix3d m1)`
Places the normalized rotational component of this transform into the 3x3 matrix argument.
`double` ```get(Matrix3d m1, Vector3d t1)```
Places the normalized rotational component of this transform into the matrix parameter; place the translational component into the vector parameter.
`void` `get(Matrix3f m1)`
Places the normalized rotational component of this transform into the 3x3 matrix argument.
`double` ```get(Matrix3f m1, Vector3d t1)```
Places the normalized rotational component of this transform into the matrix parameter; place the translational component into the vector parameter.
`float` ```get(Matrix3f m1, Vector3f t1)```
Places the normalized rotational component of this transform into the matrix parameter; place the translational component into the vector parameter.
`void` `get(Matrix4d matrix)`
Places the values of this transform into the double precision matrix argument.
`void` `get(Matrix4f matrix)`
Places the values of this transform into the single precision matrix argument.
`void` `get(Quat4d q1)`
Places the quaternion equivalent of the normalized rotational component of this transform into the quaternion parameter.
`double` ```get(Quat4d q1, Vector3d t1)```
Places the quaternion equivalent of the normalized rotational component of this transform into the quaternion parameter; places the translational component into the Vector parameter.
`void` `get(Quat4f q1)`
Places the quaternion equivalent of the normalized rotational component of this transform into the quaternion parameter.
`double` ```get(Quat4f q1, Vector3d t1)```
Places the quaternion equivalent of the normalized rotational component of this transform into the quaternion parameter; places the translational component into the Vector parameter.
`float` ```get(Quat4f q1, Vector3f t1)```
Places the quaternion equivalent of the normalized rotational component of this transform into the quaternion parameter; places the translational component into the Vector parameter.
`void` `get(Vector3d trans)`
Retrieves the translational components of this transform.
`void` `get(Vector3f trans)`
Retrieves the translational components of this transform.
`boolean` `getAutoNormalize()`
Returns the state of auto-normalization.
`int` `getBestType()`
Returns the least general type of this matrix; the order of generality from least to most is: ZERO, IDENTITY, SCALE/TRANSLATION, ORTHOGONAL, RIGID, CONGRUENT, AFFINE.
`boolean` `getDeterminantSign()`
Returns the sign of the determinant of this matrix; a return value of true indicates a non-negative determinant; a return value of false indicates a negative determinant.
`void` `getRotationScale(Matrix3d m1)`
Gets the upper 3x3 values of this matrix and places them into the matrix m1.
`void` `getRotationScale(Matrix3f m1)`
Gets the upper 3x3 values of this matrix and places them into the matrix m1.
`double` `getScale()`
Returns the uniform scale factor of this matrix.
`void` `getScale(Vector3d scale)`
Gets the possibly non-uniform scale components of the current transform and places them into the scale vector.
`int` `getType()`
Returns the type of this matrix as an or'ed bitmask of of all of the type classifications to which it belongs.
`int` `hashCode()`
Returns a hash code value based on the data values in this object.
`void` `invert()`
Inverts this transform in place.
`void` `invert(Transform3D t1)`
Sets the value of this transform to the inverse of the passed Transform3D parameter.
`void` ```lookAt(Point3d eye, Point3d center, Vector3d up)```
Helping function that specifies the position and orientation of a view matrix.
`void` `mul(double scalar)`
Multiplies each element of this transform by a scalar.
`void` ```mul(double scalar, Transform3D t1)```
Multiplies each element of transform t1 by a scalar and places the result into this.
`void` `mul(Transform3D t1)`
Sets the value of this transform to the result of multiplying itself with transform t1 (this = this * t1).
`void` ```mul(Transform3D t1, Transform3D t2)```
Sets the value of this transform to the result of multiplying transform t1 by transform t2 (this = t1*t2).
`void` `mulInverse(Transform3D t1)`
Multiplies this transform by the inverse of transform t1.
`void` ```mulInverse(Transform3D t1, Transform3D t2)```
Multiplies transform t1 by the inverse of transform t2.
`void` ```mulTransposeBoth(Transform3D t1, Transform3D t2)```
Multiplies the transpose of transform t1 by the transpose of transform t2 and places the result into this transform (this = transpose(t1) * transpose(t2)).
`void` ```mulTransposeLeft(Transform3D t1, Transform3D t2)```
Multiplies the transpose of transform t1 by transform t2 and places the result into this matrix (this = transpose(t1) * t2).
`void` ```mulTransposeRight(Transform3D t1, Transform3D t2)```
Multiplies transform t1 by the transpose of transform t2 and places the result into this transform (this = t1 * transpose(t2)).
`void` `normalize()`
Normalizes the rotational components (upper 3x3) of this matrix in place using a Singular Value Decomposition (SVD).
`void` `normalize(Transform3D t1)`
Normalizes the rotational components (upper 3x3) of transform t1 using a Singular Value Decomposition (SVD), and places the result into this transform.
`void` `normalizeCP()`
Normalizes the rotational components (upper 3x3) of this transform in place using a Cross Product (CP) normalization.
`void` `normalizeCP(Transform3D t1)`
Normalizes the rotational components (upper 3x3) of transform t1 using a Cross Product (CP) normalization, and places the result into this transform.
`void` ```ortho(double left, double right, double bottom, double top, double near, double far)```
Creates an orthographic projection transform that mimics a standard, camera-based, view-model.
`void` ```perspective(double fovx, double aspect, double zNear, double zFar)```
Creates a perspective projection transform that mimics a standard, camera-based, view-model.
`void` `rotX(double angle)`
Sets the value of this transform to a counter clockwise rotation about the x axis.
`void` `rotY(double angle)`
Sets the value of this transform to a counter clockwise rotation about the y axis.
`void` `rotZ(double angle)`
Sets the value of this transform to a counter clockwise rotation about the z axis.
`void` ```scaleAdd(double s, Transform3D t1)```
Scales this transform by a Uniform scale matrix with scale factor s and then adds transform t1 (this = S*this + t1).
`void` ```scaleAdd(double s, Transform3D t1, Transform3D t2)```
Scales transform t1 by a Uniform scale matrix with scale factor s and then adds transform t2 (this = S*t1 + t2).
`void` `set(AxisAngle4d a1)`
Sets the value of this transform to the matrix conversion of the double precision axis-angle argument; all of the matrix values are modified.
`void` `set(AxisAngle4f a1)`
Sets the value of this transform to the matrix conversion of the single precision axis-angle argument; all of the matrix values are modified.
`void` `set(double scale)`
Sets the value of this transform to a uniform scale; all of the matrix values are modified.
`void` `set(double[] matrix)`
Sets the matrix values of this transform to the matrix values in the double precision array parameter.
`void` ```set(double scale, Vector3d v1)```
Sets the value of this transform to a scale and translation matrix; the scale is not applied to the translation and all of the matrix values are modified.
`void` `set(float[] matrix)`
Sets the matrix values of this transform to the matrix values in the single precision array parameter.
`void` ```set(float scale, Vector3f v1)```
Sets the value of this transform to a scale and translation matrix; the scale is not applied to the translation and all of the matrix values are modified.
`void` `set(Matrix3d m1)`
Sets the rotational component (upper 3x3) of this transform to the matrix values in the double precision Matrix3d argument; the other elements of this transform are initialized as if this were an identity matrix (ie, affine matrix with no translational component).
`void` ```set(Matrix3d m1, Vector3d t1, double s)```
Sets the value of this matrix from the rotation expressed by the rotation matrix m1, the translation t1, and the scale s.
`void` `set(Matrix3f m1)`
Sets the rotational component (upper 3x3) of this transform to the matrix values in the single precision Matrix3f argument; the other elements of this transform are initialized as if this were an identity matrix (i.e., affine matrix with no translational component).
`void` ```set(Matrix3f m1, Vector3d t1, double s)```
Sets the value of this matrix from the rotation expressed by the rotation matrix m1, the translation t1, and the scale s.
`void` ```set(Matrix3f m1, Vector3f t1, float s)```
Sets the value of this matrix from the rotation expressed by the rotation matrix m1, the translation t1, and the scale s.
`void` `set(Matrix4d m1)`
Sets the matrix values of this transform to the matrix values in the double precision Matrix4d argument.
`void` `set(Matrix4f m1)`
Sets the matrix values of this transform to the matrix values in the single precision Matrix4f argument.
`void` `set(Quat4d q1)`
Sets the value of this transform to the matrix conversion of the double precision quaternion argument; the non-rotational components are set as if this were an identity matrix.
`void` ```set(Quat4d q1, Vector3d t1, double s)```
Sets the value of this matrix from the rotation expressed by the quaternion q1, the translation t1, and the scale s.
`void` `set(Quat4f q1)`
Sets the value of this transform to the matrix conversion of the single precision quaternion argument; the non-rotational components are set as if this were an identity matrix.
`void` ```set(Quat4f q1, Vector3d t1, double s)```
Sets the value of this matrix from the rotation expressed by the quaternion q1, the translation t1, and the scale s.
`void` ```set(Quat4f q1, Vector3f t1, float s)```
Sets the value of this matrix from the rotation expressed by the quaternion q1, the translation t1, and the scale s.
`void` `set(Transform3D t1)`
Sets the matrix, type, and state of this transform to the matrix, type, and state of transform t1.
`void` `set(Vector3d trans)`
Sets the translational value of this matrix to the Vector3d paramter values, and sets the other components of the matrix as if this transform were an identity matrix.
`void` ```set(Vector3d v1, double scale)```
Sets the value of this transform to a scale and translation matrix; the translation is scaled by the scale factor and all of the matrix values are modified.
`void` `set(Vector3f trans)`
Sets the translational value of this matrix to the Vector3f parameter values, and sets the other components of the matrix as if this transform were an identity matrix.
`void` ```set(Vector3f v1, float scale)```
Sets the value of this transform to a scale and translation matrix; the translation is scaled by the scale factor and all of the matrix values are modified.
`void` `setAutoNormalize(boolean autoNormalize)`
Sets a flag that enables or disables automatic SVD normalization.
`void` `setEuler(Vector3d euler)`
Sets the rotational component (upper 3x3) of this transform to the rotation matrix converted from the Euler angles provided; the other non-rotational elements are set as if this were an identity matrix.
`void` `setIdentity()`
Sets this transform to the identity matrix.
`void` ```setNonUniformScale(double xScale, double yScale, double zScale)```
Deprecated.
Use setScale(Vector3d) instead of setNonUniformScale; note that the setScale only modifies the scale component
`void` `setRotation(AxisAngle4d a1)`
Sets the rotational component (upper 3x3) of this transform to the matrix equivalent values of the axis-angle argument; the other elements of this transform are unchanged; any pre-existing scale in the transform is preserved.
`void` `setRotation(AxisAngle4f a1)`
Sets the rotational component (upper 3x3) of this transform to the matrix equivalent values of the axis-angle argument; the other elements of this transform are unchanged; any pre-existing scale in the transform is preserved.
`void` `setRotation(Matrix3d m1)`
Sets the rotational component (upper 3x3) of this transform to the matrix values in the double precision Matrix3d argument; the other elements of this transform are unchanged; any pre-existing scale will be preserved; the argument matrix m1 will be checked for proper normalization when this transform is internally classified.
`void` `setRotation(Matrix3f m1)`
Sets the rotational component (upper 3x3) of this transform to the matrix values in the single precision Matrix3f argument; the other elements of this transform are unchanged; any pre-existing scale will be preserved; the argument matrix m1 will be checked for proper normalization when this transform is internally classified.
`void` `setRotation(Quat4d q1)`
Sets the rotational component (upper 3x3) of this transform to the matrix equivalent values of the quaternion argument; the other elements of this transform are unchanged; any pre-existing scale in the transform is preserved.
`void` `setRotation(Quat4f q1)`
Sets the rotational component (upper 3x3) of this transform to the matrix equivalent values of the quaternion argument; the other elements of this transform are unchanged; any pre-existing scale in the transform is preserved.
`void` `setRotationScale(Matrix3d m1)`
Replaces the upper 3x3 matrix values of this transform with the values in the matrix m1.
`void` `setRotationScale(Matrix3f m1)`
Replaces the upper 3x3 matrix values of this transform with the values in the matrix m1.
`void` `setScale(double scale)`
Sets the scale component of the current transform; any existing scale is first factored out of the existing transform before the new scale is applied.
`void` `setScale(Vector3d scale)`
Sets the possibly non-uniform scale component of the current transform; any existing scale is first factored out of the existing transform before the new scale is applied.
`void` `setTranslation(Vector3d trans)`
Replaces the translational components of this transform to the values in the Vector3d argument; the other values of this transform are not modified.
`void` `setTranslation(Vector3f trans)`
Replaces the translational components of this transform to the values in the Vector3f argument; the other values of this transform are not modified.
`void` `setZero()`
Sets this transform to all zeros.
`void` `sub(Transform3D t1)`
Subtracts transform t1 from this transform and places the result into this: this = this - t1.
`void` ```sub(Transform3D t1, Transform3D t2)```
Subtracts transform t2 from transform t1 and places the result into this: this = t1 - t2.
`String` `toString()`
Returns the matrix elements of this transform as a string.
`void` `transform(Point3d point)`
Transforms the point parameter with this transform and places the result back into point.
`void` ```transform(Point3d point, Point3d pointOut)```
Transforms the point parameter with this transform and places the result into pointOut.
`void` `transform(Point3f point)`
Transforms the point parameter with this transform and places the result back into point.
`void` ```transform(Point3f point, Point3f pointOut)```
Transforms the point parameter with this transform and places the result into pointOut.
`void` `transform(Vector3d normal)`
Transforms the normal parameter by this transform and places the value back into normal.
`void` ```transform(Vector3d normal, Vector3d normalOut)```
Transforms the normal parameter by this transform and places the value into normalOut.
`void` `transform(Vector3f normal)`
Transforms the normal parameter by this transform and places the value back into normal.
`void` ```transform(Vector3f normal, Vector3f normalOut)```
Transforms the normal parameter by this transform and places the value into normalOut.
`void` `transform(Vector4d vec)`
Transform the vector vec using this Transform and place the result back into vec.
`void` ```transform(Vector4d vec, Vector4d vecOut)```
Transform the vector vec using this transform and place the result into vecOut.
`void` `transform(Vector4f vec)`
Transform the vector vec using this Transform and place the result back into vec.
`void` ```transform(Vector4f vec, Vector4f vecOut)```
Transform the vector vec using this Transform and place the result into vecOut.
`void` `transpose()`
Transposes this matrix in place.
`void` `transpose(Transform3D t1)`
Transposes transform t1 and places the value into this transform.
• ### Methods inherited from class java.lang.Object

`clone, finalize, getClass, notify, notifyAll, wait, wait, wait`
• ### Field Detail

• #### ZERO

`public static final int ZERO`
A zero matrix.
Constant Field Values
• #### IDENTITY

`public static final int IDENTITY`
An identity matrix.
Constant Field Values
• #### SCALE

`public static final int SCALE`
A Uniform scale matrix with no translation or other off-diagonal components.
Constant Field Values
• #### TRANSLATION

`public static final int TRANSLATION`
A translation-only matrix with ones on the diagonal.
Constant Field Values
• #### ORTHOGONAL

`public static final int ORTHOGONAL`
The four row vectors that make up an orthogonal matrix form a basis, meaning that they are mutually orthogonal; an orthogonal matrix with positive determinant is a pure rotation matrix; a negative determinant indicates a rotation and a reflection.
Constant Field Values
• #### RIGID

`public static final int RIGID`
This matrix is a rotation and a translation with unity scale; The upper 3x3 of the matrix is orthogonal, and there is a translation component.
Constant Field Values
• #### CONGRUENT

`public static final int CONGRUENT`
This is an angle and length preserving matrix, meaning that it can translate, rotate, and reflect about an axis, and scale by an amount that is uniform in all directions. These operations preserve the distance between any two points and the angle between any two intersecting lines.
Constant Field Values
• #### AFFINE

`public static final int AFFINE`
An affine matrix can translate, rotate, reflect, scale anisotropically, and shear. Lines remain straight, and parallel lines remain parallel, but the angle between intersecting lines can change. In order for a transform to be classified as affine, the 4th row must be: [0, 0, 0, 1].
Constant Field Values
• #### NEGATIVE_DETERMINANT

`public static final int NEGATIVE_DETERMINANT`
This matrix has a negative determinant; an orthogonal matrix with a positive determinant is a rotation matrix; an orthogonal matrix with a negative determinant is a reflection and rotation matrix.
Constant Field Values
• ### Constructor Detail

• #### Transform3D

`public Transform3D(Matrix4f m1)`
Constructs and initializes a transform from the 4 x 4 matrix. The type of the constructed transform will be classified automatically.
Parameters:
`m1` - the 4 x 4 transformation matrix
• #### Transform3D

`public Transform3D(Matrix4d m1)`
Constructs and initializes a transform from the 4 x 4 matrix. The type of the constructed transform will be classified automatically.
Parameters:
`m1` - the 4 x 4 transformation matrix
• #### Transform3D

`public Transform3D(Transform3D t1)`
Constructs and initializes a transform from the Transform3D object.
Parameters:
`t1` - the transformation object to be copied
• #### Transform3D

`public Transform3D()`
Constructs and initializes a transform to the identity matrix.
• #### Transform3D

`public Transform3D(float[] matrix)`
Constructs and initializes a transform from the float array of length 16; the top row of the matrix is initialized to the first four elements of the array, and so on. The type of the transform object is classified internally.
Parameters:
`matrix` - a float array of 16
• #### Transform3D

`public Transform3D(double[] matrix)`
Constructs and initializes a transform from the double precision array of length 16; the top row of the matrix is initialized to the first four elements of the array, and so on. The type of the transform is classified internally.
Parameters:
`matrix` - a float array of 16
• #### Transform3D

```public Transform3D(Quat4d q1,
Vector3d t1,
double s)```
Constructs and initializes a transform from the quaternion, translation, and scale values. The scale is applied only to the rotational components of the matrix (upper 3 x 3) and not to the translational components of the matrix.
Parameters:
`q1` - the quaternion value representing the rotational component
`t1` - the translational component of the matrix
`s` - the scale value applied to the rotational components
• #### Transform3D

```public Transform3D(Quat4f q1,
Vector3d t1,
double s)```
Constructs and initializes a transform from the quaternion, translation, and scale values. The scale is applied only to the rotational components of the matrix (upper 3 x 3) and not to the translational components of the matrix.
Parameters:
`q1` - the quaternion value representing the rotational component
`t1` - the translational component of the matrix
`s` - the scale value applied to the rotational components
• #### Transform3D

```public Transform3D(Quat4f q1,
Vector3f t1,
float s)```
Constructs and initializes a transform from the quaternion, translation, and scale values. The scale is applied only to the rotational components of the matrix (upper 3 x 3) and not to the translational components of the matrix.
Parameters:
`q1` - the quaternion value representing the rotational component
`t1` - the translational component of the matrix
`s` - the scale value applied to the rotational components
• #### Transform3D

```public Transform3D(Matrix3f m1,
Vector3d t1,
double s)```
Constructs and initializes a transform from the rotation matrix, translation, and scale values. The scale is applied only to the rotational component of the matrix (upper 3x3) and not to the translational component of the matrix.
Parameters:
`m1` - the rotation matrix representing the rotational component
`t1` - the translational component of the matrix
`s` - the scale value applied to the rotational components
• #### Transform3D

```public Transform3D(Matrix3d m1,
Vector3d t1,
double s)```
Constructs and initializes a transform from the rotation matrix, translation, and scale values. The scale is applied only to the rotational components of the matrix (upper 3x3) and not to the translational components of the matrix.
Parameters:
`m1` - the rotation matrix representing the rotational component
`t1` - the translational component of the matrix
`s` - the scale value applied to the rotational components
• #### Transform3D

```public Transform3D(Matrix3f m1,
Vector3f t1,
float s)```
Constructs and initializes a transform from the rotation matrix, translation, and scale values. The scale is applied only to the rotational components of the matrix (upper 3x3) and not to the translational components of the matrix.
Parameters:
`m1` - the rotation matrix representing the rotational component
`t1` - the translational component of the matrix
`s` - the scale value applied to the rotational components
• ### Method Detail

• #### getType

`public final int getType()`
Returns the type of this matrix as an or'ed bitmask of of all of the type classifications to which it belongs.
Returns:
or'ed bitmask of all of the type classifications of this transform
• #### getBestType

`public final int getBestType()`
Returns the least general type of this matrix; the order of generality from least to most is: ZERO, IDENTITY, SCALE/TRANSLATION, ORTHOGONAL, RIGID, CONGRUENT, AFFINE. If the matrix is ORTHOGONAL, calling the method getDeterminantSign() will yield more information.
Returns:
the least general matrix type
• #### getDeterminantSign

`public final boolean getDeterminantSign()`
Returns the sign of the determinant of this matrix; a return value of true indicates a non-negative determinant; a return value of false indicates a negative determinant. A value of true will be returned if the determinant is NaN. In general, an orthogonal matrix with a positive determinant is a pure rotation matrix; an orthogonal matrix with a negative determinant is a both a rotation and a reflection matrix.
Returns:
determinant sign : true means non-negative, false means negative
• #### setAutoNormalize

`public final void setAutoNormalize(boolean autoNormalize)`
Sets a flag that enables or disables automatic SVD normalization. If this flag is enabled, an automatic SVD normalization of the rotational components (upper 3x3) of this matrix is done after every subsequent matrix operation that modifies this matrix. This is functionally equivalent to calling normalize() after every subsequent call, but may be less computationally expensive. The default value for this parameter is false.
Parameters:
`autoNormalize` - the boolean state of auto normalization
• #### getAutoNormalize

`public final boolean getAutoNormalize()`
Returns the state of auto-normalization.
Returns:
boolean state of auto-normalization
• #### toString

`public String toString()`
Returns the matrix elements of this transform as a string.
Overrides:
`toString` in class `Object`
Returns:
the matrix elements of this transform
• #### setIdentity

`public final void setIdentity()`
Sets this transform to the identity matrix.
• #### setZero

`public final void setZero()`
Sets this transform to all zeros.

`public final void add(Transform3D t1)`
Adds this transform to transform t1 and places the result into this: this = this + t1.
Parameters:
`t1` - the transform to be added to this transform

```public final void add(Transform3D t1,
Transform3D t2)```
Adds transforms t1 and t2 and places the result into this transform.
Parameters:
`t1` - the transform to be added
`t2` - the transform to be added
• #### sub

`public final void sub(Transform3D t1)`
Subtracts transform t1 from this transform and places the result into this: this = this - t1.
Parameters:
`t1` - the transform to be subtracted from this transform
• #### sub

```public final void sub(Transform3D t1,
Transform3D t2)```
Subtracts transform t2 from transform t1 and places the result into this: this = t1 - t2.
Parameters:
`t1` - the left transform
`t2` - the right transform
• #### transpose

`public final void transpose()`
Transposes this matrix in place.
• #### transpose

`public final void transpose(Transform3D t1)`
Transposes transform t1 and places the value into this transform. The transform t1 is not modified.
Parameters:
`t1` - the transform whose transpose is placed into this transform
• #### set

`public final void set(Quat4f q1)`
Sets the value of this transform to the matrix conversion of the single precision quaternion argument; the non-rotational components are set as if this were an identity matrix.
Parameters:
`q1` - the quaternion to be converted
• #### set

`public final void set(Quat4d q1)`
Sets the value of this transform to the matrix conversion of the double precision quaternion argument; the non-rotational components are set as if this were an identity matrix.
Parameters:
`q1` - the quaternion to be converted
• #### setRotation

`public final void setRotation(Matrix3d m1)`
Sets the rotational component (upper 3x3) of this transform to the matrix values in the double precision Matrix3d argument; the other elements of this transform are unchanged; any pre-existing scale will be preserved; the argument matrix m1 will be checked for proper normalization when this transform is internally classified.
Parameters:
`m1` - the double precision 3x3 matrix
• #### setRotation

`public final void setRotation(Matrix3f m1)`
Sets the rotational component (upper 3x3) of this transform to the matrix values in the single precision Matrix3f argument; the other elements of this transform are unchanged; any pre-existing scale will be preserved; the argument matrix m1 will be checked for proper normalization when this transform is internally classified.
Parameters:
`m1` - the single precision 3x3 matrix
• #### setRotation

`public final void setRotation(Quat4f q1)`
Sets the rotational component (upper 3x3) of this transform to the matrix equivalent values of the quaternion argument; the other elements of this transform are unchanged; any pre-existing scale in the transform is preserved.
Parameters:
`q1` - the quaternion that specifies the rotation
• #### setRotation

`public final void setRotation(Quat4d q1)`
Sets the rotational component (upper 3x3) of this transform to the matrix equivalent values of the quaternion argument; the other elements of this transform are unchanged; any pre-existing scale in the transform is preserved.
Parameters:
`q1` - the quaternion that specifies the rotation
• #### set

`public final void set(AxisAngle4f a1)`
Sets the value of this transform to the matrix conversion of the single precision axis-angle argument; all of the matrix values are modified.
Parameters:
`a1` - the axis-angle to be converted (x, y, z, angle)
• #### set

`public final void set(AxisAngle4d a1)`
Sets the value of this transform to the matrix conversion of the double precision axis-angle argument; all of the matrix values are modified.
Parameters:
`a1` - the axis-angle to be converted (x, y, z, angle)
• #### setRotation

`public final void setRotation(AxisAngle4d a1)`
Sets the rotational component (upper 3x3) of this transform to the matrix equivalent values of the axis-angle argument; the other elements of this transform are unchanged; any pre-existing scale in the transform is preserved.
Parameters:
`a1` - the axis-angle to be converted (x, y, z, angle)
• #### setRotation

`public final void setRotation(AxisAngle4f a1)`
Sets the rotational component (upper 3x3) of this transform to the matrix equivalent values of the axis-angle argument; the other elements of this transform are unchanged; any pre-existing scale in the transform is preserved.
Parameters:
`a1` - the axis-angle to be converted (x, y, z, angle)
• #### rotX

`public void rotX(double angle)`
Sets the value of this transform to a counter clockwise rotation about the x axis. All of the non-rotational components are set as if this were an identity matrix.
Parameters:
`angle` - the angle to rotate about the X axis in radians
• #### rotY

`public void rotY(double angle)`
Sets the value of this transform to a counter clockwise rotation about the y axis. All of the non-rotational components are set as if this were an identity matrix.
Parameters:
`angle` - the angle to rotate about the Y axis in radians
• #### rotZ

`public void rotZ(double angle)`
Sets the value of this transform to a counter clockwise rotation about the z axis. All of the non-rotational components are set as if this were an identity matrix.
Parameters:
`angle` - the angle to rotate about the Z axis in radians
• #### set

`public final void set(Vector3f trans)`
Sets the translational value of this matrix to the Vector3f parameter values, and sets the other components of the matrix as if this transform were an identity matrix.
Parameters:
`trans` - the translational component
• #### set

`public final void set(Vector3d trans)`
Sets the translational value of this matrix to the Vector3d paramter values, and sets the other components of the matrix as if this transform were an identity matrix.
Parameters:
`trans` - the translational component
• #### setScale

`public final void setScale(double scale)`
Sets the scale component of the current transform; any existing scale is first factored out of the existing transform before the new scale is applied.
Parameters:
`scale` - the new scale amount
• #### setScale

`public final void setScale(Vector3d scale)`
Sets the possibly non-uniform scale component of the current transform; any existing scale is first factored out of the existing transform before the new scale is applied.
Parameters:
`scale` - the new x,y,z scale values
• #### setNonUniformScale

```public final void setNonUniformScale(double xScale,
double yScale,
double zScale)```
Deprecated. Use setScale(Vector3d) instead of setNonUniformScale; note that the setScale only modifies the scale component
Replaces the current transform with a non-uniform scale transform. All values of the existing transform are replaced.
Parameters:
`xScale` - the new X scale amount
`yScale` - the new Y scale amount
`zScale` - the new Z scale amount
• #### setTranslation

`public final void setTranslation(Vector3f trans)`
Replaces the translational components of this transform to the values in the Vector3f argument; the other values of this transform are not modified.
Parameters:
`trans` - the translational component
• #### setTranslation

`public final void setTranslation(Vector3d trans)`
Replaces the translational components of this transform to the values in the Vector3d argument; the other values of this transform are not modified.
Parameters:
`trans` - the translational component
• #### set

```public final void set(Quat4d q1,
Vector3d t1,
double s)```
Sets the value of this matrix from the rotation expressed by the quaternion q1, the translation t1, and the scale s.
Parameters:
`q1` - the rotation expressed as a quaternion
`t1` - the translation
`s` - the scale value
• #### set

```public final void set(Quat4f q1,
Vector3d t1,
double s)```
Sets the value of this matrix from the rotation expressed by the quaternion q1, the translation t1, and the scale s.
Parameters:
`q1` - the rotation expressed as a quaternion
`t1` - the translation
`s` - the scale value
• #### set

```public final void set(Quat4f q1,
Vector3f t1,
float s)```
Sets the value of this matrix from the rotation expressed by the quaternion q1, the translation t1, and the scale s.
Parameters:
`q1` - the rotation expressed as a quaternion
`t1` - the translation
`s` - the scale value
• #### set

```public final void set(Matrix3f m1,
Vector3f t1,
float s)```
Sets the value of this matrix from the rotation expressed by the rotation matrix m1, the translation t1, and the scale s. The scale is only applied to the rotational component of the matrix (upper 3x3) and not to the translational component of the matrix.
Parameters:
`m1` - the rotation matrix
`t1` - the translation
`s` - the scale value
• #### set

```public final void set(Matrix3f m1,
Vector3d t1,
double s)```
Sets the value of this matrix from the rotation expressed by the rotation matrix m1, the translation t1, and the scale s. The scale is only applied to the rotational component of the matrix (upper 3x3) and not to the translational component of the matrix.
Parameters:
`m1` - the rotation matrix
`t1` - the translation
`s` - the scale value
• #### set

```public final void set(Matrix3d m1,
Vector3d t1,
double s)```
Sets the value of this matrix from the rotation expressed by the rotation matrix m1, the translation t1, and the scale s. The scale is only applied to the rotational component of the matrix (upper 3x3) and not to the translational component of the matrix.
Parameters:
`m1` - the rotation matrix
`t1` - the translation
`s` - the scale value
• #### set

`public final void set(Transform3D t1)`
Sets the matrix, type, and state of this transform to the matrix, type, and state of transform t1.
Parameters:
`t1` - the transform to be copied
• #### set

`public final void set(double[] matrix)`
Sets the matrix values of this transform to the matrix values in the double precision array parameter. The matrix type is classified internally by the Transform3D class.
Parameters:
`matrix` - the double precision array of length 16 in row major format
• #### set

`public final void set(float[] matrix)`
Sets the matrix values of this transform to the matrix values in the single precision array parameter. The matrix type is classified internally by the Transform3D class.
Parameters:
`matrix` - the single precision array of length 16 in row major format
• #### set

`public final void set(Matrix4d m1)`
Sets the matrix values of this transform to the matrix values in the double precision Matrix4d argument. The transform type is classified internally by the Transform3D class.
Parameters:
`m1` - the double precision 4x4 matrix
• #### set

`public final void set(Matrix4f m1)`
Sets the matrix values of this transform to the matrix values in the single precision Matrix4f argument. The transform type is classified internally by the Transform3D class.
Parameters:
`m1` - the single precision 4x4 matrix
• #### set

`public final void set(Matrix3f m1)`
Sets the rotational component (upper 3x3) of this transform to the matrix values in the single precision Matrix3f argument; the other elements of this transform are initialized as if this were an identity matrix (i.e., affine matrix with no translational component).
Parameters:
`m1` - the single precision 3x3 matrix
• #### set

`public final void set(Matrix3d m1)`
Sets the rotational component (upper 3x3) of this transform to the matrix values in the double precision Matrix3d argument; the other elements of this transform are initialized as if this were an identity matrix (ie, affine matrix with no translational component).
Parameters:
`m1` - the double precision 3x3 matrix
• #### setEuler

`public final void setEuler(Vector3d euler)`
Sets the rotational component (upper 3x3) of this transform to the rotation matrix converted from the Euler angles provided; the other non-rotational elements are set as if this were an identity matrix. The euler parameter is a Vector3d consisting of three rotation angles applied first about the X, then Y then Z axis. These rotations are applied using a static frame of reference. In other words, the orientation of the Y rotation axis is not affected by the X rotation and the orientation of the Z rotation axis is not affected by the X or Y rotation.
Parameters:
`euler` - the Vector3d consisting of three rotation angles about X,Y,Z
• #### get

`public final void get(double[] matrix)`
Places the values of this transform into the double precision array of length 16. The first four elements of the array will contain the top row of the transform matrix, etc.
Parameters:
`matrix` - the double precision array of length 16
• #### get

`public final void get(float[] matrix)`
Places the values of this transform into the single precision array of length 16. The first four elements of the array will contain the top row of the transform matrix, etc.
Parameters:
`matrix` - the single precision array of length 16
• #### get

`public final void get(Matrix3d m1)`
Places the normalized rotational component of this transform into the 3x3 matrix argument.
Parameters:
`m1` - the matrix into which the rotational component is placed
• #### get

`public final void get(Matrix3f m1)`
Places the normalized rotational component of this transform into the 3x3 matrix argument.
Parameters:
`m1` - the matrix into which the rotational component is placed
• #### get

`public final void get(Quat4f q1)`
Places the quaternion equivalent of the normalized rotational component of this transform into the quaternion parameter.
Parameters:
`q1` - the quaternion into which the rotation component is placed
• #### get

`public final void get(Quat4d q1)`
Places the quaternion equivalent of the normalized rotational component of this transform into the quaternion parameter.
Parameters:
`q1` - the quaternion into which the rotation component is placed
• #### get

`public final void get(Matrix4d matrix)`
Places the values of this transform into the double precision matrix argument.
Parameters:
`matrix` - the double precision matrix
• #### get

`public final void get(Matrix4f matrix)`
Places the values of this transform into the single precision matrix argument.
Parameters:
`matrix` - the single precision matrix
• #### get

```public final double get(Quat4d q1,
Vector3d t1)```
Places the quaternion equivalent of the normalized rotational component of this transform into the quaternion parameter; places the translational component into the Vector parameter.
Parameters:
`q1` - the quaternion representing the rotation
`t1` - the translation component
Returns:
the scale component of this transform
• #### get

```public final float get(Quat4f q1,
Vector3f t1)```
Places the quaternion equivalent of the normalized rotational component of this transform into the quaternion parameter; places the translational component into the Vector parameter.
Parameters:
`q1` - the quaternion representing the rotation
`t1` - the translation component
Returns:
the scale component of this transform
• #### get

```public final double get(Quat4f q1,
Vector3d t1)```
Places the quaternion equivalent of the normalized rotational component of this transform into the quaternion parameter; places the translational component into the Vector parameter.
Parameters:
`q1` - the quaternion representing the rotation
`t1` - the translation component
Returns:
the scale component of this transform
• #### get

```public final double get(Matrix3d m1,
Vector3d t1)```
Places the normalized rotational component of this transform into the matrix parameter; place the translational component into the vector parameter.
Parameters:
`m1` - the normalized matrix representing the rotation
`t1` - the translation component
Returns:
the scale component of this transform
• #### get

```public final float get(Matrix3f m1,
Vector3f t1)```
Places the normalized rotational component of this transform into the matrix parameter; place the translational component into the vector parameter.
Parameters:
`m1` - the normalized matrix representing the rotation
`t1` - the translation component
Returns:
the scale component of this transform
• #### get

```public final double get(Matrix3f m1,
Vector3d t1)```
Places the normalized rotational component of this transform into the matrix parameter; place the translational component into the vector parameter.
Parameters:
`m1` - the normalized matrix representing the rotation
`t1` - the translation component
Returns:
the scale component of this transform
• #### getScale

`public final double getScale()`
Returns the uniform scale factor of this matrix. If the matrix has non-uniform scale factors, the largest of the x, y, and z scale factors will be returned.
Returns:
the scale factor of this matrix
• #### getScale

`public final void getScale(Vector3d scale)`
Gets the possibly non-uniform scale components of the current transform and places them into the scale vector.
Parameters:
`scale` - the vector into which the x,y,z scale values will be placed
• #### get

`public final void get(Vector3f trans)`
Retrieves the translational components of this transform.
Parameters:
`trans` - the vector that will receive the translational component
• #### get

`public final void get(Vector3d trans)`
Retrieves the translational components of this transform.
Parameters:
`trans` - the vector that will receive the translational component
• #### invert

`public final void invert(Transform3D t1)`
Sets the value of this transform to the inverse of the passed Transform3D parameter. This method uses the transform type to determine the optimal algorithm for inverting transform t1.
Parameters:
`t1` - the transform to be inverted
Throws:
`SingularMatrixException` - thrown if transform t1 is not invertible
• #### invert

`public final void invert()`
Inverts this transform in place. This method uses the transform type to determine the optimal algorithm for inverting this transform.
Throws:
`SingularMatrixException` - thrown if this transform is not invertible
• #### determinant

`public final double determinant()`
Calculates and returns the determinant of this transform.
Returns:
the double precision determinant
• #### set

`public final void set(double scale)`
Sets the value of this transform to a uniform scale; all of the matrix values are modified.
Parameters:
`scale` - the scale factor for the transform
• #### set

```public final void set(double scale,
Vector3d v1)```
Sets the value of this transform to a scale and translation matrix; the scale is not applied to the translation and all of the matrix values are modified.
Parameters:
`scale` - the scale factor for the transform
`v1` - the translation amount
• #### set

```public final void set(float scale,
Vector3f v1)```
Sets the value of this transform to a scale and translation matrix; the scale is not applied to the translation and all of the matrix values are modified.
Parameters:
`scale` - the scale factor for the transform
`v1` - the translation amount
• #### set

```public final void set(Vector3d v1,
double scale)```
Sets the value of this transform to a scale and translation matrix; the translation is scaled by the scale factor and all of the matrix values are modified.
Parameters:
`v1` - the translation amount
`scale` - the scale factor for the transform AND the translation
• #### set

```public final void set(Vector3f v1,
float scale)```
Sets the value of this transform to a scale and translation matrix; the translation is scaled by the scale factor and all of the matrix values are modified.
Parameters:
`v1` - the translation amount
`scale` - the scale factor for the transform AND the translation
• #### mul

`public final void mul(double scalar)`
Multiplies each element of this transform by a scalar.
Parameters:
`scalar` - the scalar multiplier
• #### mul

```public final void mul(double scalar,
Transform3D t1)```
Multiplies each element of transform t1 by a scalar and places the result into this. Transform t1 is not modified.
Parameters:
`scalar` - the scalar multiplier
`t1` - the original transform
• #### mul

`public final void mul(Transform3D t1)`
Sets the value of this transform to the result of multiplying itself with transform t1 (this = this * t1).
Parameters:
`t1` - the other transform
• #### mul

```public final void mul(Transform3D t1,
Transform3D t2)```
Sets the value of this transform to the result of multiplying transform t1 by transform t2 (this = t1*t2).
Parameters:
`t1` - the left transform
`t2` - the right transform
• #### mulInverse

`public final void mulInverse(Transform3D t1)`
Multiplies this transform by the inverse of transform t1. The final value is placed into this matrix (this = this*t1^-1).
Parameters:
`t1` - the matrix whose inverse is computed.
• #### mulInverse

```public final void mulInverse(Transform3D t1,
Transform3D t2)```
Multiplies transform t1 by the inverse of transform t2. The final value is placed into this matrix (this = t1*t2^-1).
Parameters:
`t1` - the left transform in the multiplication
`t2` - the transform whose inverse is computed.
• #### mulTransposeRight

```public final void mulTransposeRight(Transform3D t1,
Transform3D t2)```
Multiplies transform t1 by the transpose of transform t2 and places the result into this transform (this = t1 * transpose(t2)).
Parameters:
`t1` - the transform on the left hand side of the multiplication
`t2` - the transform whose transpose is computed
• #### mulTransposeLeft

```public final void mulTransposeLeft(Transform3D t1,
Transform3D t2)```
Multiplies the transpose of transform t1 by transform t2 and places the result into this matrix (this = transpose(t1) * t2).
Parameters:
`t1` - the transform whose transpose is computed
`t2` - the transform on the right hand side of the multiplication
• #### mulTransposeBoth

```public final void mulTransposeBoth(Transform3D t1,
Transform3D t2)```
Multiplies the transpose of transform t1 by the transpose of transform t2 and places the result into this transform (this = transpose(t1) * transpose(t2)).
Parameters:
`t1` - the transform on the left hand side of the multiplication
`t2` - the transform on the right hand side of the multiplication
• #### normalize

`public final void normalize()`
Normalizes the rotational components (upper 3x3) of this matrix in place using a Singular Value Decomposition (SVD). This operation ensures that the column vectors of this matrix are orthogonal to each other. The primary use of this method is to correct for floating point errors that accumulate over time when concatenating a large number of rotation matrices. Note that the scale of the matrix is not altered by this method.
• #### normalize

`public final void normalize(Transform3D t1)`
Normalizes the rotational components (upper 3x3) of transform t1 using a Singular Value Decomposition (SVD), and places the result into this transform. This operation ensures that the column vectors of this matrix are orthogonal to each other. The primary use of this method is to correct for floating point errors that accumulate over time when concatenating a large number of rotation matrices. Note that the scale of the matrix is not altered by this method.
Parameters:
`t1` - the source transform, which is not modified
• #### normalizeCP

`public final void normalizeCP()`
Normalizes the rotational components (upper 3x3) of this transform in place using a Cross Product (CP) normalization. This operation ensures that the column vectors of this matrix are orthogonal to each other. The primary use of this method is to correct for floating point errors that accumulate over time when concatenating a large number of rotation matrices. Note that the scale of the matrix is not altered by this method.
• #### normalizeCP

`public final void normalizeCP(Transform3D t1)`
Normalizes the rotational components (upper 3x3) of transform t1 using a Cross Product (CP) normalization, and places the result into this transform. This operation ensures that the column vectors of this matrix are orthogonal to each other. The primary use of this method is to correct for floating point errors that accumulate over time when concatenating a large number of rotation matrices. Note that the scale of the matrix is not altered by this method.
Parameters:
`t1` - the transform to be normalized
• #### equals

`public boolean equals(Transform3D t1)`
Returns true if all of the data members of transform t1 are equal to the corresponding data members in this Transform3D.
Parameters:
`t1` - the transform with which the comparison is made
Returns:
true or false
• #### equals

`public boolean equals(Object o1)`
Returns true if the Object o1 is of type Transform3D and all of the data members of o1 are equal to the corresponding data members in this Transform3D.
Overrides:
`equals` in class `Object`
Parameters:
`o1` - the object with which the comparison is made.
Returns:
true or false
• #### epsilonEquals

```public boolean epsilonEquals(Transform3D t1,
double epsilon)```
Returns true if the L-infinite distance between this matrix and matrix m1 is less than or equal to the epsilon parameter, otherwise returns false. The L-infinite distance is equal to MAX[i=0,1,2,3 ; j=0,1,2,3 ; abs[(this.m(i,j) - m1.m(i,j)]
Parameters:
`t1` - the transform to be compared to this transform
`epsilon` - the threshold value
• #### hashCode

`public int hashCode()`
Returns a hash code value based on the data values in this object. Two different Transform3D objects with identical data values (i.e., Transform3D.equals returns true) will return the same hash number. Two Transform3D objects with different data members may return the same hash value, although this is not likely.
Overrides:
`hashCode` in class `Object`
Returns:
the integer hash code value
• #### transform

```public final void transform(Vector4d vec,
Vector4d vecOut)```
Transform the vector vec using this transform and place the result into vecOut.
Parameters:
`vec` - the double precision vector to be transformed
`vecOut` - the vector into which the transformed values are placed
• #### transform

`public final void transform(Vector4d vec)`
Transform the vector vec using this Transform and place the result back into vec.
Parameters:
`vec` - the double precision vector to be transformed
• #### transform

```public final void transform(Vector4f vec,
Vector4f vecOut)```
Transform the vector vec using this Transform and place the result into vecOut.
Parameters:
`vec` - the single precision vector to be transformed
`vecOut` - the vector into which the transformed values are placed
• #### transform

`public final void transform(Vector4f vec)`
Transform the vector vec using this Transform and place the result back into vec.
Parameters:
`vec` - the single precision vector to be transformed
• #### transform

```public final void transform(Point3d point,
Point3d pointOut)```
Transforms the point parameter with this transform and places the result into pointOut. The fourth element of the point input paramter is assumed to be one.
Parameters:
`point` - the input point to be transformed
`pointOut` - the transformed point
• #### transform

`public final void transform(Point3d point)`
Transforms the point parameter with this transform and places the result back into point. The fourth element of the point input paramter is assumed to be one.
Parameters:
`point` - the input point to be transformed
• #### transform

```public final void transform(Vector3d normal,
Vector3d normalOut)```
Transforms the normal parameter by this transform and places the value into normalOut. The fourth element of the normal is assumed to be zero.
Parameters:
`normal` - the input normal to be transformed
`normalOut` - the transformed normal
• #### transform

`public final void transform(Vector3d normal)`
Transforms the normal parameter by this transform and places the value back into normal. The fourth element of the normal is assumed to be zero.
Parameters:
`normal` - the input normal to be transformed
• #### transform

```public final void transform(Point3f point,
Point3f pointOut)```
Transforms the point parameter with this transform and places the result into pointOut. The fourth element of the point input paramter is assumed to be one.
Parameters:
`point` - the input point to be transformed
`pointOut` - the transformed point
• #### transform

`public final void transform(Point3f point)`
Transforms the point parameter with this transform and places the result back into point. The fourth element of the point input paramter is assumed to be one.
Parameters:
`point` - the input point to be transformed
• #### transform

```public final void transform(Vector3f normal,
Vector3f normalOut)```
Transforms the normal parameter by this transform and places the value into normalOut. The fourth element of the normal is assumed to be zero. Note: For correct lighting results, if a transform has uneven scaling surface normals should transformed by the inverse transpose of the transform. This the responsibility of the application and is not done automatically by this method.
Parameters:
`normal` - the input normal to be transformed
`normalOut` - the transformed normal
• #### transform

`public final void transform(Vector3f normal)`
Transforms the normal parameter by this transform and places the value back into normal. The fourth element of the normal is assumed to be zero. Note: For correct lighting results, if a transform has uneven scaling surface normals should transformed by the inverse transpose of the transform. This the responsibility of the application and is not done automatically by this method.
Parameters:
`normal` - the input normal to be transformed
• #### setRotationScale

`public final void setRotationScale(Matrix3f m1)`
Replaces the upper 3x3 matrix values of this transform with the values in the matrix m1.
Parameters:
`m1` - the matrix that will be the new upper 3x3
• #### setRotationScale

`public final void setRotationScale(Matrix3d m1)`
Replaces the upper 3x3 matrix values of this transform with the values in the matrix m1.
Parameters:
`m1` - the matrix that will be the new upper 3x3

```public final void scaleAdd(double s,
Transform3D t1,
Transform3D t2)```
Scales transform t1 by a Uniform scale matrix with scale factor s and then adds transform t2 (this = S*t1 + t2).
Parameters:
`s` - the scale factor
`t1` - the transform to be scaled
`t2` - the transform to be added

```public final void scaleAdd(double s,
Transform3D t1)```
Scales this transform by a Uniform scale matrix with scale factor s and then adds transform t1 (this = S*this + t1).
Parameters:
`s` - the scale factor
`t1` - the transform to be added
• #### getRotationScale

`public final void getRotationScale(Matrix3f m1)`
Gets the upper 3x3 values of this matrix and places them into the matrix m1.
Parameters:
`m1` - the matrix that will hold the values
• #### getRotationScale

`public final void getRotationScale(Matrix3d m1)`
Gets the upper 3x3 values of this matrix and places them into the matrix m1.
Parameters:
`m1` - the matrix that will hold the values
• #### lookAt

```public void lookAt(Point3d eye,
Point3d center,
Vector3d up)```
Helping function that specifies the position and orientation of a view matrix. The inverse of this transform can be used to control the ViewPlatform object within the scene graph.
Parameters:
`eye` - the location of the eye
`center` - a point in the virtual world where the eye is looking
`up` - an up vector specifying the frustum's up direction
• #### frustum

```public void frustum(double left,
double right,
double bottom,
double top,
double near,
double far)```
Creates a perspective projection transform that mimics a standard, camera-based, view-model. This transform maps coordinates from Eye Coordinates (EC) to Clipping Coordinates (CC). Note that unlike the similar function in OpenGL, the clipping coordinates generated by the resulting transform are in a right-handed coordinate system (as are all other coordinate systems in Java 3D).

The frustum function-call establishes a view model with the eye at the apex of a symmetric view frustum. The arguments define the frustum and its associated perspective projection: (left, bottom, -near) and (right, top, -near) specify the point on the near clipping plane that maps onto the lower-left and upper-right corners of the window respectively, assuming the eye is located at (0, 0, 0).

Parameters:
`left` - the vertical line on the left edge of the near clipping plane mapped to the left edge of the graphics window
`right` - the vertical line on the right edge of the near clipping plane mapped to the right edge of the graphics window
`bottom` - the horizontal line on the bottom edge of the near clipping plane mapped to the bottom edge of the graphics window
`top` - the horizontal line on the top edge of the near
`near` - the distance to the frustum's near clipping plane. This value must be positive, (the value -near is the location of the near clip plane).
`far` - the distance to the frustum's far clipping plane. This value must be positive, and must be greater than near.
• #### perspective

```public void perspective(double fovx,
double aspect,
double zNear,
double zFar)```
Creates a perspective projection transform that mimics a standard, camera-based, view-model. This transform maps coordinates from Eye Coordinates (EC) to Clipping Coordinates (CC). Note that unlike the similar function in OpenGL, the clipping coordinates generated by the resulting transform are in a right-handed coordinate system (as are all other coordinate systems in Java 3D). Also note that the field of view is specified in radians.
Parameters:
`fovx` - specifies the field of view in the x direction, in radians
`aspect` - specifies the aspect ratio and thus the field of view in the x direction. The aspect ratio is the ratio of x to y, or width to height.
`zNear` - the distance to the frustum's near clipping plane. This value must be positive, (the value -zNear is the location of the near clip plane).
`zFar` - the distance to the frustum's far clipping plane
• #### ortho

```public void ortho(double left,
double right,
double bottom,
double top,
double near,
double far)```
Creates an orthographic projection transform that mimics a standard, camera-based, view-model. This transform maps coordinates from Eye Coordinates (EC) to Clipping Coordinates (CC). Note that unlike the similar function in OpenGL, the clipping coordinates generated by the resulting transform are in a right-handed coordinate system (as are all other coordinate systems in Java 3D).
Parameters:
`left` - the vertical line on the left edge of the near clipping plane mapped to the left edge of the graphics window
`right` - the vertical line on the right edge of the near clipping plane mapped to the right edge of the graphics window
`bottom` - the horizontal line on the bottom edge of the near clipping plane mapped to the bottom edge of the graphics window
`top` - the horizontal line on the top edge of the near clipping plane mapped to the top edge of the graphics window
`near` - the distance to the frustum's near clipping plane (the value -near is the location of the near clip plane)
`far` - the distance to the frustum's far clipping plane