Class SbMatrix
- java.lang.Object
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- com.openinventor.inventor.SbBasic
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- com.openinventor.inventor.SbMatrix
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public class SbMatrix extends SbBasic
4x4 matrix class. 4x4 matrix class/datatype used by many Open Inventor node and action classes.Matrices
The Open Inventor API uses the convention that positions and directions in 3D space are represented by row vectors. Therefore, to apply a transform matrix, the vector is post-multiplied by the matrix as shown in the following figure. Many mathematics and computer graphics books use column vector notation, however there is no functional difference between these two approaches.
Note that the commonly used terms "row major" and "column major" refer to the storage order of the matrix components in memory. This has nothing to do with how you use matrices and vectors with the Open Inventor API. Internally Open Inventor uses the same storage order as OpenGL to allow matrices to be passed efficiently to/from the GPU. When using the Open Inventor API just remember that positions are row vectors, as shown here.
[X' Y' Z' 1] = [X Y Z 1] * | m11 m12 m13 m14 | | m21 m22 m23 m24 | | m31 m32 m33 m34 | | m41 m42 m43 m44 | Some common 4x4 transform matrices look like this:
Identity | 1 0 0 0 | Translate | 1 0 0 0 | Scale | Sx 0 0 0 | RotateX | 1 0 0 0 | | 0 1 0 0 | | 0 1 0 0 | | 0 Sy 0 0 | | 0 cosT -sinT 0 | | 0 0 1 0 | | 0 0 1 0 | | 0 0 Sz 0 | | 0 sinT cosT 0 | | 0 0 0 1 | | Tx Ty Tz 1 | | 0 0 0 1 | | 0 0 0 1 | Therefore, to create a translation matrix you could initialize the
SbMatrix
object like this (or you could simply use thesetTranslate()
convenience method):SbMatrix( 1,0,0,0, 0,1,0,0, 0,0,1,0, Tx,Ty,Tz,1 ) For convenience
SbMatrix
allows its values to be accessed using 2D array syntax, like this:value = matrix.getElement( row, column ); For example, the translation X, Y, Z values in the above example can be retrieved using:
Tx = matrix[3][0] // Row 3, Column 0 Ty = matrix[3][1] // Row 3, Column 1 Tz = matrix[3][2] // Row 3, Column 2 Multiplying points
Points (positions in 3D space) are transformed by post-multiplying the row vector with the transform matrix like this:
If you need to transform a point by a matrix use theP' = P * M multVecMatrix()
method as shown here:SbMatrix M; SbVec3f src; SbVec3f dst = M.multVecMatrix( src ); SbVec3f
object as both src and dst.In
SbViewVolume
, for example, the projectToScreen() method first calls the getMatrix() method to get the combined model/view/projection matrix, then calls that object'smultVecMatrix()
method to transform the 3D point into normalized clipping space (-1 to 1). (It then does one more step to convert that position to 0..1 normalized screen space but that's not important here.)Multiplying directions
Vectors that represent a direction in 3D space rather than a position, for example surface normal vectors for geometry, can also be transformed. But in this case the translation portion of the matrix (if any) must not be used. For example, if a matrix contains the translation [10, 20, 30], then transforming the normal vector [0, 0, 1] using
multVecMatrix()
would produce the result [10, 20, 31]. However the correct result is still [0, 0, 1] because translation has no meaning for a direction vector. The methodmultDirMatrix()
is provided to transform direction vectors ignoring the translation portion of the matrix.Generally normals should be transformed by the inverse transpose of the matrix. See standard computer graphic references for the explanation.
SbMatrix M; SbVec3f src; SbVec3f dst = M.transpose().inverse().multDirMatrix( src ); Multiplying matrices
A series of transforms, for example scale, rotate and translate can be combined into a single transform matrix by multiplying the matrices together. The result of such a multiplication is order dependent. Using the row vector convention, we can say that transforms are applied from "left to right". We normally want scaling applied first, then rotation, then translation, as shown here:
P' = P * S * R * T So we would build the combined transform matrix M from scale, rotate and translate matrices S, R and T like this:
M = S * R * T Note that convenience nodes like
SoTransform
do this (combine the scale, rotate and translate) for you automatically. So you don't necessarily need to remember all the details.If you need to combine matrices yourself, you can use the
multLeft()
ormultRight()
method to multiple each matrix with the combined matrix. The name “multLeft” means to pre-multiply theSbMatrix
object with the specifiedSbMatrix
parameter, so we would combine the matrices like this:SbMatrix M, S, R, T; M = T; M.multLeft( R ); M.multLeft( S ); multLeft()
overwrites the matrix currently in theSbMatrix
object. So usually (as shown) you will start by making a copy of the first matrix as the starting point for accumulation.The name “multRight” means to post-multiply the
SbMatrix
object with the specifiedSbMatrix
parameter. So we would combine the matrices like this:SbMatrix M, S, R, T; M = S; M.multRight( R ); M.multRight( T ); multRight()
also overwrites the matrix currently in theSbMatrix
object. So usually (as shown) you will start by making a copy of the first matrix as the starting point for accumulation.
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Nested Class Summary
Nested Classes Modifier and Type Class Description static class
SbMatrix.Decomposition
static class
SbMatrix.Factorization
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Field Summary
Fields Modifier and Type Field Description float[]
array
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Constructor Summary
Constructors Constructor Description SbMatrix()
SbMatrix(float[] components)
SbMatrix(float c0, float c1, float c2, float c3, float c4, float c5, float c6, float c7, float c8, float c9, float c10, float c11, float c12, float c13, float c14, float c15)
SbMatrix(SbMatrix copyFrom)
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Method Summary
All Methods Static Methods Instance Methods Concrete Methods Modifier and Type Method Description SbMatrix.Decomposition
decompose()
Returns the translation, rotation, scale, and scale orientation components of the matrix.SbMatrix.Decomposition
decompose(SbVec3f center)
Decomposes the matrix into a translation, rotation, scale, and scale orientation.float
det3()
Returns determinant of upper-left 3x3 submatrix.float
det3(int r1, int r2, int r3, int c1, int c2, int c3)
Returns determinant of 3x3 submatrix composed of given row and column indices (0-3 for each).float
det4()
Returns determinant of entire matrix.boolean
equals(SbMatrix m, float tolerance)
Equality comparison within given tolerance, for each component.boolean
equals(java.lang.Object obj)
SbMatrix.Factorization
factor()
Factors a matrix m into 5 pieces: m = r s r^ u t, where r^ means transpose of r, and r and u are rotations, s is a scale, and t is a translation.float[]
getColumn(int col)
Gets a column of this matrix.float
getElement(int row, int column)
Gets the value at the specified row and column of this matrix.float[]
getRow(int row)
Gets a row of this matrix.float[]
getValue()
float
getValueAt(int index)
static SbMatrix
identity()
Returns an identity matrix.SbMatrix
inverse()
Returns inverse of matrix.boolean
isInvertible()
Returns true if the matrix is invertible.void
makeIdentity()
Sets matrix to be identity.SbVec3f
multDirMatrix(SbVec3f src)
Pre-multiplies the matrix by the given row vector, giving vector result.void
multiply(SbMatrix m)
Post-multiplies the matrix by the given matrix (equivalent tomultRight()
method).SbMatrix
multLeft(SbMatrix m)
Pre-multiplies matrix by the given matrix.SbLine
multLineMatrix(SbLine src)
Multiplies the given line's origin by the matrix, and the line's direction by the rotation portion of the matrix.SbVec3f
multMatrixVec(SbVec3f src)
Post-multiplies matrix by the given column vector, giving a 3D vector result.SbVec4f
multMatrixVec4(SbVec3f src)
Posts-multiplies matrix by the given column vector, giving vector result in homogeneous coordinates.SbMatrix
multRight(SbMatrix m)
Post-multiplies the matrix by the given matrix.SbVec4f
multVec4Matrix(SbVec3f src)
Pre-multiplies matrix by the given row vector, giving vector result in homogeneous coordinates.SbVec3f
multVecMatrix(SbVec3f src)
Pre-multiplies matrix by the given row vector, giving a 3D vector result.void
scale(SbVec3f scaleFactor)
Scales this matrice by the given vector.void
setElement(int row, int column, float value)
Sets the value at the specified row and column of this matrix.void
setRotate(SbRotation q)
Sets matrix to rotate by given rotation.void
setScale(float s)
Sets matrix to scale by given uniform factor.void
setScale(SbVec3f s)
Sets matrix to scale by given vector.void
setTransform(SbVec3f t, SbRotation r, SbVec3f s)
Composes the matrix based on a translation, rotation, and scale.void
setTransform(SbVec3f t, SbRotation r, SbVec3f s, SbRotation so)
Composes the matrix based on a translation, rotation, scale, and orientation for scale.void
setTransform(SbVec3f translation, SbRotation rotation, SbVec3f scaleFactor, SbRotation scaleOrientation, SbVec3f center)
Composes the matrix based on a translation, rotation, scale, orientation for scale, and center.void
setTranslate(SbVec3f t)
Sets matrix to translate by given vector.SbMatrix
setValue(float[] components)
SbMatrix
setValue(float[] components, int startIndex)
SbMatrix
setValue(float c0, float c1, float c2, float c3, float c4, float c5, float c6, float c7, float c8, float c9, float c10, float c11, float c12, float c13, float c14, float c15)
void
setValue(SbMatrix copyFrom)
void
setValue(SbMatrixd md)
Sets value from a double precision matrix.void
setValueAt(int index, float value)
SbMatrix
times(SbMatrix m2)
Multiplies two matrices, returning a matrix result.SbVec4f
times(SbVec4f v)
Multiply matrix by given vector.static SbMatrix[]
toArray(long nativeArray, long length)
void
translate(SbVec3f translation)
Translates this matrice by the given vector.SbMatrix
transpose()
Returns transpose of matrix.
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Constructor Detail
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SbMatrix
public SbMatrix(SbMatrix copyFrom)
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SbMatrix
public SbMatrix(float[] components)
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SbMatrix
public SbMatrix()
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SbMatrix
public SbMatrix(float c0, float c1, float c2, float c3, float c4, float c5, float c6, float c7, float c8, float c9, float c10, float c11, float c12, float c13, float c14, float c15)
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Method Detail
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getRow
public float[] getRow(int row)
Gets a row of this matrix.- Returns:
- an array of 4 floats.
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getColumn
public float[] getColumn(int col)
Gets a column of this matrix.- Returns:
- an array of 4 floats.
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setElement
public void setElement(int row, int column, float value)
Sets the value at the specified row and column of this matrix.
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getElement
public float getElement(int row, int column)
Gets the value at the specified row and column of this matrix.
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getValue
public float[] getValue()
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getValueAt
public float getValueAt(int index)
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setValue
public SbMatrix setValue(float[] components, int startIndex)
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setValue
public SbMatrix setValue(float[] components)
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setValue
public void setValue(SbMatrix copyFrom)
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setValue
public SbMatrix setValue(float c0, float c1, float c2, float c3, float c4, float c5, float c6, float c7, float c8, float c9, float c10, float c11, float c12, float c13, float c14, float c15)
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setValueAt
public void setValueAt(int index, float value)
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isInvertible
public boolean isInvertible()
Returns true if the matrix is invertible.
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equals
public boolean equals(SbMatrix m, float tolerance)
Equality comparison within given tolerance, for each component.
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identity
public static SbMatrix identity()
Returns an identity matrix.
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toArray
public static SbMatrix[] toArray(long nativeArray, long length)
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multiply
public void multiply(SbMatrix m)
Post-multiplies the matrix by the given matrix (equivalent tomultRight()
method). Matrix is replaced by the resulting matrix.
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scale
public void scale(SbVec3f scaleFactor)
Scales this matrice by the given vector.
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equals
public boolean equals(java.lang.Object obj)
- Overrides:
equals
in classjava.lang.Object
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setTransform
public void setTransform(SbVec3f t, SbRotation r, SbVec3f s)
Composes the matrix based on a translation, rotation, and scale. A scale orientation value of (0,0,0,1) is used. The center point for scaling and rotation is (0,0,0).
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setTransform
public void setTransform(SbVec3f t, SbRotation r, SbVec3f s, SbRotation so)
Composes the matrix based on a translation, rotation, scale, and orientation for scale. The scaleOrientation chooses the primary axes for the scale. The center point for scaling and rotation is (0,0,0).
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setTransform
public void setTransform(SbVec3f translation, SbRotation rotation, SbVec3f scaleFactor, SbRotation scaleOrientation, SbVec3f center)
Composes the matrix based on a translation, rotation, scale, orientation for scale, and center. The scaleOrientation chooses the primary axes for the scale. The center is the center point for scaling and rotation.
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transpose
public SbMatrix transpose()
Returns transpose of matrix. Matrix is not modified.
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setTranslate
public void setTranslate(SbVec3f t)
Sets matrix to translate by given vector.
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decompose
public SbMatrix.Decomposition decompose(SbVec3f center)
Decomposes the matrix into a translation, rotation, scale, and scale orientation. Any projection information is discarded. The decomposition depends upon choice of center point for rotation and scaling, which is optional as the last parameter. Note that if the center is 0, decompose() is the same asfactor()
where t is translation, u is rotation, s is scaleFactor, and r is scaleOrientation.
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det4
public float det4()
Returns determinant of entire matrix.
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det3
public float det3()
Returns determinant of upper-left 3x3 submatrix.
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det3
public float det3(int r1, int r2, int r3, int c1, int c2, int c3)
Returns determinant of 3x3 submatrix composed of given row and column indices (0-3 for each).
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factor
public SbMatrix.Factorization factor()
Factors a matrix m into 5 pieces: m = r s r^ u t, where r^ means transpose of r, and r and u are rotations, s is a scale, and t is a translation. Any projection information is returned in proj.
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translate
public void translate(SbVec3f translation)
Translates this matrice by the given vector.
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decompose
public SbMatrix.Decomposition decompose()
Returns the translation, rotation, scale, and scale orientation components of the matrix.
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inverse
public SbMatrix inverse()
Returns inverse of matrix. Results are undefined for singular matrices. Uses LU decomposition.
Matrix is not modified.
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multVec4Matrix
public SbVec4f multVec4Matrix(SbVec3f src)
Pre-multiplies matrix by the given row vector, giving vector result in homogeneous coordinates. Use this method to transform a point (position vector).
UsemultDirMatrix()
to transform a normal (direction vector).
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multMatrixVec4
public SbVec4f multMatrixVec4(SbVec3f src)
Posts-multiplies matrix by the given column vector, giving vector result in homogeneous coordinates.
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setValue
public void setValue(SbMatrixd md)
Sets value from a double precision matrix.
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multDirMatrix
public SbVec3f multDirMatrix(SbVec3f src)
Pre-multiplies the matrix by the given row vector, giving vector result. src is assumed to be a direction vector, so translation part of matrix is ignored.Note: If you need to transform surface points and normal vectors by a matrix, call
multVecMatrix()
for the points and callmultDirMatrix()
for the normals. Generally normals should be transformed by the inverse transpose of the matrix. However note that the inverse transpose is equal to the original matrix if the matrix is orthonormal, i.e. purely rotational with no scaling or shearing.
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multLineMatrix
public SbLine multLineMatrix(SbLine src)
Multiplies the given line's origin by the matrix, and the line's direction by the rotation portion of the matrix.
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multVecMatrix
public SbVec3f multVecMatrix(SbVec3f src)
Pre-multiplies matrix by the given row vector, giving a 3D vector result. The intermediate homogeneous (vec4) value is converted to 3D by dividing the X, Y and Z components by W.Use this method to transform a point (position vector).
UsemultDirMatrix()
to transform a normal (direction vector).
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setScale
public void setScale(float s)
Sets matrix to scale by given uniform factor.
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multRight
public SbMatrix multRight(SbMatrix m)
Post-multiplies the matrix by the given matrix. Matrix is replaced by the result.
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setScale
public void setScale(SbVec3f s)
Sets matrix to scale by given vector.
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multLeft
public SbMatrix multLeft(SbMatrix m)
Pre-multiplies matrix by the given matrix. Matrix is replaced by the result.
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makeIdentity
public void makeIdentity()
Sets matrix to be identity.
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multMatrixVec
public SbVec3f multMatrixVec(SbVec3f src)
Post-multiplies matrix by the given column vector, giving a 3D vector result. The intermediate homogeneous (vec4) value is converted to 3D by dividing the X, Y and Z components by W.
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setRotate
public void setRotate(SbRotation q)
Sets matrix to rotate by given rotation.
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