public class SbMatrix extends SbBasic
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 the setTranslate() 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: Note that it is safe to use the sameSbMatrix 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's multVecMatrix() 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 method multDirMatrix() 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.
However note that if the matrix is orthonormal, i.e. purely rotational with no scaling or shearing, then the inverse transpose is the same as the original matrix and it is not necessary to compute the inverse transpose.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() or multRight() method to multiple each matrix with the combined matrix. The name “multLeft” means to pre-multiply the SbMatrix object with the specified SbMatrix parameter, so we would combine the matrices like this:
Note thatSbMatrix M, S, R, T; M = T; M.multLeft( R ); M.multLeft( S );
multLeft()
overwrites the matrix currently in the SbMatrix 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 specified SbMatrix parameter. So we would combine the matrices like this:
Note thatSbMatrix M, S, R, T; M = S; M.multRight( R ); M.multRight( T );
multRight() also overwrites the matrix currently in the SbMatrix object. So usually (as shown) you will start by making a copy of the first matrix as the starting point for accumulation.
See also:
SbMatrix3, SbMatrixd, SbRotation, SbRotationd, SbVec2d, SbVec2f, SbVec2i32, SbVec2s, SbVec3d, SbVec3f, SbVec3i32, SbVec3s, SbVec4b, SbVec4d, SbVec4f, SbVec4i32, SbVec4s, SbVec4ub, SbVec4ui32, SbVec4us
| Modifier and Type | Class and Description |
|---|---|
static class |
SbMatrix.Decomposition |
static class |
SbMatrix.Factorization |
| Modifier and Type | Field and Description |
|---|---|
float[] |
array |
| Constructor and 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) |
| Modifier and Type | Method and 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(java.lang.Object obj) |
boolean |
equals(SbMatrix m,
float tolerance)
Equality comparison within given tolerance, for each component.
|
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 to
multRight() 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.
|
static SbMatrix[] |
toArray(long nativeArray,
long length) |
void |
translate(SbVec3f translation)
Translates this matrice by the given vector.
|
SbMatrix |
transpose()
Returns transpose of matrix.
|
public SbMatrix(float[] components)
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)
public SbMatrix(SbMatrix copyFrom)
public SbMatrix()
public float[] getRow(int row)
public float[] getColumn(int col)
public void setElement(int row,
int column,
float value)
public float getElement(int row,
int column)
public float[] getValue()
public void setValue(SbMatrix copyFrom)
public SbMatrix setValue(float[] components)
public SbMatrix setValue(float[] components, int startIndex)
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)
public float getValueAt(int index)
public void setValueAt(int index,
float value)
public static SbMatrix[] toArray(long nativeArray, long length)
public void setTransform(SbVec3f t, SbRotation r, SbVec3f s)
public void multiply(SbMatrix m)
multRight() method).
Matrix is replaced by the resulting matrix.public boolean equals(SbMatrix m, float tolerance)
public boolean isInvertible()
public boolean equals(java.lang.Object obj)
equals in class java.lang.Objectpublic static SbMatrix identity()
public SbMatrix.Factorization factor()
public void setScale(float s)
public float det4()
public SbMatrix inverse()
public void scale(SbVec3f scaleFactor)
public void translate(SbVec3f translation)
public void setRotate(SbRotation q)
public float det3()
public SbMatrix.Decomposition decompose(SbVec3f center)
factor() where t is translation, u is rotation, s is scaleFactor, and r is scaleOrientation. public void setTransform(SbVec3f t, SbRotation r, SbVec3f s, SbRotation so)
public void setTransform(SbVec3f translation, SbRotation rotation, SbVec3f scaleFactor, SbRotation scaleOrientation, SbVec3f center)
public void setTranslate(SbVec3f t)
public void setScale(SbVec3f s)
public float det3(int r1,
int r2,
int r3,
int c1,
int c2,
int c3)
public SbMatrix.Decomposition decompose()
public SbVec4f multMatrixVec4(SbVec3f src)
public SbVec3f multVecMatrix(SbVec3f src)
Use this method to transform a point (position vector).
Use multDirMatrix() to transform a normal (direction vector).
public SbVec4f multVec4Matrix(SbVec3f src)
multDirMatrix() to transform a normal (direction vector).public SbLine multLineMatrix(SbLine src)
public SbVec3f multDirMatrix(SbVec3f src)
Note: If you need to transform surface points and normal vectors by a matrix, call multVecMatrix() for the points and call multDirMatrix() 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.
public SbVec3f multMatrixVec(SbVec3f src)
public void makeIdentity()
public void setValue(SbMatrixd md)
public SbMatrix multLeft(SbMatrix m)
public SbMatrix multRight(SbMatrix m)
public SbMatrix transpose()
Generated on January 23, 2025, Copyright © Thermo Fisher Scientific. All rights reserved. http://www.openinventor.com