Package com.openinventor.inventor

Class SbMatrix

java.lang.Object
com.openinventor.inventor.SbBasic
com.openinventor.inventor.SbMatrix
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 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: 

  P' = P * M
If you need to transform a point by a matrix use the multVecMatrix() method as shown here: 
 SbMatrix M;
 SbVec3f  src;
 SbVec3f dst = M.multVecMatrix( src );
Note that it is safe to use the same 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. 

 SbMatrix M;
 SbVec3f  src;
 SbVec3f dst = M.transpose().inverse().multDirMatrix( src );
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.

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: 

 SbMatrix M, S, R, T;
 M = T;
 M.multLeft( R );
 M.multLeft( S );
Note that 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: 

 SbMatrix M, S, R, T;
 M = S;
 M.multRight( R );
 M.multRight( T );
Note that 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:

  • Field Details

    • array

      public final float[] array

  • Constructor Details

    • SbMatrix

      public SbMatrix(SbMatrix copyFrom)

    • SbMatrix

      public SbMatrix(float[] components)

    • SbMatrix

      public SbMatrix()

    • 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)

  • Method Details

    • getRow

      public float[] getRow(int row)
      Gets a row of this matrix.
      Returns:
      an array of 4 floats.

    • getColumn

      public float[] getColumn(int col)
      Gets a column of this matrix.
      Returns:
      an array of 4 floats.

    • setElement

      public void setElement(int row, int column, float value)
      Sets the value at the specified row and column of this matrix.

    • getElement

      public float getElement(int row, int column)
      Gets the value at the specified row and column of this matrix.

    • getValue

      public float[] getValue()

    • getValueAt

      public float getValueAt(int index)

    • setValue

      public SbMatrix setValue(float[] components, int startIndex)

    • setValue

      public SbMatrix setValue(float[] components)

    • setValue

      public void setValue(SbMatrix copyFrom)

    • 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)

    • setValueAt

      public void setValueAt(int index, float value)

    • isInvertible

      public boolean isInvertible()
      Returns true if the matrix is invertible.

    • equals

      public boolean equals(SbMatrix m, float tolerance)
      Equality comparison within given tolerance, for each component.

    • identity

      public static SbMatrix identity()
      Returns an identity matrix.

    • toArray

      public static SbMatrix[] toArray(long nativeArray, long length)

    • times

      public SbVec4f times(SbVec4f v)
      Multiply matrix by given vector. Return m * v

    • multiply

      public void multiply(SbMatrix m)
      Post-multiplies the matrix by the given matrix (equivalent to multRight() method). Matrix is replaced by the resulting matrix.

    • times

      public SbMatrix times(SbMatrix m2)
      Multiplies two matrices, returning a matrix result.

    • scale

      public void scale(SbVec3f scaleFactor)
      Scales this matrice by the given vector.

    • equals

      public boolean equals(Object obj)
      Overrides:
      equals in class Object

    • 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).

    • 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).

    • 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.

    • transpose

      public SbMatrix transpose()
      Returns transpose of matrix. Matrix is not modified.

    • setTranslate

      public void setTranslate(SbVec3f t)
      Sets matrix to translate by given vector.

    • 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 as factor() where t is translation, u is rotation, s is scaleFactor, and r is scaleOrientation.

    • det4

      public float det4()
      Returns determinant of entire matrix.

    • det3

      public float det3()
      Returns determinant of upper-left 3x3 submatrix.

    • 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).

    • 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.

    • translate

      public void translate(SbVec3f translation)
      Translates this matrice by the given vector.

    • decompose

      public SbMatrix.Decomposition decompose()
      Returns the translation, rotation, scale, and scale orientation components of the matrix.

    • inverse

      public SbMatrix inverse()
      Returns inverse of matrix. Results are undefined for singular matrices. Uses LU decomposition.
      Matrix is not modified.

    • 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).
      Use multDirMatrix() to transform a normal (direction vector).

    • multMatrixVec4

      public SbVec4f multMatrixVec4(SbVec3f src)
      Posts-multiplies matrix by the given column vector, giving vector result in homogeneous coordinates.

    • setValue

      public void setValue(SbMatrixd md)
      Sets value from a double precision matrix.

    • 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 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.

    • 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.

    • 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).
      Use multDirMatrix() to transform a normal (direction vector).

    • setScale

      public void setScale(float s)
      Sets matrix to scale by given uniform factor.

    • multRight

      public SbMatrix multRight(SbMatrix m)
      Post-multiplies the matrix by the given matrix. Matrix is replaced by the result.

    • setScale

      public void setScale(SbVec3f s)
      Sets matrix to scale by given vector.

    • multLeft

      public SbMatrix multLeft(SbMatrix m)
      Pre-multiplies matrix by the given matrix. Matrix is replaced by the result.

    • makeIdentity

      public void makeIdentity()
      Sets matrix to be identity.

    • 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.

    • setRotate

      public void setRotate(SbRotation q)
      Sets matrix to rotate by given rotation.