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The SbMatrix class is a 4x4 dimensional representation of a matrix. More...
#include <Inventor/SbLinear.h>
Static Public Member Functions | |
static SbMatrix | identity (void) |
Friends | |
SbMatrix | operator* (const SbMatrix &m1, const SbMatrix &m2) |
int | operator== (const SbMatrix &m1, const SbMatrix &m2) |
int | operator!= (const SbMatrix &m1, const SbMatrix &m2) |
Related Symbols | |
(Note that these are not member symbols.) | |
SbMatrix | operator* (const SbMatrix &m1, const SbMatrix &m2) |
int | operator== (const SbMatrix &m1, const SbMatrix &m2) |
int | operator!= (const SbMatrix &m1, const SbMatrix &m2) |
The SbMatrix class is a 4x4 dimensional representation of a matrix.
SbMatrix is used by many other classes in Coin. It provides storage for a 4x4 matrix of single-precision floating point values.
By definition, matrices in Coin should be set up in column-order mode. This is the same order as used by e.g. OpenGL, but note that books on geometry often uses the opposite row-order mode, which can confuse new-comers to the API.
Another way to think of column-order matrices is that they use post-order multiplications: that is, to concatenate a transformation from a second matrix with your current matrix, it should be multiplied on the right-hand side, i.e. with the SbMatrix::multRight() method.
If you have a matrix in row-order from some other source, it can be "converted" to column-order by transposing it with SbMatrix::transpose(). A simple example will help to explain this.
With row-order matrices, a transformation matrix with position, rotation and scale looks like this:
Where T is translation, R is rotation and S is the scale. What this means is that scale is applied first. The scaled matrix is then rotated, and finally the scaled and rotated matrix is translated. When using column-order matrices, as done in Coin, matrices are represented slightly differently; the order of multiplication is reversed:
The transformation is just the same as the row-order matrix. The only difference being the order of multiplication. To understand why this is so, consider the sample transformation:
Converting M from a row-order matrix to a column-order matrix is done as follows:
All left to be done is to remove the transpose symbols, and the matrices have been converted to column-order matrices:
This was done using the fact that:
Converting from column-order to row-order is done using the same principle.
SbMatrix::SbMatrix | ( | void | ) |
The default constructor does nothing. The matrix will be uninitialized.
Referenced by identity().
SbMatrix::SbMatrix | ( | const float | a11, |
const float | a12, | ||
const float | a13, | ||
const float | a14, | ||
const float | a21, | ||
const float | a22, | ||
const float | a23, | ||
const float | a24, | ||
const float | a31, | ||
const float | a32, | ||
const float | a33, | ||
const float | a34, | ||
const float | a41, | ||
const float | a42, | ||
const float | a43, | ||
const float | a44 | ||
) |
Constructs a matrix instance with the given initial elements.
References setValue().
SbMatrix::SbMatrix | ( | const SbMat & | matrixref | ) |
Constructs a matrix instance with the initial elements from the matrix argument.
References setValue().
SbMatrix::SbMatrix | ( | const SbMat * | matrixptr | ) |
This constructor is courtesy of the Microsoft Visual C++ compiler.
References setValue().
SbMatrix::~SbMatrix | ( | void | ) |
Default destructor does nothing.
Assignment operator. Copies the elements from m to the matrix.
References setValue().
SbMatrix::operator float * | ( | void | ) |
Return pointer to the matrix' 4x4 float array.
Assignment operator. Copies the elements from m to the matrix.
References setValue().
Copies the elements from m into the matrix.
Referenced by operator=(), operator=(), SbMatrix(), SbMatrix(), and SbMatrix().
Returns a pointer to the 2 dimensional float array with the matrix elements.
Set the matrix to be the identity matrix.
Referenced by SoGetMatrixAction::beginTraversal(), SbXfBox3f::extendBy(), SbXfBox3f::extendBy(), SoResetTransform::getMatrix(), SbProjector::SbProjector(), SbXfBox3f::SbXfBox3f(), SbXfBox3f::SbXfBox3f(), SbXfBox3f::SbXfBox3f(), setScale(), setScale(), and setTranslate().
void SbMatrix::setRotate | ( | const SbRotation & | q | ) |
Set matrix to be a rotation matrix with the given rotation.
References SbRotation::getValue().
Referenced by SoTransform::getRotationSpaceMatrix(), SoVRMLTransform::getRotationSpaceMatrix(), SoTransform::getTranslationSpaceMatrix(), SoVRMLTransform::getTranslationSpaceMatrix(), operator=(), setTransform(), and setTransform().
Return a new matrix which is the inverse matrix of this.
The user is responsible for checking that this is a valid operation to execute, by first making sure that the result of SbMatrix::det4() is not equal to zero.
References identity(), and SoDebugError::postWarning().
Referenced by SoDragger::appendScale(), SoVRMLTransform::getRotationSpaceMatrix(), SoVRMLTransform::getScaleSpaceMatrix(), SoVRMLTransform::getTranslationSpaceMatrix(), SoAntiSquish::getUnsquishingMatrix(), SoVRMLDragSensor::handleEvent(), SbProjector::setWorkingSpace(), and SbPlane::transform().
float SbMatrix::det3 | ( | int | r1, |
int | r2, | ||
int | r3, | ||
int | c1, | ||
int | c2, | ||
int | c3 | ||
) | const |
Returns the determinant of the 3x3 submatrix specified by the row and column indices.
References SoDebugError::post().
Referenced by SbXfBox3f::getVolume().
float SbMatrix::det3 | ( | void | ) | const |
Check if the m matrix is equal to this one, within the given tolerance value. The tolerance value is applied in the comparison on a component by component basis.
References SoDebugError::postWarning().
SbMatrix::operator SbMat & | ( | void | ) |
Return pointer to the matrix' 4x4 float array.
float * SbMatrix::operator[] | ( | int | i | ) |
Returns pointer to the 4 element array representing a matrix row. i should be within [0, 3].
References SoDebugError::post().
const float * SbMatrix::operator[] | ( | int | i | ) | const |
Returns pointer to the 4 element array representing a matrix row. i should be within [0, 3].
References SoDebugError::postWarning().
SbMatrix & SbMatrix::operator= | ( | const SbRotation & | q | ) |
Set matrix to be a rotation matrix with the given rotation.
References setRotate().
void SbMatrix::getValue | ( | SbMat & | m | ) | const |
Return matrix components in the SbMat structure.
Return the identity matrix.
References SbMatrix().
Referenced by SoGetBoundingBoxAction::checkResetAfter(), SoGetBoundingBoxAction::checkResetBefore(), SoCamera::doAction(), SoMatrixTransform::doAction(), SoArray::getBoundingBox(), SoLevelOfDetail::getBoundingBox(), SoMultipleCopy::getBoundingBox(), SoVRMLGroup::getBoundingBox(), SoDragger::getLocalToWorldMatrix(), SoNurbsProfile::getVertices(), SoDragger::getWorldToLocalMatrix(), SoCamera::GLRender(), SbXfBox3f::intersect(), SbDPMatrix::inverse(), inverse(), setTransform(), setTransform(), setTransform(), SoCenterballDragger::SoCenterballDragger(), SoMatrixTransform::SoMatrixTransform(), SoMultipleCopy::SoMultipleCopy(), SoTransformVec3f::SoTransformVec3f(), and SoDragger::transferMotion().
Set matrix to be a pure scaling matrix. Scale factors are specified by s.
References makeIdentity().
Referenced by setTransform(), setTransform(), and SoClipPlaneManip::setValue().
Set matrix to be a pure scaling matrix. Scale factors in x, y and z is specified by the s vector.
References makeIdentity().
Make this matrix into a pure translation matrix (no scale or rotation components) with the given vector \t as the translation.
References makeIdentity().
Referenced by SoDragger::appendRotation(), SoDragger::appendScale(), SoDragger::appendTranslation(), SoVRMLTransform::getRotationSpaceMatrix(), SoVRMLTransform::getScaleSpaceMatrix(), SoVRMLTransform::getTranslationSpaceMatrix(), setTransform(), setTransform(), setTransform(), and SoCenterballDragger::transferCenterDraggerMotion().
Set translation, rotation and scaling all at once. The resulting matrix gets calculated like this:
where S, R and T is scaling, rotation and translation matrices.
References identity(), SbRotation::identity(), multRight(), setRotate(), setScale(), and setTranslate().
Referenced by SoDragger::appendScale(), SoTransform::doAction(), SoClipPlaneManip::fieldSensorCB(), SoDirectionalLightManip::fieldSensorCB(), SoSpotLightManip::fieldSensorCB(), SoTransformManip::fieldSensorCB(), SoRotateCylindricalDragger::fieldSensorCB(), SoRotateDiscDragger::fieldSensorCB(), SoRotateSphericalDragger::fieldSensorCB(), SoScale1Dragger::fieldSensorCB(), SoScale2Dragger::fieldSensorCB(), SoScale2UniformDragger::fieldSensorCB(), SoScaleUniformDragger::fieldSensorCB(), SoAntiSquish::getUnsquishingMatrix(), SoTransform::multLeft(), SoTransform::multRight(), SoTransform::recenter(), SoVRMLTransform::recenter(), and SoDragger::workValuesIntoTransform().
void SbMatrix::setTransform | ( | const SbVec3f & | t, |
const SbRotation & | r, | ||
const SbVec3f & | s, | ||
const SbRotation & | so | ||
) |
Set translation, rotation and scaling all at once with a specified scale orientation. The resulting matrix gets calculated like this:
where Ro is the scale orientation, and S, R and T is scaling, rotation and translation.
References identity(), SbRotation::identity(), SbRotation::inverse(), multRight(), setRotate(), setScale(), and setTranslate().
void SbMatrix::setTransform | ( | const SbVec3f & | translation, |
const SbRotation & | rotation, | ||
const SbVec3f & | scaleFactor, | ||
const SbRotation & | scaleOrientation, | ||
const SbVec3f & | center | ||
) |
Set translation, rotation and scaling all at once with a specified scale orientation and center point. The resulting matrix gets calculated like this:
where Tc is the center point, Ro the scale orientation, S, R and T is scaling, rotation and translation.
References identity(), SbRotation::identity(), SbRotation::inverse(), multRight(), and setTranslate().
void SbMatrix::getTransform | ( | SbVec3f & | t, |
SbRotation & | r, | ||
SbVec3f & | s, | ||
SbRotation & | so | ||
) | const |
Factor the matrix back into its translation, rotation, scale and scaleorientation components.
Referenced by SoClipPlaneManip::fieldSensorCB(), SoDirectionalLightManip::fieldSensorCB(), SoSpotLightManip::fieldSensorCB(), SoRotateCylindricalDragger::fieldSensorCB(), SoRotateDiscDragger::fieldSensorCB(), SoRotateSphericalDragger::fieldSensorCB(), SoScale1Dragger::fieldSensorCB(), SoScale2Dragger::fieldSensorCB(), SoScale2UniformDragger::fieldSensorCB(), SoScaleUniformDragger::fieldSensorCB(), SoTransform::recenter(), SoVRMLTransform::recenter(), SoVRMLTransform::setMatrix(), SoCenterballDragger::valueChangedCB(), SoDirectionalLightDragger::valueChangedCB(), SoHandleBoxDragger::valueChangedCB(), SoJackDragger::valueChangedCB(), SoRotateCylindricalDragger::valueChangedCB(), SoRotateDiscDragger::valueChangedCB(), SoRotateSphericalDragger::valueChangedCB(), SoScale1Dragger::valueChangedCB(), SoScale2Dragger::valueChangedCB(), SoScale2UniformDragger::valueChangedCB(), SoScaleUniformDragger::valueChangedCB(), SoSpotLightDragger::valueChangedCB(), SoTabBoxDragger::valueChangedCB(), SoTrackballDragger::valueChangedCB(), SoTransformBoxDragger::valueChangedCB(), SoTransformerDragger::valueChangedCB(), SoTranslate1Dragger::valueChangedCB(), SoSpotLightManip::valueChangedCB(), SoTransformManip::valueChangedCB(), and SoDragger::workValuesIntoTransform().
void SbMatrix::getTransform | ( | SbVec3f & | translation, |
SbRotation & | rotation, | ||
SbVec3f & | scaleFactor, | ||
SbRotation & | scaleOrientation, | ||
const SbVec3f & | center | ||
) | const |
Factor the matrix back into its translation, rotation, scaleFactor and scaleorientation components. Will eliminate the center variable from the matrix.
SbBool SbMatrix::LUDecomposition | ( | int | index[4], |
float & | d | ||
) |
This function produces a permuted LU decomposition of the matrix. It uses the common single-row-pivoting strategy.
FALSE is returned if the matrix is singular, which it never is, because of small adjustment values inserted if a singularity is found (as Open Inventor does too).
The parity argument is always set to 1.0 or -1.0. Don't really know what it's for, so it's not checked for correctness.
The index[] argument returns the permutation that was done on the matrix to LU-decompose it. index[i] is the row that row i was swapped with at step i in the decomposition, so index[] is not the actual permutation of the row indexes!
BUGS: The function does not produce results that are numerically identical with those produced by Open Inventor for the same matrices, because the pivoting strategy in OI was never fully understood.
References factor().
void SbMatrix::LUBackSubstitution | ( | int | index[4], |
float | b[4] | ||
) | const |
This function does a solve on the "Ax = b" system, given that the matrix is LU-decomposed in advance. First, a forward substitution is done on the lower system (Ly = b), and then a backwards substitution is done on the upper triangular system (Ux = y).
The index[] argument is the one returned from SbMatrix::LUDecomposition(), so see that function for an explanation.
The b[] argument must contain the b vector in "Ax = b" when calling the function. After the function has solved the system, the b[] vector contains the x vector.
BUGS: As is done by Open Inventor, unsolvable x values will not return NaN but 0.
Returns the transpose of this matrix.
Referenced by SbPlane::transform().
Let this matrix be right-multiplied by m. Returns reference to self.
This is the most common multiplication / concatenation operation when using column-order matrices, as SbMatrix instances are, by definition.
Referenced by SoDragger::appendRotation(), SoDragger::appendScale(), SoDragger::appendTranslation(), SoGetBoundingBoxAction::extendBy(), SbXfBox3f::extendBy(), SoGetBoundingBoxAction::extendBy(), SoGeoLocation::getMatrix(), SoMatrixTransform::getMatrix(), SoRotation::getMatrix(), SoRotationXYZ::getMatrix(), SoScale::getMatrix(), SoSurroundScale::getMatrix(), SoTexture2Transform::getMatrix(), SoTexture3Transform::getMatrix(), SoTransform::getMatrix(), SoTranslation::getMatrix(), SoUnits::getMatrix(), SoVRMLTextureTransform::getMatrix(), SoVRMLTransform::getMatrix(), SoDragger::getPartToLocalMatrix(), SoTransform::getRotationSpaceMatrix(), SoVRMLTransform::getRotationSpaceMatrix(), SoVRMLTransform::getScaleSpaceMatrix(), SoTransform::getTranslationSpaceMatrix(), SoVRMLTransform::getTranslationSpaceMatrix(), SoAntiSquish::getUnsquishingMatrix(), SoTransform::multRight(), operator*=(), SoGetBoundingBoxAction::setCenter(), setTransform(), setTransform(), setTransform(), SbXfBox3f::transform(), and SoCenterballDragger::valueChangedCB().
Let this matrix be left-multiplied by m. Returns reference to self.
(Be aware that it is more common to use the SbMatrix::multRight() operation, when doing concatenation of transformations, as SbMatrix instances are by definition in column-order, and uses post-multiplication for common geometry operations.)
Referenced by SoDragger::appendRotation(), SoDragger::appendScale(), SoDragger::appendTranslation(), SoGeoLocation::getMatrix(), SoMatrixTransform::getMatrix(), SoRotation::getMatrix(), SoRotationXYZ::getMatrix(), SoScale::getMatrix(), SoSurroundScale::getMatrix(), SoTexture2Transform::getMatrix(), SoTexture3Transform::getMatrix(), SoTransform::getMatrix(), SoTranslation::getMatrix(), SoUnits::getMatrix(), SoVRMLTextureTransform::getMatrix(), SoVRMLTransform::getMatrix(), SoTransform::multLeft(), SoDragger::transferMotion(), SoDragger::transformMatrixLocalToWorld(), SoDragger::transformMatrixWorldToLocal(), and SoCenterballDragger::valueChangedCB().
Multiply src vector with this matrix and return the result in dst. Multiplication is done with the vector on the right side of the expression, i.e. dst = M * src.
(Be aware that it is more common to use the SbMatrix::multVecMatrix() operation, when doing vector transformations, as SbMatrix instances are by definition in column-order, and uses post-multiplication for common geometry operations.)
Multiply src vector with this matrix and return the result in dst. Multiplication is done with the vector on the left side of the expression, i.e. dst = src * M.
It is safe to let src and dst be the same SbVec3f instance.
This method can be used (using the current model matrix) to transform a point from an object coordinate systems to the world coordinate system.
This operation is what you would usually do when transforming vectors, as SbMatrix instances are, by definition, column-order matrices.
Referenced by SoHandleBoxDragger::drag(), SoRotateSphericalDragger::drag(), SoTabPlaneDragger::drag(), SoTrackballDragger::drag(), SoTranslate2Dragger::drag(), SoHandleBoxDragger::dragStart(), SoRotateSphericalDragger::dragStart(), SoTabPlaneDragger::dragStart(), SoTrackballDragger::dragStart(), SoTransformerDragger::dragStart(), SoTranslate2Dragger::dragStart(), SbXfBox3f::getCenter(), SoDragger::getLocalStartingPoint(), SoShape::getScreenSize(), SoMarkerSet::GLRender(), SoText2::GLRender(), SoVRMLDragSensor::handleEvent(), SoVRMLTouchSensor::handleEvent(), SbXfBox3f::intersect(), SbCylinderProjector::isPointInFront(), SbSphereProjector::isPointInFront(), multLineMatrix(), SbLineProjector::project(), SbPlaneProjector::project(), SoGetBoundingBoxAction::setCenter(), SbBox3f::transform(), SbPlane::transform(), and SbProjector::verifyProjection().
Multiplies src by the matrix. src is assumed to be a direction vector, and the translation components of the matrix are therefore ignored.
Multiplication is done with the vector on the left side of the expression, i.e. dst = src * M.
Referenced by SoVRMLTouchSensor::handleEvent(), SbCylinderProjector::isPointInFront(), SbSphereProjector::isPointInFront(), multLineMatrix(), SbCylinderSheetProjector::setupPlane(), SbPlaneProjector::setupPlane(), SbSphereSheetProjector::setupPlane(), SbCylinderSectionProjector::setupTolerance(), SbSphereSectionProjector::setupTolerance(), SoDirectionalLightManip::valueChangedCB(), and SoSpotLightManip::valueChangedCB().
Multiplies line point with the full matrix and multiplies the line direction with the matrix without the translation components.
References SbLine::getDirection(), SbLine::getPosition(), multDirMatrix(), and multVecMatrix().
Referenced by SbProjector::getWorkingLine(), SbLineProjector::project(), and SbPlaneProjector::project().
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
Multiplies matrix m1 with matrix m2 and returns the resultant matrix.
Compare matrices to see if they are equal. For two matrices to be equal, all their individual elements must be equal.
Compare matrices to see if they are not equal. For two matrices to not be equal, it is enough that at least one of their elements are unequal.
Multiplies matrix m1 with matrix m2 and returns the resultant matrix.
Compare matrices to see if they are equal. For two matrices to be equal, all their individual elements must be equal.
Compare matrices to see if they are not equal. For two matrices to not be equal, it is enough that at least one of their elements are unequal.
Copyright © 1998-2007 by Systems in Motion AS. All rights reserved.
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