All Math classes and functions defined in the C++ API are assigned to the MATH namespace which is nested under the XSI namespace. More...

Classes
class	CColor4f
	A color class represented by single floating values. CColor4f supports the RGBA, HSVA and HLSA color models. More...
class	CLine
	A parametric 3D line. More...
class	CMatrix3
	This class represents a double precision floating point 3 by 3 matrix. More...
class	CMatrix3f
	A class to represent a single precision floating point 3 by 3 matrix. This class is typically used for implementing custom ICE nodes. More...
class	CMatrix4
	This class represents a double precision floating point 4 by 4 matrix. More...
class	CMatrix4f
	A class to represent a single precision floating point 4 by 4 matrix. This class is typically used for implementing custom ICE nodes. More...
class	CPlane
	A parametric 3D plane. More...
class	CQuaternion
	Implementation of a quaternion q=a+bi+cj+dk. More...
class	CQuaternionf
	Implementation of a float quaternion q=a+bi+cj+dk. This class is typically used for implementing custom ICE nodes. More...
class	CRandom
	A random number sequence generator class. More...
class	CRotation
	Provides conversion facilities for various rotation representations including Euler angles, Quaternion, Axis angle and rotation matrix. More...
class	CRotationf
	Provides conversion facilities for various rotation representations including Euler angles, Quaternion, Axis angle and rotation matrix. CRotationf is typically used for implementing custom ICE nodes. More...
class	CShape
	A class representing primitive types for particles rendering. Shape objects are read-only and can be accessed with ICEAttribute properties such as ICEAttribute::GetDataArray and ICEAttribute::GetDataArray2D. More...
class	CTransformation
	This object represents a transformation which is the result of the combination of a Scaling, a Rotation and a Translation, in the S.R.T order. More...
class	CVector2f
	A 2-element vector represented by single floating point x,y coordinates. This class is typically used for implementing custom ICE nodes. More...
class	CVector3
	A 3-element vector that is represented by double precision floating point x,y,z coordinates. More...
class	CVector3Array
	The CVector3Array is an uni-dimensional array of CVector3. More...
class	CVector3f
	A 3-element vector that is represented by single floating point x,y,z coordinates. The class is used used for implementing custom ICE nodes. More...
class	CVector4
	A 4-element vector that is represented by double precision floating point x,y,z,w coordinates. More...
class	CVector4Array
	The CVector4Array is an uni-dimensional array of CVector4. More...
class	CVector4f
	A 4-element vector that is represented by single floating point x,y,z coordinates. The class is used used for implementing custom ICE nodes. More...
Functions
double	DegreesToRadians (double in_dDegrees)
double	RadiansToDegrees (double in_dRadians)
CTransformation	MapObjectPoseToWorldSpace (const CTransformation &in_transfoObjectSpace, const CTransformation &in_transfoPose)
CVector3	MapObjectOrientationToWorldSpace (const CTransformation &in_transfoObjectSpace, const CVector3 &in_vector3Orientation)
CVector3	MapObjectPositionToWorldSpace (const CTransformation &in_transfoObjectSpace, const CVector3 &in_vector3Position)
CTransformation	MapWorldPoseToObjectSpace (const CTransformation &in_transfoObjectSpace, const CTransformation &in_transfoPose)
CVector3	MapWorldOrientationToObjectSpace (const CTransformation &in_transfoObjectSpace, const CVector3 &in_vector3Orientation)
CVector3	MapWorldPositionToObjectSpace (const CTransformation &in_transfoObjectSpace, const CVector3 &in_vector3Position)
CTransformation	MapObjectPoseToObjectSpace (const CTransformation &in_transfoObjectSpace, const CTransformation &in_transfoSpace, const CTransformation &in_transfoPose)
CVector3	MapObjectOrientationToObjectSpace (const CTransformation &in_transfoObjectSpace, const CTransformation &in_transfoSpace, const CVector3 &in_vector3Orientation)
CVector3	MapObjectPositionToObjectSpace (const CTransformation &in_transfoObjectSpace, const CTransformation &in_transfoSpace, const CVector3 &in_vector3Position)

Detailed Description

All Math classes and functions defined in the C++ API are assigned to the MATH namespace which is nested under the XSI namespace.

Members of the MATH namespace can be identified explicitly with the symbol MATH for code clarity. To simplify the code however, namespace members can be referenced without the namespace symbol by using the C++ using directive.

Example:

Demonstrates using namespace

        // namespace qualification
        XSI::MATH::CVector3 v(1,1,0);

        // CVector referenced without explicit qualification
        using namespace XSI::MATH;
        CVector3 v(1,1,0);

Function Documentation

double XSI::MATH::DegreesToRadians ( double in_dDegrees ) [inline]

Converts an angle in degrees to an angle in radians.

Parameters:

in_dDegrees angle in degrees.

Returns:: Angle in radians.

double XSI::MATH::RadiansToDegrees ( double in_dRadians ) [inline]

Converts an angle in radians to an angle in degrees.

Parameters:

in_dRadians angle in radians.

Returns:: Angle in degrees.

CTransformation XSI::MATH::MapObjectPoseToWorldSpace	(	const CTransformation &	in_transfoObjectSpace,
		const CTransformation &	in_transfoPose
	)

Converts a Pose described in a given ObjectSpace to WorldSpace

Parameters:

in_transfoObjectSpace	ObjectSpace into which the pose is defined.
in_transfoPose	Pose to convert.

Returns:: The world Pose.

See also:: CTransformation, KinematicState, Kinematics::GetGlobal, Kinematics::GetLocal

Example:

Demonstrates how to use MapObjectPoseToWorldSpace

        using namespace XSI;
        using namespace MATH;
        Application app;
        Model root = app.GetActiveSceneRoot();

        X3DObject myCube;
        root.AddGeometry( L"Cube", L"MeshSurface",L"",myCube );

        KinematicState  globalKinematicState = myCube.GetKinematics().GetGlobal();
        globalKinematicState.PutParameterValue(L"posy", 4.0);
        globalKinematicState.PutParameterValue(L"posx", 2.0);

        X3DObject myCube2;
        myCube.AddGeometry( L"Cube", L"MeshSurface",L"",myCube2);

        globalKinematicState = myCube2.GetKinematics().GetGlobal();
        globalKinematicState.PutParameterValue(L"posz",3.0);
        globalKinematicState.PutParameterValue(L"rotx",45.0);

        CTransformation localTransformation =
                                myCube2.GetKinematics().GetLocal().GetTransform();
        CTransformation globalTransformation =
                                myCube.GetKinematics().GetGlobal().GetTransform();

        CVector3 translation(localTransformation.GetTranslation());

        app.LogMessage(
            L"The translation of the cube relative to its parent: x " +
            CValue(translation.GetX()).GetAsText() +
            L" y " +
            CValue(translation.GetY()).GetAsText() +
            L" z " +
            CValue(translation.GetZ()).GetAsText());

        CTransformation worldTransformation =
                        MapObjectPoseToWorldSpace(  globalTransformation,
                                                    localTransformation);

        translation = worldTransformation.GetTranslation();

        app.LogMessage( L"The translation of the cube relative to " +
                        CString(L"the origin of the universe: x ") +
                        CValue(translation.GetX()).GetAsText() +
                        L" y " + CValue(translation.GetY()).GetAsText() +
                        L" z " + CValue(translation.GetZ()).GetAsText());

CVector3 XSI::MATH::MapObjectOrientationToWorldSpace	(	const CTransformation &	in_transfoObjectSpace,
		const CVector3 &	in_vector3Orientation
	)

Converts an Orientation described in a given ObjectSpace to WorldSpace.

Parameters:

in_transfoObjectSpace	ObjectSpace in which the orientation is defined.
in_vector3Orientation	Orientation to convert.

Returns:: The world orientation.

See also:: CTransformation, KinematicState, Kinematics::GetGlobal, Kinematics::GetLocal

Example:

Demonstrates MapObjectOrientationToWorldSpace

        using namespace XSI;
        using namespace MATH;
        Application app;
        Model root = app.GetActiveSceneRoot();

        X3DObject myCube;
        root.AddGeometry( L"Cube", L"MeshSurface",L"",myCube );

        KinematicState  globalKinematicState = myCube.GetKinematics().GetGlobal();
        globalKinematicState.PutParameterValue(L"posy", 4.0);
        globalKinematicState.PutParameterValue(L"posx", 2.0);
        globalKinematicState.PutParameterValue(L"rotx", 45.0);

        CTransformation localTransformation =
                                myCube.GetKinematics().GetLocal().GetTransform();

        PolygonMesh mesh = myCube.GetActivePrimitive().GetGeometry();
        CVector3Array normalArray = mesh.GetPolygons().GetNormalArray();
        CVector3 orientation(normalArray[1]);

        CVector3 worldOrientation =
                    MapObjectOrientationToWorldSpace(   localTransformation,
                                                        orientation);

        app.LogMessage(
                L"The second polygon normal corresponds to ( " +
                CValue(RadiansToDegrees(worldOrientation.GetX())).GetAsText() +
                L", " +
                CValue(RadiansToDegrees(worldOrientation.GetY())).GetAsText() +
                L", " +
                CValue(RadiansToDegrees(worldOrientation.GetZ())).GetAsText() +
                L") in the world space" );

CVector3 XSI::MATH::MapObjectPositionToWorldSpace	(	const CTransformation &	in_transfoObjectSpace,
		const CVector3 &	in_vector3Position
	)

Converts a Position described in a given ObjectSpace to WorldSpace.

Parameters:

in_transfoObjectSpace	ObjectSpace in which the position is defined.
in_vector3Position	Position to convert.

Returns:: The world position.

See also:: CTransformation, KinematicState, Kinematics::GetGlobal, Kinematics::GetLocal

Example:

Demonstrates MapObjectPositionToWorldSpace

        using namespace XSI;
        using namespace MATH;
        Application app;
        Model root = app.GetActiveSceneRoot();

        X3DObject myCube;
        root.AddGeometry( L"Cube", L"MeshSurface",L"",myCube );

        KinematicState  globalKinematicState = myCube.GetKinematics().GetGlobal();
        globalKinematicState.PutParameterValue(L"posy", 4.0);
        globalKinematicState.PutParameterValue(L"posx", 2.0);

        CTransformation localTransformation = myCube.GetKinematics().GetLocal().GetTransform();

        CPointRefArray pointArray = myCube.GetActivePrimitive().GetGeometry().GetPoints();
        CVector3 position(Point(pointArray.GetItem(0)).GetPosition());

        app.LogMessage(L"The local position is: X " +
                      CValue(position.GetX()).GetAsText() + CString(L" Y ") +
                      CValue(position.GetY()).GetAsText() + CString(L" Z ") +
                      CValue(position.GetZ()).GetAsText());

        CVector3 worldPosition =
                        MapObjectPositionToWorldSpace(  localTransformation,
                                                        position);

        app.LogMessage(L"The world position is: X " +
                      CValue(worldPosition.GetX()).GetAsText() + CString(L" Y ") +
                      CValue(worldPosition.GetY()).GetAsText() + CString(L" Z ") +
                      CValue(worldPosition.GetZ()).GetAsText());

CTransformation XSI::MATH::MapWorldPoseToObjectSpace	(	const CTransformation &	in_transfoObjectSpace,
		const CTransformation &	in_transfoPose
	)

Converts a Pose described in WorldSpace to a different ObjectSpace

Parameters:

in_transfoObjectSpace	ObjectSpace in which the position is defined.
in_transfoPose	Pose to convert.

Returns:: The converted Pose.

CVector3 XSI::MATH::MapWorldOrientationToObjectSpace	(	const CTransformation &	in_transfoObjectSpace,
		const CVector3 &	in_vector3Orientation
	)

Converts an orientation described in WorldSpace to a different ObjectSpace.

Parameters:

in_transfoObjectSpace	ObjectSpace in which the position is defined.
in_vector3Orientation	Orientation to convert.

Returns:: The converted orientation.

CVector3 XSI::MATH::MapWorldPositionToObjectSpace	(	const CTransformation &	in_transfoObjectSpace,
		const CVector3 &	in_vector3Position
	)

Converts a position described in WorldSpace to a position in a different ObjectSpace.

Parameters:

in_transfoObjectSpace	ObjectSpace in which we want to convert the position.
in_vector3Position	Position to convert.

Returns:: The converted position.

See also:: CTransformation, KinematicState, Kinematics::GetGlobal, Kinematics::GetLocal

Example:

Demonstrates MapWorldPositionToObjectSpace

        using namespace XSI;
        using namespace MATH;
        Application app;
        Model root = app.GetActiveSceneRoot();

        X3DObject myCube;
        root.AddGeometry( L"Cube", L"MeshSurface", L"", myCube );

        KinematicState  globalKinematicState = myCube.GetKinematics().GetGlobal();
        globalKinematicState.PutParameterValue(L"posy", 4.0);
        globalKinematicState.PutParameterValue(L"posx", 2.0);
        globalKinematicState.PutParameterValue(L"rotx", 30.0);

        CTransformation localTransformation =
                                myCube.GetKinematics().GetLocal().GetTransform();
        CVector3 position(1.0,1.0,1.0);
        CVector3 convertedPosition =
                    MapWorldPositionToObjectSpace(  localTransformation,
                                                    position);

        app.LogMessage(L"The position (1,1,1) is (" +
                    CValue(convertedPosition.GetX()).GetAsText() + L", " +
                    CValue(convertedPosition.GetY()).GetAsText() + L", " +
                    CValue(convertedPosition.GetZ()).GetAsText() +
                    L" in the cube object space");

CTransformation XSI::MATH::MapObjectPoseToObjectSpace	(	const CTransformation &	in_transfoObjectSpace,
		const CTransformation &	in_transfoSpace,
		const CTransformation &	in_transfoPose
	)

Converts a pose described in an ObjectSpace to a pose in a different ObjectSpace.

Parameters:

in_transfoObjectSpace	ObjectSpace in which the pose is described.
in_transfoSpace	Space in which we want to convert the pose.
in_transfoPose	Pose to convert.

Returns:: The converted transformation.

See also:: CTransformation, KinematicState, Kinematics::GetGlobal, Kinematics::GetLocal

Example:

Demonstrates MapObjectPoseToObjectSpace

        using namespace XSI;
        using namespace MATH;
        Application app;
        Model root = app.GetActiveSceneRoot();

        X3DObject myCube;
        root.AddGeometry( L"Cube", L"MeshSurface", L"",myCube );

        KinematicState  globalKinematicState = myCube.GetKinematics().GetGlobal();
        globalKinematicState.PutParameterValue(L"posy", 4.0);
        globalKinematicState.PutParameterValue(L"posx", 2.0);

        X3DObject myCube2;
        myCube.AddGeometry( L"Cube", L"MeshSurface", L"", myCube2 );

        globalKinematicState = myCube2.GetKinematics().GetGlobal();
        globalKinematicState.PutParameterValue(L"posz", 3.0);
        globalKinematicState.PutParameterValue(L"rotz", 45.0);

        X3DObject myCone;
        root.AddGeometry( L"Cone", L"MeshSurface", L"",myCone );

        globalKinematicState = myCube2.GetKinematics().GetGlobal();
        globalKinematicState.PutParameterValue(L"posy", -2.0);
        globalKinematicState.PutParameterValue(L"rotz", 90.0);

        CTransformation localTransformation =
                            myCube2.GetKinematics().GetLocal().GetTransform();
        CTransformation parentTransformation =
                            myCube.GetKinematics().GetGlobal().GetTransform();
        CVector3 translation(localTransformation.GetTranslation());
        CTransformation destinationTransformation =
                            myCone.GetKinematics().GetGlobal().GetTransform();

        app.LogMessage(
            L"The translation of the cube relative to its parent: x " +
            CValue(translation.GetX()).GetAsText() + CString(L" Y ") +
            CValue(translation.GetY()).GetAsText() + CString(L" Z ") +
            CValue(translation.GetZ()).GetAsText());

        CTransformation convertedTranformation =
                MapObjectPoseToObjectSpace( parentTransformation,
                                            destinationTransformation,
                                            localTransformation);

        translation = convertedTranformation.GetTranslation();

        app.LogMessage(
            L"The translation of the cube relative to the cone: x " +
            CValue(translation.GetX()).GetAsText() + CString(L" Y ") +
            CValue(translation.GetY()).GetAsText() + CString(L" Z ") +
            CValue(translation.GetZ()).GetAsText());

CVector3 XSI::MATH::MapObjectOrientationToObjectSpace	(	const CTransformation &	in_transfoObjectSpace,
		const CTransformation &	in_transfoSpace,
		const CVector3 &	in_vector3Orientation
	)

Converts an orientation described in an ObjectSpace to an orientation in a different ObjectSpace.

Parameters:

in_transfoObjectSpace	ObjectSpace in which the orientation is described.
in_transfoSpace	Space in which we want to convert the orientation.
in_vector3Orientation	Orientation to convert.

See also:: CTransformation, KinematicState, Kinematics::GetGlobal, Kinematics::GetLocal

Example:

Demonstrates MapObjectOrientationToObjectSpace

        using namespace XSI;
        using namespace MATH;
        Application app;
        Model root = app.GetActiveSceneRoot();

        X3DObject myCube;
        root.AddGeometry( L"Cube", L"MeshSurface", L"",myCube );

        KinematicState  globalKinematicState = myCube.GetKinematics().GetGlobal();
        globalKinematicState.PutParameterValue(L"posy", 4.0);
        globalKinematicState.PutParameterValue(L"posx", 2.0);

        X3DObject myCube2;
        myCube.AddGeometry( L"Cube", L"MeshSurface", L"",myCube2 );

        globalKinematicState = myCube2.GetKinematics().GetGlobal();
        globalKinematicState.PutParameterValue(L"posz", 3.0);
        globalKinematicState.PutParameterValue(L"rotz", 45.0);

        X3DObject myCone;
        root.AddGeometry( L"Cone", L"MeshSurface", L"", myCone );

        globalKinematicState = myCube2.GetKinematics().GetGlobal();
        globalKinematicState.PutParameterValue(L"posy", -2.0);
        globalKinematicState.PutParameterValue(L"rotz", 90.0);

        CTransformation localTransformation =
                                myCube2.GetKinematics().GetLocal().GetTransform();

        PolygonMesh myMesh = myCube.GetActivePrimitive().GetGeometry();
        CVector3Array normalArray = myMesh.GetPolygons().GetNormalArray();

        CVector3 orientation(normalArray[1]);

        CTransformation destinationTransformation =
                                myCone.GetKinematics().GetGlobal().GetTransform();

        CVector3 convertedOrientation =
            MapObjectOrientationToObjectSpace(  localTransformation,
                                                destinationTransformation,
                                                orientation);

        app.LogMessage(L"The second face of the cube normal vector " +
                CString(L"represented in the cone referential( " )+
                CValue(RadiansToDegrees(convertedOrientation.GetX())).GetAsText()
                + L", " +
                CValue(RadiansToDegrees(convertedOrientation.GetY())).GetAsText()
                + L", " +
                CValue(RadiansToDegrees(convertedOrientation.GetZ())).GetAsText() +
                L" ) in the cube object space");

CVector3 XSI::MATH::MapObjectPositionToObjectSpace	(	const CTransformation &	in_transfoObjectSpace,
		const CTransformation &	in_transfoSpace,
		const CVector3 &	in_vector3Position
	)

Converts a position described in an ObjectSpace to a position in a different ObjectSpace.

Parameters:

in_transfoObjectSpace	ObjectSpace in which the position is described.
in_transfoSpace	Space in which we want to convert the position.
in_vector3Position	Position to convert.

Returns:: The converted position.

See also:: CTransformation, KinematicState, GetGlobal, GetLocal

Example:

Demonstrates MapObjectPositionToObjectSpace

        using namespace XSI;
        using namespace MATH;
        //Forward declaration
        bool Above(X3DObject&, X3DObject&);

        Application app;
        Model root = app.GetActiveSceneRoot();

        X3DObject myCube;
        root.AddGeometry( L"Cube", L"MeshSurface", L"", myCube );

        KinematicState globalKinematicState = myCube.GetKinematics().GetGlobal();
        globalKinematicState.PutParameterValue(L"posy", 4.0);
        globalKinematicState.PutParameterValue(L"posx", 2.0);

        X3DObject myGrid;
        oRoot.AddGeometry( L"Grid", L"MeshSurface", L"",myGrid );
        myCube.GetKinematics().GetGlobal().PutParameterValue(L"posy",-2.0);

        if( Above(myCube,myGrid)
            app.LogMessage(L"The cube is above the grid");
        else
            app.LogMessage(L"The cube is below the grid");

        //Function that returns true if in_obj1 is above in_obj2.
        //Which means that all " y" values of in_obj1 vertices relative to
        //in_obj2 are bigger than in_obj2 "y" values
        bool Above(X3DObject& in_obj1, X3DObject& in_obj2)
        {
            double biggestY(0.0);

            CVector3Array positionArray;
            CVector3Array::iterater it;
            Geometry myGeom = in_obj1.GetActivePrimitive().GetGeoemtry()
            myGeom.Points().PositionArray(positionArray);

            //Determine the upper position in obj1;
            for(LONG i = 0; i < positionArray.GetCount(); ++i)
            {
                if(positionArray[i].GetY() > biggestY)
                { biggestY = positionArray[i].GetY();}
            }

            CTransformation globalTransformation1,globalTransformation2;
            globalTransformation1 = in_obj1.GetKinematics().GetGlobal().GetTransform();
            globalTransformation2 = in_obj2.GetKinematics().GetGlobal().GetTransform();

            Geometry myGeom = in_obj2.GetActivePrimitive().GetGeometry();
            myGeom.Points().PositionArray(positionArray);

            CVector3 convertedPosition;
            //Determine if all vertices of in_obj1 are above in_obj2
            i= 0;
            for(; i < positionArray.GetCount(); ++i)
            {
                convertdPosition =
                    MapObjectPositionToObjectSpace( globalTransformation1,
                                                    globalTransformation2,
                                                    positionArray[i]);

                if(convertdPosition.GetY() < biggestY)
                { return false;}
            }

            return true;
        }

Classes

Functions

Detailed Description

Function Documentation