A UnitInertia matrix is a unit-mass inertia matrix; you can convert it to an Inertia by multiplying it by the actual body mass.
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| | UnitInertia_ () |
| | Default is a NaN-ed out mess to avoid accidents, even in Release mode. More...
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| | UnitInertia_ (const RealP &moment) |
| | Create a principal unit inertia matrix with identical diagonal elements. More...
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| | UnitInertia_ (const Vec3P &moments, const Vec3P &products=Vec3P(0)) |
| | Create a unit inertia matrix from a vector of the moments of inertia (the inertia matrix diagonal) and optionally a vector of the products of inertia (the off-diagonals). More...
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| | UnitInertia_ (const RealP &xx, const RealP &yy, const RealP &zz) |
| | Create a principal unit inertia matrix (only non-zero on diagonal). More...
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| | UnitInertia_ (const RealP &xx, const RealP &yy, const RealP &zz, const RealP &xy, const RealP &xz, const RealP &yz) |
| | This is a general unit inertia matrix. More...
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| | UnitInertia_ (const SymMat33P &m) |
| | Construct a UnitInertia from a symmetric 3x3 matrix. More...
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| | UnitInertia_ (const Mat33P &m) |
| | Construct a UnitInertia from a 3x3 symmetric matrix. More...
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| | UnitInertia_ (const Inertia_< P > &I) |
| | Construct a UnitInertia matrix from an Inertia matrix. More...
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| UnitInertia_ & | setUnitInertia (const RealP &xx, const RealP &yy, const RealP &zz) |
| | Set a UnitInertia matrix to have only principal moments (that is, it will be diagonal). More...
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| UnitInertia_ & | setUnitInertia (const Vec3P &moments, const Vec3P &products=Vec3P(0)) |
| | Set principal moments and optionally off-diagonal terms. More...
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| UnitInertia_ & | setUnitInertia (const RealP &xx, const RealP &yy, const RealP &zz, const RealP &xy, const RealP &xz, const RealP &yz) |
| | Set this UnitInertia to a general matrix. More...
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| UnitInertia_ | shiftToCentroid (const Vec3P &CF) const |
| | Assuming that this unit inertia matrix is currently taken about some (implicit) frame F's origin OF, produce a new unit inertia matrix which is the same as this one except measured about the body's centroid CF. More...
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| UnitInertia_ & | shiftToCentroidInPlace (const Vec3P &CF) |
| | Assuming that this unit inertia matrix is currently taken about some (implicit) frame F's origin OF, modify it so that it is instead taken about the body's centroid CF. More...
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| UnitInertia_ | shiftFromCentroid (const Vec3P &p) const |
| | Assuming that the current UnitInertia G is a central inertia (that is, it is inertia about the body centroid CF), create a new object that is the same as this one except shifted to some other point p measured from the centroid. More...
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| UnitInertia_ & | shiftFromCentroidInPlace (const Vec3P &p) |
| | Assuming that the current UnitInertia G is a central inertia (that is, it is inertia about the body centroid CF), shift it in place to some other point p measured from the centroid. More...
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| UnitInertia_ | reexpress (const Rotation_< P > &R_FB) const |
| | Return a new unit inertia matrix like this one but re-expressed in another frame (leaving the origin point unchanged). More...
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| UnitInertia_ | reexpress (const InverseRotation_< P > &R_FB) const |
| | Rexpress using an inverse rotation to avoid having to convert it. More...
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| UnitInertia_ & | reexpressInPlace (const Rotation_< P > &R_FB) |
| | Re-express this unit inertia matrix in another frame, changing the object in place; see reexpress() if you want to leave this object unmolested and get a new one instead. More...
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| UnitInertia_ & | reexpressInPlace (const InverseRotation_< P > &R_FB) |
| | Rexpress using an inverse rotation to avoid having to convert it. More...
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| | operator const SymMat33P & () const |
| | This is an implicit conversion to const SymMat33. More...
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| const Inertia_< P > & | asUnitInertia () const |
| | Recast this UnitInertia matrix as a unit inertia matrix. More...
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| UnitInertia_ & | setFromUnitInertia (const Inertia_< P > &I) |
| | Set from a unit inertia matrix. More...
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| | Inertia_ () |
| | Default is a NaN-ed out mess to avoid accidents, even in Release mode. More...
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| | Inertia_ (const RealP &moment) |
| | Create a principal inertia matrix with identical diagonal elements, like a sphere where moment=2/5 m r^2, or a cube where moment=1/6 m s^2, with m the total mass, r the sphere's radius and s the length of a side of the cube. More...
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| | Inertia_ (const Vec3P &p, const RealP &mass) |
| | Create an Inertia matrix for a point mass at a given location, measured from the origin OF of the implicit frame F, and expressed in F. More...
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| | Inertia_ (const Vec3P &moments, const Vec3P &products=Vec3P(0)) |
| | Create an inertia matrix from a vector of the moments of inertia (the inertia matrix diagonal) and optionally a vector of the products of inertia (the off-diagonals). More...
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| | Inertia_ (const RealP &xx, const RealP &yy, const RealP &zz) |
| | Create a principal inertia matrix (only non-zero on diagonal). More...
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| | Inertia_ (const RealP &xx, const RealP &yy, const RealP &zz, const RealP &xy, const RealP &xz, const RealP &yz) |
| | This is a general inertia matrix. More...
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| | Inertia_ (const SymMat33P &I) |
| | Construct an Inertia from a symmetric 3x3 matrix. More...
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| | Inertia_ (const Mat33P &m) |
| | Construct an Inertia matrix from a 3x3 symmetric matrix. More...
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| Inertia_ & | setInertia (const RealP &xx, const RealP &yy, const RealP &zz) |
| | Set an inertia matrix to have only principal moments (that is, it will be diagonal). More...
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| Inertia_ & | setInertia (const Vec3P &moments, const Vec3P &products=Vec3P(0)) |
| | Set principal moments and optionally off-diagonal terms. More...
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| Inertia_ & | setInertia (const RealP &xx, const RealP &yy, const RealP &zz, const RealP &xy, const RealP &xz, const RealP &yz) |
| | Set this Inertia to a general matrix. More...
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| Inertia_ & | operator+= (const Inertia_ &I) |
| | Add in another inertia matrix. More...
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| Inertia_ & | operator-= (const Inertia_ &I) |
| | Subtract off another inertia matrix. More...
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| Inertia_ & | operator*= (const P &s) |
| | Multiply this inertia matrix by a scalar. Cost is 6 flops. More...
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| Inertia_ & | operator/= (const P &s) |
| | Divide this inertia matrix by a scalar. More...
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| Inertia_ | shiftToMassCenter (const Vec3P &CF, const RealP &mass) const |
| | Assume that the current inertia is about the F frame's origin OF, and expressed in F. More...
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| Inertia_ & | shiftToMassCenterInPlace (const Vec3P &CF, const RealP &mass) |
| | Assume that the current inertia is about the F frame's origin OF, and expressed in F. More...
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| Inertia_ | shiftFromMassCenter (const Vec3P &p, const RealP &mass) const |
| | Assuming that the current inertia I is a central inertia (that is, it is inertia about the body center of mass CF), shift it to some other point p measured from the center of mass. More...
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| Inertia_ & | shiftFromMassCenterInPlace (const Vec3P &p, const RealP &mass) |
| | Assuming that the current inertia I is a central inertia (that is, it is inertia about the body center of mass CF), shift it to some other point p measured from the center of mass. More...
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| Inertia_ | reexpress (const Rotation_< P > &R_FB) const |
| | Return a new inertia matrix like this one but re-expressed in another frame (leaving the origin point unchanged). More...
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| Inertia_ | reexpress (const InverseRotation_< P > &R_FB) const |
| | Rexpress using an inverse rotation to avoid having to convert it. More...
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| Inertia_ & | reexpressInPlace (const Rotation_< P > &R_FB) |
| | Re-express this inertia matrix in another frame, changing the object in place; see reexpress() if you want to leave this object unmolested and get a new one instead. More...
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| Inertia_ & | reexpressInPlace (const InverseRotation_< P > &R_FB) |
| | Rexpress in place using an inverse rotation to avoid having to convert it. More...
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| RealP | trace () const |
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| | operator const SymMat33P & () const |
| | This is an implicit conversion to a const SymMat33. More...
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| const SymMat33P & | asSymMat33 () const |
| | Obtain a reference to the underlying symmetric matrix type. More...
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| Mat33P | toMat33 () const |
| | Expand the internal packed representation into a full 3x3 symmetric matrix with all elements set. More...
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| const Vec3P & | getMoments () const |
| | Obtain the inertia moments (diagonal of the Inertia matrix) as a Vec3 ordered xx, yy, zz. More...
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| const Vec3P & | getProducts () const |
| | Obtain the inertia products (off-diagonals of the Inertia matrix) as a Vec3 with elements ordered xy, xz, yz. More...
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| bool | isNaN () const |
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| bool | isInf () const |
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| bool | isFinite () const |
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| bool | isNumericallyEqual (const Inertia_< P > &other) const |
| | Compare this inertia matrix with another one and return true if they are close to within a default numerical tolerance. More...
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| bool | isNumericallyEqual (const Inertia_< P > &other, double tol) const |
| | Compare this inertia matrix with another one and return true if they are close to within a specified numerical tolerance. More...
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| static bool | isValidUnitInertiaMatrix (const SymMat33P &m) |
| | Test some conditions that must hold for a valid UnitInertia matrix. More...
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These are UnitInertia matrix factories for some common 3D solids.
Each defines its own frame aligned (when possible) with principal moments. Each has unit mass and its center of mass located at the origin (usually). Use this with shiftFromCentroid() to move it somewhere else, and with reexpress() to express the UnitInertia matrix in another frame.
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| static UnitInertia_ | pointMassAtOrigin () |
| | Create a UnitInertia matrix for a point located at the origin – that is, an all-zero matrix. More...
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| static UnitInertia_ | pointMassAt (const Vec3P &p) |
| | Create a UnitInertia matrix for a point of unit mass located at a given location measured from origin OF and expressed in F (where F is the implicit frame of this UnitInertia matrix). More...
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| static UnitInertia_ | sphere (const RealP &r) |
| | Create a UnitInertia matrix for a unit mass sphere of radius r centered at the origin. More...
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| static UnitInertia_ | cylinderAlongZ (const RealP &r, const RealP &hz) |
| | Unit-mass cylinder aligned along z axis; use radius and half-length. More...
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| static UnitInertia_ | cylinderAlongY (const RealP &r, const RealP &hy) |
| | Unit-mass cylinder aligned along y axis; use radius and half-length. More...
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| static UnitInertia_ | cylinderAlongX (const RealP &r, const RealP &hx) |
| | Unit-mass cylinder aligned along x axis; use radius and half-length. More...
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| static UnitInertia_ | brick (const RealP &hx, const RealP &hy, const RealP &hz) |
| | Unit-mass brick given by half-lengths in each direction. More...
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| static UnitInertia_ | brick (const Vec3P &halfLengths) |
| | Alternate interface to brick() that takes a Vec3 for the half lengths. More...
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| static UnitInertia_ | ellipsoid (const RealP &hx, const RealP &hy, const RealP &hz) |
| | Unit-mass ellipsoid given by half-lengths in each direction. More...
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| static UnitInertia_ | ellipsoid (const Vec3P &halfLengths) |
| | Alternate interface to ellipsoid() that takes a Vec3 for the half lengths. More...
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| static bool | isValidInertiaMatrix (const SymMat33P &m) |
| | Test some conditions that must hold for a valid Inertia matrix. More...
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| static Inertia_ | pointMassAtOrigin () |
| | Create an Inertia matrix for a point located at the origin – that is, an all-zero matrix. More...
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| static Inertia_ | pointMassAt (const Vec3P &p, const RealP &m) |
| | Create an Inertia matrix for a point of a given mass, located at a given location measured from the origin of the implicit F frame. More...
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| static Inertia_ | sphere (const RealP &r) |
| | Create a UnitInertia matrix for a unit mass sphere of radius r centered at the origin. More...
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| static Inertia_ | cylinderAlongZ (const RealP &r, const RealP &hz) |
| | Unit-mass cylinder aligned along z axis; use radius and half-length. More...
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| static Inertia_ | cylinderAlongY (const RealP &r, const RealP &hy) |
| | Unit-mass cylinder aligned along y axis; use radius and half-length. More...
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| static Inertia_ | cylinderAlongX (const RealP &r, const RealP &hx) |
| | Unit-mass cylinder aligned along x axis; use radius and half-length. More...
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| static Inertia_ | brick (const RealP &hx, const RealP &hy, const RealP &hz) |
| | Unit-mass brick given by half-lengths in each direction. More...
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| static Inertia_ | brick (const Vec3P &halfLengths) |
| | Alternate interface to brick() that takes a Vec3 for the half lengths. More...
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| static Inertia_ | ellipsoid (const RealP &hx, const RealP &hy, const RealP &hz) |
| | Unit-mass ellipsoid given by half-lengths in each direction. More...
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| static Inertia_ | ellipsoid (const Vec3P &halfLengths) |
| | Alternate interface to ellipsoid() that takes a Vec3 for the half lengths. More...
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| const UnitInertia_< P > & | getAsUnitInertia () const |
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| UnitInertia_< P > & | updAsUnitInertia () |
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| void | errChk (const char *methodName) const |
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| SymMat33P | I_OF_F |
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| template<class P > |
| Inertia_< P > | operator+ (const Inertia_< P > &l, const Inertia_< P > &r) |
| | Add two compatible inertia matrices, meaning they must be taken about the same point and expressed in the same frame. More...
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| template<class P > |
| Inertia_< P > | operator- (const Inertia_< P > &l, const Inertia_< P > &r) |
| | Subtract from one inertia matrix another one which is compatible, meaning that both must be taken about the same point and expressed in the same frame. More...
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| template<class P > |
| Inertia_< P > | operator* (const Inertia_< P > &i, const P &r) |
| | Multiply an inertia matrix by a scalar. More...
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| template<class P > |
| Inertia_< P > | operator* (const P &r, const Inertia_< P > &i) |
| | Multiply an inertia matrix by a scalar. More...
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| template<class P > |
| Inertia_< P > | operator* (const Inertia_< P > &i, int r) |
| | Multiply an inertia matrix by a scalar given as an int. More...
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| template<class P > |
| Inertia_< P > | operator* (int r, const Inertia_< P > &i) |
| | Multiply an inertia matrix by a scalar given as an int. More...
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| template<class P > |
| Inertia_< P > | operator/ (const Inertia_< P > &i, const P &r) |
| | Divide an inertia matrix by a scalar. More...
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| template<class P > |
| Inertia_< P > | operator/ (const Inertia_< P > &i, int r) |
| | Divide an inertia matrix by a scalar provided as an int. More...
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| template<class P > |
| Vec< 3, P > | operator* (const Inertia_< P > &I, const Vec< 3, P > &w) |
| | Multiply an inertia matrix I on the right by a vector w giving the vector result I*w. More...
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| bool | operator== (const Inertia_< P > &i1, const Inertia_< P > &i2) |
| | Compare two inertia matrices for exact (bitwise) equality. More...
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| template<class P > |
| std::ostream & | operator<< (std::ostream &o, const Inertia_< P > &inertia) |
| | Output a human-readable representation of an inertia matrix to the indicated stream. More...
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template<class P>
class SimTK::UnitInertia_< P >
A UnitInertia matrix is a unit-mass inertia matrix; you can convert it to an Inertia by multiplying it by the actual body mass.
Functionality is limited here to those few operations which ensure unit mass; most operations on a UnitInertia matrix result in a general Inertia instead. You can use a UnitInertia object wherever an Inertia is expected but not vice versa.
When constructing a UnitInertia matrix, note that we cannot verify that it actually has unit mass because every legal Inertia matrix can be viewed as the UnitInertia matrix for some differently-scaled object.
Unit inertia matrices are sometimes called "gyration" matrices; we will often represent them with the symbol "G" to avoid confusion with general inertia matrices for which the symbol "I" (or sometimes "J") is used.
Abbreviations
Typedefs exist for the most common invocations of UnitInertia_<P>:
Inheritance diagram for SimTK::UnitInertia_< P >:
1.8.8 
