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OpenVDB
9.0.1
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Namespaces | |
| internal | |
| mat3_internal | |
| pcg | |
Classes | |
| class | AffineMap |
| A general linear transform using homogeneous coordinates to perform rotation, scaling, shear and translation. More... | |
| class | BaseStencil |
| class | BBox |
| Axis-aligned bounding box. More... | |
| struct | BIAS_SCHEME |
| struct | BIAS_SCHEME< FIRST_BIAS > |
| struct | BIAS_SCHEME< HJWENO5_BIAS > |
| struct | BIAS_SCHEME< SECOND_BIAS > |
| struct | BIAS_SCHEME< THIRD_BIAS > |
| struct | BIAS_SCHEME< WENO5_BIAS > |
| class | BoxStencil |
| class | CompoundMap |
| Creates the composition of two maps, each of which could be a composition. In the case that each component of the composition classified as linear an acceleration AffineMap is stored. More... | |
| struct | Conversion |
| Dummy class for tag dispatch of conversion constructors. More... | |
| class | Coord |
| Signed (x, y, z) 32-bit integer coordinates. More... | |
| class | CoordBBox |
| Axis-aligned bounding box of signed integer coordinates. More... | |
| struct | CPT |
| Compute the closest-point transform to a level set. More... | |
| struct | CPT_RANGE |
| Compute the closest-point transform to a level set. More... | |
| struct | Curl |
| Compute the curl of a vector-valued grid using differencing of various orders in the space defined by the range of the map. More... | |
| struct | Curl< UniformScaleMap, CD_2ND > |
| Full template specialization of Curl. More... | |
| struct | Curl< UniformScaleMap, DiffScheme > |
| Partial template specialization of Curl. More... | |
| struct | Curl< UniformScaleTranslateMap, CD_2ND > |
| Full template specialization of Curl. More... | |
| struct | Curl< UniformScaleTranslateMap, DiffScheme > |
| Partial template specialization of Curl. More... | |
| class | CurvatureStencil |
| struct | D1 |
| struct | D1< BD_1ST > |
| struct | D1< BD_2ND > |
| struct | D1< BD_3RD > |
| struct | D1< BD_HJWENO5 > |
| struct | D1< BD_WENO5 > |
| struct | D1< CD_2ND > |
| struct | D1< CD_2NDT > |
| struct | D1< CD_4TH > |
| struct | D1< CD_6TH > |
| struct | D1< FD_1ST > |
| struct | D1< FD_2ND > |
| struct | D1< FD_3RD > |
| struct | D1< FD_HJWENO5 > |
| struct | D1< FD_WENO5 > |
| struct | D1Vec |
| struct | D1Vec< CD_2ND > |
| struct | D1Vec< CD_2NDT > |
| struct | D1Vec< CD_4TH > |
| struct | D1Vec< CD_6TH > |
| struct | D2 |
| struct | D2< CD_FOURTH > |
| struct | D2< CD_SECOND > |
| struct | D2< CD_SIXTH > |
| class | DDA |
| A Digital Differential Analyzer specialized for OpenVDB grids. More... | |
| struct | Delta |
| Delta for small floating-point offsets. More... | |
| struct | Delta< double > |
| struct | Delta< float > |
| class | DenseStencil |
| Dense stencil of a given width. More... | |
| struct | Divergence |
| Compute the divergence of a vector-valued grid using differencing of various orders, the result defined with respect to the range-space of the map. More... | |
| struct | Divergence< ScaleMap, CD_2ND > |
| struct | Divergence< ScaleMap, DiffScheme > |
| struct | Divergence< ScaleTranslateMap, CD_2ND > |
| struct | Divergence< ScaleTranslateMap, DiffScheme > |
| struct | Divergence< TranslationMap, DiffScheme > |
| struct | Divergence< UniformScaleMap, CD_2ND > |
| struct | Divergence< UniformScaleMap, DiffScheme > |
| struct | Divergence< UniformScaleTranslateMap, CD_2ND > |
| struct | Divergence< UniformScaleTranslateMap, DiffScheme > |
| class | Extrema |
| This class computes the minimum and maximum values of a population of floating-point values. More... | |
| class | FourthOrderDenseStencil |
| class | GenericMap |
| A wrapper that holds a MapBase::ConstPtr and exposes a reduced set of functionality needed by the mathematical operators. More... | |
| struct | Gradient |
Center difference gradient operators, defined with respect to the range-space of the map. More... | |
| struct | Gradient< ScaleMap, CD_2ND > |
| struct | Gradient< ScaleTranslateMap, CD_2ND > |
| struct | Gradient< TranslationMap, DiffScheme > |
| struct | Gradient< UniformScaleMap, CD_2ND > |
| struct | Gradient< UniformScaleTranslateMap, CD_2ND > |
| struct | GradientBiased |
| Biased gradient operators, defined with respect to the range-space of the map. More... | |
| struct | GradientNormSqrd |
| struct | GradientNormSqrd< UniformScaleMap, GradScheme > |
| Partial template specialization of GradientNormSqrd. More... | |
| struct | GradientNormSqrd< UniformScaleTranslateMap, GradScheme > |
| Partial template specialization of GradientNormSqrd. More... | |
| class | GradStencil |
| class | Histogram |
| This class computes a histogram, with a fixed interval width, of a population of floating-point values. More... | |
| struct | is_diagonal_jacobian |
| struct | is_double |
| struct | is_double< double > |
| struct | is_linear |
| Map traits. More... | |
| struct | is_linear< AffineMap > |
| struct | is_linear< CompoundMap< T1, T2 > > |
| struct | is_linear< ScaleMap > |
| struct | is_linear< ScaleTranslateMap > |
| struct | is_linear< TranslationMap > |
| struct | is_linear< UniformScaleMap > |
| struct | is_linear< UniformScaleTranslateMap > |
| struct | is_linear< UnitaryMap > |
| struct | is_scale |
| struct | is_scale< ScaleMap > |
| struct | is_scale_translate |
| struct | is_scale_translate< ScaleTranslateMap > |
| struct | is_uniform_diagonal_jacobian |
| struct | is_uniform_scale |
| struct | is_uniform_scale< UniformScaleMap > |
| struct | is_uniform_scale_translate |
| struct | is_uniform_scale_translate< TranslationMap > |
| struct | is_uniform_scale_translate< UniformScaleTranslateMap > |
| struct | is_vec3d |
| struct | is_vec3d< Vec3d > |
| struct | ISCurl |
| Curl operator defined in index space using various first derivative schemes. More... | |
| struct | ISDivergence |
| Divergence operator defined in index space using various first derivative schemes. More... | |
| struct | ISGradient |
| Gradient operators defined in index space of various orders. More... | |
| struct | ISGradientBiased |
Biased Gradient Operators, using upwinding defined by the Vec3Bias input. More... | |
| struct | ISGradientNormSqrd |
| struct | ISLaplacian |
| Laplacian defined in index space, using various center-difference stencils. More... | |
| struct | ISLaplacian< CD_FOURTH > |
| struct | ISLaplacian< CD_SECOND > |
| struct | ISLaplacian< CD_SIXTH > |
| struct | ISMeanCurvature |
| Compute the mean curvature in index space. More... | |
| struct | ISOpMagnitude |
| Adapter for vector-valued index-space operators to return the vector magnitude. More... | |
| struct | Laplacian |
| Compute the Laplacian at a given location in a grid using finite differencing of various orders. The result is defined in the range of the map. More... | |
| struct | Laplacian< ScaleMap, DiffScheme > |
| struct | Laplacian< ScaleTranslateMap, DiffScheme > |
| struct | Laplacian< TranslationMap, DiffScheme > |
| struct | Laplacian< UniformScaleMap, DiffScheme > |
| struct | Laplacian< UniformScaleTranslateMap, DiffScheme > |
| struct | Laplacian< UnitaryMap, DiffScheme > |
| struct | LevelSetHDDA |
| Helper class that implements Hierarchical Digital Differential Analyzers and is specialized for ray intersections with level sets. More... | |
| struct | LevelSetHDDA< TreeT,-1 > |
| Specialization of Hierarchical Digital Differential Analyzer class that intersects a ray against the voxels of a level set. More... | |
| struct | MapAdapter |
| Adapter to associate a map with a world-space operator, giving it the same call signature as an index-space operator. More... | |
| class | MapBase |
| Abstract base class for maps. More... | |
| class | MapRegistry |
| Threadsafe singleton object for accessing the map type-name dictionary. Associates a map type-name with a factory function. More... | |
| class | Mat |
| class | Mat2 |
| class | Mat3 |
| 3x3 matrix class. More... | |
| class | Mat4 |
| 4x4 -matrix class. More... | |
| struct | MeanCurvature |
| Compute the mean curvature. More... | |
| struct | MeanCurvature< TranslationMap, DiffScheme2, DiffScheme1 > |
| struct | MeanCurvature< UniformScaleMap, DiffScheme2, DiffScheme1 > |
| struct | MeanCurvature< UniformScaleTranslateMap, DiffScheme2, DiffScheme1 > |
| class | MinMax |
| Templated class to compute the minimum and maximum values. More... | |
| class | NineteenPointStencil |
| class | NonlinearFrustumMap |
| This map is composed of three steps. First it will take a box of size (Lx X Ly X Lz) defined by a member data bounding box and map it into a frustum with near plane (1 X Ly/Lx) and prescribed depth Then this frustum is transformed by an internal second map: most often a uniform scale, but other effects can be achieved by accumulating translation, shear and rotation: these are all applied to the second map. More... | |
| struct | OpMagnitude |
| Adapter for vector-valued world-space operators to return the vector magnitude. More... | |
| struct | promote |
| class | QuantizedUnitVec |
| Unit vector occupying only 16 bits. More... | |
| class | Quat |
| class | Rand01 |
| Simple generator of random numbers over the range [0, 1) More... | |
| class | RandInt |
| Simple random integer generator. More... | |
| class | Ray |
| class | ScaleMap |
| A specialized Affine transform that scales along the principal axis the scaling need not be uniform in the three-directions. More... | |
| class | ScaleTranslateMap |
| A specialized Affine transform that scales along the principal axis the scaling need not be uniform in the three-directions, and then translates the result. More... | |
| class | SecondOrderDenseStencil |
| class | SevenPointStencil |
| class | SixthOrderDenseStencil |
| class | Stats |
| This class computes statistics (minimum value, maximum value, mean, variance and standard deviation) of a population of floating-point values. More... | |
| class | ThirteenPointStencil |
| struct | Tolerance |
| Tolerance for floating-point comparison. More... | |
| struct | Tolerance< double > |
| struct | Tolerance< float > |
| class | Transform |
| class | TranslationMap |
| A specialized linear transform that performs a translation. More... | |
| class | Tuple |
| class | UniformScaleMap |
| A specialized Affine transform that scales along the principal axis the scaling is uniform in the three-directions. More... | |
| class | UniformScaleTranslateMap |
| A specialized Affine transform that uniformaly scales along the principal axis and then translates the result. More... | |
| class | UnitaryMap |
| A specialized linear transform that performs a unitary maping i.e. rotation and or reflection. More... | |
| class | Vec2 |
| class | Vec3 |
| class | Vec4 |
| class | VolumeHDDA |
| Helper class that implements Hierarchical Digital Differential Analyzers for ray intersections against a generic volume. More... | |
| class | VolumeHDDA< TreeT, RayT, 0 > |
| Specialization of Hierarchical Digital Differential Analyzer class that intersects against the leafs or tiles of a generic volume. More... | |
| class | WenoStencil |
| This is a special 19-point stencil that supports optimal fifth-order WENO upwinding, second-order central differencing, Laplacian, and zero-crossing test. More... | |
Typedefs | |
| using | half = internal::half |
| using | UnitaryAndTranslationMap = CompoundMap< UnitaryMap, TranslationMap > |
| using | SpectralDecomposedMap = CompoundMap< CompoundMap< UnitaryMap, ScaleMap >, UnitaryMap > |
| using | SymmetricMap = SpectralDecomposedMap |
| using | FullyDecomposedMap = CompoundMap< SymmetricMap, UnitaryAndTranslationMap > |
| using | PolarDecomposedMap = CompoundMap< SymmetricMap, UnitaryMap > |
| using | Mat3s = Mat3< float > |
| using | Mat3d = Mat3< double > |
| using | Mat3f = Mat3d |
| using | Mat4s = Mat4< float > |
| using | Mat4d = Mat4< double > |
| using | Mat4f = Mat4d |
| using | Random01 = Rand01< double, std::mt19937 > |
| using | RandomInt = RandInt< int, std::mt19937 > |
| using | Quats = Quat< float > |
| using | Quatd = Quat< double > |
| using | Vec2i = Vec2< int32_t > |
| using | Vec2ui = Vec2< uint32_t > |
| using | Vec2s = Vec2< float > |
| using | Vec2d = Vec2< double > |
| using | Vec3i = Vec3< int32_t > |
| using | Vec3ui = Vec3< uint32_t > |
| using | Vec3s = Vec3< float > |
| using | Vec3d = Vec3< double > |
| using | Vec4i = Vec4< int32_t > |
| using | Vec4ui = Vec4< uint32_t > |
| using | Vec4s = Vec4< float > |
| using | Vec4d = Vec4< double > |
Functions | |
| template<typename Vec3T > | |
| std::ostream & | operator<< (std::ostream &os, const BBox< Vec3T > &b) |
| std::ostream & | operator<< (std::ostream &os, const Coord &xyz) |
| Coord | Abs (const Coord &xyz) |
| std::ostream & | operator<< (std::ostream &os, const CoordBBox &b) |
| template<typename RayT , Index Log2Dim> | |
| std::ostream & | operator<< (std::ostream &os, const DDA< RayT, Log2Dim > &dda) |
| Output streaming of the Ray class. More... | |
| std::string | dsSchemeToString (DScheme dss) |
| DScheme | stringToDScheme (const std::string &s) |
| std::string | dsSchemeToMenuName (DScheme dss) |
| std::string | biasedGradientSchemeToString (BiasedGradientScheme bgs) |
| BiasedGradientScheme | stringToBiasedGradientScheme (const std::string &s) |
| std::string | biasedGradientSchemeToMenuName (BiasedGradientScheme bgs) |
| std::string | temporalIntegrationSchemeToString (TemporalIntegrationScheme tis) |
| TemporalIntegrationScheme | stringToTemporalIntegrationScheme (const std::string &s) |
| std::string | temporalIntegrationSchemeToMenuName (TemporalIntegrationScheme tis) |
| template<typename ValueType > | |
| ValueType | WENO5 (const ValueType &v1, const ValueType &v2, const ValueType &v3, const ValueType &v4, const ValueType &v5, float scale2=0.01f) |
| Implementation of nominally fifth-order finite-difference WENO. More... | |
| template<typename Real > | |
| Real | GodunovsNormSqrd (bool isOutside, Real dP_xm, Real dP_xp, Real dP_ym, Real dP_yp, Real dP_zm, Real dP_zp) |
| template<typename Real > | |
| Real | GodunovsNormSqrd (bool isOutside, const Vec3< Real > &gradient_m, const Vec3< Real > &gradient_p) |
| OPENVDB_API SharedPtr< SymmetricMap > | createSymmetricMap (const Mat3d &m) |
| Utility methods. More... | |
| OPENVDB_API SharedPtr< FullyDecomposedMap > | createFullyDecomposedMap (const Mat4d &m) |
| General decomposition of a Matrix into a Unitary (e.g. rotation) following a Symmetric (e.g. stretch & shear) More... | |
| OPENVDB_API SharedPtr< PolarDecomposedMap > | createPolarDecomposedMap (const Mat3d &m) |
| Decomposes a general linear into translation following polar decomposition. More... | |
| OPENVDB_API SharedPtr< MapBase > | simplify (SharedPtr< AffineMap > affine) |
| reduces an AffineMap to a ScaleMap or a ScaleTranslateMap when it can More... | |
| OPENVDB_API Mat4d | approxInverse (const Mat4d &mat) |
| Returns the left pseudoInverse of the input matrix when the 3x3 part is symmetric otherwise it zeros the 3x3 and reverses the translation. More... | |
| template<class MatType > | |
| MatType | rotation (const Quat< typename MatType::value_type > &q, typename MatType::value_type eps=static_cast< typename MatType::value_type >(1.0e-8)) |
| Return the rotation matrix specified by the given quaternion. More... | |
| template<class MatType > | |
| MatType | rotation (Axis axis, typename MatType::value_type angle) |
| Return a matrix for rotation by angle radians about the given axis. More... | |
| template<class MatType > | |
| MatType | rotation (const Vec3< typename MatType::value_type > &_axis, typename MatType::value_type angle) |
| Return a matrix for rotation by angle radians about the given axis. More... | |
| template<class MatType > | |
| Vec3< typename MatType::value_type > | eulerAngles (const MatType &mat, RotationOrder rotationOrder, typename MatType::value_type eps=static_cast< typename MatType::value_type >(1.0e-8)) |
| Return the Euler angles composing the given rotation matrix. More... | |
| template<typename MatType , typename ValueType1 , typename ValueType2 > | |
| MatType | rotation (const Vec3< ValueType1 > &_v1, const Vec3< ValueType2 > &_v2, typename MatType::value_type eps=static_cast< typename MatType::value_type >(1.0e-8)) |
| Return a rotation matrix that maps v1 onto v2 about the cross product of v1 and v2. More... | |
| template<class MatType > | |
| MatType | scale (const Vec3< typename MatType::value_type > &s) |
| Return a matrix that scales by s. More... | |
| template<class MatType > | |
| Vec3< typename MatType::value_type > | getScale (const MatType &mat) |
| Return a Vec3 representing the lengths of the passed matrix's upper 3×3's rows. More... | |
| template<class MatType > | |
| MatType | unit (const MatType &mat, typename MatType::value_type eps=1.0e-8) |
| Return a copy of the given matrix with its upper 3×3 rows normalized. More... | |
| template<class MatType > | |
| MatType | unit (const MatType &in, typename MatType::value_type eps, Vec3< typename MatType::value_type > &scaling) |
| Return a copy of the given matrix with its upper 3×3 rows normalized, and return the length of each of these rows in scaling. More... | |
| template<class MatType > | |
| MatType | shear (Axis axis0, Axis axis1, typename MatType::value_type shear) |
| Set the matrix to a shear along axis0 by a fraction of axis1. More... | |
| template<class MatType > | |
| MatType | skew (const Vec3< typename MatType::value_type > &skew) |
| Return a matrix as the cross product of the given vector. More... | |
| template<class MatType > | |
| MatType | aim (const Vec3< typename MatType::value_type > &direction, const Vec3< typename MatType::value_type > &vertical) |
| Return an orientation matrix such that z points along direction, and y is along the direction / vertical plane. More... | |
| template<class MatType > | |
| MatType | snapMatBasis (const MatType &source, Axis axis, const Vec3< typename MatType::value_type > &direction) |
| This function snaps a specific axis to a specific direction, preserving scaling. More... | |
| template<class MatType > | |
| MatType & | padMat4 (MatType &dest) |
| Write 0s along Mat4's last row and column, and a 1 on its diagonal. More... | |
| template<typename MatType > | |
| void | sqrtSolve (const MatType &aA, MatType &aB, double aTol=0.01) |
| Solve for A=B*B, given A. More... | |
| template<typename MatType > | |
| void | powSolve (const MatType &aA, MatType &aB, double aPower, double aTol=0.01) |
| template<typename MatType > | |
| bool | isIdentity (const MatType &m) |
| Determine if a matrix is an identity matrix. More... | |
| template<typename MatType > | |
| bool | isInvertible (const MatType &m) |
| Determine if a matrix is invertible. More... | |
| template<typename MatType > | |
| bool | isSymmetric (const MatType &m) |
| Determine if a matrix is symmetric. More... | |
| template<typename MatType > | |
| bool | isUnitary (const MatType &m) |
| Determine if a matrix is unitary (i.e., rotation or reflection). More... | |
| template<typename MatType > | |
| bool | isDiagonal (const MatType &mat) |
| Determine if a matrix is diagonal. More... | |
| template<typename MatType > | |
| MatType::ValueType | lInfinityNorm (const MatType &matrix) |
| Return the L∞ norm of an N×N matrix. More... | |
| template<typename MatType > | |
| MatType::ValueType | lOneNorm (const MatType &matrix) |
| Return the L1 norm of an N×N matrix. More... | |
| template<typename MatType > | |
| bool | polarDecomposition (const MatType &input, MatType &unitary, MatType &positive_hermitian, unsigned int MAX_ITERATIONS=100) |
| Decompose an invertible 3×3 matrix into a unitary matrix followed by a symmetric matrix (positive semi-definite Hermitian), i.e., M = U * S. More... | |
| template<unsigned SIZE, typename T > | |
| bool | cwiseLessThan (const Mat< SIZE, T > &m0, const Mat< SIZE, T > &m1) |
| template<unsigned SIZE, typename T > | |
| bool | cwiseGreaterThan (const Mat< SIZE, T > &m0, const Mat< SIZE, T > &m1) |
| template<typename T0 , typename T1 > | |
| Mat3< typename promote< T0, T1 >::type > | operator* (const Mat3< T0 > &m0, const Mat3< T1 > &m1) |
| Multiply m0 by m1 and return the resulting matrix. More... | |
| template<typename T > | |
| Mat3< T > | outerProduct (const Vec3< T > &v1, const Vec3< T > &v2) |
| template<typename T , typename T0 > | |
| Mat3< T > | powLerp (const Mat3< T0 > &m1, const Mat3< T0 > &m2, T t) |
| template<typename T > | |
| bool | diagonalizeSymmetricMatrix (const Mat3< T > &input, Mat3< T > &Q, Vec3< T > &D, unsigned int MAX_ITERATIONS=250) |
| Use Jacobi iterations to decompose a symmetric 3x3 matrix (diagonalize and compute eigenvectors) More... | |
| template<typename T > | |
| Mat3< T > | Abs (const Mat3< T > &m) |
| template<typename Type1 , typename Type2 > | |
| Mat3< Type1 > | cwiseAdd (const Mat3< Type1 > &m, const Type2 s) |
| template<typename T > | |
| bool | cwiseLessThan (const Mat3< T > &m0, const Mat3< T > &m1) |
| template<typename T > | |
| bool | cwiseGreaterThan (const Mat3< T > &m0, const Mat3< T > &m1) |
| template<typename T0 , typename T1 > | |
| Vec3< T1 > | transformNormal (const Mat4< T0 > &m, const Vec3< T1 > &n) |
| template<typename T > | |
| bool | isAffine (const Mat4< T > &m) |
| template<typename T > | |
| bool | hasTranslation (const Mat4< T > &m) |
| template<typename T > | |
| Mat4< T > | Abs (const Mat4< T > &m) |
| template<typename Type1 , typename Type2 > | |
| Mat4< Type1 > | cwiseAdd (const Mat4< Type1 > &m, const Type2 s) |
| template<typename T > | |
| bool | cwiseLessThan (const Mat4< T > &m0, const Mat4< T > &m1) |
| template<typename T > | |
| bool | cwiseGreaterThan (const Mat4< T > &m0, const Mat4< T > &m1) |
| template<typename Type1 , typename Type2 > | |
| auto | cwiseAdd (const Type1 &v, const Type2 s) |
| Componentwise adder for POD types. More... | |
| template<typename Type1 , typename Type2 > | |
| bool | cwiseLessThan (const Type1 &a, const Type2 &b) |
| Componentwise less than for POD types. More... | |
| template<typename Type1 , typename Type2 > | |
| bool | cwiseGreaterThan (const Type1 &a, const Type2 &b) |
| Componentwise greater than for POD types. More... | |
| template<typename T > | |
| constexpr T | pi () |
| Pi constant taken from Boost to match old behaviour. More... | |
| template<> | |
| constexpr float | pi () |
| template<> | |
| constexpr double | pi () |
| template<> | |
| constexpr long double | pi () |
| template<typename T > | |
| T | negative (const T &val) |
| Return the unary negation of the given value. More... | |
| template<> | |
| bool | negative (const bool &val) |
| Return the negation of the given boolean. More... | |
| template<> | |
| std::string | negative (const std::string &val) |
| Return the "negation" of the given string. More... | |
| template<typename Type > | |
| Type | Clamp (Type x, Type min, Type max) |
| Return x clamped to [min, max]. More... | |
| template<typename Type > | |
| Type | Clamp01 (Type x) |
| Return x clamped to [0, 1]. More... | |
| template<typename Type > | |
| bool | ClampTest01 (Type &x) |
Return true if x is outside [0,1]. More... | |
| template<typename Type > | |
| Type | SmoothUnitStep (Type x) |
| Return 0 if x < 0, 1 if x > 1 or else (3 − 2 x) x². More... | |
| template<typename Type > | |
| Type | SmoothUnitStep (Type x, Type min, Type max) |
| Return 0 if x < min, 1 if x > max or else (3 − 2 t) t², where t = (x − min)/(max − min). More... | |
| template<typename Type > | |
| bool | isZero (const Type &x) |
Return true if x is exactly equal to zero. More... | |
| template<typename Type > | |
| bool | isApproxZero (const Type &x) |
Return true if x is equal to zero to within the default floating-point comparison tolerance. More... | |
| template<typename Type > | |
| bool | isApproxZero (const Type &x, const Type &tolerance) |
Return true if x is equal to zero to within the given tolerance. More... | |
| template<typename Type > | |
| bool | isNegative (const Type &x) |
Return true if x is less than zero. More... | |
| template<> | |
| bool | isNegative< bool > (const bool &) |
| bool | isFinite (const float x) |
Return true if x is finite. More... | |
| template<typename Type , typename std::enable_if< std::is_arithmetic< Type >::value, int >::type = 0> | |
| bool | isFinite (const Type &x) |
Return true if x is finite. More... | |
| bool | isInfinite (const float x) |
Return true if x is an infinity value (either positive infinity or negative infinity). More... | |
| template<typename Type , typename std::enable_if< std::is_arithmetic< Type >::value, int >::type = 0> | |
| bool | isInfinite (const Type &x) |
Return true if x is an infinity value (either positive infinity or negative infinity). More... | |
| bool | isNan (const float x) |
Return true if x is a NaN (Not-A-Number) value. More... | |
| template<typename Type , typename std::enable_if< std::is_arithmetic< Type >::value, int >::type = 0> | |
| bool | isNan (const Type &x) |
Return true if x is a NaN (Not-A-Number) value. More... | |
| template<typename Type > | |
| bool | isApproxEqual (const Type &a, const Type &b, const Type &tolerance) |
Return true if a is equal to b to within the given tolerance. More... | |
| template<typename Type > | |
| bool | isApproxEqual (const Type &a, const Type &b) |
Return true if a is equal to b to within the default floating-point comparison tolerance. More... | |
| template<> | |
| bool | isApproxEqual< bool > (const bool &a, const bool &b) |
| template<> | |
| bool | isApproxEqual< bool > (const bool &a, const bool &b, const bool &) |
| template<> | |
| bool | isApproxEqual< std::string > (const std::string &a, const std::string &b) |
| template<> | |
| bool | isApproxEqual< std::string > (const std::string &a, const std::string &b, const std::string &) |
| template<typename Type > | |
| bool | isApproxLarger (const Type &a, const Type &b, const Type &tolerance) |
Return true if a is larger than b to within the given tolerance, i.e., if b - a < tolerance. More... | |
| template<typename T0 , typename T1 > | |
| bool | isExactlyEqual (const T0 &a, const T1 &b) |
Return true if a is exactly equal to b. More... | |
| template<typename Type > | |
| bool | isRelOrApproxEqual (const Type &a, const Type &b, const Type &absTol, const Type &relTol) |
| template<> | |
| bool | isRelOrApproxEqual (const bool &a, const bool &b, const bool &, const bool &) |
| int32_t | floatToInt32 (const float aFloatValue) |
| int64_t | doubleToInt64 (const double aDoubleValue) |
| bool | isUlpsEqual (const double aLeft, const double aRight, const int64_t aUnitsInLastPlace) |
| bool | isUlpsEqual (const float aLeft, const float aRight, const int32_t aUnitsInLastPlace) |
| template<typename Type > | |
| Type | Pow2 (Type x) |
| Return x2. More... | |
| template<typename Type > | |
| Type | Pow3 (Type x) |
| Return x3. More... | |
| template<typename Type > | |
| Type | Pow4 (Type x) |
| Return x4. More... | |
| template<typename Type > | |
| Type | Pow (Type x, int n) |
| Return xn. More... | |
| template<typename Type > | |
| const Type & | Max (const Type &a, const Type &b) |
| Return the maximum of two values. More... | |
| template<typename Type > | |
| const Type & | Max (const Type &a, const Type &b, const Type &c) |
| Return the maximum of three values. More... | |
| template<typename Type > | |
| const Type & | Max (const Type &a, const Type &b, const Type &c, const Type &d) |
| Return the maximum of four values. More... | |
| template<typename Type > | |
| const Type & | Max (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e) |
| Return the maximum of five values. More... | |
| template<typename Type > | |
| const Type & | Max (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e, const Type &f) |
| Return the maximum of six values. More... | |
| template<typename Type > | |
| const Type & | Max (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e, const Type &f, const Type &g) |
| Return the maximum of seven values. More... | |
| template<typename Type > | |
| const Type & | Max (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e, const Type &f, const Type &g, const Type &h) |
| Return the maximum of eight values. More... | |
| template<typename Type > | |
| const Type & | Min (const Type &a, const Type &b) |
| Return the minimum of two values. More... | |
| template<typename Type > | |
| const Type & | Min (const Type &a, const Type &b, const Type &c) |
| Return the minimum of three values. More... | |
| template<typename Type > | |
| const Type & | Min (const Type &a, const Type &b, const Type &c, const Type &d) |
| Return the minimum of four values. More... | |
| template<typename Type > | |
| const Type & | Min (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e) |
| Return the minimum of five values. More... | |
| template<typename Type > | |
| const Type & | Min (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e, const Type &f) |
| Return the minimum of six values. More... | |
| template<typename Type > | |
| const Type & | Min (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e, const Type &f, const Type &g) |
| Return the minimum of seven values. More... | |
| template<typename Type > | |
| const Type & | Min (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e, const Type &f, const Type &g, const Type &h) |
| Return the minimum of eight values. More... | |
| template<typename Type > | |
| Type | Exp (const Type &x) |
| Return ex. More... | |
| template<typename Type > | |
| int | Sign (const Type &x) |
| Return the sign of the given value as an integer (either -1, 0 or 1). More... | |
| template<typename Type > | |
| bool | SignChange (const Type &a, const Type &b) |
Return true if a and b have different signs. More... | |
| template<typename Type > | |
| bool | ZeroCrossing (const Type &a, const Type &b) |
Return true if the interval [a, b] includes zero, i.e., if either a or b is zero or if they have different signs. More... | |
| template<typename Type > | |
| Type | RoundUp (Type x, Type base) |
| Return x rounded up to the nearest multiple of base. More... | |
| template<typename Type > | |
| Type | RoundDown (Type x, Type base) |
| Return x rounded down to the nearest multiple of base. More... | |
| template<typename Type > | |
| Type | EuclideanRemainder (Type x) |
| template<typename Type > | |
| Type | IntegerPart (Type x) |
| Return the integer part of x. More... | |
| template<typename Type > | |
| Type | FractionalPart (Type x) |
| Return the fractional part of x. More... | |
| template<typename Type > | |
| Type | Chop (Type x, Type delta) |
| Return x if it is greater or equal in magnitude than delta. Otherwise, return zero. More... | |
| template<typename Type > | |
| Type | Truncate (Type x, unsigned int digits) |
| Return x truncated to the given number of decimal digits. More... | |
| template<typename T > | |
| auto | PrintCast (const T &val) -> typename std::enable_if<!std::is_same< T, int8_t >::value &&!std::is_same< T, uint8_t >::value, const T & >::type |
| 8-bit integer values print to std::ostreams as characters. Cast them so that they print as integers instead. More... | |
| int32_t | PrintCast (int8_t val) |
| uint32_t | PrintCast (uint8_t val) |
| template<typename Type > | |
| Type | Inv (Type x) |
| Return the inverse of x. More... | |
| template<typename Vec3T > | |
| size_t | MinIndex (const Vec3T &v) |
| Return the index [0,1,2] of the smallest value in a 3D vector. More... | |
| template<typename Vec3T > | |
| size_t | MaxIndex (const Vec3T &v) |
| Return the index [0,1,2] of the largest value in a 3D vector. More... | |
| OPENVDB_API Vec3d | closestPointOnTriangleToPoint (const Vec3d &a, const Vec3d &b, const Vec3d &c, const Vec3d &p, Vec3d &uvw) |
Closest Point on Triangle to Point. Given a triangle abc and a point p, return the point on abc closest to p and the corresponding barycentric coordinates. More... | |
| OPENVDB_API Vec3d | closestPointOnSegmentToPoint (const Vec3d &a, const Vec3d &b, const Vec3d &p, double &t) |
Closest Point on Line Segment to Point. Given segment ab and point p, return the point on ab closest to p and t the parametric distance to b. More... | |
| template<typename T > | |
| Quat< T > | slerp (const Quat< T > &q1, const Quat< T > &q2, T t, T tolerance=0.00001) |
| Linear interpolation between the two quaternions. More... | |
| template<typename S , typename T > | |
| Quat< T > | operator* (S scalar, const Quat< T > &q) |
| Multiply each element of the given quaternion by scalar and return the result. More... | |
| template<typename T , typename T0 > | |
| Mat3< T > | slerp (const Mat3< T0 > &m1, const Mat3< T0 > &m2, T t) |
| Interpolate between m1 and m2. Converts to quaternion form and uses slerp m1 and m2 must be rotation matrices! More... | |
| template<typename T , typename T0 > | |
| Mat3< T > | bezLerp (const Mat3< T0 > &m1, const Mat3< T0 > &m2, const Mat3< T0 > &m3, const Mat3< T0 > &m4, T t) |
| template<typename RealT > | |
| std::ostream & | operator<< (std::ostream &os, const Ray< RealT > &r) |
| Output streaming of the Ray class. More... | |
| OPENVDB_API void | calculateBounds (const Transform &t, const Vec3d &minWS, const Vec3d &maxWS, Vec3d &minIS, Vec3d &maxIS) |
| Calculate an axis-aligned bounding box in index space from an axis-aligned bounding box in world space. More... | |
| OPENVDB_API std::ostream & | operator<< (std::ostream &, const Transform &) |
| template<typename ResolvedMapType , typename OpType > | |
| void | doProcessTypedMap (Transform &transform, OpType &op) |
| Helper function used internally by processTypedMap() More... | |
| template<typename ResolvedMapType , typename OpType > | |
| void | doProcessTypedMap (const Transform &transform, OpType &op) |
| Helper function used internally by processTypedMap() More... | |
| template<typename TransformType , typename OpType > | |
| bool | processTypedMap (TransformType &transform, OpType &op) |
| Utility function that, given a generic map pointer, calls a functor on the fully-resoved map. More... | |
| template<int SIZE, typename T0 , typename T1 > | |
| bool | operator< (const Tuple< SIZE, T0 > &t0, const Tuple< SIZE, T1 > &t1) |
| template<int SIZE, typename T0 , typename T1 > | |
| bool | operator> (const Tuple< SIZE, T0 > &t0, const Tuple< SIZE, T1 > &t1) |
| template<int SIZE, typename T > | |
| Tuple< SIZE, T > | Abs (const Tuple< SIZE, T > &t) |
| template<int SIZE, typename T > | |
| bool | isNan (const Tuple< SIZE, T > &t) |
Return true if a Nan is present in the tuple. More... | |
| template<int SIZE, typename T > | |
| bool | isInfinite (const Tuple< SIZE, T > &t) |
Return true if an Inf is present in the tuple. More... | |
| template<int SIZE, typename T > | |
| bool | isFinite (const Tuple< SIZE, T > &t) |
Return true if no Nan or Inf values are present. More... | |
| template<int SIZE, typename T > | |
| bool | isZero (const Tuple< SIZE, T > &t) |
Return true if all elements are exactly equal to zero. More... | |
| template<int SIZE, typename T > | |
| std::ostream & | operator<< (std::ostream &ostr, const Tuple< SIZE, T > &classname) |
| Write a Tuple to an output stream. More... | |
| template<typename S , typename T > | |
| Vec2< typename promote< S, T >::type > | operator* (S scalar, const Vec2< T > &v) |
| Multiply each element of the given vector by scalar and return the result. More... | |
| template<typename S , typename T > | |
| Vec2< typename promote< S, T >::type > | operator* (const Vec2< T > &v, S scalar) |
| Multiply each element of the given vector by scalar and return the result. More... | |
| template<typename T0 , typename T1 > | |
| Vec2< typename promote< T0, T1 >::type > | operator* (const Vec2< T0 > &v0, const Vec2< T1 > &v1) |
| Multiply corresponding elements of v0 and v1 and return the result. More... | |
| template<typename S , typename T > | |
| Vec2< typename promote< S, T >::type > | operator/ (S scalar, const Vec2< T > &v) |
| Divide scalar by each element of the given vector and return the result. More... | |
| template<typename S , typename T > | |
| Vec2< typename promote< S, T >::type > | operator/ (const Vec2< T > &v, S scalar) |
| Divide each element of the given vector by scalar and return the result. More... | |
| template<typename T0 , typename T1 > | |
| Vec2< typename promote< T0, T1 >::type > | operator/ (const Vec2< T0 > &v0, const Vec2< T1 > &v1) |
| Divide corresponding elements of v0 and v1 and return the result. More... | |
| template<typename T0 , typename T1 > | |
| Vec2< typename promote< T0, T1 >::type > | operator+ (const Vec2< T0 > &v0, const Vec2< T1 > &v1) |
| Add corresponding elements of v0 and v1 and return the result. More... | |
| template<typename S , typename T > | |
| Vec2< typename promote< S, T >::type > | operator+ (const Vec2< T > &v, S scalar) |
| Add scalar to each element of the given vector and return the result. More... | |
| template<typename T0 , typename T1 > | |
| Vec2< typename promote< T0, T1 >::type > | operator- (const Vec2< T0 > &v0, const Vec2< T1 > &v1) |
| Subtract corresponding elements of v0 and v1 and return the result. More... | |
| template<typename S , typename T > | |
| Vec2< typename promote< S, T >::type > | operator- (const Vec2< T > &v, S scalar) |
| Subtract scalar from each element of the given vector and return the result. More... | |
| template<typename T > | |
| T | angle (const Vec2< T > &v1, const Vec2< T > &v2) |
| template<typename T > | |
| bool | isApproxEqual (const Vec2< T > &a, const Vec2< T > &b) |
| template<typename T > | |
| bool | isApproxEqual (const Vec2< T > &a, const Vec2< T > &b, const Vec2< T > &eps) |
| template<typename T > | |
| Vec2< T > | Abs (const Vec2< T > &v) |
| template<typename T > | |
| void | orthonormalize (Vec2< T > &v1, Vec2< T > &v2) |
| template<typename T > | |
| Vec2< T > | minComponent (const Vec2< T > &v1, const Vec2< T > &v2) |
| Return component-wise minimum of the two vectors. More... | |
| template<typename T > | |
| Vec2< T > | maxComponent (const Vec2< T > &v1, const Vec2< T > &v2) |
| Return component-wise maximum of the two vectors. More... | |
| template<typename T > | |
| Vec2< T > | Exp (Vec2< T > v) |
| Return a vector with the exponent applied to each of the components of the input vector. More... | |
| template<typename T > | |
| Vec2< T > | Log (Vec2< T > v) |
| Return a vector with log applied to each of the components of the input vector. More... | |
| template<typename T0 , typename T1 > | |
| bool | operator== (const Vec3< T0 > &v0, const Vec3< T1 > &v1) |
| Equality operator, does exact floating point comparisons. More... | |
| template<typename T0 , typename T1 > | |
| bool | operator!= (const Vec3< T0 > &v0, const Vec3< T1 > &v1) |
| Inequality operator, does exact floating point comparisons. More... | |
| template<typename S , typename T > | |
| Vec3< typename promote< S, T >::type > | operator* (S scalar, const Vec3< T > &v) |
| Multiply each element of the given vector by scalar and return the result. More... | |
| template<typename S , typename T > | |
| Vec3< typename promote< S, T >::type > | operator* (const Vec3< T > &v, S scalar) |
| Multiply each element of the given vector by scalar and return the result. More... | |
| template<typename T0 , typename T1 > | |
| Vec3< typename promote< T0, T1 >::type > | operator* (const Vec3< T0 > &v0, const Vec3< T1 > &v1) |
| Multiply corresponding elements of v0 and v1 and return the result. More... | |
| template<typename S , typename T > | |
| Vec3< typename promote< S, T >::type > | operator/ (S scalar, const Vec3< T > &v) |
| Divide scalar by each element of the given vector and return the result. More... | |
| template<typename S , typename T > | |
| Vec3< typename promote< S, T >::type > | operator/ (const Vec3< T > &v, S scalar) |
| Divide each element of the given vector by scalar and return the result. More... | |
| template<typename T0 , typename T1 > | |
| Vec3< typename promote< T0, T1 >::type > | operator/ (const Vec3< T0 > &v0, const Vec3< T1 > &v1) |
| Divide corresponding elements of v0 and v1 and return the result. More... | |
| template<typename T0 , typename T1 > | |
| Vec3< typename promote< T0, T1 >::type > | operator+ (const Vec3< T0 > &v0, const Vec3< T1 > &v1) |
| Add corresponding elements of v0 and v1 and return the result. More... | |
| template<typename S , typename T > | |
| Vec3< typename promote< S, T >::type > | operator+ (const Vec3< T > &v, S scalar) |
| Add scalar to each element of the given vector and return the result. More... | |
| template<typename T0 , typename T1 > | |
| Vec3< typename promote< T0, T1 >::type > | operator- (const Vec3< T0 > &v0, const Vec3< T1 > &v1) |
| Subtract corresponding elements of v0 and v1 and return the result. More... | |
| template<typename S , typename T > | |
| Vec3< typename promote< S, T >::type > | operator- (const Vec3< T > &v, S scalar) |
| Subtract scalar from each element of the given vector and return the result. More... | |
| template<typename T > | |
| T | angle (const Vec3< T > &v1, const Vec3< T > &v2) |
| template<typename T > | |
| bool | isApproxEqual (const Vec3< T > &a, const Vec3< T > &b) |
| template<typename T > | |
| bool | isApproxEqual (const Vec3< T > &a, const Vec3< T > &b, const Vec3< T > &eps) |
| template<typename T > | |
| Vec3< T > | Abs (const Vec3< T > &v) |
| template<typename T > | |
| void | orthonormalize (Vec3< T > &v1, Vec3< T > &v2, Vec3< T > &v3) |
| template<typename T > | |
| Vec3< T > | minComponent (const Vec3< T > &v1, const Vec3< T > &v2) |
| Return component-wise minimum of the two vectors. More... | |
| template<typename T > | |
| Vec3< T > | maxComponent (const Vec3< T > &v1, const Vec3< T > &v2) |
| Return component-wise maximum of the two vectors. More... | |
| template<typename T > | |
| Vec3< T > | Exp (Vec3< T > v) |
| Return a vector with the exponent applied to each of the components of the input vector. More... | |
| template<typename T > | |
| Vec3< T > | Log (Vec3< T > v) |
| Return a vector with log applied to each of the components of the input vector. More... | |
| template<typename T0 , typename T1 > | |
| bool | operator== (const Vec4< T0 > &v0, const Vec4< T1 > &v1) |
| Equality operator, does exact floating point comparisons. More... | |
| template<typename T0 , typename T1 > | |
| bool | operator!= (const Vec4< T0 > &v0, const Vec4< T1 > &v1) |
| Inequality operator, does exact floating point comparisons. More... | |
| template<typename S , typename T > | |
| Vec4< typename promote< S, T >::type > | operator* (S scalar, const Vec4< T > &v) |
| Multiply each element of the given vector by scalar and return the result. More... | |
| template<typename S , typename T > | |
| Vec4< typename promote< S, T >::type > | operator* (const Vec4< T > &v, S scalar) |
| Multiply each element of the given vector by scalar and return the result. More... | |
| template<typename T0 , typename T1 > | |
| Vec4< typename promote< T0, T1 >::type > | operator* (const Vec4< T0 > &v0, const Vec4< T1 > &v1) |
| Multiply corresponding elements of v0 and v1 and return the result. More... | |
| template<typename S , typename T > | |
| Vec4< typename promote< S, T >::type > | operator/ (S scalar, const Vec4< T > &v) |
| Divide scalar by each element of the given vector and return the result. More... | |
| template<typename S , typename T > | |
| Vec4< typename promote< S, T >::type > | operator/ (const Vec4< T > &v, S scalar) |
| Divide each element of the given vector by scalar and return the result. More... | |
| template<typename T0 , typename T1 > | |
| Vec4< typename promote< T0, T1 >::type > | operator/ (const Vec4< T0 > &v0, const Vec4< T1 > &v1) |
| Divide corresponding elements of v0 and v1 and return the result. More... | |
| template<typename T0 , typename T1 > | |
| Vec4< typename promote< T0, T1 >::type > | operator+ (const Vec4< T0 > &v0, const Vec4< T1 > &v1) |
| Add corresponding elements of v0 and v1 and return the result. More... | |
| template<typename S , typename T > | |
| Vec4< typename promote< S, T >::type > | operator+ (const Vec4< T > &v, S scalar) |
| Add scalar to each element of the given vector and return the result. More... | |
| template<typename T0 , typename T1 > | |
| Vec4< typename promote< T0, T1 >::type > | operator- (const Vec4< T0 > &v0, const Vec4< T1 > &v1) |
| Subtract corresponding elements of v0 and v1 and return the result. More... | |
| template<typename S , typename T > | |
| Vec4< typename promote< S, T >::type > | operator- (const Vec4< T > &v, S scalar) |
| Subtract scalar from each element of the given vector and return the result. More... | |
| template<typename T > | |
| bool | isApproxEqual (const Vec4< T > &a, const Vec4< T > &b) |
| template<typename T > | |
| bool | isApproxEqual (const Vec4< T > &a, const Vec4< T > &b, const Vec4< T > &eps) |
| template<typename T > | |
| Vec4< T > | Abs (const Vec4< T > &v) |
| template<typename T > | |
| Vec4< T > | minComponent (const Vec4< T > &v1, const Vec4< T > &v2) |
| Return component-wise minimum of the two vectors. More... | |
| template<typename T > | |
| Vec4< T > | maxComponent (const Vec4< T > &v1, const Vec4< T > &v2) |
| Return component-wise maximum of the two vectors. More... | |
| template<typename T > | |
| Vec4< T > | Exp (Vec4< T > v) |
| Return a vector with the exponent applied to each of the components of the input vector. More... | |
| template<typename T > | |
| Vec4< T > | Log (Vec4< T > v) |
| Return a vector with log applied to each of the components of the input vector. More... | |
| template<typename T > | |
| Vec3< typename promote< T, typename Coord::ValueType >::type > | operator+ (const Vec3< T > &v0, const Coord &v1) |
| Allow a Coord to be added to or subtracted from a Vec3. More... | |
| template<typename T > | |
| Vec3< typename promote< T, typename Coord::ValueType >::type > | operator+ (const Coord &v1, const Vec3< T > &v0) |
| Allow a Coord to be added to or subtracted from a Vec3. More... | |
| template<typename T > | |
| Vec3< typename promote< T, Coord::ValueType >::type > | operator- (const Vec3< T > &v0, const Coord &v1) |
| Allow a Coord to be subtracted from a Vec3. More... | |
| template<typename T > | |
| Vec3< typename promote< T, Coord::ValueType >::type > | operator- (const Coord &v1, const Vec3< T > &v0) |
| Allow a Coord to be subtracted from a Vec3. More... | |
| std::string | operator+ (const std::string &s, bool) |
Needed to support the (zeroVal<ValueType>() + val) idiom when ValueType is std::string. More... | |
| std::string | operator+ (const std::string &s, int) |
Needed to support the (zeroVal<ValueType>() + val) idiom when ValueType is std::string. More... | |
| std::string | operator+ (const std::string &s, float) |
Needed to support the (zeroVal<ValueType>() + val) idiom when ValueType is std::string. More... | |
| std::string | operator+ (const std::string &s, double) |
Needed to support the (zeroVal<ValueType>() + val) idiom when ValueType is std::string. More... | |
| int32_t | Abs (int32_t i) |
| Return the absolute value of the given quantity. More... | |
| int64_t | Abs (int64_t i) |
| Return the absolute value of the given quantity. More... | |
| float | Abs (float x) |
| Return the absolute value of the given quantity. More... | |
| double | Abs (double x) |
| Return the absolute value of the given quantity. More... | |
| long double | Abs (long double x) |
| Return the absolute value of the given quantity. More... | |
| uint32_t | Abs (uint32_t i) |
| Return the absolute value of the given quantity. More... | |
| uint64_t | Abs (uint64_t i) |
| Return the absolute value of the given quantity. More... | |
| bool | Abs (bool b) |
| Return the absolute value of the given quantity. More... | |
| template<typename T > | |
| std::enable_if< std::is_same< T, size_t >::value, T >::type | Abs (T i) |
| Return the absolute value of the given quantity. More... | |
| float | Pow (float b, float e) |
| Return be. More... | |
| double | Pow (double b, double e) |
| Return be. More... | |
| float | Sin (const float &x) |
| Return sin x. More... | |
| double | Sin (const double &x) |
| Return sin x. More... | |
| float | Cos (const float &x) |
| Return cos x. More... | |
| double | Cos (const double &x) |
| Return cos x. More... | |
| float | Sqrt (float x) |
| Return the square root of a floating-point value. More... | |
| double | Sqrt (double x) |
| Return the square root of a floating-point value. More... | |
| long double | Sqrt (long double x) |
| Return the square root of a floating-point value. More... | |
| float | Cbrt (float x) |
| Return the cube root of a floating-point value. More... | |
| double | Cbrt (double x) |
| Return the cube root of a floating-point value. More... | |
| long double | Cbrt (long double x) |
| Return the cube root of a floating-point value. More... | |
| int | Mod (int x, int y) |
| Return the remainder of x / y. More... | |
| float | Mod (float x, float y) |
| Return the remainder of x / y. More... | |
| double | Mod (double x, double y) |
| Return the remainder of x / y. More... | |
| long double | Mod (long double x, long double y) |
| Return the remainder of x / y. More... | |
| template<typename Type > | |
| Type | Remainder (Type x, Type y) |
| Return the remainder of x / y. More... | |
| float | RoundUp (float x) |
| Return x rounded up to the nearest integer. More... | |
| double | RoundUp (double x) |
| Return x rounded up to the nearest integer. More... | |
| long double | RoundUp (long double x) |
| Return x rounded up to the nearest integer. More... | |
| float | RoundDown (float x) |
| Return x rounded down to the nearest integer. More... | |
| double | RoundDown (double x) |
| Return x rounded down to the nearest integer. More... | |
| long double | RoundDown (long double x) |
| Return x rounded down to the nearest integer. More... | |
| float | Round (float x) |
| Return x rounded to the nearest integer. More... | |
| double | Round (double x) |
| Return x rounded to the nearest integer. More... | |
| long double | Round (long double x) |
| Return x rounded to the nearest integer. More... | |
| int | Floor (float x) |
| Return the floor of x. More... | |
| int | Floor (double x) |
| Return the floor of x. More... | |
| int | Floor (long double x) |
| Return the floor of x. More... | |
| int | Ceil (float x) |
| Return the ceiling of x. More... | |
| int | Ceil (double x) |
| Return the ceiling of x. More... | |
| int | Ceil (long double x) |
| Return the ceiling of x. More... | |
| using half = internal::half |
| using PolarDecomposedMap = CompoundMap<SymmetricMap, UnitaryMap> |
| using SymmetricMap = SpectralDecomposedMap |
| enum Axis |
| enum BiasedGradientScheme |
| enum DDScheme |
| enum DScheme |
| enum RotationOrder |
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Return the absolute value of the given quantity.
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Return the absolute value of the given quantity.
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Return the absolute value of the given quantity.
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Return the absolute value of the given quantity.
|
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Return the absolute value of the given quantity.
|
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Return the absolute value of the given quantity.
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Return the absolute value of the given quantity.
|
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Return the absolute value of the given quantity.
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Return the absolute value of the given quantity.
| MatType openvdb::v9_0::math::aim | ( | const Vec3< typename MatType::value_type > & | direction, |
| const Vec3< typename MatType::value_type > & | vertical | ||
| ) |
Return an orientation matrix such that z points along direction, and y is along the direction / vertical plane.
Angle between two vectors, the result is between [0, pi], e.g. float a = Vec2f::angle(v1,v2);
Angle between two vectors, the result is between [0, pi], e.g. double a = Vec3d::angle(v1,v2);
| OPENVDB_API Mat4d openvdb::v9_0::math::approxInverse | ( | const Mat4d & | mat | ) |
Returns the left pseudoInverse of the input matrix when the 3x3 part is symmetric otherwise it zeros the 3x3 and reverses the translation.
| Mat3<T> openvdb::v9_0::math::bezLerp | ( | const Mat3< T0 > & | m1, |
| const Mat3< T0 > & | m2, | ||
| const Mat3< T0 > & | m3, | ||
| const Mat3< T0 > & | m4, | ||
| T | t | ||
| ) |
Interpolate between m1 and m4 by converting m1 ... m4 into quaternions and treating them as control points of a Bezier curve using slerp in place of lerp in the De Castlejeau evaluation algorithm. Just like a cubic Bezier curve, this will interpolate m1 at t = 0 and m4 at t = 1 but in general will not pass through m2 and m3. Unlike a standard Bezier curve this curve will not have the convex hull property. m1 ... m4 must be rotation matrices!
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| OPENVDB_API void openvdb::v9_0::math::calculateBounds | ( | const Transform & | t, |
| const Vec3d & | minWS, | ||
| const Vec3d & | maxWS, | ||
| Vec3d & | minIS, | ||
| Vec3d & | maxIS | ||
| ) |
Calculate an axis-aligned bounding box in index space from an axis-aligned bounding box in world space.
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Return the cube root of a floating-point value.
|
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Return the cube root of a floating-point value.
|
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Return the cube root of a floating-point value.
|
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Return the ceiling of x.
|
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Return the ceiling of x.
|
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Return the ceiling of x.
|
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Return x if it is greater or equal in magnitude than delta. Otherwise, return zero.
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Return x clamped to [min, max].
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Return x clamped to [0, 1].
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Return true if x is outside [0,1].
| OPENVDB_API Vec3d openvdb::v9_0::math::closestPointOnSegmentToPoint | ( | const Vec3d & | a, |
| const Vec3d & | b, | ||
| const Vec3d & | p, | ||
| double & | t | ||
| ) |
Closest Point on Line Segment to Point. Given segment ab and point p, return the point on ab closest to p and t the parametric distance to b.
| a | The segment's first vertex point. |
| b | The segment's second vertex point. |
| p | Point to compute the closest point on ab for. |
| t | Parametric distance to b. |
| OPENVDB_API Vec3d openvdb::v9_0::math::closestPointOnTriangleToPoint | ( | const Vec3d & | a, |
| const Vec3d & | b, | ||
| const Vec3d & | c, | ||
| const Vec3d & | p, | ||
| Vec3d & | uvw | ||
| ) |
Closest Point on Triangle to Point. Given a triangle abc and a point p, return the point on abc closest to p and the corresponding barycentric coordinates.
Algorithms from "Real-Time Collision Detection" pg 136 to 142 by Christer Ericson. The closest point is obtained by first determining which of the triangles' Voronoi feature regions p is in and then computing the orthogonal projection of p onto the corresponding feature.
| a | The triangle's first vertex point. |
| b | The triangle's second vertex point. |
| c | The triangle's third vertex point. |
| p | Point to compute the closest point on abc for. |
| uvw | Barycentric coordinates, computed and returned. |
|
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Return cos x.
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Return cos x.
| OPENVDB_API SharedPtr<FullyDecomposedMap> openvdb::v9_0::math::createFullyDecomposedMap | ( | const Mat4d & | m | ) |
General decomposition of a Matrix into a Unitary (e.g. rotation) following a Symmetric (e.g. stretch & shear)
| OPENVDB_API SharedPtr<PolarDecomposedMap> openvdb::v9_0::math::createPolarDecomposedMap | ( | const Mat3d & | m | ) |
Decomposes a general linear into translation following polar decomposition.
T U S where:
T: Translation U: Unitary (rotation or reflection) S: Symmetric
| OPENVDB_API SharedPtr<SymmetricMap> openvdb::v9_0::math::createSymmetricMap | ( | const Mat3d & | m | ) |
Utility methods.
Create a SymmetricMap from a symmetric matrix. Decomposes the map into Rotation Diagonal Rotation^T
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Componentwise adder for POD types.
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Componentwise greater than for POD types.
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Componentwise less than for POD types.
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Use Jacobi iterations to decompose a symmetric 3x3 matrix (diagonalize and compute eigenvectors)
This is based on the "Efficient numerical diagonalization of Hermitian 3x3 matrices" Joachim Kopp. arXiv.org preprint: physics/0610206 with the addition of largest pivot
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Helper function used internally by processTypedMap()
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Helper function used internally by processTypedMap()
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Return the euclidean remainder of x. Note unlike % operator this will always return a positive result
| Vec3<typename MatType::value_type> openvdb::v9_0::math::eulerAngles | ( | const MatType & | mat, |
| RotationOrder | rotationOrder, | ||
| typename MatType::value_type | eps = static_cast<typename MatType::value_type>(1.0e-8) |
||
| ) |
Return the Euler angles composing the given rotation matrix.
Optional axes arguments describe in what order elementary rotations are applied. Note that in our convention, XYZ means Rz * Ry * Rx. Because we are using rows rather than columns to represent the local axes of a coordinate frame, the interpretation from a local reference point of view is to first rotate about the x axis, then about the newly rotated y axis, and finally by the new local z axis. From a fixed reference point of view, the interpretation is to rotate about the stationary world z, y, and x axes respectively.
Irrespective of the Euler angle convention, in the case of distinct axes, eulerAngles() returns the x, y, and z angles in the corresponding x, y, z components of the returned Vec3. For the XZX convention, the left X value is returned in Vec3.x, and the right X value in Vec3.y. For the ZXZ convention the left Z value is returned in Vec3.z and the right Z value in Vec3.y
Examples of reconstructing r from its Euler angle decomposition
v = eulerAngles(r, ZYX_ROTATION); rx.setToRotation(Vec3d(1,0,0), v[0]); ry.setToRotation(Vec3d(0,1,0), v[1]); rz.setToRotation(Vec3d(0,0,1), v[2]); r = rx * ry * rz;
v = eulerAngles(r, ZXZ_ROTATION); rz1.setToRotation(Vec3d(0,0,1), v[2]); rx.setToRotation (Vec3d(1,0,0), v[0]); rz2.setToRotation(Vec3d(0,0,1), v[1]); r = rz2 * rx * rz1;
v = eulerAngles(r, XZX_ROTATION); rx1.setToRotation (Vec3d(1,0,0), v[0]); rx2.setToRotation (Vec3d(1,0,0), v[1]); rz.setToRotation (Vec3d(0,0,1), v[2]); r = rx2 * rz * rx1;
Return a vector with the exponent applied to each of the components of the input vector.
Return a vector with the exponent applied to each of the components of the input vector.
Return a vector with the exponent applied to each of the components of the input vector.
|
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Return ex.
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|
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Return the floor of x.
|
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Return the floor of x.
|
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Return the floor of x.
|
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Return the fractional part of x.
| Vec3<typename MatType::value_type> openvdb::v9_0::math::getScale | ( | const MatType & | mat | ) |
Return a Vec3 representing the lengths of the passed matrix's upper 3×3's rows.
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|
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Return the integer part of x.
|
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Return the inverse of x.
|
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|
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Return true if a is equal to b to within the given tolerance.
|
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Return true if a is equal to b to within the default floating-point comparison tolerance.
|
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|
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|
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|
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|
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|
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|
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|
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Return true if a is larger than b to within the given tolerance, i.e., if b - a < tolerance.
|
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Return true if x is equal to zero to within the default floating-point comparison tolerance.
|
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Return true if x is equal to zero to within the given tolerance.
|
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Determine if a matrix is diagonal.
|
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Return true if a is exactly equal to b.
|
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Return true if no Nan or Inf values are present.
|
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Return true if x is finite.
|
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Return true if x is finite.
|
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Determine if a matrix is an identity matrix.
|
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Return true if an Inf is present in the tuple.
|
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Return true if x is an infinity value (either positive infinity or negative infinity).
|
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Return true if x is an infinity value (either positive infinity or negative infinity).
|
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Determine if a matrix is invertible.
|
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Return true if a Nan is present in the tuple.
|
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Return true if x is a NaN (Not-A-Number) value.
|
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Return true if x is a NaN (Not-A-Number) value.
|
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Return true if x is less than zero.
|
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|
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|
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|
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Determine if a matrix is symmetric.
This implicitly uses math::isApproxEqual() to determine equality.
|
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|
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|
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Determine if a matrix is unitary (i.e., rotation or reflection).
|
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Return true if all elements are exactly equal to zero.
|
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Return true if x is exactly equal to zero.
| MatType::ValueType openvdb::v9_0::math::lInfinityNorm | ( | const MatType & | matrix | ) |
Return the L∞ norm of an N×N matrix.
Return a vector with log applied to each of the components of the input vector.
Return a vector with log applied to each of the components of the input vector.
Return a vector with log applied to each of the components of the input vector.
| MatType::ValueType openvdb::v9_0::math::lOneNorm | ( | const MatType & | matrix | ) |
Return the L1 norm of an N×N matrix.
|
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Return the maximum of two values.
|
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Return the maximum of three values.
|
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Return the maximum of four values.
|
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Return the maximum of five values.
|
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Return the maximum of six values.
|
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Return the maximum of seven values.
|
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Return the maximum of eight values.
Return component-wise maximum of the two vectors.
Return component-wise maximum of the two vectors.
Return component-wise maximum of the two vectors.
| size_t openvdb::v9_0::math::MaxIndex | ( | const Vec3T & | v | ) |
Return the index [0,1,2] of the largest value in a 3D vector.
If two components of the input vector are equal and larger than the third component, the largest index of the two is always returned. If all three vector components are equal the largest index, i.e. 2, is returned. In other words the return value corresponds to the largest index of the largest vector components.
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Return the minimum of two values.
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Return the minimum of three values.
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Return the minimum of four values.
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Return the minimum of five values.
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Return the minimum of six values.
|
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Return the minimum of seven values.
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Return the minimum of eight values.
Return component-wise minimum of the two vectors.
Return component-wise minimum of the two vectors.
Return component-wise minimum of the two vectors.
| size_t openvdb::v9_0::math::MinIndex | ( | const Vec3T & | v | ) |
Return the index [0,1,2] of the smallest value in a 3D vector.
If two components of the input vector are equal and smaller than the third component, the largest index of the two is always returned. If all three vector components are equal the largest index, i.e. 2, is returned. In other words the return value corresponds to the largest index of the of the smallest vector components.
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Return the remainder of x / y.
|
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Return the remainder of x / y.
|
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Return the remainder of x / y.
|
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Return the remainder of x / y.
|
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Return the unary negation of the given value.
|
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Return the negation of the given boolean.
|
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Return the "negation" of the given string.
Inequality operator, does exact floating point comparisons.
Inequality operator, does exact floating point comparisons.
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Multiply each element of the given vector by scalar and return the result.
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Multiply each element of the given vector by scalar and return the result.
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Multiply corresponding elements of v0 and v1 and return the result.
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Multiply each element of the given vector by scalar and return the result.
|
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Multiply each element of the given vector by scalar and return the result.
|
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Multiply corresponding elements of v0 and v1 and return the result.
|
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Multiply each element of the given vector by scalar and return the result.
|
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Multiply each element of the given vector by scalar and return the result.
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Multiply corresponding elements of v0 and v1 and return the result.
Multiply each element of the given quaternion by scalar and return the result.
| Mat3<typename promote<T0, T1>::type> openvdb::v9_0::math::operator* | ( | const Mat3< T0 > & | m0, |
| const Mat3< T1 > & | m1 | ||
| ) |
Multiply m0 by m1 and return the resulting matrix.
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Needed to support the (zeroVal<ValueType>() + val) idiom when ValueType is std::string.
|
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Needed to support the (zeroVal<ValueType>() + val) idiom when ValueType is std::string.
|
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Needed to support the (zeroVal<ValueType>() + val) idiom when ValueType is std::string.
|
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Needed to support the (zeroVal<ValueType>() + val) idiom when ValueType is std::string.
|
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Add corresponding elements of v0 and v1 and return the result.
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Add scalar to each element of the given vector and return the result.
|
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Add corresponding elements of v0 and v1 and return the result.
|
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Add scalar to each element of the given vector and return the result.
|
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|
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Add corresponding elements of v0 and v1 and return the result.
|
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Add scalar to each element of the given vector and return the result.
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Subtract corresponding elements of v0 and v1 and return the result.
|
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Subtract scalar from each element of the given vector and return the result.
|
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Subtract corresponding elements of v0 and v1 and return the result.
|
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Subtract scalar from each element of the given vector and return the result.
|
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Subtract corresponding elements of v0 and v1 and return the result.
|
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Subtract scalar from each element of the given vector and return the result.
|
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Divide scalar by each element of the given vector and return the result.
|
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Divide each element of the given vector by scalar and return the result.
|
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Divide corresponding elements of v0 and v1 and return the result.
|
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Divide scalar by each element of the given vector and return the result.
|
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Divide each element of the given vector by scalar and return the result.
|
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Divide corresponding elements of v0 and v1 and return the result.
|
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Divide scalar by each element of the given vector and return the result.
|
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Divide each element of the given vector by scalar and return the result.
|
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Divide corresponding elements of v0 and v1 and return the result.
|
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Output streaming of the Ray class.
| OPENVDB_API std::ostream& openvdb::v9_0::math::operator<< | ( | std::ostream & | , |
| const Transform & | |||
| ) |
| std::ostream& openvdb::v9_0::math::operator<< | ( | std::ostream & | ostr, |
| const Tuple< SIZE, T > & | classname | ||
| ) |
Write a Tuple to an output stream.
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Output streaming of the Ray class.
|
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Equality operator, does exact floating point comparisons.
Equality operator, does exact floating point comparisons.
Orthonormalize vectors v1 and v2 and store back the resulting basis e.g. Vec2f::orthonormalize(v1,v2);
Orthonormalize vectors v1, v2 and v3 and store back the resulting basis e.g. Vec3d::orthonormalize(v1,v2,v3);
Returns outer product of v1, v2, i.e. v1 v2^T if v1 and v2 are column vectors, e.g. M = Mat3f::outerproduct(v1,v2);
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Write 0s along Mat4's last row and column, and a 1 on its diagonal.
Useful initialization when we're initializing just the 3×3 block.
|
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Pi constant taken from Boost to match old behaviour.
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| bool openvdb::v9_0::math::polarDecomposition | ( | const MatType & | input, |
| MatType & | unitary, | ||
| MatType & | positive_hermitian, | ||
| unsigned int | MAX_ITERATIONS = 100 |
||
| ) |
Decompose an invertible 3×3 matrix into a unitary matrix followed by a symmetric matrix (positive semi-definite Hermitian), i.e., M = U * S.
If det(U) = 1 it is a rotation, otherwise det(U) = -1, meaning there is some part reflection. See "Computing the polar decomposition with applications" Higham, N.J. - SIAM J. Sc. Stat Comput 7(4):1160-1174
| Type openvdb::v9_0::math::Pow | ( | Type | x, |
| int | n | ||
| ) |
Return xn.
|
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Return be.
|
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Return be.
|
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Return x2.
|
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Return x3.
|
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Return x4.
Interpolate the rotation between m1 and m2 using Mat::powSolve. Unlike slerp, translation is not treated independently. This results in smoother animation results.
|
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8-bit integer values print to std::ostreams as characters. Cast them so that they print as integers instead.
|
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| bool openvdb::v9_0::math::processTypedMap | ( | TransformType & | transform, |
| OpType & | op | ||
| ) |
Utility function that, given a generic map pointer, calls a functor on the fully-resoved map.
Usage:
false if the grid type is unknown or unhandled.
|
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Return the remainder of x / y.
| MatType openvdb::v9_0::math::rotation | ( | const Quat< typename MatType::value_type > & | q, |
| typename MatType::value_type | eps = static_cast<typename MatType::value_type>(1.0e-8) |
||
| ) |
Return the rotation matrix specified by the given quaternion.
The quaternion is normalized and used to construct the matrix. Note that the matrix is transposed to match post-multiplication semantics.
| MatType openvdb::v9_0::math::rotation | ( | Axis | axis, |
| typename MatType::value_type | angle | ||
| ) |
Return a matrix for rotation by angle radians about the given axis.
| axis | The axis (one of X, Y, Z) to rotate about. |
| angle | The rotation angle, in radians. |
| MatType openvdb::v9_0::math::rotation | ( | const Vec3< typename MatType::value_type > & | _axis, |
| typename MatType::value_type | angle | ||
| ) |
Return a matrix for rotation by angle radians about the given axis.
|
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Return x rounded to the nearest integer.
|
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Return x rounded to the nearest integer.
|
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Return x rounded to the nearest integer.
|
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Return x rounded down to the nearest integer.
|
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Return x rounded down to the nearest integer.
|
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Return x rounded down to the nearest integer.
|
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Return x rounded down to the nearest multiple of base.
|
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Return x rounded up to the nearest integer.
|
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Return x rounded up to the nearest integer.
|
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Return x rounded up to the nearest integer.
|
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Return x rounded up to the nearest multiple of base.
| MatType openvdb::v9_0::math::scale | ( | const Vec3< typename MatType::value_type > & | s | ) |
Return a matrix that scales by s.
Set the matrix to a shear along axis0 by a fraction of axis1.
| axis0 | The fixed axis of the shear. |
| axis1 | The shear axis. |
| shear | The shear factor. |
|
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Return the sign of the given value as an integer (either -1, 0 or 1).
|
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Return true if a and b have different signs.
| OPENVDB_API SharedPtr<MapBase> openvdb::v9_0::math::simplify | ( | SharedPtr< AffineMap > | affine | ) |
reduces an AffineMap to a ScaleMap or a ScaleTranslateMap when it can
|
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Return sin x.
|
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Return sin x.
| MatType openvdb::v9_0::math::skew | ( | const Vec3< typename MatType::value_type > & | skew | ) |
Return a matrix as the cross product of the given vector.
| Quat<T> openvdb::v9_0::math::slerp | ( | const Quat< T > & | q1, |
| const Quat< T > & | q2, | ||
| T | t, | ||
| T | tolerance = 0.00001 |
||
| ) |
Linear interpolation between the two quaternions.
Interpolate between m1 and m2. Converts to quaternion form and uses slerp m1 and m2 must be rotation matrices!
|
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Return 0 if x < 0, 1 if x > 1 or else (3 − 2 x) x².
|
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Return 0 if x < min, 1 if x > max or else (3 − 2 t) t², where t = (x − min)/(max − min).
|
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This function snaps a specific axis to a specific direction, preserving scaling.
It does this using minimum energy, thus posing a unique solution if basis & direction aren't parallel.
|
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Return the square root of a floating-point value.
|
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Return the square root of a floating-point value.
|
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Return the square root of a floating-point value.
|
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Solve for A=B*B, given A.
Denman-Beavers square root iteration
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Return x truncated to the given number of decimal digits.
| MatType openvdb::v9_0::math::unit | ( | const MatType & | mat, |
| typename MatType::value_type | eps = 1.0e-8 |
||
| ) |
Return a copy of the given matrix with its upper 3×3 rows normalized.
This can be geometrically interpreted as a matrix with no scaling along its major axes.
| MatType openvdb::v9_0::math::unit | ( | const MatType & | in, |
| typename MatType::value_type | eps, | ||
| Vec3< typename MatType::value_type > & | scaling | ||
| ) |
Return a copy of the given matrix with its upper 3×3 rows normalized, and return the length of each of these rows in scaling.
This can be geometrically interpretted as a matrix with no scaling along its major axes, and the scaling in the input vector
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Implementation of nominally fifth-order finite-difference WENO.
This function returns the numerical flux. See "High Order Finite Difference and Finite Volume WENO Schemes and Discontinuous Galerkin Methods for CFD" - Chi-Wang Shu ICASE Report No 2001-11 (page 6). Also see ICASE No 97-65 for a more complete reference (Shu, 1997). Given v1 = f(x-2dx), v2 = f(x-dx), v3 = f(x), v4 = f(x+dx) and v5 = f(x+2dx), return an interpolated value f(x+dx/2) with the special property that ( f(x+dx/2) - f(x-dx/2) ) / dx = df/dx (x) + error, where the error is fifth-order in smooth regions: O(dx) <= error <=O(dx^5)
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Return true if the interval [a, b] includes zero, i.e., if either a or b is zero or if they have different signs.
1.8.11