See IMP.algebra for more information.

Classes
class	BoundedGridRangeD

class	BoundingBoxD
	An axis-aligned bounding box. More...

class	Cone3D

class	ConnollySurfacePoint

class	Cylinder3D

class	DefaultEmbeddingD

struct	DenseFloatLogGridKD

struct	DenseGrid3D

class	DenseGridStorageD

struct	DenseIntLogGrid3D

class	DynamicNearestNeighbor3D

class	Ellipsoid3D

class	EuclideanVectorKDMetric

class	ExtendedGridIndexD
	An index in an infinite grid on space. More...

class	FixedXYZ
	A simple class for returning XYZ Euler angles. More...

class	Gaussian3D

class	GeometricPrimitiveD

class	GridD
	A voxel grid in d-dimensional space space. More...

class	GridIndexD
	Represent a real cell in a grid (one within the bounding box) More...

class	LinearFit2D
	Calculate line that fits best the input data points (Linear least squares) More...

class	LogEmbeddingD

class	MaxVectorKDMetric

class	NearestNeighborD

class	ParabolicFit2D
	Calculate parabola that fits best the input data points. More...

class	Plane3D

class	PrincipalComponentAnalysisD

class	ReferenceFrame3D
	A reference frame in 3D. More...

class	Reflection3D
	Reflect about a plane in 3D. More...

class	Rotation2D
	Stores a 2D rotation matrix. More...

class	Rotation3D
	3D rotation class. More...

class	Segment3D

struct	SparseGrid3D

class	SparseGridStorageD

struct	SparseUnboundedGrid3D

struct	SparseUnboundedGridD

class	SphereD

class	SpherePatch3D

class	SphericalVector3D
	Class to represent a 3D point in spherical coordinates. More...

class	Transformation2D
	Simple 2D transformation class. More...

class	Transformation3D
	Simple 3D transformation class. More...

class	Triangle3D

class	UnboundedGridRangeD

class	VectorBaseD
	A Cartesian vector in D-dimensions. More...

class	VectorD
	A Cartesian vector in D-dimensions. More...

class	VectorKDMetric

Typedefs
typedef std::pair< Vector3D, double >	AxisAnglePair

typedef BoundingBoxD< 1 >	BoundingBox1D

typedef IMP::base::Vector < BoundingBox1D >	BoundingBox1Ds

typedef BoundingBoxD< 2 >	BoundingBox2D

typedef IMP::base::Vector < BoundingBox2D >	BoundingBox2Ds

typedef BoundingBoxD< 3 >	BoundingBox3D

typedef IMP::base::Vector < BoundingBox3D >	BoundingBox3Ds

typedef BoundingBoxD< 4 >	BoundingBox4D

typedef IMP::base::Vector < BoundingBox4D >	BoundingBox4Ds

typedef BoundingBoxD< 5 >	BoundingBox5D

typedef IMP::base::Vector < BoundingBox5D >	BoundingBox5Ds

typedef BoundingBoxD< 6 >	BoundingBox6D

typedef IMP::base::Vector < BoundingBox6D >	BoundingBox6Ds

typedef BoundingBoxD<-1 >	BoundingBoxKD

typedef IMP::base::Vector < BoundingBoxKD >	BoundingBoxKDs

typedef IMP::base::Vector< Cone3D >	Cone3Ds

typedef IMP::base::Vector < ConnollySurfacePoint >	ConnollySurfacePoints

typedef IMP::base::Vector < Cylinder3D >	Cylinder3Ds

typedef IMP::base::Vector < Ellipsoid3D >	Ellipsoid3Ds

typedef IMP::base::Vector < Gaussian3D >	Gaussian3Ds

typedef IMP::base::Vector < LinearFit2D >	LinearFit2Ds

typedef IMP::base::Vector < ParabolicFit2D >	ParabolicFit2Ds

typedef IMP::base::Vector < Plane3D >	Plane3Ds

typedef IMP::base::Vector < ReferenceFrame3D >	ReferenceFrame3Ds

typedef IMP::base::Vector < Reflection3D >	Reflection3Ds

typedef IMP::base::Vector < Rotation2D >	Rotation2Ds

typedef IMP::base::Vector < Rotation3D >	Rotation3Ds

typedef IMP::base::Vector < Segment3D >	Segment3Ds

typedef SphereD< 1 >	Sphere1D

typedef IMP::base::Vector < Sphere1D >	Sphere1Ds

typedef SphereD< 2 >	Sphere2D

typedef IMP::base::Vector < Sphere2D >	Sphere2Ds

typedef SphereD< 3 >	Sphere3D

typedef IMP::base::Vector < Sphere3D >	Sphere3Ds

typedef SphereD< 4 >	Sphere4D

typedef IMP::base::Vector < Sphere4D >	Sphere4Ds

typedef SphereD< 5 >	Sphere5D

typedef IMP::base::Vector < Sphere5D >	Sphere5Ds

typedef SphereD< 6 >	Sphere6D

typedef IMP::base::Vector < Sphere6D >	Sphere6Ds

typedef SphereD<-1 >	SphereKD

typedef IMP::base::Vector < SphereKD >	SphereKDs

typedef IMP::base::Vector < SpherePatch3D >	SpherePatch3Ds

typedef IMP::base::Vector < SphericalVector3D >	SphericalVector3Ds

typedef IMP::base::Vector < Transformation2D >	Transformation2Ds

typedef IMP::base::Vector < Transformation3D >	Transformation3Ds

typedef IMP::base::Vector < Triangle3D >	Triangle3Ds

typedef VectorD< 1 >	Vector1D

typedef base::Vector< VectorD< 1 > >	Vector1Ds

typedef VectorD< 2 >	Vector2D

typedef base::Vector< VectorD< 2 > >	Vector2Ds

typedef VectorD< 3 >	Vector3D

typedef base::Vector< VectorD< 3 > >	Vector3Ds

typedef VectorD< 4 >	Vector4D

typedef base::Vector< VectorD< 4 > >	Vector4Ds

typedef VectorD< 5 >	Vector5D

typedef base::Vector< VectorD< 5 > >	Vector5Ds

typedef VectorD< 6 >	Vector6D

typedef base::Vector< VectorD< 6 > >	Vector6Ds

typedef VectorD<-1 >	VectorKD

typedef IMP::base::Vector < IMP::base::Pointer < VectorKDMetric > >	VectorKDMetrics

typedef IMP::base::Vector < IMP::base::WeakPointer < VectorKDMetric > >	VectorKDMetricsTemp

typedef base::Vector< VectorD<-1 > >	VectorKDs

Functions
template<int D>
int	compare (const VectorD< D > &a, const VectorD< D > &b)
	lexicographic comparison of two vectors More...

Rotation2D	compose (const Rotation2D &a, const Rotation2D &b)
	compose two rotations a and b More...

Transformation3D	compose (const Transformation3D &a, const Transformation3D &b)
	compose two transformations More...

Transformation2D	compose (const Transformation2D &a, const Transformation2D &b)
	compose two transformations More...

Rotation3D	compose (const Rotation3D &a, const Rotation3D &b)

Transformation3Ds	get_alignments_from_first_to_second (const PrincipalComponentAnalysisD< 3 > &pca1, const PrincipalComponentAnalysisD< 3 > &pca2)

bool	get_are_almost_equal (const double a, const double b, const double epsilon)
	Compares two values (intended for doubles) More...

bool	get_are_colinear (const Vector3D &p1, const Vector3D &p2, const Vector3D &p3)
	Return true if the three points are co-linear.

double	get_area (const SpherePatch3D &g)

double	get_area (const Plane3D &g)

template<class Geometry >
double	get_area (const Geometry &)
	Compute the area of any surface object.

std::pair< Vector3D, double >	get_axis_and_angle (const Rotation3D &rot)
	Decompose a Rotation3D object into a rotation around an axis. More...

double	get_ball_radius_from_volume_3d (double volume)
	Return the radius of a sphere with a given volume. More...

template<int D>
VectorD< D >	get_basis_vector_d (unsigned int coordinate)
	Return the basis vector for the given coordinate. More...

VectorD<-1 >	get_basis_vector_kd (int D, unsigned int coordinate)
	Return a dynamically sized basis vector.

BoundingBoxD< 3 >	get_bounding_box (const SpherePatch3D &g)

BoundingBoxD< 3 >	get_bounding_box (const Segment3D &g)

BoundingBoxD< 3 >	get_bounding_box (const Cone3D &g)

BoundingBoxD< 3 >	get_bounding_box (const Ellipsoid3D &g)

BoundingBoxD< 3 >	get_bounding_box (const Cylinder3D &g)

BoundingBoxD< 3 >	get_bounding_box (const Plane3D &g)

template<int D>
BoundingBoxD< D >	get_bounding_box (const SphereD< D > &g)

template<int D>
BoundingBoxD< D >	get_bounding_box (const BoundingBoxD< D > &g)

template<class Geometry >
BoundingBoxD< 3 >	get_bounding_box (const Geometry &)
	Compute the bounding box of any geometric object.

template<int D, class Storage , class Value , class Embedding >
BoundingBoxD< D >	get_bounding_box (const GridD< D, Storage, Value, Embedding > &g)

template<int D>
const BoundingBoxD< D > &	get_bounding_box_d_geometry (const BoundingBoxD< D > &g)

double	get_closer_power_of_2 (double x)
	Closest power of 2 for a number, not necessarily higher.

const Cone3D &	get_cone_3d_geometry (const Cone3D &g)

ConnollySurfacePoints	get_connolly_surface (const algebra::Sphere3Ds &spheres, double density, double probe_radius)

template<typename T >
T	get_constrained (const T x, const T x0, const T xF)
	Constrains a value between two given limits.

IMP_Eigen::Matrix3d	get_covariance (const Gaussian3D &g)

template<unsigned int D>
BoundingBoxD< D >	get_cube_d (double radius)
	Cube with radius of length `radius`. More...

BoundingBoxD<-1 >	get_cube_kd (unsigned int d, double radius)
	Cube with radius of length `side`. More...

const Cylinder3D &	get_cylinder_3d_geometry (const Cylinder3D &g)

std::string	get_data_path (std::string file_name)
	Return the full path to installed data. More...

double	get_distance (const Plane3D &pln, const Vector3D &p)
	Return the distance between a plane and a point in 3D. More...

double	get_distance (const Segment3D &s, const Vector3D &p)
	Get the distance between a segment and a point. More...

double	get_distance (const Segment3D &a, const Segment3D &b)
	Get the distance between two segments. More...

template<int D>
double	get_distance (const SphereD< D > &a, const SphereD< D > &b)
	Return the distance between the two spheres if they are disjoint. More...

template<int D>
double	get_distance (const VectorD< D > &v1, const VectorD< D > &v2)
	compute the distance between two vectors More...

double	get_distance (const Rotation3D &r0, const Rotation3D &r1)
	Return a distance between the two rotations. More...

IntPairs	get_edges (const BoundingBoxD< 3 > &)
	Return the edges of the box as indices into the vertices list. More...

template<int D>
VectorD< D >	get_elementwise_product (const algebra::VectorD< D > &a, const algebra::VectorD< D > &b)

template<int D>
VectorD< D >	get_elementwise_product (const Ints &a, const algebra::VectorD< D > &b)

const Ellipsoid3D &	get_ellipsoid_3d_geometry (const Ellipsoid3D &g)

Sphere3D	get_enclosing_sphere (const Sphere3Ds &ss)
	Return a sphere containing the listed spheres. More...

Sphere3D	get_enclosing_sphere (const Vector3Ds &ss)
	Return a sphere containing the listed spheres. More...

std::string	get_example_path (std::string file_name)
	Return the path to installed example data for this module. More...

Gaussian3D	get_gaussian_from_covariance (const IMP_Eigen::Matrix3d &covariance, const Vector3D &center)

Rotation2D	get_identity_rotation_2d ()
	Builds an identity rotation in 2D.

Rotation3D	get_identity_rotation_3d ()
	Return a rotation that does not do anything. More...

Transformation2D	get_identity_transformation_2d ()
	Returns a transformation that does not do anything. More...

Transformation3D	get_identity_transformation_3d ()
	Return a transformation that does not do anything. More...

template<int D>
bool	get_interiors_intersect (const SphereD< D > &a, const SphereD< D > &b)
	Return true if the two balls bounded by the two spheres interesect. More...

template<int D>
bool	get_interiors_intersect (const BoundingBoxD< D > &a, const BoundingBoxD< D > &b)
	Return true if they intersect. More...

Rotation3D	get_interpolated (const Rotation3D &a, const Rotation3D &b, double f)
	Interpolate between two rotations. More...

template<int D>
BoundingBoxD< D >	get_intersection (const BoundingBoxD< D > &a, const BoundingBoxD< D > &b)
	Return the intersecting bounding box. More...

Triangle3D	get_largest_triangle (const Vector3Ds &points)
	Return the largest triangle defined by 3 points from the input. More...

template<int D, class Storage , class Value , class Embedding >
Value	get_linearly_interpolated (const GridD< D, Storage, Value, Embedding > &g, const VectorD< D > &pt)

template<int D>
double	get_maximum_length (const BoundingBoxD< D > &a)
	Return the maximum axis aligned extent. More...

float	get_next_larger_power_of_2 (float x)
	Closest power of 2 that can contain a number x.

double	get_next_larger_power_of_2 (double x)
	Closest power of 2 that can contain a number x.

template<int D>
VectorD< D >	get_ones_vector_d (double v=1)
	Return a vector of ones (or another constant)

template<int D>
VectorD< D >	get_ones_vector_kd (unsigned int Di, double v=1)
	Return a vector of ones (or another constant) More...

const Plane3D &	get_plane_3d_geometry (const Plane3D &g)

template<int D>
double	get_power_distance (const SphereD< D > &a, const SphereD< D > &b)
	Return the power distance between the two spheres. More...

template<int D>
PrincipalComponentAnalysisD< D >	get_principal_components (const base::Vector< VectorD< D > > &ps)
	Perform principal components analysis on a set of vectors. More...

Transformation3D	get_random_local_transformation (Vector3D origin, double max_translation=5., double max_angle_in_rad=0.26)
	Get a local transformation. More...

Rotation2D	get_random_rotation_2d ()
	Builds an identity rotation in 2D.

Rotation3D	get_random_rotation_3d ()
	Pick a rotation at random from all possible rotations. More...

Rotation3D	get_random_rotation_3d (const Rotation3D &center, double distance)
	Pick a rotation at random near the provided one. More...

DenseGrid3D< float >	get_rasterized (const Gaussian3Ds &gmm, const Floats &weights, double cell_width, const BoundingBox3D &bb)

Vector3D	get_reflected (const Plane3D &pln, const Vector3D &p)
	return the point reflected about the plane

double	get_relative_projection_on_segment (const Segment3D &s, const algebra::Vector3D &p)

template<class Vector3DsOrXYZs0 , class Vector3DsOrXYZs1 >
double	get_rmsd (const Vector3DsOrXYZs0 &m1, const Vector3DsOrXYZs1 &m2)

template<class Vector3DsOrXYZs0 , class Vector3DsOrXYZs1 >
double	get_rmsd_transforming_first (const Transformation3D &tr, const Vector3DsOrXYZs0 &m1, const Vector3DsOrXYZs1 &m2)
	Calculate the root mean square deviation between two sets of 3D points. More...

Rotation3D	get_rotation_about_axis (const Vector3D &axis, double angle)
	Generate a Rotation3D object from a rotation around an axis. More...

Rotation3D	get_rotation_about_normalized_axis (const Vector3D &axis_norm, double angle)

Transformation3D	get_rotation_about_point (const Vector3D &point, const Rotation3D &rotation)
	Generate a Transformation3D object from a rotation around a point. More...

Transformation2D	get_rotation_about_point (const Vector2D &point, const Rotation2D &rotation)
	Generates a Transformation2D object from a rotation around a point. More...

Rotation3D	get_rotation_from_matrix (double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)
	Generate a Rotation3D object from a rotation matrix. More...

Rotation3D	get_rotation_from_matrix (IMP_Eigen::Matrix3d m)
	Generate a Rotation3D object from a rotation matrix. More...

Rotation3D	get_rotation_from_vector4d (const VectorD< 4 > &v)
	Compute a rotatation from an unnormalized quaternion. More...

Rotation3D	get_rotation_from_x_y_axes (const Vector3D &x, const Vector3D &y)

Rotation3D	get_rotation_taking_first_to_second (const Vector3D &v1, const Vector3D &v2)
	Create a rotation from the first vector to the second one. More...

Rotation2D	get_rotation_to_x_axis (const Vector2D &v)

template<typename T >
int	get_rounded (const T &x)
	Rounds a number to next integer. More...

const Segment3D &	get_segment_3d_geometry (const Segment3D &g)

template<typename T >
int	get_sign (const T &x)
	Sign of a number. 1 if the number is higher or equal to 0 and -1 otherwise.

Sphere3Ds	get_simplified_from_volume (Sphere3Ds in, double maximum_allowed_error_angstroms)

template<int D>
const SphereD< D > &	get_sphere_d_geometry (const SphereD< D > &g)

const SpherePatch3D &	get_sphere_patch_3d_geometry (const SpherePatch3D &g)

double	get_squared (double x)

template<int D>
double	get_squared_distance (const VectorD< D > &v1, const VectorD< D > &v2)
	compute the squared distance between two vectors More...

double	get_surface_area (const Cone3D &g)

double	get_surface_area (const Ellipsoid3D &g)

double	get_surface_area (const Cylinder3D &g)

double	get_surface_area (const SphereD< 3 > &g)

double	get_surface_area (const BoundingBoxD< 3 > &g)

template<class Geometry >
double	get_surface_area (const Geometry &)
	Compute the surface area of any volumetric object.

FloatPair	get_surface_area_and_volume (const algebra::Sphere3Ds &ss)

Transformation3D	get_transformation_3d (const Transformation2D &t2d)
	Builds a 3D transformation from a 2D one. More...

template<class Vector3DsOrXYZs0 , class Vector3DsOrXYZs1 >
IMP::algebra::Transformation3D	get_transformation_aligning_first_to_second (const Vector3DsOrXYZs0 &source, const Vector3DsOrXYZs1 &target)
	Compute the rigid transform bringing the first point set to the second. More...

Transformation2D	get_transformation_aligning_pair (const Vector2Ds &set_from, const Vector2Ds &set_to)

Transformation3D	get_transformation_from_first_to_second (const ReferenceFrame3D &a, const ReferenceFrame3D &b)

Transformation3D	get_transformation_from_first_triangle_to_second (Triangle3D first_tri, Triangle3D second_tri)
	Return a transformation between two triangles.

ReferenceFrame3D	get_transformed (const ReferenceFrame3D &rf, const Transformation3D &tr)

BoundingBoxD< 3 >	get_transformed (const BoundingBoxD< 3 > &bb, const Transformation3D &tr)
	Return a bounding box containing the transformed box.

template<class Storage , class Embedding >
const Storage::Value	get_trilinearly_interpolated (const GridD< 3, Storage, typename Storage::Value, Embedding > &g, const Vector3D &v, const typename Storage::Value &outside=0)
	Use trilinear interpolation to compute a smoothed value at v. More...

Rotation3Ds	get_uniform_cover_rotations_3d (unsigned int num_points)
	Cover the space of rotations evenly. More...

Vector3Ds	get_uniform_surface_cover (const Sphere3Ds &in, double points_per_square_angstrom)

algebra::Rotation3Ds	get_uniformly_sampled_rotations (double delta)
	Generates a nondegenerate set of Euler angles with a delta resolution. More...

template<int D>
BoundingBoxD< D >	get_union (BoundingBoxD< D > a, const BoundingBoxD< D > &b)
	Return the union bounding box. More...

template<unsigned int D>
BoundingBoxD< D >	get_unit_bounding_box_d ()
	Box with radius one. More...

BoundingBoxD<-1 >	get_unit_bounding_box_kd (unsigned int d)
	Box with radius one. More...

template<unsigned int D>
SphereD< D >	get_unit_sphere_d ()

SphereD<-1 >	get_unit_sphere_kd (unsigned int d)

template<class VT >
VT	get_unit_vector (VT vt)

template<int D>
VectorD< D >	get_vector_geometry (const SphereD< D > &s)

template<class C >
const VectorD< C::DIMENSION > &	get_vector_geometry (const C &g)

template<int D>
base::Vector< VectorD< D > >	get_vertices (const BoundingBoxD< D > &bb)
	Return a list of the 8 bounding points for the bounding box. More...

double	get_volume (const Cone3D &g)

double	get_volume (const Ellipsoid3D &g)

double	get_volume (const Cylinder3D &g)

double	get_volume (const SphereD< 3 > &g)

template<int D>
double	get_volume (const BoundingBoxD< D > &bb)

double	get_volume (const BoundingBoxD< 3 > &g)

template<class Geometry >
double	get_volume (const Geometry &)
	Compute the volume of any volumetric object.

template<int D>
VectorD< D >	get_zero_vector_d ()
	Return a vector of zeros.

template<int D>
VectorD< D >	get_zero_vector_kd (int Di)
	Return a dynamically sized vector of zeros.

template<int D>
VectorD< D >	operator* (double s, VectorD< D > o)

template<int D>
void	set_bounding_box_d_geometry (BoundingBoxD< D > &g, const BoundingBoxD< D > &v)

void	set_cone_3d_geometry (Cone3D &g, const Cone3D &v)

void	set_cylinder_3d_geometry (Cylinder3D &g, const Cylinder3D &v)

void	set_ellipsoid_3d_geometry (Ellipsoid3D &g, const Ellipsoid3D &v)

void	set_plane_3d_geometry (Plane3D &g, const Plane3D &v)

void	set_segment_3d_geometry (Segment3D &g, const Segment3D &gi)

template<int D>
void	set_sphere_d_geometry (SphereD< D > &g, const SphereD< D > &v)

void	set_sphere_patch_3d_geometry (SpherePatch3D &g, const SpherePatch3D &v)

template<class C , class E >
void	set_vector_geometry (C &g, const E &v)

Variables
static const double	PI = 3.1415926535897931
	the constant pi

Standard module methods
All `IMP` modules have a set of standard methods to help get information about the module and about files associated with the module.
std::string	get_module_version ()

std::string	get_module_name ()

Endian
`IMP` provides a variety of functionality to manage byte order in input and output data.
void	reversed_read (void *dest, size_t size, size_t nitems, std::ifstream &f, bool reverse)
	Reads from file in normal or reverse order. More...

void	reversed_write (const void *src, size_t size, size_t nitems, std::ofstream &f, bool reverse=false)
	Writes to a file in normal or reversed order. More...

template<class T >
void	get_swapped_endian (T &x)
	Conversion between little and big endian. Goes both ways.

bool	get_is_big_endian ()
	Returns 1 if machine is big endian else 0.

bool	get_is_little_endian ()
	Returns 1 if machine is little endian else 0.

Simple geometric IO
These functions write geometry to text files, one line per geometric primitive. Each line has the form “x y z” for points or “x y z r” for spheres. We can easily add general dimension support if requested.. Lines beginning with "#" are treated as comments.
void	write_pts (const Vector3Ds &vs, base::TextOutput out)
	Write a set of 3D vectors to a file. More...

Vector3Ds	read_pts (base::TextInput input)
	Read a set of 3D vectors from a file. More...

void	write_spheres (const Sphere3Ds &vs, base::TextOutput out)
	Write a set of 3d spheres to a file. More...

Sphere3Ds	read_spheres (base::TextInput input)
	Read a set of 3d spheres from a file. More...

Python Only
The following functions are only availale in Python as the equivalent C++ functionality is provided via template functions or in other ways that don't directly map to python.
typedef Grid3D< int, SparseGridStorage3D< int, BoundedGridStorage3D > >	SparseIntGrid3D

typedef Grid3D< int, SparseGridStorage3D< int, UnboundedGridStorage3D > >	SparseUnboundedIntGrid3D

typedef Grid3D< double, DenseGridStorage3D< double > >	DenseDoubleGrid3D

typedef Grid3D< float, DenseGridStorage3D< float > >	DenseFloatGrid3D

Transformation3D	get_transformation_aligning_first_to_second (Vector3Ds a, Vector3Ds b)

Euler Angles
There are many conventions for how to define Euler angles, based on choices of which of the x,y,z axis to use in what order and whether the rotation axis is in the body frame (and hence affected by previous rotations) or in in a fixed frame. See http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles for a general description. All Euler angles are specified in radians. Only x-y-z order is currently supported. To convert Euler angles in a different order, one can compose a Rotation3D from three rotations using get_rotation_about_axis function.
typedef IMP::base::Vector < FixedXYZ >	FixedXYZs

Rotation3D	get_rotation_from_fixed_xyz (double xr, double yr, double zr)
	Initialize a rotation in x-y-z order from three angles. More...

Rotation3D	get_rotation_from_fixed_zxz (double phi, double theta, double psi)
	Initialize a rotation from euler angles. More...

Rotation3D	get_rotation_from_fixed_zyz (double Rot, double Tilt, double Psi)
	Generate a rotation object from Euler Angles. More...

FixedXYZ	get_fixed_xyz_from_rotation (const Rotation3D &r)
	The inverse of rotation_from_fixed_xyz() More...

Shortest segments
These methods return the shortest segment connecting two geometric objects. Such segments can be used to give the direction of the derivative of the distance between the two objects. The 0 point on the segment is in the first passed object and the 1 point is in the second.
Segment3D	get_shortest_segment (const Segment3D &s, const Vector3D &p)

Segment3D	get_shortest_segment (const Segment3D &sa, const Segment3D &sb)

3D Vectors
We provide a specialization of VectorD for 3-space and several additional functions on it.
Vector3D	get_vector_product (const Vector3D &p1, const Vector3D &p2)
	Returns the vector product (cross product) of two vectors. More...

Vector3D	get_orthogonal_vector (const Vector3D &v)
	Return a vector that is perpendicular to the given vector. More...

Vector3D	get_centroid (const Vector3Ds &ps)
	Returns the centroid of a set of vectors. More...

double	get_radius_of_gyration (const Vector3Ds &ps)
	Return the radius of gyration of a set of points. More...

Vector Generators
These functions generate vector objects. Some of the methods, those with random in their name, generate a single vector chosen uniformly from the specified domain. Others, the cover methods, generate a set of points distributed (somewhat) evenly over the domain.
template<int D>
VectorD< D >	get_random_vector_in (const BoundingBoxD< D > &bb)
	Generate a random vector in a box with uniform density. More...

template<int D>
VectorD< D >	get_random_vector_on (const BoundingBoxD< D > &bb)
	Generate a random vector on a box with uniform density. More...

template<int D>
VectorD< D >	get_random_vector_in (const SphereD< D > &s)
	Generate a random vector in a sphere with uniform density. More...

VectorD< 2 >	get_random_vector_in (const SphereD< 2 > &s)

Vector3D	get_random_vector_in (const Cylinder3D &c)
	Generate a random vector in a cylinder with uniform density. More...

VectorD< 3 >	get_random_vector_on_unit_sphere ()

template<int D>
VectorD< D >	get_random_vector_on (const SphereD< D > &s)
	Generate a random vector on a sphere with uniform density. More...

template<int D>
base::Vector< VectorD< D > >	get_uniform_surface_cover (const SphereD< D > &s, unsigned int n)
	Generate a set of vectors which covers a sphere uniformly. More...

Vector3Ds	get_uniform_surface_cover (const Cylinder3D &cyl, int number_of_points)
	Generate a set of 3d points that uniformly cover a cylinder. More...

template<int D>
base::Vector< VectorD< D > >	get_uniform_upper_hemisphere_cover (const SphereD< D > &s, unsigned int n)
	Generate a set of 3D points that uniformly cover a hemisphere. More...

Vector3Ds	get_grid_surface_cover (const Cylinder3D &cyl, int number_of_cycles, int number_of_points_on_cycle)
	Generate a grid of 3d points on a cylinder surface. More...

Vector3Ds	get_uniform_surface_cover (const SpherePatch3D &sph, unsigned int number_of_points)
	Generate a set of 3d points that uniformly cover a patch of a sphere. More...

Vector3Ds	get_uniform_surface_cover (const Cone3D &cone, unsigned int number_of_points)

template<int D>
base::Vector< VectorD< D > >	get_grid_interior_cover_by_spacing (const BoundingBoxD< D > &bb, double s)

Vector3Ds	get_random_chain (unsigned int n, double r, const Vector3D &start=Vector3D(0, 0, 0), const Sphere3Ds &obstacles=Sphere3Ds())
	Generate a random chain with no collisions. More...

Norms
We define a number of standard, \(L^p\), norms on VectorD. \(L^1\) is the Manhattan distance, the sum of the components \(L^2\) is the standard Euclidean length \(L^{\inf}\) is the maximum of the components
template<int D>
double	get_l2_norm (const VectorD< D > &v)

template<int D>
double	get_l1_norm (const VectorD< D > &v)

template<int D>
double	get_linf_norm (const VectorD< D > &v)

Typedef Documentation

typedef BoundingBoxD<1> IMP::algebra::BoundingBox1D

Typedef for python.

Definition at line 160 of file BoundingBoxD.h.

typedef IMP::base::Vector< BoundingBox1D > IMP::algebra::BoundingBox1Ds

Pass or store a set of BoundingBox1D .

Definition at line 160 of file BoundingBoxD.h.

typedef BoundingBoxD<2> IMP::algebra::BoundingBox2D

Typedef for python.

Definition at line 160 of file BoundingBoxD.h.

typedef IMP::base::Vector< BoundingBox2D > IMP::algebra::BoundingBox2Ds

Pass or store a set of BoundingBox2D .

Definition at line 160 of file BoundingBoxD.h.

typedef BoundingBoxD<3> IMP::algebra::BoundingBox3D

Typedef for python.

Definition at line 160 of file BoundingBoxD.h.

typedef IMP::base::Vector< BoundingBox3D > IMP::algebra::BoundingBox3Ds

Pass or store a set of BoundingBox3D .

Definition at line 160 of file BoundingBoxD.h.

typedef BoundingBoxD<4> IMP::algebra::BoundingBox4D

Typedef for python.

Definition at line 160 of file BoundingBoxD.h.

typedef IMP::base::Vector< BoundingBox4D > IMP::algebra::BoundingBox4Ds

Pass or store a set of BoundingBox4D .

Definition at line 160 of file BoundingBoxD.h.

typedef BoundingBoxD<5> IMP::algebra::BoundingBox5D

Typedef for python.

Definition at line 160 of file BoundingBoxD.h.

typedef IMP::base::Vector< BoundingBox5D > IMP::algebra::BoundingBox5Ds

Pass or store a set of BoundingBox5D .

Definition at line 160 of file BoundingBoxD.h.

typedef BoundingBoxD<6> IMP::algebra::BoundingBox6D

Typedef for python.

Definition at line 160 of file BoundingBoxD.h.

typedef IMP::base::Vector< BoundingBox6D > IMP::algebra::BoundingBox6Ds

Pass or store a set of BoundingBox6D .

Definition at line 160 of file BoundingBoxD.h.

typedef BoundingBoxD<-1> IMP::algebra::BoundingBoxKD

Typedef for python.

Definition at line 160 of file BoundingBoxD.h.

typedef IMP::base::Vector< BoundingBoxKD > IMP::algebra::BoundingBoxKDs

Pass or store a set of BoundingBoxKD .

Definition at line 160 of file BoundingBoxD.h.

typedef IMP::base::Vector< Cone3D > IMP::algebra::Cone3Ds

Pass or store a set of Cone3D .

Definition at line 62 of file Cone3D.h.

typedef IMP::base::Vector< ConnollySurfacePoint > IMP::algebra::ConnollySurfacePoints

Pass or store a set of ConnollySurfacePoint .

Definition at line 46 of file algebra/connolly_surface.h.

typedef IMP::base::Vector< Cylinder3D > IMP::algebra::Cylinder3Ds

Pass or store a set of Cylinder3D .

Definition at line 77 of file Cylinder3D.h.

typedef Grid3D<double, DenseGridStorage3D<double> > IMP::algebra::DenseDoubleGrid3D

A grid of doubles over a region of space.

Definition at line 91 of file algebra/python_only.h.

typedef Grid3D<float, DenseGridStorage3D<float> > IMP::algebra::DenseFloatGrid3D

A grid of floats over a region of space.

Definition at line 94 of file algebra/python_only.h.

typedef IMP::base::Vector< Ellipsoid3D > IMP::algebra::Ellipsoid3Ds

Pass or store a set of Ellipsoid3D .

Definition at line 65 of file Ellipsoid3D.h.

typedef IMP::base::Vector< FixedXYZ > IMP::algebra::FixedXYZs

Pass or store a set of FixedXYZ .

Definition at line 430 of file Rotation3D.h.

typedef IMP::base::Vector< Gaussian3D > IMP::algebra::Gaussian3Ds

Pass or store a set of Gaussian3D .

Definition at line 41 of file Gaussian3D.h.

typedef IMP::base::Vector< LinearFit2D > IMP::algebra::LinearFit2Ds

Pass or store a set of LinearFit2D .

Definition at line 52 of file LinearFit.h.

typedef IMP::base::Vector< ParabolicFit2D > IMP::algebra::ParabolicFit2Ds

Pass or store a set of ParabolicFit2D .

Definition at line 54 of file ParabolicFit.h.

typedef IMP::base::Vector< Plane3D > IMP::algebra::Plane3Ds

Pass or store a set of Plane3D .

Definition at line 82 of file Plane3D.h.

typedef IMP::base::Vector< ReferenceFrame3D > IMP::algebra::ReferenceFrame3Ds

Pass or store a set of ReferenceFrame3D .

Definition at line 80 of file ReferenceFrame3D.h.

typedef IMP::base::Vector< Reflection3D > IMP::algebra::Reflection3Ds

Pass or store a set of Reflection3D .

Definition at line 34 of file Reflection3D.h.

typedef IMP::base::Vector< Rotation2D > IMP::algebra::Rotation2Ds

Pass or store a set of Rotation2D .

Definition at line 114 of file Rotation2D.h.

typedef IMP::base::Vector< Rotation3D > IMP::algebra::Rotation3Ds

Pass or store a set of Rotation3D .

Definition at line 224 of file Rotation3D.h.

typedef IMP::base::Vector< Segment3D > IMP::algebra::Segment3Ds

Pass or store a set of Segment3D .

Definition at line 51 of file Segment3D.h.

typedef Grid3D<int, SparseGridStorage3D<int, BoundedGridStorage3D> > IMP::algebra::SparseIntGrid3D

A sparse grid of integers over a bounded region of space.

Definition at line 84 of file algebra/python_only.h.

typedef Grid3D<int, SparseGridStorage3D<int, UnboundedGridStorage3D> > IMP::algebra::SparseUnboundedIntGrid3D

A sparse grid of integers over all of space.

Definition at line 88 of file algebra/python_only.h.

typedef SphereD<1> IMP::algebra::Sphere1D

Typedef for python.

Definition at line 89 of file SphereD.h.

typedef IMP::base::Vector< Sphere1D > IMP::algebra::Sphere1Ds

Pass or store a set of Sphere1D .

Definition at line 89 of file SphereD.h.

typedef SphereD<2> IMP::algebra::Sphere2D

Typedef for python.

Definition at line 89 of file SphereD.h.

typedef IMP::base::Vector< Sphere2D > IMP::algebra::Sphere2Ds

Pass or store a set of Sphere2D .

Definition at line 89 of file SphereD.h.

typedef SphereD<3> IMP::algebra::Sphere3D

Typedef for python.

Definition at line 89 of file SphereD.h.

typedef IMP::base::Vector< Sphere3D > IMP::algebra::Sphere3Ds

Pass or store a set of Sphere3D .

Definition at line 89 of file SphereD.h.

typedef SphereD<4> IMP::algebra::Sphere4D

Typedef for python.

Definition at line 89 of file SphereD.h.

typedef IMP::base::Vector< Sphere4D > IMP::algebra::Sphere4Ds

Pass or store a set of Sphere4D .

Definition at line 89 of file SphereD.h.

typedef SphereD<5> IMP::algebra::Sphere5D

Typedef for python.

Definition at line 89 of file SphereD.h.

typedef IMP::base::Vector< Sphere5D > IMP::algebra::Sphere5Ds

Pass or store a set of Sphere5D .

Definition at line 89 of file SphereD.h.

typedef SphereD<6> IMP::algebra::Sphere6D

Typedef for python.

Definition at line 89 of file SphereD.h.

typedef IMP::base::Vector< Sphere6D > IMP::algebra::Sphere6Ds

Pass or store a set of Sphere6D .

Definition at line 89 of file SphereD.h.

typedef SphereD<-1> IMP::algebra::SphereKD

Typedef for python.

Definition at line 89 of file SphereD.h.

typedef IMP::base::Vector< SphereKD > IMP::algebra::SphereKDs

Pass or store a set of SphereKD .

Definition at line 89 of file SphereD.h.

typedef IMP::base::Vector< SpherePatch3D > IMP::algebra::SpherePatch3Ds

Pass or store a set of SpherePatch3D .

Definition at line 50 of file SpherePatch3D.h.

typedef IMP::base::Vector< SphericalVector3D > IMP::algebra::SphericalVector3Ds

Pass or store a set of SphericalVector3D .

Definition at line 80 of file SphericalVector3D.h.

typedef IMP::base::Vector< Transformation2D > IMP::algebra::Transformation2Ds

Pass or store a set of Transformation2D .

Definition at line 117 of file Transformation2D.h.

typedef IMP::base::Vector< Transformation3D > IMP::algebra::Transformation3Ds

Pass or store a set of Transformation3D .

Definition at line 85 of file Transformation3D.h.

typedef IMP::base::Vector< Triangle3D > IMP::algebra::Triangle3Ds

Pass or store a set of Triangle3D .

Definition at line 41 of file Triangle3D.h.

typedef VectorD<1> IMP::algebra::Vector1D

1D vector typedef for swig

Definition at line 387 of file VectorD.h.

typedef base::Vector<VectorD<1> > IMP::algebra::Vector1Ds

1D vectors typedef for swig

Definition at line 389 of file VectorD.h.

typedef VectorD<2> IMP::algebra::Vector2D

2D vector typedef for swig

Definition at line 391 of file VectorD.h.

typedef base::Vector<VectorD<2> > IMP::algebra::Vector2Ds

2D vectors typedef for swig

Definition at line 393 of file VectorD.h.

typedef VectorD<3> IMP::algebra::Vector3D

3D vector typedef for swig

Examples:: grid.cpp.

Definition at line 395 of file VectorD.h.

typedef base::Vector<VectorD<3> > IMP::algebra::Vector3Ds

3D vectors typedef for swig

Definition at line 397 of file VectorD.h.

typedef VectorD<4> IMP::algebra::Vector4D

4D vector typedef for swig

Definition at line 399 of file VectorD.h.

typedef base::Vector<VectorD<4> > IMP::algebra::Vector4Ds

4D vectors typedef for swig

Definition at line 401 of file VectorD.h.

typedef VectorD<5> IMP::algebra::Vector5D

5D vector typedef for swig

Definition at line 403 of file VectorD.h.

typedef base::Vector<VectorD<5> > IMP::algebra::Vector5Ds

5D vectors typedef for swig

Definition at line 405 of file VectorD.h.

typedef VectorD<6> IMP::algebra::Vector6D

6D vector typedef for swig

Definition at line 407 of file VectorD.h.

typedef base::Vector<VectorD<6> > IMP::algebra::Vector6Ds

6D vector typedef for swig

Definition at line 409 of file VectorD.h.

typedef VectorD<-1> IMP::algebra::VectorKD

KD vector typedef for swig

Definition at line 411 of file VectorD.h.

typedef IMP::base::Vector<IMP::base::Pointer< VectorKDMetric > > IMP::algebra::VectorKDMetrics

Store a set of objects.

Definition at line 32 of file vector_metrics.h.

typedef IMP::base::Vector<IMP::base::WeakPointer< VectorKDMetric > > IMP::algebra::VectorKDMetricsTemp

Pass a set of objects. See VectorKDMetric

Definition at line 32 of file vector_metrics.h.

typedef base::Vector<VectorD<-1> > IMP::algebra::VectorKDs

KD vectors typedef for swig

Definition at line 413 of file VectorD.h.

Function Documentation

template<int D>

int IMP::algebra::compare	(	const VectorD< D > &	a,
		const VectorD< D > &	b
	)

Note that this is not very reliable and probably should not be used. See VectorD

Definition at line 179 of file VectorD.h.

Rotation2D IMP::algebra::compose	(	const Rotation2D &	a,
		const Rotation2D &	b
	)

For any vector v (a*b)*v = a*(b*v).

Definition at line 108 of file Rotation2D.h.

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Transformation3D IMP::algebra::compose	(	const Transformation3D &	a,
		const Transformation3D &	b
	)

For any vector v (a*b)*v = a*(b*v). See Transformation3D

Definition at line 109 of file Transformation3D.h.

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Transformation2D IMP::algebra::compose	(	const Transformation2D &	a,
		const Transformation2D &	b
	)

For any vector v (a*b)*v = a*(b*v). See Transformation2D

Definition at line 144 of file Transformation2D.h.

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Rotation3D IMP::algebra::compose	(	const Rotation3D &	a,
		const Rotation3D &	b
	)

See Rotation3D

Definition at line 348 of file Rotation3D.h.

Transformation3Ds IMP::algebra::get_alignments_from_first_to_second	(	const PrincipalComponentAnalysisD< 3 > &	pca1,
		const PrincipalComponentAnalysisD< 3 > &	pca2
	)

Get all possible alignments of the first principal component system to the second one

bool IMP::algebra::get_are_almost_equal	(	const double	a,
		const double	b,
		const double	epsilon
	)

epsilon is the tolerance allowed to consider the values as equal

Definition at line 108 of file algebra/utility.h.

double IMP::algebra::get_area ( const SpherePatch3D & g )

See SpherePatch3D

Definition at line 50 of file SpherePatch3D.h.

double IMP::algebra::get_area ( const Plane3D & g )

See Plane3D

Definition at line 82 of file Plane3D.h.

std::pair<Vector3D, double> IMP::algebra::get_axis_and_angle ( const Rotation3D & rot )

Decompose a Rotation3D object into a rotation around an axis. For all identity rotations, returns the axis [1,0,0] and the angle 0.0.

Note: http://en.wikipedia.org/wiki/Rotation_matrix; www.euclideanspace.com/maths/geometry/rotations/conversions/ angleToQuaternion/index.htm See Rotation3D

Returns: axis direction and rotation about the axis in Radians

double IMP::algebra::get_ball_radius_from_volume_3d ( double volume )

See Sphere3D

Definition at line 35 of file Sphere3D.h.

template<int D>

VectorD<D> IMP::algebra::get_basis_vector_d ( unsigned int coordinate )

Return the unit vector pointing in the direction of the requested coordinate. That is

get_basis_vector_d<3>(2)== Vector3D(0,0,1);

See VectorD

Definition at line 222 of file VectorD.h.

BoundingBoxD<3> IMP::algebra::get_bounding_box ( const SpherePatch3D & g )

See SpherePatch3D

Definition at line 50 of file SpherePatch3D.h.

BoundingBoxD<3> IMP::algebra::get_bounding_box ( const Segment3D & g )

See Segment3D

Definition at line 51 of file Segment3D.h.

BoundingBoxD<3> IMP::algebra::get_bounding_box ( const Cone3D & g )

See Cone3D

Definition at line 62 of file Cone3D.h.

BoundingBoxD<3> IMP::algebra::get_bounding_box ( const Ellipsoid3D & g )

See Ellipsoid3D

Definition at line 65 of file Ellipsoid3D.h.

BoundingBoxD<3> IMP::algebra::get_bounding_box ( const Cylinder3D & g )

See Cylinder3D

Definition at line 77 of file Cylinder3D.h.

BoundingBoxD<3> IMP::algebra::get_bounding_box ( const Plane3D & g )

See Plane3D

Definition at line 82 of file Plane3D.h.

template<int D>

BoundingBoxD<D> IMP::algebra::get_bounding_box ( const SphereD< D > & g )

See Sphere

Definition at line 89 of file SphereD.h.

template<int D>

BoundingBoxD<D> IMP::algebra::get_bounding_box ( const BoundingBoxD< D > & g )

See BoundingBox

Definition at line 160 of file BoundingBoxD.h.

template<int D>

const BoundingBoxD<D>& IMP::algebra::get_bounding_box_d_geometry ( const BoundingBoxD< D > & g )

See BoundingBox

Definition at line 160 of file BoundingBoxD.h.

Vector3D IMP::algebra::get_centroid ( const Vector3Ds & ps )

See Vector3D

Definition at line 56 of file Vector3D.h.

const Cone3D& IMP::algebra::get_cone_3d_geometry ( const Cone3D & g )

See Cone3D

Definition at line 62 of file Cone3D.h.

ConnollySurfacePoints IMP::algebra::get_connolly_surface	(	const algebra::Sphere3Ds &	spheres,
		double	density,
		double	probe_radius
	)

M.L. Connolly, "Solvent-accessible surfaces of proteins and nucleic acids", Science, 221, p709-713 (1983).

M.L. Connolly, "Analytical molecular surface calculation", J. Appl. Cryst. 16, p548-558 (1983).

See also get_uniform_surface_cover(const IMP::algebra::Sphere3Ds&, double) for a faster alternative.

IMP_Eigen::Matrix3d IMP::algebra::get_covariance ( const Gaussian3D & g )

Return the covariance matrix from a given set of standard deviations in the passed reference frame.

template<unsigned int D>

BoundingBoxD<D> IMP::algebra::get_cube_d ( double radius )

See BoundingBoxD

Definition at line 178 of file BoundingBoxD.h.

BoundingBoxD<-1> IMP::algebra::get_cube_kd	(	unsigned int	d,
		double	radius
	)

See BoundingBoxD

Definition at line 185 of file BoundingBoxD.h.

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const Cylinder3D& IMP::algebra::get_cylinder_3d_geometry ( const Cylinder3D & g )

See Cylinder3D

Definition at line 77 of file Cylinder3D.h.

std::string IMP::algebra::get_data_path ( std::string file_name )

Each module has its own data directory, so be sure to use the version of this function in the correct module. To read the data file "data_library" that was placed in the data directory of module "mymodule", do something like

std::ifstream in(IMP::mymodule::get_data_path("data_library"));

This will ensure that the code works when IMP is installed or used via the setup_environment.sh script.

double IMP::algebra::get_distance	(	const Plane3D &	pln,
		const Vector3D &	p
	)

See Plane3D

Examples:: grid.cpp.

Definition at line 67 of file Plane3D.h.

double IMP::algebra::get_distance	(	const Segment3D &	s,
		const Vector3D &	p
	)

See Segment3D

double IMP::algebra::get_distance	(	const Segment3D &	a,
		const Segment3D &	b
	)

See Segment3D

template<int D>

double IMP::algebra::get_distance	(	const SphereD< D > &	a,
		const SphereD< D > &	b
	)

If they intersect, the distances are not meaningful. See SphereD

Definition at line 105 of file SphereD.h.

template<int D>

double IMP::algebra::get_distance	(	const VectorD< D > &	v1,
		const VectorD< D > &	v2
	)

See VectorD

Definition at line 209 of file VectorD.h.

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double IMP::algebra::get_distance	(	const Rotation3D &	r0,
		const Rotation3D &	r1
	)

The distance runs between 0 and 1. More precisely, the distance returned is distance between the two quaternion vectors properly normalized, divided by sqrt(2).

A vector with distance d from the unit vector represents a rotation of

\( \theta= \cos^{-1}\left(1-\sqrt{2}d\right)\) See Rotation3D

Definition at line 242 of file Rotation3D.h.

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IntPairs IMP::algebra::get_edges ( const BoundingBoxD< 3 > & )

See BoundingBoxD

Definition at line 289 of file BoundingBoxD.h.

template<int D>

VectorD<D> IMP::algebra::get_elementwise_product	(	const algebra::VectorD< D > &	a,
		const algebra::VectorD< D > &	b
	)

See VectorD Return the vector that is the elementwise product of the two.

Definition at line 432 of file VectorD.h.

template<int D>

VectorD<D> IMP::algebra::get_elementwise_product	(	const Ints &	a,
		const algebra::VectorD< D > &	b
	)

See VectorD Return the vector that is the elementwise product of the two.

Definition at line 445 of file VectorD.h.

const Ellipsoid3D& IMP::algebra::get_ellipsoid_3d_geometry ( const Ellipsoid3D & g )

See Ellipsoid3D

Definition at line 65 of file Ellipsoid3D.h.

Sphere3D IMP::algebra::get_enclosing_sphere ( const Sphere3Ds & ss )

See Sphere3D

Note: This method produces tighter bounding spheres if CGAL is used.

Sphere3D IMP::algebra::get_enclosing_sphere ( const Vector3Ds & ss )

See Sphere3D See Vector3D

Note: This method produces tighter bounding spheres if CGAL is used.

std::string IMP::algebra::get_example_path ( std::string file_name )

Each module has its own example directory, so be sure to use the version of this function in the correct module. For example to read the file example_protein.pdb located in the examples directory of the IMP::atom module, do

IMP::atom::read_pdb(IMP::atom::get_example_path("example_protein.pdb",

model));

This will ensure that the code works when IMP is installed or used via the setup_environment.sh script.

FixedXYZ IMP::algebra::get_fixed_xyz_from_rotation ( const Rotation3D & r )

See Also: rotation_from_fixed_xyz() See Rotation3D See FixesXYZ

Gaussian3D IMP::algebra::get_gaussian_from_covariance	(	const IMP_Eigen::Matrix3d &	covariance,
		const Vector3D &	center
	)

Return a Gaussian centered at the origin from a covariance matrix.

template<int D>

base::Vector<VectorD<D> > IMP::algebra::get_grid_interior_cover_by_spacing	(	const BoundingBoxD< D > &	bb,
		double	s
	)

Cover the interior of the bounding box by equal sized parallelograms of approximately full-width s, returning the list of centers of the cubes.

Definition at line 170 of file vector_generators.h.

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Vector3Ds IMP::algebra::get_grid_surface_cover	(	const Cylinder3D &	cyl,
		int	number_of_cycles,
		int	number_of_points_on_cycle
	)

See Vector3D See Cylinder3D

Rotation3D IMP::algebra::get_identity_rotation_3d ( )

See Rotation3D

Definition at line 228 of file Rotation3D.h.

Transformation2D IMP::algebra::get_identity_transformation_2d ( )

See Transformation2D

Definition at line 123 of file Transformation2D.h.

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Transformation3D IMP::algebra::get_identity_transformation_3d ( )

See Transformation3D

Definition at line 89 of file Transformation3D.h.

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template<int D>

bool IMP::algebra::get_interiors_intersect	(	const SphereD< D > &	a,
		const SphereD< D > &	b
	)

See SphereD

Definition at line 125 of file SphereD.h.

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template<int D>

bool IMP::algebra::get_interiors_intersect	(	const BoundingBoxD< D > &	a,
		const BoundingBoxD< D > &	b
	)

See BoundingBoxD

Definition at line 193 of file BoundingBoxD.h.

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Rotation3D IMP::algebra::get_interpolated	(	const Rotation3D &	a,
		const Rotation3D &	b,
		double	f
	)

It f ==0, return b, if f==1 return a. See Rotation3D

Definition at line 445 of file Rotation3D.h.

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template<int D>

BoundingBoxD<D> IMP::algebra::get_intersection	(	const BoundingBoxD< D > &	a,
		const BoundingBoxD< D > &	b
	)

See BoundingBoxD

Definition at line 207 of file BoundingBoxD.h.

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Triangle3D IMP::algebra::get_largest_triangle ( const Vector3Ds & points )

See Triangle3D

template<int D, class Storage , class Value , class Embedding >

Value IMP::algebra::get_linearly_interpolated	(	const GridD< D, Storage, Value, Embedding > &	g,
		const VectorD< D > &	pt
	)

Get the value from the grid with linear interpolation. Values outside the bounding box are snapped to the bounding box (effectively extending the boundary values out to infinity).

Examples:: grid.cpp.

Definition at line 23 of file grid_utility.h.

template<int D>

double IMP::algebra::get_maximum_length ( const BoundingBoxD< D > & a )

See BoundingBoxD

Definition at line 244 of file BoundingBoxD.h.

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template<int D>

VectorD<-1 > IMP::algebra::get_ones_vector_kd	(	unsigned int	Di,
		double	v = `1`
	)

Di must equal D.

Definition at line 289 of file VectorD.h.

Vector3D IMP::algebra::get_orthogonal_vector ( const Vector3D & v )

Or, if you are Israeli, it is a vertical vector. See Vector3D

Definition at line 39 of file Vector3D.h.

const Plane3D& IMP::algebra::get_plane_3d_geometry ( const Plane3D & g )

See Plane3D

Definition at line 82 of file Plane3D.h.

template<int D>

double IMP::algebra::get_power_distance	(	const SphereD< D > &	a,
		const SphereD< D > &	b
	)

The power distance is the square of the distance between the centers minus the sum of the square of the radii. See SphereD

Definition at line 116 of file SphereD.h.

template<int D>

PrincipalComponentAnalysisD<D> IMP::algebra::get_principal_components ( const base::Vector< VectorD< D > > & ps )

See PrincipalComponentAnalysis

Definition at line 109 of file eigen_analysis.h.

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double IMP::algebra::get_radius_of_gyration ( const Vector3Ds & ps )

See Also: IMP::atom::get_radius_of_gyration()

Definition at line 65 of file Vector3D.h.

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Vector3Ds IMP::algebra::get_random_chain	(	unsigned int	n,
		double	r,
		const Vector3D &	start = `Vector3D(0, 0, 0)`,
		const Sphere3Ds &	obstacles = `Sphere3Ds()`
	)

This function generates a random chain, starting at (0,0,0) with n particles each with radius r. Consecutive particles are approximately distance 2r apart and no pair of particles is closer than 2r.

If an obstacles parameter is provided then chain spheres also don't intersect the obstacle spheres.

Note: The current implementation is not very clever and can be made more clever if needed.

Transformation3D IMP::algebra::get_random_local_transformation	(	Vector3D	origin,
		double	max_translation = `5.`,
		double	max_angle_in_rad = `0.26`
	)

Note: randomly select an axis that passes to the input point and rotate around it

Parameters

[in]	origin	the origin of the rotation
[in]	max_translation	detault value is 5
[in]	max_angle_in_rad	default value is 15 degree in radians

Rotation3D IMP::algebra::get_random_rotation_3d ( )

See Rotation3D

Rotation3D IMP::algebra::get_random_rotation_3d	(	const Rotation3D &	center,
		double	distance
	)

This method generates a rotation that is within the provided distance of center.

Parameters

[in]	center	The center of the rotational volume
[in]	distance	See get_distance(const Rotation3D&,const Rotation3D&) for a full definition.

Note: The cost of this operation increases as distance goes to 0.

See Rotation3D

template<int D>

VectorD<D> IMP::algebra::get_random_vector_in ( const BoundingBoxD< D > & bb )

See BoundingBoxD See VectorD

Definition at line 39 of file vector_generators.h.

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template<int D>

VectorD<D> IMP::algebra::get_random_vector_in ( const SphereD< D > & s )

See VectorD See SphereD

Definition at line 57 of file vector_generators.h.

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VectorD<2> IMP::algebra::get_random_vector_in ( const SphereD< 2 > & s )

Generates a random vector in a circle with uniform density with respect to the area of the circle

Parameters

s	a 2D sphere (circle)

See VectorD See SphereD

Vector3D IMP::algebra::get_random_vector_in ( const Cylinder3D & c )

See VectorD See Cylinder3D

template<int D>

VectorD<D> IMP::algebra::get_random_vector_on ( const BoundingBoxD< D > & bb )

See BoundingBoxD See VectorD

Definition at line 48 of file vector_generators.h.

template<int D>

VectorD<D> IMP::algebra::get_random_vector_on ( const SphereD< D > & s )

See VectorD See SphereD

Definition at line 100 of file vector_generators.h.

VectorD<3> IMP::algebra::get_random_vector_on_unit_sphere ( )

returns a random vector on a sphere of radius 1 with uniform density and implementation optimized for the 3D + unit vector case

Definition at line 91 of file vector_generators.h.

DenseGrid3D<float> IMP::algebra::get_rasterized	(	const Gaussian3Ds &	gmm,
		const Floats &	weights,
		double	cell_width,
		const BoundingBox3D &	bb
	)

Rasterize the gaussians to a grid.

double IMP::algebra::get_relative_projection_on_segment	(	const Segment3D &	s,
		const algebra::Vector3D &	p
	)

Returns f, the 'relative' projection of a point p onto the line that contains s. Formally, the projection of p onto the line through s is s[0]+f*(s[1]-s[0]) f is in the range [0..1] if the projection of p is inside s.

Parameters

s	segment in 3D
p	point in 3D

Returns: the 'relative' project of p onto the line containing s

template<class Vector3DsOrXYZs0 , class Vector3DsOrXYZs1 >

double IMP::algebra::get_rmsd	(	const Vector3DsOrXYZs0 &	m1,
		const Vector3DsOrXYZs1 &	m2
	)

Se get_rmsd_transforming_first().

Definition at line 47 of file algebra/distance.h.

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template<class Vector3DsOrXYZs0 , class Vector3DsOrXYZs1 >

double IMP::algebra::get_rmsd_transforming_first	(	const Transformation3D &	tr,
		const Vector3DsOrXYZs0 &	m1,
		const Vector3DsOrXYZs1 &	m2
	)

Note: the function assumes correspondence between the two sets of points and does not perform rigid alignment.

See generic geometry for more information.

Definition at line 27 of file algebra/distance.h.

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Rotation3D IMP::algebra::get_rotation_about_axis	(	const Vector3D &	axis,
		double	angle
	)

Parameters

[in]	axis	the rotation axis passes through (0,0,0)
[in]	angle	the rotation angle in radians in the clockwise direction

Note: http://en.wikipedia.org/wiki/Rotation_matrix; www.euclideanspace.com/maths/geometry/rotations/conversions/ angleToQuaternion/index.htm See Rotation3D

Rotation3D IMP::algebra::get_rotation_about_normalized_axis	(	const Vector3D &	axis_norm,
		double	angle
	)

Generate a Rotation3D object from a rotation around an axis that is assumed to be normalized

Parameters

[in]	axis_norm	the normalized rotation axis passing through (0,0,0)
[in]	angle	the rotation angle in radians in the clockwise direction

Note: http://en.wikipedia.org/wiki/Rotation_matrix; www.euclideanspace.com/maths/geometry/rotations/conversions/ angleToQuaternion/index.htm See Rotation3D

Transformation3D IMP::algebra::get_rotation_about_point	(	const Vector3D &	point,
		const Rotation3D &	rotation
	)

Rotate about a point rather than the origin.

Parameters

[in]	point	Center to rotate about
[in]	rotation	The rotation to perform

See Transformation3D

Definition at line 100 of file Transformation3D.h.

Transformation2D IMP::algebra::get_rotation_about_point	(	const Vector2D &	point,
		const Rotation2D &	rotation
	)

Generates a Transformation2D to rotate about a point rather than the origin.

Parameters

[in]	point	Center to rotate about
[in]	rotation	The rotation to perform (defined taking the origin as reference, not the new point). See Transformation2D

Definition at line 135 of file Transformation2D.h.

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Rotation3D IMP::algebra::get_rotation_from_fixed_xyz	(	double	xr,
		double	yr,
		double	zr
	)

Parameters

[in]	xr	Rotation around the X axis in radians
[in]	yr	Rotation around the Y axis in radians
[in]	zr	Rotation around the Z axis in radians

Note: The three rotations are represented in the original (fixed) coordinate frame. See Rotation3D See FixedXYZ

Rotation3D IMP::algebra::get_rotation_from_fixed_zxz	(	double	phi,
		double	theta,
		double	psi
	)

Parameters

[in]	phi	Rotation around the Z axis in radians
[in]	theta	Rotation around the X axis in radians
[in]	psi	Rotation around the Z axis in radians

Note: The first rotation is by an angle phi about the z-axis. The second rotation is by an angle theta in [0,pi] about the former x-axis , and the third rotation is by an angle psi about the former z-axis. See Rotation3D

Rotation3D IMP::algebra::get_rotation_from_fixed_zyz	(	double	Rot,
		double	Tilt,
		double	Psi
	)

Note: The first rotation is by an angle about the z-axis. The second rotation is by an angle about the new y-axis. The third rotation is by an angle about the new z-axis.

Parameters

[in]	Rot	First Euler angle (radians) defining the rotation (Z axis)
[in]	Tilt	Second Euler angle (radians) defining the rotation (Y axis)
[in]	Psi	Third Euler angle (radians) defining the rotation (Z axis) See Rotation3D

Rotation3D IMP::algebra::get_rotation_from_matrix	(	double	m00,
		double	m01,
		double	m02,
		double	m10,
		double	m11,
		double	m12,
		double	m20,
		double	m21,
		double	m22
	)

See Rotation3D

Rotation3D IMP::algebra::get_rotation_from_matrix ( IMP_Eigen::Matrix3d m )

See Rotation3D

Rotation3D IMP::algebra::get_rotation_from_vector4d ( const VectorD< 4 > & v )

See Rotation3D

Definition at line 341 of file Rotation3D.h.

Rotation3D IMP::algebra::get_rotation_from_x_y_axes	(	const Vector3D &	x,
		const Vector3D &	y
	)

Return the rotation which takes the native x and y axes to the given x and y axes. The two axis must be perpendicular unit vectors.

Rotation3D IMP::algebra::get_rotation_taking_first_to_second	(	const Vector3D &	v1,
		const Vector3D &	v2
	)

See Rotation3D

Rotation2D IMP::algebra::get_rotation_to_x_axis ( const Vector2D & v )

Builds the rotation that transforms the vector X of the origin of coordinates into the given vector

Definition at line 100 of file Rotation2D.h.

template<typename T >

int IMP::algebra::get_rounded ( const T & x )

The result is of type integer but the argument can be of any type. Some examples:

a = round(-0.7); // a = -1
a = round(-0.2); // a = 0
a = round(0.2); // a = 0
a = round(0.7); // a = 1

Definition at line 43 of file algebra/utility.h.

const Segment3D& IMP::algebra::get_segment_3d_geometry ( const Segment3D & g )

See Segment3D

Definition at line 51 of file Segment3D.h.

Segment3D IMP::algebra::get_shortest_segment	(	const Segment3D &	s,
		const Vector3D &	p
	)

See Segment3D See Vector3D

Segment3D IMP::algebra::get_shortest_segment	(	const Segment3D &	sa,
		const Segment3D &	sb
	)

See Segment3D

Sphere3Ds IMP::algebra::get_simplified_from_volume	(	Sphere3Ds	in,
		double	maximum_allowed_error_angstroms
	)

Return a set of balls that approximates the surface of the passed set within the error tolerance.

The any point in the old surface will be within roughly maximum_allowed_error_angstroms of a point in the new surface and any point outside the old volume will be within roughly maximum_allowed_error_angstroms of a point outside the new volume.

Note: The name may change if someone thinks up a better one.

template<int D>

const SphereD<D>& IMP::algebra::get_sphere_d_geometry ( const SphereD< D > & g )

See Sphere

Definition at line 89 of file SphereD.h.

const SpherePatch3D& IMP::algebra::get_sphere_patch_3d_geometry ( const SpherePatch3D & g )

See SpherePatch3D

Definition at line 50 of file SpherePatch3D.h.

template<int D>

double IMP::algebra::get_squared_distance	(	const VectorD< D > &	v1,
		const VectorD< D > &	v2
	)

See VectorD

Definition at line 201 of file VectorD.h.

double IMP::algebra::get_surface_area ( const Cone3D & g )

See Cone3D

Definition at line 62 of file Cone3D.h.

double IMP::algebra::get_surface_area ( const Ellipsoid3D & g )

See Ellipsoid3D

Definition at line 65 of file Ellipsoid3D.h.

double IMP::algebra::get_surface_area ( const Cylinder3D & g )

See Cylinder3D

Definition at line 77 of file Cylinder3D.h.

double IMP::algebra::get_surface_area ( const SphereD< 3 > & g )

See Sphere

Definition at line 89 of file SphereD.h.

double IMP::algebra::get_surface_area ( const BoundingBoxD< 3 > & g )

See BoundingBox

Definition at line 160 of file BoundingBoxD.h.

FloatPair IMP::algebra::get_surface_area_and_volume ( const algebra::Sphere3Ds & ss )

Return the surface area and volume of the union of the balls bounded by the spheres. This method requires CGAL to work.

Transformation3D IMP::algebra::get_transformation_3d ( const Transformation2D & t2d )

Note: The 3D transformation is built with the 2D rotation becoming a rotation around the z axis.

template<class Vector3DsOrXYZs0 , class Vector3DsOrXYZs1 >

IMP::algebra::Transformation3D IMP::algebra::get_transformation_aligning_first_to_second	(	const Vector3DsOrXYZs0 &	source,
		const Vector3DsOrXYZs1 &	target
	)

The points are assumed to be corresponding (that is, from[0] is aligned to to[0] etc.). The alignment computed is that which minimized the sum of squared distances between corresponding points. Return the

\[ \textit{argmin}_T \sum \left|T\left(f\left[i\right]\right)-t[i]\right|^2 \]

If the point sets lie in a 1 or 2 dimensional subspace, the alignment algorithm is unstable and not guaranteed to work. A warning is printed in this case.

See generic geometry for more information.

See Transformation3D

See Also: Vector3D

Definition at line 42 of file geometric_alignment.h.

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Transformation3D IMP::algebra::get_transformation_aligning_first_to_second	(	Vector3Ds	a,
		Vector3Ds	b
	)

Equivalent to

IMP::algebra::get_transformation_aligning_first_to_second(a,b);

Transformation2D IMP::algebra::get_transformation_aligning_pair	(	const Vector2Ds &	set_from,
		const Vector2Ds &	set_to
	)

Builds the transformation required to obtain a set of points from the first one

Note: The function assumes that the relative distances between points are conserved.

template<class Storage , class Embedding >

const Storage::Value IMP::algebra::get_trilinearly_interpolated	(	const GridD< 3, Storage, typename Storage::Value, Embedding > &	g,
		const Vector3D &	v,
		const typename Storage::Value &	outside = `0`
	)

The voxel values are assumed to be at the center of the voxel and the passed outside value is used for voxels outside the grid. The type Voxel must support get_linearly_interpolated().

See Also: get_linearly_interpolated() See GridD

Definition at line 36 of file grid_utility.h.

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Rotation3Ds IMP::algebra::get_uniform_cover_rotations_3d ( unsigned int num_points )

If you care about the distance between samples instead of the number of samples, the "surface area" of the set of rotations is pi^2. If you allocate each sample a volume of 4/3 pi d^3 (to space them d apart), Then you want 3/4 pi/d^3 points.

Creates at least num_points rotations.

template<int D>

base::Vector<VectorD<D> > IMP::algebra::get_uniform_surface_cover	(	const SphereD< D > &	s,
		unsigned int	n
	)

The function is currently pretty slow, especially in non-optimized builds. Complain if this bugs you. We might be able to do better, at least in 3D.

Creates at least the requested number of points.

Note: This predicates will produce guaranteed correct results if IMP.cgal is available (the results will be unreliable if it is not).

See VectorD See SphereD

Definition at line 116 of file vector_generators.h.

Vector3Ds IMP::algebra::get_uniform_surface_cover	(	const Cylinder3D &	cyl,
		int	number_of_points
	)

See VectorD See Cylinder3D

Vector3Ds IMP::algebra::get_uniform_surface_cover	(	const SpherePatch3D &	sph,
		unsigned int	number_of_points
	)

Note: the implementation can be improved See SpherePatch3D See VectorD

Vector3Ds IMP::algebra::get_uniform_surface_cover	(	const Cone3D &	cone,
		unsigned int	number_of_points
	)

See VectorD See Cone3D

Vector3Ds IMP::algebra::get_uniform_surface_cover	(	const Sphere3Ds &	in,
		double	points_per_square_angstrom
	)

Return a cover of the surface of the volume defined by a union of balls bounded by the spheres.

This is effectively a sampling of the solvent exposed surface of a set of spheres. The density of points has approximately the passed value.

This method is much faster than get_connolly_surface().

template<int D>

base::Vector<VectorD<D> > IMP::algebra::get_uniform_upper_hemisphere_cover	(	const SphereD< D > &	s,
		unsigned int	n
	)

The points all lie on the upper hemisphere, eg, all their z coordinates are greater than those of the center of the sphere.

Definition at line 134 of file vector_generators.h.

algebra::Rotation3Ds IMP::algebra::get_uniformly_sampled_rotations ( double delta )

Parameters

[in] delta sample every delta angles in radians.

template<int D>

BoundingBoxD<D> IMP::algebra::get_union	(	BoundingBoxD< D >	a,
		const BoundingBoxD< D > &	b
	)

This is the same as doing a+b. See BoundingBoxD

Definition at line 236 of file BoundingBoxD.h.

template<unsigned int D>

BoundingBoxD<D> IMP::algebra::get_unit_bounding_box_d ( )

See BoundingBoxD

Definition at line 165 of file BoundingBoxD.h.

BoundingBoxD<-1> IMP::algebra::get_unit_bounding_box_kd ( unsigned int d )

See BoundingBoxD

Definition at line 171 of file BoundingBoxD.h.

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template<class VT >

VT IMP::algebra::get_unit_vector ( VT vt )

Returns a unit vector pointing at the same direction as this vector.

Note: If the magnitude of this vector is smaller than 1e-12 (an arbitrarily selected small number), returns a unit vector pointing at a random direction

Definition at line 242 of file VectorBaseD.h.

template<class C >

const VectorD<C::DIMENSION>& IMP::algebra::get_vector_geometry ( const C & g )

See VectorD See generic geometry for more information.

Definition at line 418 of file VectorD.h.

Vector3D IMP::algebra::get_vector_product	(	const Vector3D &	p1,
		const Vector3D &	p2
	)

See Vector3D

Definition at line 31 of file Vector3D.h.

template<int D>

base::Vector<VectorD<D> > IMP::algebra::get_vertices ( const BoundingBoxD< D > & bb )

See BoundingBoxD

Definition at line 256 of file BoundingBoxD.h.

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double IMP::algebra::get_volume ( const Cone3D & g )

See Cone3D

Definition at line 62 of file Cone3D.h.

double IMP::algebra::get_volume ( const Ellipsoid3D & g )

See Ellipsoid3D

Definition at line 65 of file Ellipsoid3D.h.

double IMP::algebra::get_volume ( const Cylinder3D & g )

See Cylinder3D

Definition at line 77 of file Cylinder3D.h.

double IMP::algebra::get_volume ( const SphereD< 3 > & g )

See Sphere

Definition at line 89 of file SphereD.h.

template<int D>

double IMP::algebra::get_volume ( const BoundingBoxD< D > & bb )

See BoundingBoxD

Definition at line 147 of file BoundingBoxD.h.

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double IMP::algebra::get_volume ( const BoundingBoxD< 3 > & g )

See BoundingBox

Definition at line 160 of file BoundingBoxD.h.

template<int D>

VectorD<D> IMP::algebra::operator*	(	double	s,
		VectorD< D >	o
	)

See VectorD

Definition at line 193 of file VectorD.h.

Vector3Ds IMP::algebra::read_pts ( base::TextInput input )

See Also: write_pts See VectorD

Sphere3Ds IMP::algebra::read_spheres ( base::TextInput input )

See Also: write_pts See SphereD

void IMP::algebra::reversed_read	(	void *	dest,
		size_t	size,
		size_t	nitems,
		std::ifstream &	f,
		bool	reverse
	)

If the reverse parameter is true, the data will be read in reverse order.

void IMP::algebra::reversed_write	(	const void *	src,
		size_t	size,
		size_t	nitems,
		std::ofstream &	f,
		bool	reverse = `false`
	)

This function is the same as fread from C, but at the end there is a flag saying if data should be read in reverse order or not.

If the reverse parameter is true, the data will be written in reverse order.

template<int D>

void IMP::algebra::set_bounding_box_d_geometry	(	BoundingBoxD< D > &	g,
		const BoundingBoxD< D > &	v
	)

See BoundingBox

Definition at line 160 of file BoundingBoxD.h.

void IMP::algebra::set_cone_3d_geometry	(	Cone3D &	g,
		const Cone3D &	v
	)

See Cone3D

Definition at line 62 of file Cone3D.h.

void IMP::algebra::set_cylinder_3d_geometry	(	Cylinder3D &	g,
		const Cylinder3D &	v
	)

See Cylinder3D

Definition at line 77 of file Cylinder3D.h.

void IMP::algebra::set_ellipsoid_3d_geometry	(	Ellipsoid3D &	g,
		const Ellipsoid3D &	v
	)

See Ellipsoid3D

Definition at line 65 of file Ellipsoid3D.h.

void IMP::algebra::set_plane_3d_geometry	(	Plane3D &	g,
		const Plane3D &	v
	)

See Plane3D

Definition at line 82 of file Plane3D.h.

template<int D>

void IMP::algebra::set_sphere_d_geometry	(	SphereD< D > &	g,
		const SphereD< D > &	v
	)

See Sphere

Definition at line 89 of file SphereD.h.

void IMP::algebra::set_sphere_patch_3d_geometry	(	SpherePatch3D &	g,
		const SpherePatch3D &	v
	)

See SpherePatch3D

Definition at line 50 of file SpherePatch3D.h.

template<class C , class E >

void IMP::algebra::set_vector_geometry	(	C &	g,
		const E &	v
	)

See VectorD See generic geometry for more information.

Definition at line 423 of file VectorD.h.

void IMP::algebra::write_pts	(	const Vector3Ds &	vs,
		base::TextOutput	out
	)

See Also: read_pts See VectorD

void IMP::algebra::write_spheres	(	const Sphere3Ds &	vs,
		base::TextOutput	out
	)

See Also: read_pts See SphereD

Classes

Typedefs

Functions

Variables

Standard module methods

Endian

Simple geometric IO

Python Only

Euler Angles

Shortest segments

3D Vectors

Vector Generators

Norms

Typedef Documentation

Function Documentation