General purpose algebraic and geometric methods that are expected to be used by a wide variety of IMP modules. More...

Detailed Description

General purpose algebraic and geometric methods that are expected to be used by a wide variety of IMP modules.

Geometric primitives

IMP has a number of geometric primitives. They support the following namespace functions as appropriate

In addition, they cannot be compared against one another due to floating point implementation issues (eg Vector3D v=v2 does not imply v==v2).

Geometric primitives are not put into a defined state by their constructor. Such classes mimic POD types (int, float etc) in C++ and are optimized for efficiency. All operations on a default initialized instance other than assigning to it from a non-default initialized instance should be assumed to be invalid.

Geometry and dimensions

Many of the geometric primitives and operations in IMP are written to work in any dimension. In C++, this is implemented via templates (such as IMP::algebra::VectorD). In the Python side, the different dimensions are named explicitly instead. That means, a 2-D point is IMP::algebra::VectorD<2> in C++, and IMP::algebra::Vector2D in Python and the function IMP::algebra::get_basis_vector_d<3>() in C++ becomes IMP.algebra.get_basis_vector_3d() in Python. Similarly, a collection of 2D points is IMP::Vector<IMP::algebra::VectorD<2> > in C++ and IMP.algebra.Vector2Ds in Python, which as with all collections, look like Python lists. For convenience, we provide typedefs in C++ to the IMP::algebra::Vector2D and IMP::algebra::Vector2Ds style names.

Generic geometry

Geometry in IMP can be stored in a variety of ways. For example, a point in 3D can be stored using an IMP::algebra::VectorD<3> or using an IMP::core::XYZ particle. It is often useful to be able to write algorithms that work on sets of points without worrying how they are stored, the Generic Geometry layer provides that. It works using a set of functions get_vector_3d() and set_vector_3d() which manipulate the geometry in terms of the IMP::algebra representation of the geometry in question. That is, get_vector_3d() returns a IMP::algebra::VectorD<3> for both an IMP::algebra::Vector3D and a IMP::core::XYZ. Algorithms take their arguments as C++ templates and use the generic geometry methods to manipulate the geometry. And versions of the function for both types of storage are exported to Python, so one could also write generic functions in Python.

For example, IMP::atom::get_rmsd() takes any combination of IMP::algebra::Vector3Ds or IMP::core::XYZs or IMP::core::XYZsTemp as arguments. Versions for all combinations of those are exported to Python.

ANN

ANN is a library implementing fast nearest neighbor searches. Certain data structures will be faster if it is installed. While compilation of the library from source is quite straightforward, it is not available as a package for common platforms. In addition, ANN must be built as a shared library rather than a static library.

Eigen

We ship a copy of Eigen as part of IMP as Eigen support varies quite considerably across platforms and it is header-only and so easy to ship. Our version of Eigen has been patched to move everything to the IMP_Eigen namespace and preprocessor symbols to start with IMP_EIGEN_ so that things do not conflict with system installs of Eigen.

Info

Author(s): Daniel Russel, Keren Lasker, Ben Webb, Javier Angel Velázquez-Muriel

Maintainer: benmwebb

License: LGPL This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

Publications:

See main IMP papers list.

Classes
class	BoundedGridRangeD

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

class	Cone3D
	Represent a cone in 3D. More...

class	ConnollySurfacePoint
	Represent a point on the Connolly surface. More...

class	Cylinder3D
	Represent a cylinder in 3D. More...

class	DefaultEmbeddingD
	Embed a grid as an evenly spaced axis aligned grid. More...

struct	DenseFloatLogGridKD

struct	DenseGrid3D
	A dense grid of values. More...

class	DenseGridStorageD

struct	DenseIntLogGrid3D

class	DynamicNearestNeighbor3D
	Provide an incremental nearest neighbor search function. More...

class	Ellipsoid3D
	Represent an ellipsoid in 3D. More...

class	EuclideanVectorKDMetric
	The l2 norm on the distance vector. More...

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

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

class	Gaussian3D
	A Gaussian distribution in 3D. More...

class	GeometricPrimitiveD
	Base class for geometric types. More...

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

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

class	Line3D
	Simple implementation of lines in 3D. More...

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

class	LogEmbeddingD

class	MaxVectorKDMetric

class	NearestNeighborD
	Build a structure for finding nearest neighbors. More...

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

class	Plane3D
	Represent a plane in 3D. More...

class	PrincipalComponentAnalysisD
	Represent an eigen analysis of some data. More...

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

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

class	Rotation2D
	Represent a rotation in 2D space. More...

class	Rotation3D
	3D rotation class. More...

class	Segment3D
	Simple implementation of segments in 3D. More...

struct	SparseGrid3D
	A sparse grid of values. More...

class	SparseGridStorageD

struct	SparseUnboundedGrid3D
	A sparse, infinite grid of values. More...

struct	SparseUnboundedGridD
	A sparse, infinite grid of values. More...

class	SphereD
	Represent a sphere in D-dimensions. More...

class	SpherePatch3D
	A sphere patch is defined as all points above the plane and on the sphere. More...

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

class	Torus3D
	Represent a torus in 3D. More...

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

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

class	Triangle3D
	Represent a triangle in 3D. More...

class	UnboundedGridRangeD

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

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

class	VectorKDMetric
	The base class for a metric on VectorKDs. More...

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

typedef BoundingBoxD< 1 >	BoundingBox1D
	Typedef for Python. More...

typedef IMP::Vector < BoundingBox1D >	BoundingBox1Ds

typedef BoundingBoxD< 2 >	BoundingBox2D
	Typedef for Python. More...

typedef IMP::Vector < BoundingBox2D >	BoundingBox2Ds

typedef BoundingBoxD< 3 >	BoundingBox3D
	Typedef for Python. More...

typedef IMP::Vector < BoundingBox3D >	BoundingBox3Ds

typedef BoundingBoxD< 4 >	BoundingBox4D
	Typedef for Python. More...

typedef IMP::Vector < BoundingBox4D >	BoundingBox4Ds

typedef BoundingBoxD< 5 >	BoundingBox5D
	Typedef for Python. More...

typedef IMP::Vector < BoundingBox5D >	BoundingBox5Ds

typedef BoundingBoxD< 6 >	BoundingBox6D
	Typedef for Python. More...

typedef IMP::Vector < BoundingBox6D >	BoundingBox6Ds

typedef BoundingBoxD<-1 >	BoundingBoxKD
	Typedef for Python. More...

typedef IMP::Vector < BoundingBoxKD >	BoundingBoxKDs

typedef IMP::Vector< Cone3D >	Cone3Ds

typedef IMP::Vector < ConnollySurfacePoint >	ConnollySurfacePoints

typedef IMP::Vector< Cylinder3D >	Cylinder3Ds

typedef IMP::Vector< Ellipsoid3D >	Ellipsoid3Ds

typedef IMP::Vector< Gaussian3D >	Gaussian3Ds

typedef IMP::Vector< Line3D >	Line3Ds

typedef IMP::Vector< LinearFit2D >	LinearFit2Ds

typedef IMP::Vector < ParabolicFit2D >	ParabolicFit2Ds

typedef IMP::Vector< Plane3D >	Plane3Ds

typedef IMP::Vector < ReferenceFrame3D >	ReferenceFrame3Ds

typedef IMP::Vector< Reflection3D >	Reflection3Ds

typedef IMP::Vector< Rotation2D >	Rotation2Ds

typedef IMP::Vector< Rotation3D >	Rotation3Ds

typedef IMP::Vector< Segment3D >	Segment3Ds

typedef SphereD< 1 >	Sphere1D
	Typedef for Python. More...

typedef IMP::Vector< Sphere1D >	Sphere1Ds

typedef SphereD< 2 >	Sphere2D
	Typedef for Python. More...

typedef IMP::Vector< Sphere2D >	Sphere2Ds

typedef SphereD< 3 >	Sphere3D
	Typedef for Python. More...

typedef IMP::Vector< Sphere3D >	Sphere3Ds

typedef SphereD< 4 >	Sphere4D
	Typedef for Python. More...

typedef IMP::Vector< Sphere4D >	Sphere4Ds

typedef SphereD< 5 >	Sphere5D
	Typedef for Python. More...

typedef IMP::Vector< Sphere5D >	Sphere5Ds

typedef SphereD< 6 >	Sphere6D
	Typedef for Python. More...

typedef IMP::Vector< Sphere6D >	Sphere6Ds

typedef SphereD<-1 >	SphereKD
	Typedef for Python. More...

typedef IMP::Vector< SphereKD >	SphereKDs

typedef IMP::Vector < SpherePatch3D >	SpherePatch3Ds

typedef IMP::Vector < SphericalVector3D >	SphericalVector3Ds

typedef IMP::Vector< Torus3D >	Torus3Ds

typedef IMP::Vector < Transformation2D >	Transformation2Ds

typedef IMP::Vector < Transformation3D >	Transformation3Ds

typedef IMP::Vector< Triangle3D >	Triangle3Ds

typedef VectorD< 1 >	Vector1D

typedef Vector< VectorD< 1 > >	Vector1Ds

typedef VectorD< 2 >	Vector2D

typedef Vector< VectorD< 2 > >	Vector2Ds

typedef VectorD< 3 >	Vector3D

typedef Vector< VectorD< 3 > >	Vector3Ds

typedef VectorD< 4 >	Vector4D

typedef Vector< VectorD< 4 > >	Vector4Ds

typedef VectorD< 5 >	Vector5D

typedef Vector< VectorD< 5 > >	Vector5Ds

typedef VectorD< 6 >	Vector6D

typedef Vector< VectorD< 6 > >	Vector6Ds

typedef VectorD<-1 >	VectorKD

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

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

typedef 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)
	Get all alignments of the first principal component system to the second one. More...

double	get_angle (const Line3D &a, const Line3D &b)
	Get angle in radians between two lines around their closest points. More...

bool	get_are_almost_equal (const double a, const double b, const double epsilon)
	Compare two values for "almost equal" (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. More...

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

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. More...

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

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

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

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)
	Constrain a value between two given limits. More...

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...

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

double	get_distance (const Line3D &s, const Vector3D &p)
	Get closest distance between a line and a point. More...

double	get_distance (const Line3D &a, const Line3D &b)
	Get the closest distance between two lines. 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)
	Return the vector that is the elementwise product of the two. More...

template<int D>
VectorD< D >	get_elementwise_product (const Ints &a, const algebra::VectorD< D > &b)
	Return the vector that is the elementwise product of the two. More...

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 vectors. More...

Gaussian3D	get_gaussian_from_covariance (const IMP_Eigen::Matrix3d &covariance, const Vector3D &center)
	Return a Gaussian centered at the origin from a covariance matrix. More...

Rotation2D	get_identity_rotation_2d ()
	Build an identity rotation in 2D. More...

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

Transformation2D	get_identity_transformation_2d ()
	Return 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 intersect. 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)
	Get the value from the grid with linear interpolation. More...

template<class VT >
double	get_magnitude_and_normalize_in_place (VT &vt)
	Returns the magnitude of vt and turns it to a unit vector in place. More...

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. More...

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

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

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

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 Vector< VectorD< D > > &ps)
	Perform principal components analysis on a set of vectors. More...

Vector3D	get_projected (const Line3D &l, const Vector3D &p)
	Project a point onto the line. More...

algebra::Segment3D	get_projected (const Line3D &l, const algebra::Segment3D &s)
	Project a segment onto a line. 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 ()
	Build an identity rotation in 2D. More...

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< double >	get_rasterized (const Gaussian3Ds &gmm, const Floats &weights, double cell_width, const BoundingBox3D &bb)
	Rasterize the Gaussians to a grid. More...

DenseGrid3D< double >	get_rasterized_fast (const Gaussian3Ds &gmm, const Floats &weights, double cell_width, const BoundingBox3D &bb, double factor=2.5)
	Rasterize the Gaussians to a grid. More...

Vector3D	get_reflected (const Plane3D &pln, const Vector3D &p)
	Return the point reflected about the plane. More...

double	get_relative_projection_on_segment (const Segment3D &s, const algebra::Vector3D &p)
	Return the 'relative' projection of a point p onto the line that contains s. More...

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)
	Generate 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 rotation 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...

algebra::Segment3D	get_segment_connecting_first_to_second (const Line3D &a, const Line3D &b)
	Get shortest possible segment from the first line to the second. More...

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. More...

Sphere3Ds	get_simplified_from_volume (Sphere3Ds in, double maximum_allowed_error_angstroms)
	Get a set of balls that approximates the surface of the passed set. More...

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...

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

FloatPair	get_surface_area_and_volume (const algebra::Sphere3Ds &ss)
	Get surface area & volume of the union of the balls bounded by the spheres. More...

Transformation3D	get_transformation_3d (const Transformation2D &t2d)
	Build 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. More...

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. More...

algebra::Line3D	get_transformed (const algebra::Line3D &l, const Transformation3D &tr)

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

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>
Vector< VectorD< D > >	get_vertices (const BoundingBoxD< D > &bb)
	Return a list of the 2^D bounding points for the bounding box. More...

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

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

template<class Vector3DsOrXYZs0 , class Vector3DsOrXYZs1 >
double	get_weighted_rmsd (const Vector3DsOrXYZs0 &m1, const Vector3DsOrXYZs1 &m2, const Floats &weights)

template<class Vector3DsOrXYZs0 , class Vector3DsOrXYZs1 >
double	get_weighted_rmsd_transforming_first (const Transformation3D &tr, const Vector3DsOrXYZs0 &m1, const Vector3DsOrXYZs1 &m2, const Floats &weights)

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

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

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

void	set_line_3d_geometry (Line3D &g, const Line3D &gi)

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

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

Variables
static const double	PI = 3.1415926535897931
	the constant pi More...

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

std::string	get_module_name ()

std::string	get_data_path (std::string file_name)
	Return the full path to one of this module's data files. More...

std::string	get_example_path (std::string file_name)
	Return the full path to one of this module's example files. More...

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...

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

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

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, TextOutput out)
	Write a set of 3D vectors to a file. More...

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

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

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

Python Only
The following functions are only available 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::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)
	Return 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)
	Return 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>
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>
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>
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 176 of file BoundingBoxD.h.

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

Pass or store a set of BoundingBox1D .

Definition at line 176 of file BoundingBoxD.h.

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

Typedef for Python.

Definition at line 176 of file BoundingBoxD.h.

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

Pass or store a set of BoundingBox2D .

Definition at line 176 of file BoundingBoxD.h.

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

Typedef for Python.

Definition at line 176 of file BoundingBoxD.h.

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

Pass or store a set of BoundingBox3D .

Definition at line 176 of file BoundingBoxD.h.

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

Typedef for Python.

Definition at line 176 of file BoundingBoxD.h.

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

Pass or store a set of BoundingBox4D .

Definition at line 176 of file BoundingBoxD.h.

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

Typedef for Python.

Definition at line 176 of file BoundingBoxD.h.

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

Pass or store a set of BoundingBox5D .

Definition at line 176 of file BoundingBoxD.h.

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

Typedef for Python.

Definition at line 176 of file BoundingBoxD.h.

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

Pass or store a set of BoundingBox6D .

Definition at line 176 of file BoundingBoxD.h.

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

Typedef for Python.

Definition at line 176 of file BoundingBoxD.h.

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

Pass or store a set of BoundingBoxKD .

Definition at line 176 of file BoundingBoxD.h.

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

Pass or store a set of Cone3D .

Definition at line 64 of file Cone3D.h.

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

Pass or store a set of ConnollySurfacePoint .

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

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

Pass or store a set of Cylinder3D .

Definition at line 78 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::Vector< Ellipsoid3D > IMP::algebra::Ellipsoid3Ds

Pass or store a set of Ellipsoid3D .

Definition at line 46 of file Ellipsoid3D.h.

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

Pass or store a set of FixedXYZ .

Definition at line 465 of file Rotation3D.h.

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

Pass or store a set of Gaussian3D .

Definition at line 43 of file Gaussian3D.h.

typedef IMP::Vector< Line3D > IMP::algebra::Line3Ds

Pass or store a set of Line3D .

Definition at line 70 of file Line3D.h.

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

Pass or store a set of LinearFit2D .

Definition at line 52 of file LinearFit.h.

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

Pass or store a set of ParabolicFit2D .

Definition at line 54 of file ParabolicFit.h.

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

Pass or store a set of Plane3D .

Definition at line 78 of file Plane3D.h.

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

Pass or store a set of ReferenceFrame3D .

Definition at line 82 of file ReferenceFrame3D.h.

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

Pass or store a set of Reflection3D .

Definition at line 32 of file Reflection3D.h.

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

Pass or store a set of Rotation2D .

Definition at line 114 of file Rotation2D.h.

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

Pass or store a set of Rotation3D .

Definition at line 240 of file Rotation3D.h.

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

Pass or store a set of Segment3D .

Definition at line 46 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 88 of file SphereD.h.

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

Pass or store a set of Sphere1D .

Definition at line 88 of file SphereD.h.

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

Typedef for Python.

Definition at line 88 of file SphereD.h.

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

Pass or store a set of Sphere2D .

Definition at line 88 of file SphereD.h.

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

Typedef for Python.

Definition at line 88 of file SphereD.h.

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

Pass or store a set of Sphere3D .

Definition at line 88 of file SphereD.h.

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

Typedef for Python.

Definition at line 88 of file SphereD.h.

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

Pass or store a set of Sphere4D .

Definition at line 88 of file SphereD.h.

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

Typedef for Python.

Definition at line 88 of file SphereD.h.

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

Pass or store a set of Sphere5D .

Definition at line 88 of file SphereD.h.

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

Typedef for Python.

Definition at line 88 of file SphereD.h.

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

Pass or store a set of Sphere6D .

Definition at line 88 of file SphereD.h.

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

Typedef for Python.

Definition at line 88 of file SphereD.h.

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

Pass or store a set of SphereKD .

Definition at line 88 of file SphereD.h.

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

Pass or store a set of SpherePatch3D .

Definition at line 48 of file SpherePatch3D.h.

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

Pass or store a set of SphericalVector3D .

Definition at line 78 of file SphericalVector3D.h.

typedef IMP::Vector< Torus3D > IMP::algebra::Torus3Ds

Pass or store a set of Torus3D .

Definition at line 61 of file Torus3D.h.

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

Pass or store a set of Transformation2D .

Definition at line 118 of file Transformation2D.h.

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

Pass or store a set of Transformation3D .

Definition at line 98 of file Transformation3D.h.

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

A vector of reference-counting object pointers.

Definition at line 31 of file vector_metrics.h.

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

A vector of weak (non reference-counting) pointers to specified objects.

See Also: VectorKDMetric

Definition at line 31 of file vector_metrics.h.

typedef 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
	)

lexicographic comparison of two vectors

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

See Also: VectorD

Definition at line 179 of file VectorD.h.

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

Compose two rotations a and 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
	)

Compose two transformations.

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

See Also: Transformation3D

Definition at line 122 of file Transformation3D.h.

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

Compose two transformations.

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

See Also: Transformation2D

Definition at line 144 of file Transformation2D.h.

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

See Also: Rotation3D

Definition at line 383 of file Rotation3D.h.

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

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

double IMP::algebra::get_angle	(	const Line3D &	a,
		const Line3D &	b
	)

Get angle in radians between two lines around their closest points.

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

Compare two values for "almost equal" (intended for doubles)

epsilon is the tolerance allowed to consider the values as equal

Definition at line 107 of file algebra/utility.h.

bool IMP::algebra::get_are_colinear	(	const Vector3D &	p1,
		const Vector3D &	p2,
		const Vector3D &	p3
	)

Return true if the three points are co-linear.

template<class Geometry >

double IMP::algebra::get_area ( const Geometry & )

Compute the area of any surface object.

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 Also: Rotation3D

Returns: axis direction and rotation about the axis in Radians

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

Return the radius of a sphere with a given volume.

See Also: 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 basis vector for the given 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 Also: VectorD

Definition at line 222 of file VectorD.h.

VectorD<-1> IMP::algebra::get_basis_vector_kd	(	int	D,
		unsigned int	coordinate
	)

Return a dynamically sized basis vector.

Definition at line 235 of file VectorD.h.

template<class Geometry >

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

Compute the bounding box of any geometric object.

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

Return the centroid of a set of vectors.

See Also: Vector3D

Definition at line 68 of file Vector3D.h.

double IMP::algebra::get_closer_power_of_2 ( double x )

Closest power of 2 for a number, not necessarily higher.

Definition at line 90 of file algebra/utility.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.

template<typename T >

T IMP::algebra::get_constrained	(	const T	x,
		const T	x0,
		const T	xF
	)

Constrain a value between two given limits.

Definition at line 65 of file algebra/utility.h.

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 )

Cube with radius of length radius.

See Also: BoundingBoxD

Definition at line 194 of file BoundingBoxD.h.

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

Cube with radius of length side.

See Also: BoundingBoxD

Definition at line 201 of file BoundingBoxD.h.

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

Return the full path to one of this module's data files.

To read the data file "data_library" that was placed in the data directory of this module, do something like

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

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

Note: Each module has its own data directory, so be sure to use this function from the correct module.

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

Get the distance between a segment and a point.

See Also: Segment3D

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

Return the distance between a plane and a point in 3D.

See Also: Plane3D

Definition at line 63 of file Plane3D.h.

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

Get the distance between two segments.

See Also: Segment3D

double IMP::algebra::get_distance	(	const Line3D &	s,
		const Vector3D &	p
	)

Get closest distance between a line and a point.

Examples:: grid.cpp.

double IMP::algebra::get_distance	(	const Line3D &	a,
		const Line3D &	b
	)

Get the closest distance between two lines.

template<int D>

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

Return the distance between the two spheres if they are disjoint.

If they intersect, the distances are not meaningful.

See Also: SphereD

Definition at line 104 of file SphereD.h.

template<int D>

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

Compute the distance between two vectors.

See Also: VectorD

Definition at line 209 of file VectorD.h.

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

Return a distance between the two rotations.

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 Also: Rotation3D

Definition at line 258 of file Rotation3D.h.

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

Return the edges of the box as indices into the vertices list.

See Also: BoundingBoxD

Definition at line 307 of file BoundingBoxD.h.

template<int D>

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

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

See Also: VectorD

Definition at line 431 of file VectorD.h.

template<int D>

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

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

See Also: VectorD

Definition at line 443 of file VectorD.h.

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

Return a sphere containing the listed spheres.

See Also: Sphere3D

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

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

Return a sphere containing the listed vectors.

See Also: Sphere3D; Vector3D

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

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

Return the full path to one of this module's example files.

To read the example file "example_protein.pdb" that was placed in the examples directory of this module, do something like

std::ifstream in(IMP::algebra::get_example_path("example_protein.pdb"));

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

Note: Each module has its own example directory, so be sure to use this function from the correct module.

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

The inverse of rotation_from_fixed_xyz()

See Also: rotation_from_fixed_xyz(); Rotation3D; 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>

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
	)

Generate a grid of 3d points on a cylinder surface.

See Also: Vector3D; Cylinder3D

Rotation2D IMP::algebra::get_identity_rotation_2d ( )

Build an identity rotation in 2D.

Definition at line 90 of file Rotation2D.h.

Rotation3D IMP::algebra::get_identity_rotation_3d ( )

Return a rotation that does not do anything.

See Also: Rotation3D

Definition at line 244 of file Rotation3D.h.

Transformation2D IMP::algebra::get_identity_transformation_2d ( )

Return a transformation that does not do anything.

See Also: Transformation2D

Definition at line 123 of file Transformation2D.h.

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Transformation3D IMP::algebra::get_identity_transformation_3d ( )

Return a transformation that does not do anything.

See Also: Transformation3D

Definition at line 102 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
	)

Return true if the two balls bounded by the two spheres intersect.

See Also: SphereD

Definition at line 124 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
	)

Return true if they intersect.

See Also: BoundingBoxD

Definition at line 209 of file BoundingBoxD.h.

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

Interpolate between two rotations.

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

See Also: Rotation3D

Definition at line 480 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
	)

Return the intersecting bounding box.

See Also: BoundingBoxD

Definition at line 223 of file BoundingBoxD.h.

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bool IMP::algebra::get_is_big_endian ( )

Returns 1 if machine is big endian else 0.

bool IMP::algebra::get_is_little_endian ( )

Returns 1 if machine is little endian else 0.

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

Return the largest triangle defined by 3 points from the input.

See Also: 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<class VT >

double IMP::algebra::get_magnitude_and_normalize_in_place ( VT & vt )

Returns the magnitude of vt and turns it to a unit vector in place.

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

Definition at line 256 of file VectorBaseD.h.

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template<int D>

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

Return the maximum axis aligned extent.

See Also: BoundingBoxD

Definition at line 262 of file BoundingBoxD.h.

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float IMP::algebra::get_next_larger_power_of_2 ( float x )

Closest power of 2 that can contain a number x.

Definition at line 72 of file algebra/utility.h.

double IMP::algebra::get_next_larger_power_of_2 ( double x )

Closest power of 2 that can contain a number x.

Definition at line 81 of file algebra/utility.h.

template<int D>

VectorD<D> IMP::algebra::get_ones_vector_d ( double v = 1 )

Return a vector of ones (or another constant)

Definition at line 277 of file VectorD.h.

template<int D>

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

Return a vector of ones (or another constant)

Di must equal D.

Definition at line 289 of file VectorD.h.

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

Return a vector that is perpendicular to the given vector.

Note: This is occasionally referred to in the code as a "vertical" vector.

See Also: Vector3D

Definition at line 51 of file Vector3D.h.

template<int D>

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

Return the power distance between the two spheres.

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

See Also: SphereD

Definition at line 115 of file SphereD.h.

template<int D>

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

Perform principal components analysis on a set of vectors.

See Also: PrincipalComponentAnalysis

Definition at line 109 of file eigen_analysis.h.

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Vector3D IMP::algebra::get_projected	(	const Line3D &	l,
		const Vector3D &	p
	)

Project a point onto the line.

This is equivalent to the point on the line closest to the provided point.

algebra::Segment3D IMP::algebra::get_projected	(	const Line3D &	l,
		const algebra::Segment3D &	s
	)

Project a segment onto a line.

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

Return the radius of gyration of a set of points.

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

Definition at line 77 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()`
	)

Generate a random chain with no collisions.

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`
	)

Get a local transformation.

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

Parameters

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

Rotation2D IMP::algebra::get_random_rotation_2d ( )

Build an identity rotation in 2D.

Definition at line 93 of file Rotation2D.h.

Rotation3D IMP::algebra::get_random_rotation_3d ( )

Pick a rotation at random from all possible rotations.

See Also: Rotation3D

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

Pick a rotation at random near the provided one.

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 Also: Rotation3D

template<int D>

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

Generate a random vector in a box with uniform density.

See Also: BoundingBoxD; 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 )

Generate a random vector in a sphere with uniform density.

See Also: VectorD; 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 Also: VectorD; SphereD

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

Generate a random vector in a cylinder with uniform density.

See Also: VectorD; Cylinder3D

template<int D>

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

Generate a random vector on a box with uniform density.

See Also: BoundingBoxD; 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 )

Generate a random vector on a sphere with uniform density.

See Also: VectorD; 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<double> IMP::algebra::get_rasterized	(	const Gaussian3Ds &	gmm,
		const Floats &	weights,
		double	cell_width,
		const BoundingBox3D &	bb
	)

Rasterize the Gaussians to a grid.

DenseGrid3D<double> IMP::algebra::get_rasterized_fast	(	const Gaussian3Ds &	gmm,
		const Floats &	weights,
		double	cell_width,
		const BoundingBox3D &	bb,
		double	factor = `2.5`
	)

Rasterize the Gaussians to a grid.

The result is an approximation, but is obtained significantly faster. Good for quickly checking a GMM.

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

Return the point reflected about the plane.

Definition at line 68 of file Plane3D.h.

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

Return 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' projection of p onto the line containing s

template<class Vector3DsOrXYZs0 , class Vector3DsOrXYZs1 >

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

See 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
	)

Calculate the root mean square deviation between two sets of 3D points.

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
	)

Generate a Rotation3D object from a rotation around an axis.

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 Also: Rotation3D

Definition at line 309 of file Rotation3D.h.

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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 Also: Rotation3D

Definition at line 283 of file Rotation3D.h.

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

Generate a Transformation3D object from a rotation around a point.

Rotate about a point rather than the origin.

Parameters

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

See Also: Transformation3D

Definition at line 113 of file Transformation3D.h.

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

Generate a Transformation2D object from a rotation around a point.

Generate 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 Also: 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
	)

Initialize a rotation in x-y-z order from three angles.

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 Also: Rotation3D; FixedXYZ

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

Initialize a rotation from Euler angles.

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 Also: Rotation3D

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

Generate a rotation object from Euler Angles.

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 Also: 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
	)

Generate a Rotation3D object from a rotation matrix.

See Also: Rotation3D

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

Generate a Rotation3D object from a rotation matrix.

See Also: Rotation3D

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

Compute a rotation from an unnormalized quaternion.

See Also: Rotation3D

Definition at line 376 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 axes must be perpendicular unit vectors.

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

Create a rotation from the first vector to the second one.

See Also: Rotation3D

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

Build 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 )

Rounds a number to next integer.

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.

algebra::Segment3D IMP::algebra::get_segment_connecting_first_to_second	(	const Line3D &	a,
		const Line3D &	b
	)

Get shortest possible segment from the first line to the second.

Note: If the lines are parallel, this segment is not unique and is chosen so that the segment passes closest to the origin.

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

See Also: Segment3D; Vector3D

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

See Also: Segment3D

template<typename T >

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

Sign of a number. 1 if the number is higher or equal to 0 and -1 otherwise.

Definition at line 25 of file algebra/utility.h.

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

Get a set of balls that approximates the surface of the passed set.

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>

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

Compute the squared distance between two vectors.

See Also: VectorD

Definition at line 201 of file VectorD.h.

template<class Geometry >

double IMP::algebra::get_surface_area ( const Geometry & )

Compute the surface area of any volumetric object.

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

Get surface area & 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 )

Build a 3D transformation from a 2D one.

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
	)

Compute the rigid transform bringing the first point set to the second.

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

Returns: 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 Also: Transformation3D; Vector3D

Definition at line 45 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.

Transformation3D IMP::algebra::get_transformation_from_first_triangle_to_second	(	Triangle3D	first_tri,
		Triangle3D	second_tri
	)

Return a transformation between two triangles.

BoundingBoxD<3> IMP::algebra::get_transformed	(	const BoundingBoxD< 3 > &	bb,
		const Transformation3D &	tr
	)

Return a bounding box containing the transformed box.

Definition at line 154 of file Transformation3D.h.

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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`
	)

Use trilinear interpolation to compute a smoothed value at v.

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(); 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 )

Cover the space of rotations evenly.

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>

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

Generate a set of vectors which covers a sphere uniformly.

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 Also: VectorD; SphereD

Definition at line 116 of file vector_generators.h.

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

Generate a set of 3d points that uniformly cover a cylinder.

See Also: VectorD; Cylinder3D

Vector3Ds IMP::algebra::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.

Note: the implementation can be improved

See Also: SpherePatch3D; VectorD

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

See Also: VectorD; 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>

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

Generate a set of 3D points that uniformly cover a hemisphere.

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 )

Generates a nondegenerate set of Euler angles with a delta resolution.

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
	)

Return the union bounding box.

This is the same as doing a+b.

See Also: BoundingBoxD

Definition at line 254 of file BoundingBoxD.h.

template<unsigned int D>

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

Box with radius one.

See Also: BoundingBoxD

Definition at line 181 of file BoundingBoxD.h.

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

Box with radius one.

See Also: BoundingBoxD

Definition at line 187 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 229 of file VectorBaseD.h.

template<class C >

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

See Also: 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
	)

Return the vector product (cross product) of two vectors.

See Also: Vector3D

Definition at line 31 of file Vector3D.h.

template<int D>

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

Return a list of the 2^D bounding points for the bounding box.

See Also: BoundingBoxD

Definition at line 274 of file BoundingBoxD.h.

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template<int D>

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

See BoundingBoxD.

Definition at line 163 of file BoundingBoxD.h.

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template<class Geometry >

double IMP::algebra::get_volume ( const Geometry & )

Compute the volume of any volumetric object.

template<class Vector3DsOrXYZs0 , class Vector3DsOrXYZs1 >

double IMP::algebra::get_weighted_rmsd	(	const Vector3DsOrXYZs0 &	m1,
		const Vector3DsOrXYZs1 &	m2,
		const Floats &	weights
	)

See get_weighted_rmsd_transforming_first().

Definition at line 83 of file algebra/distance.h.

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template<int D>

VectorD<D> IMP::algebra::get_zero_vector_d ( )

Return a vector of zeros.

Definition at line 251 of file VectorD.h.

template<int D>

VectorD<-1 > IMP::algebra::get_zero_vector_kd ( int Di )

Return a dynamically sized vector of zeros.

Definition at line 262 of file VectorD.h.

template<int D>

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

See Also: VectorD

Definition at line 193 of file VectorD.h.

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

Read a set of 3D vectors from a file.

See Also: write_pts; VectorD

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

Read a set of 3D spheres from a file.

See Also: write_pts; SphereD

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

Reads from file in normal or reverse order.

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`
	)

Writes to a file in normal or reversed order.

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

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

template<class C , class E >

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

See Also: VectorD See generic geometry for more information.

Definition at line 423 of file VectorD.h.

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

Write a set of 3D vectors to a file.

See Also: read_pts; VectorD

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

Write a set of 3D spheres to a file.

See Also: read_pts; SphereD

Variable Documentation

const double IMP::algebra::PI = 3.1415926535897931

static

the constant pi

Definition at line 21 of file algebra/constants.h.

Detailed Description

Geometric primitives

Geometry and dimensions

Generic geometry

ANN

Eigen

Info

Classes

Typedefs

Functions

Variables

Standard module functions

Endian

Simple geometric IO

Python Only

Euler Angles

Shortest segments

3D Vectors

Vector Generators

Norms

Typedef Documentation

Function Documentation

Variable Documentation