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IMP Reference Guide  develop.4056850,2019/07/19
The Integrative Modeling Platform
IMP::algebra Namespace Reference

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.

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:

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< Cone3DCone3Ds
 
typedef IMP::Vector
< ConnollySurfacePoint
ConnollySurfacePoints
 
typedef IMP::Vector< Cylinder3DCylinder3Ds
 
typedef IMP::Vector< Ellipsoid3DEllipsoid3Ds
 
typedef IMP::Vector< Gaussian3DGaussian3Ds
 
typedef IMP::Vector< Line3DLine3Ds
 
typedef IMP::Vector< LinearFit2DLinearFit2Ds
 
typedef IMP::Vector
< ParabolicFit2D
ParabolicFit2Ds
 
typedef IMP::Vector< Plane3DPlane3Ds
 
typedef IMP::Vector
< ReferenceFrame3D
ReferenceFrame3Ds
 
typedef IMP::Vector< Reflection3DReflection3Ds
 
typedef IMP::Vector< Rotation2DRotation2Ds
 
typedef IMP::Vector< Rotation3DRotation3Ds
 
typedef IMP::Vector< Segment3DSegment3Ds
 
typedef SphereD< 1 > Sphere1D
 Typedef for Python. More...
 
typedef IMP::Vector< Sphere1DSphere1Ds
 
typedef SphereD< 2 > Sphere2D
 Typedef for Python. More...
 
typedef IMP::Vector< Sphere2DSphere2Ds
 
typedef SphereD< 3 > Sphere3D
 Typedef for Python. More...
 
typedef IMP::Vector< Sphere3DSphere3Ds
 
typedef SphereD< 4 > Sphere4D
 Typedef for Python. More...
 
typedef IMP::Vector< Sphere4DSphere4Ds
 
typedef SphereD< 5 > Sphere5D
 Typedef for Python. More...
 
typedef IMP::Vector< Sphere5DSphere5Ds
 
typedef SphereD< 6 > Sphere6D
 Typedef for Python. More...
 
typedef IMP::Vector< Sphere6DSphere6Ds
 
typedef SphereD<-1 > SphereKD
 Typedef for Python. More...
 
typedef IMP::Vector< SphereKDSphereKDs
 
typedef IMP::Vector
< SpherePatch3D
SpherePatch3Ds
 
typedef IMP::Vector
< SphericalVector3D
SphericalVector3Ds
 
typedef IMP::Vector< Torus3DTorus3Ds
 
typedef IMP::Vector
< Transformation2D
Transformation2Ds
 
typedef IMP::Vector
< Transformation3D
Transformation3Ds
 
typedef IMP::Vector< Triangle3DTriangle3Ds
 
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 >
get_constrained (const T x, const T x0, const T xF)
 Constrain a value between two given limits. More...
 
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 Eigen::Matrix3d &covariance, const Vector3D &center)
 Return a Gaussian centered at the origin from a covariance matrix. More...
 
Eigen::MatrixXd get_gradient_of_composed_with_respect_to_first (const Rotation3D &q, const Rotation3D &p, bool projected=true)
 Get gradient of quaternion product with respect to first quaternion. More...
 
Eigen::MatrixXd get_gradient_of_composed_with_respect_to_second (const Rotation3D &q, const Rotation3D &p, bool projected=true)
 Get gradient of quaternion product with respect to second quaternion. 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 (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< FixedXYZFixedXYZs
 
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 for Python.

Definition at line 176 of file BoundingBoxD.h.

Pass or store a set of BoundingBox1D .

Definition at line 176 of file BoundingBoxD.h.

Typedef for Python.

Definition at line 176 of file BoundingBoxD.h.

Pass or store a set of BoundingBox2D .

Definition at line 176 of file BoundingBoxD.h.

Typedef for Python.

Definition at line 176 of file BoundingBoxD.h.

Pass or store a set of BoundingBox3D .

Definition at line 176 of file BoundingBoxD.h.

Typedef for Python.

Definition at line 176 of file BoundingBoxD.h.

Pass or store a set of BoundingBox4D .

Definition at line 176 of file BoundingBoxD.h.

Typedef for Python.

Definition at line 176 of file BoundingBoxD.h.

Pass or store a set of BoundingBox5D .

Definition at line 176 of file BoundingBoxD.h.

Typedef for Python.

Definition at line 176 of file BoundingBoxD.h.

Pass or store a set of BoundingBox6D .

Definition at line 176 of file BoundingBoxD.h.

Typedef for Python.

Definition at line 176 of file BoundingBoxD.h.

Pass or store a set of BoundingBoxKD .

Definition at line 176 of file BoundingBoxD.h.

Pass or store a set of Cone3D .

Definition at line 64 of file Cone3D.h.

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.

Pass or store a set of Ellipsoid3D .

Definition at line 46 of file Ellipsoid3D.h.

Pass or store a set of FixedXYZ .

Definition at line 530 of file Rotation3D.h.

Pass or store a set of Gaussian3D .

Definition at line 43 of file Gaussian3D.h.

Pass or store a set of Line3D .

Definition at line 70 of file Line3D.h.

Pass or store a set of LinearFit2D .

Definition at line 52 of file LinearFit.h.

Pass or store a set of ParabolicFit2D .

Definition at line 54 of file ParabolicFit.h.

Pass or store a set of Plane3D .

Definition at line 78 of file Plane3D.h.

Pass or store a set of ReferenceFrame3D .

Definition at line 95 of file ReferenceFrame3D.h.

Pass or store a set of Reflection3D .

Definition at line 32 of file Reflection3D.h.

Pass or store a set of Rotation2D .

Definition at line 114 of file Rotation2D.h.

Pass or store a set of Rotation3D .

Definition at line 272 of file Rotation3D.h.

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 for Python.

Definition at line 96 of file SphereD.h.

Pass or store a set of Sphere1D .

Definition at line 96 of file SphereD.h.

Typedef for Python.

Definition at line 96 of file SphereD.h.

Pass or store a set of Sphere2D .

Definition at line 96 of file SphereD.h.

Typedef for Python.

Definition at line 96 of file SphereD.h.

Pass or store a set of Sphere3D .

Definition at line 96 of file SphereD.h.

Typedef for Python.

Definition at line 96 of file SphereD.h.

Pass or store a set of Sphere4D .

Definition at line 96 of file SphereD.h.

Typedef for Python.

Definition at line 96 of file SphereD.h.

Pass or store a set of Sphere5D .

Definition at line 96 of file SphereD.h.

Typedef for Python.

Definition at line 96 of file SphereD.h.

Pass or store a set of Sphere6D .

Definition at line 96 of file SphereD.h.

Typedef for Python.

Definition at line 96 of file SphereD.h.

Pass or store a set of SphereKD .

Definition at line 96 of file SphereD.h.

Pass or store a set of SpherePatch3D .

Definition at line 48 of file SpherePatch3D.h.

Pass or store a set of SphericalVector3D .

Definition at line 78 of file SphericalVector3D.h.

Pass or store a set of Torus3D .

Definition at line 61 of file Torus3D.h.

Pass or store a set of Transformation2D .

Definition at line 118 of file Transformation2D.h.

Pass or store a set of Transformation3D .

Definition at line 98 of file Transformation3D.h.

Pass or store a set of Triangle3D .

Definition at line 41 of file Triangle3D.h.

1D vector typedef for swig

Definition at line 387 of file VectorD.h.

1D vectors typedef for swig

Definition at line 389 of file VectorD.h.

2D vector typedef for swig

Definition at line 391 of file VectorD.h.

2D vectors typedef for swig

Definition at line 393 of file VectorD.h.

3D vector typedef for swig

Examples:
grid.cpp.

Definition at line 395 of file VectorD.h.

3D vectors typedef for swig

Definition at line 397 of file VectorD.h.

4D vector typedef for swig

Definition at line 399 of file VectorD.h.

4D vectors typedef for swig

Definition at line 401 of file VectorD.h.

5D vector typedef for swig

Definition at line 403 of file VectorD.h.

5D vectors typedef for swig

Definition at line 405 of file VectorD.h.

6D vector typedef for swig

Definition at line 407 of file VectorD.h.

6D vector typedef for swig

Definition at line 409 of file VectorD.h.

KD vector typedef for swig

Definition at line 411 of file VectorD.h.

A vector of reference-counting object pointers.

Definition at line 31 of file vector_metrics.h.

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

See Also
VectorKDMetric

Definition at line 31 of file vector_metrics.h.

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 448 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 
)

The algorithm is taken from Connolly's original MS program, which is freely distributable and Copyright 1983, Michael Connolly.

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.

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 112 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 323 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 Eigen::Matrix3d &  covariance,
const Vector3D &  center 
)

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

Eigen::MatrixXd IMP::algebra::get_gradient_of_composed_with_respect_to_first ( const Rotation3D &  q,
const Rotation3D &  p,
bool  projected = true 
)

Get gradient of quaternion product with respect to first quaternion.

Given the rotation \(R(p)\) followed by \(R(q)\), where \(p\) and \(q\) are quaternions, the quaternion of the composed rotation \(R(s)=R(q) R(p)\) can be expressed through the Hamilton product of the two quaternions \(s(q,p) = q p\). This function returns the matrix \(M = \nabla_q s(q, p)\) with elements \(M_{ij}=\frac{d s_i}{d q_j}\).

Parameters
[in]qrotation corresponding to first quaternion
[in]protation corresponding to second quaternion
[in]projectedproject derivative onto tangent space to \(q\). Equivalent to differentiating wrt \(\frac{q_i}{\|q\|}\) instead of \(q_i\).
Eigen::MatrixXd IMP::algebra::get_gradient_of_composed_with_respect_to_second ( const Rotation3D &  q,
const Rotation3D &  p,
bool  projected = true 
)

Get gradient of quaternion product with respect to second quaternion.

Given the rotation \(R(p)\) followed by \(R(q)\), where \(p\) and \(q\) are quaternions, the quaternion of the composed rotation \(R(s)=R(q) R(p)\) can be expressed through the Hamilton product of the two quaternions \(s(q,p) = q p\). This function returns the matrix \(\nabla_p s(q, p)\) with elements \(M_{ij}=\frac{d s_i}{d p_j}\).

Parameters
[in]qrotation corresponding to first quaternion
[in]protation corresponding to second quaternion
[in]projectedproject derivative onto tangent space to \(p\). Equivalent to differentiating wrt \(\frac{p_i}{\|p\|}\) instead of \(p_i\).
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 309 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 132 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 545 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 260 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 123 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]originthe origin of the rotation
[in]max_translationdefault value is 5
[in]max_angle_in_raddefault 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]centerThe center of the rotational volume
[in]distanceSee 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
sa 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
ssegment in 3D
ppoint 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]axisthe rotation axis passes through (0,0,0)
[in]anglethe 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 374 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_normthe normalized rotation axis passing through (0,0,0)
[in]anglethe 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 348 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]pointCenter to rotate about
[in]rotationThe 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]pointCenter to rotate about
[in]rotationThe 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]xrRotation around the X axis in radians
[in]yrRotation around the Y axis in radians
[in]zrRotation 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]phiRotation around the Z axis in radians
[in]thetaRotation around the X axis in radians
[in]psiRotation 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]RotFirst Euler angle (radians) defining the rotation (Z axis)
[in]TiltSecond Euler angle (radians) defining the rotation (Y axis)
[in]PsiThird 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 ( 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 441 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 
)
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 
)
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]deltasample 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.