WFMath (3) - Linux Manuals
WFMath: Generic library namespace.
NAME
WFMath - Generic library namespace.
SYNOPSIS
Classes
class AxisBox
A dim dimensional axis-aligned box.
class Ball
A dim dimensional ball.
struct ColinearVectors
An error thrown by certain functions when passed parallel vectors.
struct ParseError
An error thrown by operator>>() when it fails to parse wfmath types.
class Point
A dim dimensional point.
class Polygon< 2 >
The 2D specialization of the Polygon<> template.
class Polygon
A polygon, all of whose points lie in a plane, embedded in dim dimensions.
class Quaternion
A normalized quaterion.
class RotBox
A dim dimensional box, lying at an arbitrary angle.
class RotMatrix
A dim dimensional rotation matrix. Technically, a member of the group O(dim).
class Segment
A line segment embedded in dim dimensions.
class TimeDiff
The difference between two timestamps.
class TimeStamp
A time stamp.
class Vector
A dim dimensional vector.
class ZeroPrimitive
Utility class for providing zero primitives. This class will only work with simple structures such as Vector or Point which provide a m_elem structure. In order for it to access the m_elem structure it must be declared as a friend class of the class it will provide an instance of.
class Shape
A fake class which documents the generic parts of the WFMath interface.
Typedefs
typedef float CoordType
Basic floating point type.
Functions
template<const int dim, template< class, class > class container> AxisBox< dim > BoundingBox (const container< AxisBox< dim >, std::allocator< AxisBox< dim > > > &c)
Get the axis-aligned bounding box for a set of boxes.
template<const int dim, template< class, class > class container> AxisBox< dim > BoundingBox (const container< Point< dim >, std::allocator< Point< dim > > > &c)
Get the axis-aligned bounding box for a set of points.
template<const int dim, template< class, class > class container> Ball< dim > BoundingSphere (const container< Point< dim >, std::allocator< Point< dim > > > &c)
get the minimal bounding sphere for a set of points
template<const int dim, template< class, class > class container> Ball< dim > BoundingSphereSloppy (const container< Point< dim >, std::allocator< Point< dim > > > &c)
get a bounding sphere for a set of points
template<class C > bool Equal (const C &c1, const C &c2, double epsilon=WFMATH_EPSILON)
Test for equality up to precision epsilon.
template<const int dim, template< class, class > class container> Point< dim > Barycenter (const container< Point< dim >, std::allocator< Point< dim > > > &c)
Find the center of a set of points, all weighted equally.
template<const int dim, template< class, class > class container, template< class, class > class container2> Point< dim > Barycenter (const container< Point< dim >, std::allocator< Point< dim > > > &c, const container2< CoordType, std::allocator< CoordType > > &weights)
Find the center of a set of points with the given weights.
template<const int dim> Point< dim > Midpoint (const Point< dim > &p1, const Point< dim > &p2, CoordType dist=0.5)
double GaussianConditional (double mean, double stddev, double val)
Gives the conditional probability of the Gaussian distribution at position val.
double Gaussian (double mean, double stddev, double val)
Gives the value of the Gaussian distribution at position val.
double PoissonConditional (double mean, unsigned int step)
Gives the conditional probability of the Poisson distribution at position step.
double Poisson (double mean, unsigned int step)
Gives the value of the Poisson distribution at position step.
double LogFactorial (unsigned int n)
Gives the natural log of n!
double Factorial (unsigned int n)
Gives n!
double LogGamma (double z)
The natural log of Euler's Gamma function.
double Gamma (double z)
Euler's Gamma function.
template<const int dim> RotMatrix< dim > Prod (const RotMatrix< dim > &m1, const RotMatrix< dim > &m2)
returns m1 * m2
template<const int dim> RotMatrix< dim > ProdInv (const RotMatrix< dim > &m1, const RotMatrix< dim > &m2)
returns m1 * m2^-1
template<const int dim> RotMatrix< dim > InvProd (const RotMatrix< dim > &m1, const RotMatrix< dim > &m2)
returns m1^-1 * m2
template<const int dim> RotMatrix< dim > InvProdInv (const RotMatrix< dim > &m1, const RotMatrix< dim > &m2)
returns m1^-1 * m2^-1
template<const int dim> Vector< dim > Prod (const RotMatrix< dim > &m, const Vector< dim > &v)
returns m * v
template<const int dim> Vector< dim > InvProd (const RotMatrix< dim > &m, const Vector< dim > &v)
returns m^-1 * v
template<const int dim> Vector< dim > Prod (const Vector< dim > &v, const RotMatrix< dim > &m)
returns v * m
template<const int dim> Vector< dim > ProdInv (const Vector< dim > &v, const RotMatrix< dim > &m)
return v * m^-1
template<const int dim> RotMatrix< dim > operator* (const RotMatrix< dim > &m1, const RotMatrix< dim > &m2)
returns m1 * m2
template<class C > void Shuffle (std::vector< C > &v)
Randomly reorder the contents of a std::vector.
template<class C > std::string ToString (const C &c, unsigned int precision=6)
Output a WFMath type as a string.
template<class C > void FromString (C &c, const std::string &s, unsigned int precision=6)
Parse a WFMath type from a string.
CoordType Cross (const Vector< 2 > &v1, const Vector< 2 > &v2)
2D only: get the z component of the cross product of two vectors
Vector< 3 > Cross (const Vector< 3 > &v1, const Vector< 3 > &v2)
3D only: get the cross product of two vectors
template<const int dim> bool Parallel (const Vector< dim > &v1, const Vector< dim > &v2, bool &same_dir)
Check if two vectors are parallel.
template<const int dim> bool Parallel (const Vector< dim > &v1, const Vector< dim > &v2)
Check if two vectors are parallel.
template<const int dim> bool Perpendicular (const Vector< dim > &v1, const Vector< dim > &v2)
Check if two vectors are perpendicular.
Variables
const double Pi = 3.14159265358979323846264338327950288419716939937508
The constant pi.
const double SqrtPi = 1.77245385090551602729816748334114518279754945612237
The square root of pi.
const double LogPi = 1.14472988584940017414342735135305871164729481291530
The natural logarithm of pi.
const double Sqrt2 = 1.41421356237309504880168872420969807856967187537693
The square root of 2.
const double Sqrt3 = 1.73205080756887729352744634150587236694280525381037
The square root of 3.
const double Log2 = 0.69314718055994530941723212145817656807550013436025
The natural logarithm of 2.
Detailed Description
Generic library namespace.
Timing related primitives in a portable fashion - note this is for interval / elapsed time measurement, not displaying a human readable time.
Function Documentation
template<const int dim, template< class, class > class container, template< class, class > class container2> Point< dim > WFMath::Barycenter (const container< Point< dim >, std::allocator< Point< dim > > > & c, const container2< CoordType, std::allocator< CoordType > > & weights) [inline]
Find the center of a set of points with the given weights.
If the number of points and the number of weights are not equal, the excess of either is ignored. The weights (or that subset which is used, if there are more weights than points), must not sum to zero.
References WFMath::Point< dim >::setValid().
template<class C > bool WFMath::Equal (const C & c1, const C & c2, double epsilon = WFMATH_EPSILON) [inline]
Test for equality up to precision epsilon.
Returns true if the difference between the numbers is less than epsilon. Note that epsilon is multiplied by 2 raised to the power of the exponent of the smaller number. So, for example, Equal(0.00010000, 0.00010002, 1.0e-4) will not compare equal, but Equal(0.00010000, 0.00010002, 1.0e-3) will.
template<class C > void WFMath::FromString (C & c, const std::string & s, unsigned int precision = 6) [inline]
Parse a WFMath type from a string.
This uses operator>>() in its backend.
double WFMath::GaussianConditional (double mean, double stddev, double val)
Gives the conditional probability of the Gaussian distribution at position val.
The probability that a Gaussian random variable will fall between val and val + delta, given that it is already known to be not less than val, is given by this function multiplied by delta (for small delta).
template<const int dim> Point< dim > WFMath::Midpoint (const Point< dim > & p1, const Point< dim > & p2, CoordType dist = 0.5) [inline]
The default value of 0.5 for dist gives the midpoint. A value of 0 gives p1, and 1 gives p2. Values of dist outside the [0, 1] range are allowed, and give points on the line which are not on the segment bounded by p1 and p2.
Referenced by BoundingSphereSloppy().
template<const int dim> bool WFMath::Parallel (const Vector< dim > & v1, const Vector< dim > & v2) [inline]
Check if two vectors are parallel.
Convienience wrapper if you don't care about same_dir
template<const int dim> bool WFMath::Parallel (const Vector< dim > & v1, const Vector< dim > & v2, bool & same_dir) [inline]
Check if two vectors are parallel.
Returns true if the vectors are parallel. For parallel vectors, same_dir is set to true if they point the same direction, and false if they point opposite directions
References Equal(), and WFMath::Vector< dim >::sqrMag().
double WFMath::PoissonConditional (double mean, unsigned int step)
Gives the conditional probability of the Poisson distribution at position step.
Returns the probability that a Poisson random variable will have value step, given that it is already known not to be less than step.
template<const int dim> Vector< dim > WFMath::Prod (const Vector< dim > & v, const RotMatrix< dim > & m) [inline]
returns v * m
This is the function to use to rotate a Vector v using a Matrix m
template<class C > void WFMath::Shuffle (std::vector< C > & v) [inline]
Randomly reorder the contents of a std::vector.
For things like shuffling a deck of cards, etc.
template<class C > std::string WFMath::ToString (const C & c, unsigned int precision = 6) [inline]
Output a WFMath type as a string.
This uses operator<<() in its backend.
Author
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