hyperpoint.cpp File Reference

basic computations in non-Euclidean geometry More...

#include "hyper.h"

Classes
struct	hr::hyperpoint
	A point in our continuous space Originally used for representing points in the hyperbolic plane. Currently used for all kinds of supported spaces, as well as for all vector spaces (up to 4 dimensions). We are using the normalized homogeneous coordinates, which allows us to work with most geometries in HyperRogue in a uniform way. More...
struct	hr::transmatrix
	A matrix acting on hr::hyperpoint Since we are using homogeneous coordinates for hr::hyperpoint, rotations and translations can be represented as matrix multiplications. Other applications of matrices in HyperRogue (in dimension up to 4) are also implemented using transmatrix. More...

Namespaces
	hr

Macros
#define	C0   (MDIM == 3 ? C02 : C03)
#define	M_PI   3.14159265358979
#define	Cx1   (GDIM==2?Cx12:Cx13)

Enumerations
enum	iePrecision { iLazy, iTable }

Functions
constexpr transmatrix	hr::diag (ld a, ld b, ld c, ld d)
hyperpoint	hr::hpxyz (ld x, ld y, ld z)
hyperpoint	hr::hpxyz3 (ld x, ld y, ld z, ld w)
constexpr hyperpoint	hr::point3 (ld x, ld y, ld z)
constexpr hyperpoint	hr::point31 (ld x, ld y, ld z)
constexpr hyperpoint	hr::point2 (ld x, ld y)
EX ld	hr::squar (ld x)
EX int	hr::sig (int z)
EX int	hr::curvature ()
EX ld	hr::sin_auto (ld x)
EX ld	hr::asin_auto (ld x)
EX ld	hr::acos_auto (ld x)
EX ld	hr::volume_auto (ld r)
EX ld	hr::asin_clamp (ld x)
EX ld	hr::asin_auto_clamp (ld x)
EX ld	hr::acos_auto_clamp (ld x)
EX ld	hr::cos_auto (ld x)
EX ld	hr::tan_auto (ld x)
EX ld	hr::atan_auto (ld x)
EX ld	hr::atan2_auto (ld y, ld x)
EX ld	hr::edge_of_triangle_with_angles (ld alpha, ld beta, ld gamma)
EX hyperpoint	hr::hpxy (ld x, ld y)
EX hyperpoint	hr::hpxy3 (ld x, ld y, ld z)
EX bool	hr::zero_d (int d, hyperpoint h)
EX ld	hr::intval (const hyperpoint &h1, const hyperpoint &h2)
EX ld	hr::quickdist (const hyperpoint &h1, const hyperpoint &h2)
EX ld	hr::sqhypot_d (int d, const hyperpoint &h)
EX ld	hr::hypot_d (int d, const hyperpoint &h)
EX ld	hr::zlevel (const hyperpoint &h)
EX ld	hr::hypot_auto (ld x, ld y)
EX hyperpoint	hr::normalize (hyperpoint H)
EX hyperpoint	hr::normalize_flat (hyperpoint h)
EX hyperpoint	hr::mid (const hyperpoint &H1, const hyperpoint &H2)
EX hyperpoint	hr::midz (const hyperpoint &H1, const hyperpoint &H2)
EX transmatrix	hr::cspin (int a, int b, ld alpha)
EX transmatrix	hr::spin (ld alpha)
EX transmatrix	hr::random_spin ()
EX transmatrix	hr::eupush (ld x, ld y)
EX transmatrix	hr::eupush (hyperpoint h)
EX transmatrix	hr::eupush3 (ld x, ld y, ld z)
EX transmatrix	hr::euscalezoom (hyperpoint h)
EX transmatrix	hr::euaffine (hyperpoint h)
EX transmatrix	hr::cpush (int cid, ld alpha)
EX transmatrix	hr::xpush (ld alpha)
EX bool	hr::eqmatrix (transmatrix A, transmatrix B, ld eps IS(.01))
EX hyperpoint	hr::orthogonal_move (const hyperpoint &h, ld z)
EX transmatrix	hr::ypush (ld alpha)
EX transmatrix	hr::zpush (ld z)
EX transmatrix	hr::matrix3 (ld a, ld b, ld c, ld d, ld e, ld f, ld g, ld h, ld i)
EX transmatrix	hr::matrix4 (ld a, ld b, ld c, ld d, ld e, ld f, ld g, ld h, ld i, ld j, ld k, ld l, ld m, ld n, ld o, ld p)
EX void	hr::swapmatrix (transmatrix &T)
EX void	hr::swapmatrix (hyperpoint &h)
EX transmatrix	hr::parabolic1 (ld u)
EX transmatrix	hr::parabolic13 (ld u, ld v)
EX hyperpoint	hr::parabolic10 (hyperpoint h)
EX hyperpoint	hr::deparabolic10 (const hyperpoint h)
EX transmatrix	hr::spintoc (const hyperpoint &H, int t, int f)
EX transmatrix	hr::rspintoc (const hyperpoint &H, int t, int f)
EX transmatrix	hr::spintox (const hyperpoint &H)
EX transmatrix	hr::rspintox (const hyperpoint &H)
EX transmatrix	hr::pushxto0 (const hyperpoint &H)
EX void	hr::set_column (transmatrix &T, int i, const hyperpoint &H)
EX transmatrix	hr::build_matrix (hyperpoint h1, hyperpoint h2, hyperpoint h3, hyperpoint h4)
EX transmatrix	hr::rpushxto0 (const hyperpoint &H)
EX transmatrix	hr::ggpushxto0 (const hyperpoint &H, ld co)
EX transmatrix	hr::gpushxto0 (const hyperpoint &H)
EX transmatrix	hr::rgpushxto0 (const hyperpoint &H)
EX void	hr::fixmatrix (transmatrix &T)
	Fix the numerical inaccuracies in the isometry T The nature of hyperbolic geometry makes the computations numerically unstable. The numerical errors tend to accumulate, eventually destroying the projection. This function fixes this problem by replacing T with a 'correct' isometry.
EX ld	hr::det (const transmatrix &T)
void	hr::inverse_error (const transmatrix &T)
EX transmatrix	hr::inverse (const transmatrix &T)
EX pair< ld, hyperpoint >	hr::product_decompose (hyperpoint h)
EX ld	hr::hdist0 (const hyperpoint &mh)
EX ld	hr::circlelength (ld r)
EX ld	hr::hdist (const hyperpoint &h1, const hyperpoint &h2)
EX hyperpoint	hr::mscale (const hyperpoint &t, double fac)
EX transmatrix	hr::mscale (const transmatrix &t, double fac)
EX transmatrix	hr::xyscale (const transmatrix &t, double fac)
EX transmatrix	hr::xyzscale (const transmatrix &t, double fac, double facz)
EX transmatrix	hr::mzscale (const transmatrix &t, double fac)
EX hyperpoint	hr::mid3 (hyperpoint h1, hyperpoint h2, hyperpoint h3)
EX hyperpoint	hr::mid_at (hyperpoint h1, hyperpoint h2, ld v)
EX hyperpoint	hr::mid_at_actual (hyperpoint h, ld v)
EX hyperpoint	hr::orthogonal_of_C0 (hyperpoint h0, hyperpoint h1, hyperpoint h2)
EX hyperpoint	hr::zshift (hyperpoint x, ld z)
EX hyperpoint	hr::hpxd (ld d, ld x, ld y, ld z)
EX ld	hr::signum (ld x)
EX bool	hr::asign (ld y1, ld y2)
EX ld	hr::xcross (ld x1, ld y1, ld x2, ld y2)
EX transmatrix	hr::parallel_transport (const transmatrix Position, const transmatrix &ori, const hyperpoint direction, int precision IS(100))
EX void	hr::apply_parallel_transport (transmatrix &Position, const transmatrix orientation, const hyperpoint direction)
EX void	hr::rotate_object (transmatrix &Position, transmatrix &orientation, transmatrix R)
EX transmatrix	hr::spin_towards (const transmatrix Position, transmatrix &ori, const hyperpoint goal, int dir, int back)
EX ld	hr::ortho_error (transmatrix T)
EX transmatrix	hr::transpose (transmatrix T)
hyperpoint	hr::slr::xyz_point (ld x, ld y, ld z)
hyperpoint	hr::slr::polar (ld r, ld theta, ld phi)
hyperpoint	hr::cpush0 (int c, ld x)
hyperpoint	hr::xspinpush0 (ld alpha, ld x)
hyperpoint	hr::xpush0 (ld x)
hyperpoint	hr::ypush0 (ld x)
hyperpoint	hr::zpush0 (ld x)
hyperpoint	hr::tC0 (const transmatrix &T)
EX hyperpoint	hr::ctangent (int c, ld x)
EX hyperpoint	hr::xtangent (ld x)
EX hyperpoint	hr::ztangent (ld z)
EX hyperpoint	hr::tangent_length (hyperpoint dir, ld length)
EX hyperpoint	hr::direct_exp (hyperpoint v, int steps)
EX hyperpoint	hr::inverse_exp (const hyperpoint h, iePrecision p, bool just_direction IS(true))
EX ld	hr::geo_dist (const hyperpoint h1, const hyperpoint h2, iePrecision p)
EX hyperpoint	hr::lp_iapply (const hyperpoint h)
EX hyperpoint	hr::lp_apply (const hyperpoint h)
EX hyperpoint	hr::smalltangent ()
EX void	hr::cyclefix (ld &a, ld b)
EX ld	hr::raddif (ld a, ld b)
EX int	hr::bucketer (ld x)
EX int	hr::bucketer (hyperpoint h)

Variables
constexpr hyperpoint	hr::Hypc = hyperpoint(0, 0, 0, 0)
constexpr transmatrix	hr::Id = diag(1,1,1,1)
constexpr transmatrix	hr::Zero = diag(0,0,0,0)
constexpr transmatrix	hr::Mirror = diag(1,-1,1,1)
constexpr transmatrix	hr::MirrorY = diag(1,-1,1,1)
constexpr transmatrix	hr::MirrorX = diag(-1,1,1,1)
constexpr transmatrix	hr::MirrorZ = diag(1,1,-1,1)
constexpr transmatrix	hr::pispin = diag(-1,-1,1,1)
constexpr transmatrix	hr::centralsym = diag(-1,-1,-1,-1)
constexpr hyperpoint	hr::C02 = hyperpoint(0,0,1,0)
constexpr hyperpoint	hr::C03 = hyperpoint(0,0,0,1)
constexpr hyperpoint	hr::Cx12 = hyperpoint(1,0,1.41421356237,0)
constexpr hyperpoint	hr::Cx13 = hyperpoint(1,0,0,1.41421356237)

Detailed Description

basic computations in non-Euclidean geometry

This implements hyperpoint (a point in non-Euclidean space), transmatrix (a transformation matrix), and various basic routines related to them: rotations, translations, inverses and determinants, etc. For nonisotropic geometries, it rather refers to nonisotropic.cpp.

Macro Definition Documentation

C0

#define C0   (MDIM == 3 ? C02 : C03)

C0 is the origin in our space