nonisotropic.cpp File Reference

nonisotropic spaces (Solv and Nil) More...

#include "hyper.h"

Classes
struct	hr::sn::tabled_inverses
struct	hr::sn::hrmap_solnih
struct	hr::nilv::mvec
struct	hr::nilv::nilstructure
struct	hr::nilv::hrmap_nil
struct	hr::hybrid::hrmap_hybrid
struct	hr::product::hrmap_product
struct	hr::rots::hrmap_rotation_space

Namespaces
	hr

Macros
#define	S0(x, y, z)   get_int(x, y, z)[t]
#define	S1(x, y)   (S0(x,y,az) * (bz-iz) + S0(x,y,bz) * (iz-az))
#define	S2(x)   (S1(x,ay) * (by-iy) + S1(x,by) * (iy-ay))
#define	PIU(x)   hr::hybrid::in_underlying_geometry([&] { return (x); })

Typedefs
typedef array< float, 3 >	hr::sn::compressed_point

Functions
bool	hr::nisot::local_perspective_used ()
EX transmatrix	hr::nisot::translate (hyperpoint h)
EX bool	hr::sn::in ()
EX eGeometry	hr::sn::geom ()
hyperpoint	hr::sn::decompress (compressed_point p)
compressed_point	hr::sn::compress (hyperpoint h)
EX ld	hr::sn::x_to_ix (ld u)
EX ld	hr::sn::ix_to_x (ld ix)
EX ld	hr::sn::z_to_iz (ld z)
EX ld	hr::sn::iz_to_z (ld iz)
EX hyperpoint	hr::sn::azeq_to_table (hyperpoint x)
EX hyperpoint	hr::sn::table_to_azeq (hyperpoint x)
EX pair< heptagon *, heptagon * >	hr::sn::getcoord (heptagon *h)
EX heptagon *	hr::sn::get_at (heptagon *h1, heptagon *h2, bool gen)
hyperpoint	hr::sn::christoffel (const hyperpoint at, const hyperpoint velocity, const hyperpoint transported)
EX hyperpoint	hr::sn::get_inverse_exp_symsol (hyperpoint h, bool lazy, bool just_direction)
EX hyperpoint	hr::sn::get_inverse_exp_nsym (hyperpoint h, bool lazy, bool just_direction)
EX bool	hr::sn::in_table_range (hyperpoint h)
EX tabled_inverses &	hr::sn::get_tabled ()
EX int	hr::sn::approx_distance (heptagon *h1, heptagon *h2)
hyperpoint	hr::nilv::christoffel (const hyperpoint Position, const hyperpoint Velocity, const hyperpoint Transported)
EX hyperpoint	hr::nilv::formula_exp (hyperpoint v)
EX hyperpoint	hr::nilv::get_inverse_exp (hyperpoint h, int iterations)
hyperpoint	hr::nilv::mvec_to_point (mvec m)
EX nilstructure &	hr::nilv::current_ns ()
EX transmatrix	hr::nilv::adjmatrix (int i)
EX mvec	hr::nilv::get_coord (heptagon *h)
EX heptagon *	hr::nilv::get_heptagon_at (mvec m)
EX void	hr::nilv::set_flags ()
EX hyperpoint	hr::nilv::on_geodesic (hyperpoint s0, hyperpoint s1, ld x)
EX color_t	hr::nilv::colorize (cell *c, char whichCanvas)
EX void	hr::nilv::prepare_niltorus3 ()
EX void	hr::nilv::show_niltorus3 ()
EX bool	hr::in_s2xe ()
EX bool	hr::in_h2xe ()
EX bool	hr::in_e2xe ()
EX eGeometryClass	hr::hybrid::under_class ()
EX void	hr::hybrid::configure (eGeometry g)
EX void	hr::hybrid::reconfigure ()
template<class T >
auto	hr::hybrid::in_actual (const T &t) -> decltype(t())
hrmap_hybrid *	hr::hybrid::hmap ()
EX cell *	hr::hybrid::get_at (cell *base, int level)
EX pair< cell *, int >	hr::hybrid::get_where (cell *c)
EX void	hr::hybrid::find_cell_connection (cell *c, int d)
EX hrmap *	hr::hybrid::get_umap ()
template<class T >
auto	hr::hybrid::in_underlying_geometry (const T &f) -> decltype(f())
EX hyperpoint	hr::hybrid::get_corner (cell *c, int i, int next, ld z)
EX int	hr::hybrid::wall_offset (cell *c)
EX void	hr::hybrid::will_link (cell *c)
EX void	hr::hybrid::link ()
EX int	hr::hybrid::celldistance (cell *c1, cell *c2)
EX hyperpoint	hr::product::inverse_exp (hyperpoint h)
EX hyperpoint	hr::product::direct_exp (hyperpoint h)
EX bool	hr::product::validate_spin ()
EX void	hr::product::show_config ()
EX hyperpoint	hr::slr::from_phigans (hyperpoint h)
EX hyperpoint	hr::slr::to_phigans (hyperpoint h)
hyperpoint	hr::slr::christoffel (const hyperpoint Position, const hyperpoint Velocity, const hyperpoint Transported)
EX transmatrix	hr::slr::translate (hyperpoint h)
hyperpoint	hr::slr::polar (ld r, ld theta, ld phi)
hyperpoint	hr::slr::xyz_point (ld x, ld y, ld z)
ld	hr::slr::rootsin (ld square, ld s)
ld	hr::slr::asin_it (ld z, int it)
ld	hr::slr::arootsin (ld square, ld v, int it)
ld	hr::slr::roottan (ld square, ld s)
hyperpoint	hr::slr::geodesic_polar (ld alpha, ld beta, ld s)
EX hyperpoint	hr::slr::formula_exp (hyperpoint h)
void	hr::slr::find_alpha (ld phi, ld r, ld theta, ld &alpha, ld &s, ld &beta)
EX hyperpoint	hr::slr::get_inverse_exp (hyperpoint h, ld index IS(0))
EX transmatrix	hr::rots::uxpush (ld x)
EX transmatrix	hr::rots::uypush (ld y)
EX transmatrix	hr::rots::uzpush (ld z)
EX transmatrix	hr::rots::qtm (hyperpoint h)
EX void	hr::rots::draw_underlying (bool cornermode)
EX hyperpoint	hr::nisot::christoffel (const hyperpoint at, const hyperpoint velocity, const hyperpoint transported)
EX bool	hr::nisot::in_table_range (hyperpoint h)
EX void	hr::nisot::geodesic_step (hyperpoint &at, hyperpoint &velocity)
EX hyperpoint	hr::nisot::numerical_exp (hyperpoint v, int steps)
EX transmatrix	hr::nisot::parallel_transport_bare (transmatrix Pos, hyperpoint h)
EX void	hr::nisot::fixmatrix (transmatrix &T)
EX transmatrix	hr::nisot::parallel_transport (const transmatrix Position, const hyperpoint direction)
EX transmatrix	hr::nisot::spin_towards (const transmatrix Position, const hyperpoint goal)
EX hrmap *	hr::nisot::new_map ()

Variables
EX bool	hr::nisot::geodesic_movement = true
EX string	hr::sn::common
EX string	hr::sn::shader_symsol
EX string	hr::sn::shader_nsymsol
EX string	hr::sn::shader_nsym
EX ld	hr::sn::solrange_xy = 15
EX ld	hr::sn::solrange_z = 4
EX tabled_inverses	hr::sn::solt = sn::tabled_inverses("solv-geodesics.dat")
EX tabled_inverses	hr::sn::niht = sn::tabled_inverses("shyp-geodesics.dat")
EX tabled_inverses	hr::sn::sont = sn::tabled_inverses("ssol-geodesics.dat")
EX string	hr::nilv::nilshader
EX ld	hr::nilv::nilwidth = 1
nilstructure	hr::nilv::ns6
nilstructure	hr::nilv::ns8
EX array< int, 3 >	hr::nilv::nilperiod
EX array< int, 3 >	hr::nilv::nilperiod_edit
int	hr::nilv::S7_edit
EX eGeometry	hr::hybrid::underlying
EX geometry_information *	hr::hybrid::underlying_cgip
EX hrmap *	hr::hybrid::pmap
EX geometry_information *	hr::hybrid::pcgip
EX eGeometry	hr::hybrid::actual_geometry
vector< cell * >	hr::hybrid::to_link
EX bool	hr::hybrid::in_link = false
int	hr::product::z0
EX bool	hr::product::current_spin_invalid
EX int	hr::product::csteps
EX int	hr::product::cspin
EX bool	hr::product::cmirror
EX ld	hr::slr::range_xy = 2
EX int	hr::slr::steps = 15
EX string	hr::slr::slshader
EX ld	hr::rots::underlying_scale = 0
auto	hr::nisot::config

Detailed Description

nonisotropic spaces (Solv and Nil)

Function Documentation

christoffel()

hyperpoint hr::slr::christoffel	(	const hyperpoint	Position,
		const hyperpoint	Velocity,
		const hyperpoint	Transported
	)

in the 'phigans' model

asin_it()

ld hr::slr::asin_it	(	ld	z,
		int	it
	)

it==0 is standard asin, it==1 is the next solution (PI-asin)

qtm()

EX transmatrix hr::rots::qtm

(

hyperpoint

h

)

reinterpret the given point of rotspace as a rotation matrix in the underlying geometry

Variable Documentation

common

EX string hr::sn::common

Initial value:

= 
    "uniform mediump sampler3D tInvExpTable;"    
    "uniform mediump float PRECX, PRECY, PRECZ;"
 
    "float x_to_ix(float u) {"
    "  if(u < 1e-6) return 0.;"
    "  float diag = u*u/2.;"
   
    "  float x = diag;"
    "  float y = u;"
    "  float z = diag+1.;"
    
    "  x /= (1.+z);"
    "  y /= (1.+z);"
    
    "  return 0.5 - atan((0.5-x) / y) / 3.1415926535897932384626433832795;"
    "  }"
    
    "float z_to_iz_s(float z) {"
      "return sinh(z) / (1. + cosh(z));"
      "}"
    
    "float z_to_iz_ns(float z) {"
      "z = sinh(z) / (1. + cosh(z));"
      "return (z+1.)/2.;"
      "}"

shader_symsol

EX string hr::sn::shader_symsol

Initial value:

= sn::common +
 
    "vec4 inverse_exp(vec4 h) {"
    
    "float ix = h[0] >= 0. ? x_to_ix(h[0]) : x_to_ix(-h[0]);"
    "float iy = h[1] >= 0. ? x_to_ix(h[1]) : x_to_ix(-h[1]);"
    "float iz = z_to_iz_s(h[2]);"
    
    "if(h[2] < 1e-6) { iz = -iz; float s = ix; ix = iy; iy = s; }"
    "if(iz < 0.) iz = 0.;"
    
    "vec4 res;"
 
    "float cx = ix*(1.-1./PRECX) + .5/PRECX;"
    "float cy = iy*(1.-1./PRECY) + .5/PRECY;"
    "float cz = iz*(1.-1./PRECZ) + .5/PRECZ;"
 
    
    "if(ix > .65 + iz * .25 && iy > .55) res = vec4(0.,0.,0.,1.); "
    
     "else "
  
      "res = texture3D(tInvExpTable, vec3(cx, cy, cz));"
 
    "if(h[2] < 1e-6) { res.xy = res.yx; res[2] = -res[2]; }"
    "if(h[0] < 0.) res[0] = -res[0];"
    "if(h[1] < 0.) res[1] = -res[1];"
    
    "return res;"
    "}"

shader_nsym

EX string hr::sn::shader_nsym

Initial value:

= sn::common +
 
    "vec4 inverse_exp(vec4 h) {"
    
    "float ix = h[0] >= 0. ? x_to_ix(h[0]) : x_to_ix(-h[0]);"
    "float iy = h[1] >= 0. ? x_to_ix(h[1]) : x_to_ix(-h[1]);"
    "float iz = z_to_iz_ns(h[2]);"
    
    "vec4 res;"
 
    "float cx = ix*(1.-1./PRECX) + .5/PRECX;"
    "float cy = iy*(1.-1./PRECY) + .5/PRECY;"
    "float cz = iz*(1.-1./PRECZ) + .5/PRECZ;"
 
    "res = texture3D(tInvExpTable, vec3(cx, cy, cz));"
 
    "if(h[0] < 0.) res[0] = -res[0];"
    "if(h[1] < 0.) res[1] = -res[1];"
    
    "return res;"
    "}"

nilshader

EX string hr::nilv::nilshader

Initial value:

= 
    "vec4 inverse_exp(vec4 h) {"
      "float wmin, wmax;"
      "float side = h[2] - h[0] * h[1] / 2.;"
      "if(h[0]*h[0] + h[1]*h[1] < 1e-12) return vec4(h[0], h[1], h[2], 1);"
      "if(side > 1e-6) { wmin = 0.; wmax = 2.*PI; }"
      "else if(side < -1e-6) { wmin = -2.*PI; wmax = 0.; }"
      "else return vec4(h[0], h[1], 0., 1.);"
      "float at = h[0] != 0. ? atan(h[1] / h[0]) : PI/2.;"
      "float b = abs(h[0]) > abs(h[1]) ? h[0] / 2. / cos(at) : h[1] / 2. / sin(at);"
      "float s = sin(2. * at);"
 
      "for(int it=0; it<50; it++) {"
        "float w = (wmin + wmax) / 2.;"
        
        "float z = b * b * (s + (abs(w) < .1 ? w/3. + w*w*w/90. + w*w*w*w*w/2520.: (sin(w) - w)/(cos(w) - 1.))) + w;"
        "if(h[2] > z) wmin = w;"
        "else wmax = w;"
        "}"
 
      "float w = (wmin + wmax) / 2.;"
      "float alpha = at - w/2.;"
      "float c = b / sin(w/2.);"
      "return vec4(c*w*cos(alpha), c*w*sin(alpha), w, 1.);"
      "}"

ns6

nilstructure hr::nilv::ns6

Initial value:

= {
    {{ mvec(-1,0,0), mvec(0,-1,0), mvec(0,0,-1), mvec(1,0,0), mvec(0,1,0), mvec(0,0,1) }},
  
    {{
    { point31(-0.5,-0.5,-0.25), point31(-0.5,-0.5,0.75), point31(-0.5,0.5,0.25), point31(-0.5,0.5,-0.75), },
    { point31(0.5,-0.5,-0.5), point31(0.5,-0.5,0.5), point31(-0.5,-0.5,0.5), point31(-0.5,-0.5,-0.5), },
    { point31(0,0,-0.5), point31(-0.5,0.5,-0.75), point31(-0.5,-0.5,-0.25), point31(0,0,-0.5), point31(-0.5,-0.5,-0.25), point31(-0.5,-0.5,-0.5), point31(0,0,-0.5), point31(-0.5,-0.5,-0.5), point31(0.5,-0.5,-0.5), point31(0,0,-0.5), point31(0.5,-0.5,-0.5), point31(0.5,-0.5,-0.75), point31(0,0,-0.5), point31(0.5,-0.5,-0.75), point31(0.5,0.5,-0.25), point31(0,0,-0.5), point31(0.5,0.5,-0.25), point31(0.5,0.5,-0.5), point31(0,0,-0.5), point31(0.5,0.5,-0.5), point31(-0.5,0.5,-0.5), point31(0,0,-0.5), point31(-0.5,0.5,-0.5), point31(-0.5,0.5,-0.75), },
    { point31(0.5,0.5,-0.25), point31(0.5,0.5,0.75), point31(0.5,-0.5,0.25), point31(0.5,-0.5,-0.75), },
    { point31(-0.5,0.5,-0.5), point31(-0.5,0.5,0.5), point31(0.5,0.5,0.5), point31(0.5,0.5,-0.5), },
    { point31(0,0,0.5), point31(-0.5,0.5,0.25), point31(-0.5,-0.5,0.75), point31(0,0,0.5), point31(-0.5,-0.5,0.75), point31(-0.5,-0.5,0.5), point31(0,0,0.5), point31(-0.5,-0.5,0.5), point31(0.5,-0.5,0.5), point31(0,0,0.5), point31(0.5,-0.5,0.5), point31(0.5,-0.5,0.25), point31(0,0,0.5), point31(0.5,-0.5,0.25), point31(0.5,0.5,0.75), point31(0,0,0.5), point31(0.5,0.5,0.75), point31(0.5,0.5,0.5), point31(0,0,0.5), point31(0.5,0.5,0.5), point31(-0.5,0.5,0.5), point31(0,0,0.5), point31(-0.5,0.5,0.5), point31(-0.5,0.5,0.25), },
    }}
    }

ns8

nilstructure hr::nilv::ns8

Initial value:

= {
    {{ mvec(-1,0,0), mvec(-1,0,1), mvec(0,-1,0), mvec(0,0,-1), mvec(1,0,0), mvec(1,0,-1), mvec(0,1,0), mvec(0,0,1) }},
  
    {{
      { point31(-0.5,-0.5,-0.25), point31(-0.5,-0.5,0.75), point31(-0.5,0.5,-0.25), },
      { point31(-0.5,-0.5,0.75), point31(-0.5,0.5,0.75), point31(-0.5,0.5,-0.25), },
      { point31(-0.5,-0.5,-0.25), point31(-0.5,-0.5,0.75), point31(0.5,-0.5,0.25), point31(0.5,-0.5,-0.75), },
      { point31(-0.5,-0.5,-0.25), point31(-0.5,0.5,-0.25), point31(0.5,0.5,-0.75), point31(0.5,-0.5,-0.75), },
      { point31(0.5,0.5,0.25), point31(0.5,-0.5,0.25), point31(0.5,-0.5,-0.75), },
      { point31(0.5,0.5,-0.75), point31(0.5,0.5,0.25), point31(0.5,-0.5,-0.75), },
      { point31(-0.5,0.5,0.75), point31(-0.5,0.5,-0.25), point31(0.5,0.5,-0.75), point31(0.5,0.5,0.25), },
      { point31(-0.5,-0.5,0.75), point31(-0.5,0.5,0.75), point31(0.5,0.5,0.25), point31(0.5,-0.5,0.25), },
      }}
    }