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ico.gs
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*
* Help is in the end of this script.
*
*
function ico( args )
_version='0.01b1'
rc = gsfallow( 'on' )
set_const()
if( args = '' )
help()
return
endif
*---------- arguements ----------*
*
*----- default (1)
*
gl = -999
xo = -999
yo = -999
hp_fill = 0
_hp_color = 'colorful'
_color_kind = 'blue->red->yellow->green->magenta->orange->purple->aqua->maroon->lime'
_color_num = 10
hp_mark = 0
_hp_mark_size = 0.2
hp_number = 0
tri_fill = 0
tri_mark = 0
_tri_mark_size = 0.2
tri_number = 0
_tri_color = 'basic-region'
hp_line = 0
_hp_line_color = 1
_hp_line_thick = 2
tri_line = 0
_tri_line_color = 1
_tri_line_thick = 2
rotx = 0
roty = 0
rotz = 0
_verbose = 0
* direction of light ( (0,0,-1): light source from eye )
_ix = 0
_iy = 0
_iz = -1
_size = 2.5
_lsmask_land = 3
_lsmask_sea = 4
*----- user-specidife
*
i = 1
while( 1 )
arg = subwrd( args, i )
i = i + 1
if( arg = '' ) ; break ; endif
while( 1 )
if( arg = '-hp-fill' ) ; hp_fill = 1 ; break ; endif
if( arg = '-hp-color' ) ; _hp_color = subwrd( args, i ) ; i=i+1 ; break ; endif
if( arg = '-color-kind' ) ; _color_kind = subwrd( args, i ) ; i=i+1 ; break ; endif
if( arg = '-color-num' ) ; _color_num = subwrd( args, i ) ; i=i+1 ; break ; endif
if( arg = '-hp-number' ) ; hp_number = 1 ; break ; endif
if( arg = '-hp-mark' ) ; hp_mark = 1 ; break ; endif
if( arg = '-hp-mark-size' ) ; _hp_mark_size = subwrd( args, i ) ; i=i+1 ; break ; endif
if( arg = '-tri-fill' ) ; tri_fill = 1 ; break ; endif
if( arg = '-tri-color' )
_tri_color = subwrd( args, i )
i=i+1
if( _tri_color = 'rgb' )
_tri_color = _tri_color % ' ' % subwrd( args, i ) ; i=i+1
_tri_color = _tri_color % ' ' % subwrd( args, i ) ; i=i+1
_tri_color = _tri_color % ' ' % subwrd( args, i ) ; i=i+1
endif
break
endif
if( arg = '-tri-mark' ) ; tri_mark = 1 ; break ; endif
if( arg = '-tri-mark-size' ) ; _tri_mark_size = subwrd( args, i ) ; i=i+1 ; break ; endif
if( arg = '-tri-number' ) ; tri_number = 1 ; break ; endif
if( arg = '-hp-line' ) ; hp_line = 1 ; break ; endif
if( arg = '-hp-line-color' ) ; _hp_line_color = subwrd( args, i ) ; i=i+1 ; break ; endif
if( arg = '-hp-line-thick' ) ; _hp_line_thick = subwrd( args, i ) ; i=i+1 ; break ; endif
if( arg = '-tri-line' ) ; tri_line = 1 ; break ; endif
if( arg = '-tri-line-color' ) ; _tri_line_color = subwrd( args, i ) ; i=i+1 ; break ; endif
if( arg = '-tri-line-thick' ) ; _tri_line_thick = subwrd( args, i ) ; i=i+1 ; break ; endif
if( arg = '-rotx' ) ; rotx = subwrd( args, i ) ; i=i+1 ; break ; endif
if( arg = '-roty' ) ; roty = subwrd( args, i ) ; i=i+1 ; break ; endif
if( arg = '-rotz' ) ; rotz = subwrd( args, i ) ; i=i+1 ; break ; endif
if( arg = '-size' ) ; _size = subwrd( args, i ) ; i=i+1 ; break ; endif
if( arg = '-light' )
_ix = subwrd( args, i ) ; i=i+1
_iy = subwrd( args, i ) ; i=i+1
_iz = subwrd( args, i ) ; i=i+1
break ; endif
if( arg = '-lsmask-color' )
_lsmask_land = subwrd( args, i ) ; i=i+1
_lsmask_sea = subwrd( args, i ) ; i=i+1
break ; endif
if( arg = '-verbose' | arg = '-v' ) ; _verbose = 1 ; break ; endif
if( valnum(arg) = 1 & gl = -999) ; gl = arg ; break ; endif
if( valnum(arg) != 0 & xo = -999) ; xo = arg ; break ; endif
if( valnum(arg) != 0 & yo = -999) ; yo = arg ; break ; endif
say "syntax error: " % arg
exit
endwhile
endwhile
*
*----- default (2)
*
if( gl = -999 ) ; gl = 0 ; endif
if( xo = -999 ) ; xo = 3 ; endif
if( yo = -999 ) ; yo = 4 ; endif
if( hp_fill + tri_fill + hp_line + tri_line = 0 ) ; tri_line = 1 ; endif
*---------- arguements ----------*
if( _tri_color = 'lsmask' | _hp_color = 'lsmask' )
_lsmask_latmin = qctlinfo( 1, 'ydef', 3 )
_lsmask_latmax = -_lsmask_latmin
endif
create( gl )
rotate( rotx, roty, rotz )
if( tri_fill = 1 ) ; dtris( xo, yo, 'tri-fill' ) ; endif
if( hp_fill = 1 ) ; dtris( xo, yo, 'hp-fill' ) ; endif
if( tri_line = 1 ) ; dtris( xo, yo, 'tri-line' ) ; endif
if( hp_line = 1 ) ; dtris( xo, yo, 'hp-line' ) ; endif
if( tri_mark = 1 ) ; dtris( xo, yo, 'tri-mark' ) ; endif
if( hp_mark = 1 ) ; dtris( xo, yo, 'hp-mark' ) ; endif
if( tri_number = 1 ) ; dtris( xo, yo, 'tri-number' ) ; endif
if( hp_number = 1 ) ; dtris( xo, yo, 'hp-number' ) ; endif
return
*************************************************
*
* set constants
*
function set_const()
_pi = 4 * math_atan( 1.0 )
_d2r = _pi / 180.0
_r2d = 180.0 / _pi
return
*************************************************
*
* create icosahedral grid
*
function create( gl )
create_basic()
create_basic_tri()
while( gl > 0 )
plus_glevel()
gl = gl - 1
endwhile
_rotfinx = 0
_rotfiny = 0
_rotfinz = 0
if( _verbose = 1 )
print_x()
print_vlink()
print_trin()
endif
return
*************************************************
*
* make icosahedron (i.e. rl=0)
*
function create_basic()
*
* calculate (x,y,z) relative to O(0,0,0)
*
* reference:http://www1.ocn.ne.jp/~km31/solid_sei20.htm
*
* consider regular pentagon
*
x = _size / 2 * math_tan( 54*_d2r )
*
theta = math_acos( x / (math_sqrt(3.0)/2.0)/_size )
*
h = x * math_tan( theta )
*
theta_p = math_asin( h / _size )
*
* radius of the sphere
_r = h / ( 1 - math_cos(2*theta_p) )
*
if( _verbose = 1 )
say 'basic patameters'
say ' x = ' % x
say ' theta = ' % (theta*_r2d)
say ' h = ' % h
say ' theta_p = ' % (theta_p*_r2d)
say ' r = ' % _r
endif
*
* (_x.n, _y.n, _z.n): n-th vertex
* _vlink.n.i: neighboring vertex of n-th vertex (1<=i<=6)
* =-999: not defined
* counterclockwise for i = 1 -> 6
* _br.n: number unique for each basic region
*
* "top of the " icosahedron
_x.1 = 0.0 ; _y.1 = 0.0 ; _z.1 = _r
_vlink.1.1 = 2 ; _vlink.1.2 = 3 ; _vlink.1.3 = 4
_vlink.1.4 = 5 ; _vlink.1.5 = 6 ; _vlink.1.6 = -999
_br.1 = 1
_x.2 = _size * math_cos(theta_p)
_y.2 = 0.0
_z.2 = _r - h
_vlink.2.1 = 1 ; _vlink.2.2 = 6 ; _vlink.2.3 = 12
_vlink.2.4 = 8 ; _vlink.2.5 = 3 ; _vlink.2.6 = -999
_br.2 = 2
i = 3
while( i <= 6 )
imm = i - 1
_x.i = _x.imm * math_cos(72*_d2r) - _y.imm * math_sin(72*_d2r)
_y.i = _x.imm * math_sin(72*_d2r) + _y.imm * math_cos(72*_d2r)
_z.i = _r - h
_vlink.i.1 = 1 ; _vlink.i.2 = i-1 ; _vlink.i.3 = i+5
_vlink.i.4 = i+6 ; _vlink.i.5 = math_mod(i-1,5)+2 ; _vlink.i.6 = -999
_br.i = i
i = i + 1
endwhile
* "bottom of the" icosahedron
_x.7 = 0.0 ; _y.7 = 0.0 ; _z.7 = -_r
_vlink.7.1 = 12 ; _vlink.7.2 = 11 ; _vlink.7.3 = 10
_vlink.7.4 = 9 ; _vlink.7.5 = 8 ; _vlink.7.6 = -999
_br.7 = -1
_x.8 = _x.2 * math_cos(36*_d2r) - _y.2 * math_sin(36*_d2r)
_y.8 = _x.2 * math_sin(36*_d2r) + _y.2 * math_sin(36*_d2r)
_z.8 = -(_r - h)
_vlink.8.1 = 7 ; _vlink.8.2 = 9 ; _vlink.8.3 = 3
_vlink.8.4 = 2 ; _vlink.8.5 = 12 ; _vlink.8.6 = -999
_br.8 = -2
i = 9
while( i <= 12 )
imm = i - 1
_x.i = _x.imm * math_cos(72*_d2r) - _y.imm * math_sin(72*_d2r)
_y.i = _x.imm * math_sin(72*_d2r) + _y.imm * math_cos(72*_d2r)
_z.i = -(_r - h)
_vlink.i.1 = 7 ; _vlink.i.2 = math_mod(i-7,5)+8 ; _vlink.i.3 = math_mod(i-7,5)+2
_vlink.i.4 = i-6 ; _vlink.i.5 = i-1 ; _vlink.i.6 = -999
_br.i = -i+6
i = i + 1
endwhile
_xn = 12
_xh.1.1 = -999
return
*************************************************
*
* set triangle
* _trin.n.i: vertex number.
* position vector = [ _x.{_trin.n.i}, _y.{_trin.n.i}, _z.{_trin.n.i} ]
* n: n-th triangle
* i: i-th vertex (1<=i<=3)
* seeing from outside, _trin.n.1 - _trin.n.2 - _trin.n.3 should be counter-clockwise
function create_basic_tri()
n = 1
i = 1
while( i <= 5 )
_trin.n.1 = 1
_trin.n.2 = i + 1
_trin.n.3 = math_mod(i,5) + 2
* _tribr.n: the number unique for each basic region
_tribr.n = n
n = n + 1
i = i + 1
endwhile
i = 1
while( i <= 5 )
_trin.n.1 = 7
_trin.n.2 = math_mod(i,5) + 8
_trin.n.3 = i + 7
_tribr.n = n
n = n + 1
i = i + 1
endwhile
i = 1
while( i <= 5 )
* 8 3 2
* 9 4 3
_trin.n.1 = i + 7
_trin.n.2 = math_mod(i,5) + 2
_trin.n.3 = i + 1
_tribr.n = n - 10
n = n + 1
i = i + 1
endwhile
i = 1
while( i <= 5 )
* 3 8 9
* 4 9 10
* 5 10 11
* 6 11 12
* 2 12 8
_trin.n.1 = math_mod(i+0,5) + 2
_trin.n.2 = i + 7
_trin.n.3 = math_mod(i+0,5) + 8
_tribr.n = n - 10
n = n + 1
i = i + 1
endwhile
_trin = n - 1
return
*************************************************
*
* glevel++
*
function plus_glevel()
say "glevel++"
*----- save on temporary buffer
i = 1
while( i <= _trin )
j = 1
while( j <= 3 )
tmptrin.i.j = _trin.i.j
j = j + 1
endwhile
tmptribr.i = _tribr.i
i = i + 1
endwhile
tmptrin = _trin
_trin = 0
i = 1
while( i <= _xn )
j = 1
while( j <= 6 )
tmpvlink.i.j = _vlink.i.j
j = j + 1
endwhile
i = i + 1
endwhile
tmpxn = _xn
*----- add new vertex between the previous vertices
i = 1
while( i <= tmpxn )
j = 1
while( j <= 6 )
if( i < tmpvlink.i.j )
_xn = _xn + 1
i2 = tmpvlink.i.j
_x._xn = 0.5 * ( _x.i + _x.i2 )
_y._xn = 0.5 * ( _y.i + _y.i2 )
_z._xn = 0.5 * ( _z.i + _z.i2 )
scale = _r / math_sqrt( _x._xn*_x._xn + _y._xn*_y._xn + _z._xn*_z._xn )
_x._xn = _x._xn * scale
_y._xn = _y._xn * scale
_z._xn = _z._xn * scale
if( _br.i <= 1 ) ; _br._xn = _br.i2
else ; _br._xn = _br.i ; endif
_br._xn = -999
if( _br._xn = -999 & math_abs(_br.i) = 1 ) ; _br._xn = _br.i2 ; endif
if( _br._xn = -999 & math_abs(_br.i2) = 1 ) ; _br._xn = _br.i ; endif
if( _br._xn = -999 & _br.i * _br.i2 > 0 & math_abs(_br.i)-math_abs(_br.i2) = 4 ) ; _br._xn = _br.i ; endif
if( _br._xn = -999 & _br.i * _br.i2 > 0 & math_abs(_br.i2)-math_abs(_br.i) = 4 ) ; _br._xn = _br.i2 ; endif
if( _br._xn = -999 & _br.i * _br.i2 < 0 & _br.i+_br.i2 = 0 )
if( _br.i > 0 ) ; _br._xn = _br.i
else ; _br._xn = _br.i2 ; endif
endif
if( _br._xn = -999 & _br.i * _br.i2 < 0 )
if( _br.i > 0 ) ; _br._xn = _br.i2
else ; _br._xn = _br.i ; endif
endif
if( _br._xn = -999 )
if( math_abs(_br.i) <= math_abs(_br.i2) ) ; _br._xn = _br.i
else ; _br._xn = _br.i2 ; endif
endif
* reconnect
_vlink.i.j = _xn
* say 'reconnect: ' % i % ' ' % j % ' ' % _xn
* n1, n2 -> return j, where _vlink.n1.j = n2
* here, i, i2 -> k (NO!!!: because of tmpvlink)
* k = get_vlink_2( i, i2 )
k = 1
while( k <= 6 )
if( tmpvlink.i2.k = i )
_vlink.i2.k = _xn
* say 'reconnect: ' % i2 % ' ' % k % ' ' % _xn
break
endif
k = k + 1
endwhile
* for _xn (only for i and i2)
_vlink._xn.1 = i
_vlink._xn.4 = i2
endif
j = j + 1
endwhile
i = i + 1
endwhile
* for _xn (except for i and i2)
i = tmpxn + 1
while( i <= _xn )
n1 = _vlink.i.1
j = 1
while( j <= 6 )
if( _vlink.n1.j = i ) ; break ; endif
if( j = 6 ) ; say 'error!' ; exit ; endif
j = j + 1
endwhile
j2 = j - 1
if( j2 <= 0 ) ; j2 = j2 + 6 ; endif
if( _vlink.n1.j2 = -999 ) ; j2 = j2 - 1; endif
_vlink.i.2 = _vlink.n1.j2
j2 = j + 1
if( j2 > 6 | _vlink.n1.j2 = -999 ) ; j2 = 1 ; endif
_vlink.i.6 = _vlink.n1.j2
n4 = _vlink.i.4
j = 1
while( j <= 6 )
if( _vlink.n4.j = i ) ; break ; endif
if( j = 6 ) ; say 'error!' ; exit ; endif
j = j + 1
endwhile
j2 = j - 1
if( j2 <= 0 ) ; j2 = j2 + 6 ; endif
if( _vlink.n4.j2 = -999 ) ; j2 = j2 - 1; endif
_vlink.i.5 = _vlink.n4.j2
j2 = j + 1
if( j2 > 6 | _vlink.n4.j2 = -999 ) ; j2 = 1 ; endif
_vlink.i.3 = _vlink.n4.j2
i = i + 1
endwhile
if( _verbose = 1 )
print_x()
print_vlink()
endif
i = 1
n = 1
while( i <= tmptrin )
n1 = tmptrin.i.1
n2 = tmptrin.i.2
n3 = tmptrin.i.3
* between n1 and n2 (search for k toward n2 tmpvlink.n1.k)
k12 = 1
while( k12 <= 6 )
if( tmpvlink.n1.k12 = n2 ) ; break ; endif
if( k12 = 6 ) ; say 'error' ; exit ; endif
k12 = k12 + 1
endwhile
* between n2 and n3
k23 = 1
while( k23 <= 6 )
if( tmpvlink.n2.k23 = n3 ) ; break ; endif
if( k23 = 6 ) ; say 'error' ; exit ; endif
k23 = k23 + 1
endwhile
* between n3 and n1
k31 = 1
while( k31 <= 6 )
if( tmpvlink.n3.k31 = n1 ) ; break ; endif
if( k31 = 6 ) ; say 'error' ; exit ; endif
k31 = k31 + 1
endwhile
_trin.n.1 = n1
_trin.n.2 = _vlink.n1.k12
_trin.n.3 = _vlink.n3.k31
_tribr.n = tmptribr.i
n = n + 1
_trin.n.1 = n2
_trin.n.2 = _vlink.n2.k23
_trin.n.3 = _vlink.n1.k12
_tribr.n = tmptribr.i
n = n + 1
_trin.n.1 = n3
_trin.n.2 = _vlink.n3.k31
_trin.n.3 = _vlink.n2.k23
_tribr.n = tmptribr.i
n = n + 1
_trin.n.1 = _vlink.n1.k12
_trin.n.2 = _vlink.n2.k23
_trin.n.3 = _vlink.n3.k31
_tribr.n = tmptribr.i
n = n + 1
i = i + 1
endwhile
_trin = n - 1
_xh.1.1 = -999
if( _verbose = 1 ) ; print_trin() ; endif
return
*************************************************
*
* draw
*
function dtris( xo, yo, type )
type.1 = rgnwrd( type, 1, 1, '-' )
type.2 = rgnwrd( type, 2, 2, '-' )
if( _color_kind != '' )
'color 2 '_color_num' 1 -kind '_color_kind
endif
*---------- triangle ----------*
if( type.1 = 'tri' )
n = 1
while( n <= _trin )
n1 = _trin.n.1
n2 = _trin.n.2
n3 = _trin.n.3
* if 1-2-3 is clockwise -> not draw
theta1 = arg( _x.n2-_x.n1, _y.n2-_y.n1 )
theta2 = arg( _x.n3-_x.n1, _y.n3-_y.n1 )
theta = math_fmod( theta2 - theta1 + 2*_pi, 2*_pi )
if( theta > _pi ) ; n = n + 1 ; continue ; endif
* if( theta < _pi ) ; n = n + 1 ; continue ; endif
*----- filled triangle or mark at the center of the triangle -----*
if( type.2 = 'fill' | type.2 = 'mark' | type.2 = 'number' )
color = -999
if( valnum(_tri_color) = 1 )
color = _tri_color
endif
if( subwrd(_tri_color,1) = 'rgb' )
'set rgb 50 'subwrd(_tri_color,2)' 'subwrd(_tri_color,3)' 'subwrd(_tri_color,4)
color = 50
endif
if( _tri_color = 'colorful' )
* color = math_mod(n,10) + 16
color = math_mod(n,_color_num) + 16
endif
if( _tri_color = 'basic-region' )
color = math_mod(_tribr.n-1,10) + 16
endif
if( _tri_color = 'lsmask' )
lsmask = ( get_lsmask( _x.n1, _y.n1, _z.n1 ) + get_lsmask( _x.n2, _y.n2, _z.n2 ) + get_lsmask( _x.n3, _y.n3, _z.n3 ) ) / 3.0
if( lsmask < 0.5 ) ; color = _lsmask_sea
else ; color = _lsmask_land ; endif
endif
if( _tri_color = 'light' )
* alpha = theta_from_light( n1, n2, n3 )
alpha = theta_from_light( _x.n1, _y.n1, _z.n1, _x.n2, _y.n2, _z.n2, _x.n3, _y.n3, _z.n3 )
b = alpha2bri( alpha )
'set rgb 50 'b' 'b' 'b
color = 50
endif
if( color = -999 ) ; say 'error in color' ; exit ; endif
'set line 'color' 1'
if( type.2 = 'fill' )
'draw polyf '_x.n1+xo' '_y.n1+yo' '_x.n2+xo' '_y.n2+yo' '_x.n3+xo' '_y.n3+yo
endif
*---- mark -----*
if( type.2 = 'mark' )
x = ( _x.n1 + _x.n2 + _x.n3 ) / 3.0 + xo
y = ( _y.n1 + _y.n2 + _y.n3 ) / 3.0 + yo
'draw mark 3 'x' 'y' '_tri_mark_size
endif
*---- triangle number -----*
if( type.2 = 'number' )
'setfont huge'
'set string 'color
x = ( _x.n1 + _x.n2 + _x.n3 ) / 3.0 + xo
y = ( _y.n1 + _y.n2 + _y.n3 ) / 3.0 + yo
'draw string 'x' 'y' 'n
endif
* if( _tri_color = 'light' )
* xpos = (_x.n1 + _x.n2 + _x.n3) / 3.0 + xo
* ypos = (_y.n1 + _y.n2 + _y.n3) / 3.0 + yo
* 'setfont normal'
* 'draw string 'xpos' 'ypos' 'math_nint(alpha*_r2d)
* endif
endif
*----- line triangle -----*
if( type.2 = 'line' )
'set line '_tri_line_color' 1 '_tri_line_thick
'drawpoly '_x.n1+xo' '_y.n1+yo' '_x.n2+xo' '_y.n2+yo' '_x.n3+xo' '_y.n3+yo
endif
n = n + 1
endwhile
endif
*---------- hexagonal/pentagonal ----------*
if( type.1 = 'hp' )
if( _xh.1.1 = -999 ) ; create_hp() ; endif
n = 1
while( n <= _xn )
theta1 = arg( _xh.n.2-_xh.n.1, _yh.n.2-_yh.n.1 )
theta2 = arg( _xh.n.3-_xh.n.1, _yh.n.3-_yh.n.1 )
theta = math_fmod( theta2 - theta1 + 2*_pi, 2*_pi )
if( theta > _pi ) ; n = n + 1 ; continue ; endif
* if( theta < _pi ) ; n = n + 1 ; continue ; endif
str = ''
xc = 0 ; yc = 0 ; zc = 0
j = 1
while( j <= 6 )
if( _xh.n.j = -999 | _yh.n.j = -999 ) ; break ; endif
str = str % ' ' % _xh.n.j+xo % ' ' % _yh.n.j+yo
j = j + 1
endwhile
jn = j - 1
*----- filled hp or mark at the center of the hp -----*
if( type.2 = 'fill' | type.2 = 'mark' | type.2 = 'number' )
color = -999
if( valnum(_hp_color) = 1 )
color = _hp_color
endif
if( _hp_color = 'colorful' )
* color = math_mod(n,10) + 16
color = math_mod(n,_color_num) + 16
endif
if( _hp_color = 'lsmask' )
lsmask = 0
j = 1
while( j <= jn )
lsmask = lsmask + get_lsmask( _xh.n.j, _yh.n.j, _zh.n.j )
j = j + 1
endwhile
lsmask = lsmask + get_lsmask( _x.n, _y.n, _z.n )
lsmask = lsmask / (jn+1)
if( lsmask < 0.5 ) ; color = _lsmask_sea
else ; color = _lsmask_land ; endif
endif
if( _hp_color = 'light' )
alpha = theta_from_light( _xh.n.1, _yh.n.1, _zh.n.1, _xh.n.2, _yh.n.2, _zh.n.2, _xh.n.3, _yh.n.3, _zh.n.3 )
b = alpha2bri( alpha )
'set rgb 50 'b' 'b' 'b
color = 50
endif
if( _hp_color = 'basic-region' )
* 1<=_br.n<=6: NH, -1>=_br.n>=-6: SH
* _br.n=1 or -1: poles
color = _br.n + 7
if( _color_kind != '' )
color = 16
if( _br.n >= 2 ) ; color = _br.n + 15 ; endif
if( _br.n <= -2 ) ; color = _br.n + 28 ; endif
endif
endif
if( color = -999 ) ; say 'error in color' ; exit ; endif
'set line 'color' 1'
*---- filled -----*
if( type.2 = 'fill' )
'draw polyf 'str
endif
*---- mark -----*
if( type.2 = 'mark' )
'draw mark 3 '_x.n+xo' '_y.n+yo' '_hp_mark_size
endif
*---- number -----*
if( type.2 = 'number' )
'setfont huge'
'set string 'color
* 'draw string '_x.n+xo' '_y.n+yo' 'n
'draw string '_x.n+xo' '_y.n+yo' 'n'('_br.n')'
endif
endif
if( type.2 = 'line' )
'set line '_hp_line_color' 1 '_hp_line_thick
'drawpoly 'str
endif
n = n + 1
endwhile
endif
return
*
* note: creation of triangle grid and rotation should be finished before it is invoked.
*
function create_hp()
say "creating hexagonal-pentagonal grid"
n = 1
while( n <= _xn )
j = 1
_xh.n.6 = -999
_yh.n.6 = -999
_zh.n.6 = -999
while( j <= 6 )
if( _vlink.n.j = -999 ) ; break ; endif
jpp = j + 1
if( jpp > 6 ) ; jpp =1 ; endif
if( _vlink.n.jpp = -999 ) ; jpp =1 ; endif
n1 = n
n2 = _vlink.n.j
n3 = _vlink.n.jpp
* say n1 % ', ' % n2 % ',' % n3
zeta = 30 * _d2r
len = math_sqrt( (_x.n1-_x.n2)*(_x.n1-_x.n2) + (_y.n1-_y.n2)*(_y.n1-_y.n2) + (_z.n1-_z.n2)*(_z.n1-_z.n2) )
p = len / (2 * math_cos(zeta) )
q = len * math_cos(zeta) - p
xm = 0.5 * ( _x.n2 + _x.n3 )
ym = 0.5 * ( _y.n2 + _y.n3 )
zm = 0.5 * ( _z.n2 + _z.n3 )
x = ( q * _x.n1 + p * xm ) / ( p + q )
y = ( q * _y.n1 + p * ym ) / ( p + q )
z = ( q * _z.n1 + p * zm ) / ( p + q )
scale = _r / math_sqrt( x*x + y*y + z*z )
_xh.n.j = x * scale
_yh.n.j = y * scale
_zh.n.j = z * scale
j = j + 1
endwhile
n = n + 1
endwhile
return
*
* calculate angle relative to the toward-eye-direction
* alpha is always positive except for no reflection case
*
*function theta_from_light( n1, n2, n3 )
function theta_from_light( x1, y1, z1, x2, y2, z2, x3, y3, z3 )
*
* A = (ax,ay,az)
* B = (bx,by,bz)
* AB = A x B: vector perpendicular to the surface
* ax = _x.n2 - _x.n1 ; ay = _y.n2 - _y.n1 ; az = _z.n2 - _z.n1
* bx = _x.n3 - _x.n1 ; by = _y.n3 - _y.n1 ; bz = _z.n3 - _z.n1
ax = x2 - x1 ; ay = y2 - y1 ; az = z2 - z1
bx = x3 - x1 ; by = y3 - y1 ; bz = z3 - z1
abx = ay * bz - az * by
aby = az * bx - ax * bz
abz = ax * by - ay * bx
* say 'for ' % n % 'th triangle'
* say ' (ax,ay,az) = (' % math_format("%8.3f",ax) % ',' % math_format("%8.3f",ay) % ',' math_format("%8.3f",az) % ')'
* say ' (bx,by,bz) = (' % math_format("%8.3f",bx) % ',' % math_format("%8.3f",by) % ',' math_format("%8.3f",bz) % ')'
* say ' (abx,aby,abz) = (' % math_format("%8.3f",abx) % ',' % math_format("%8.3f",aby) % ',' math_format("%8.3f",abz) % ')'
* 'set line 1' ; 'arrow 3 2 '3+ax' '2+ay
* 'set line 2' ; 'arrow 3 2 '3+bx' '2+by
* I = (_ix,_iy,_iz) : source of light
* _ix = 1 ; _iy = 0 ; _iz = 0
* E = (ex,ey,ez) : line of sight ( positive toward eye )
ex = 0 ; ey = 0 ; ez = 1
*abx = -1 ; aby = 0 ; abz = 1
* 'set line 3' ; 'arrow 3 2 '3+abx' '2+aby
* 'set line 4' ; 'arrow 3 3 '3+_ix' '3+_iy
*----- rotate vectors to make AxB parallel to z-axis
* get angle for rotation on x-y plane to make aby=0
theta_z = arg( abx, aby )
if( theta_z = 9999 ) ; theta_z = 0 ; endif
tmpx = abx * math_cos(-theta_z) - aby * math_sin(-theta_z)
tmpy = abx * math_sin(-theta_z) + aby * math_cos(-theta_z)
tmpz = abz
* get angle for rotation on z-x plane to make abx=0
theta_y = arg( tmpz, tmpx )
if( theta_y = 9999 ) ; theta_y = 0 ; endif
r_abz = tmpz * math_cos(-theta_y) - tmpx * math_sin(-theta_y)
r_abx = tmpz * math_sin(-theta_y) + tmpx * math_cos(-theta_y)
r_aby = tmpy
* say ' (r_abx,r_aby,r_abz) = (' % math_format("%8.3f",r_abx) % ',' % math_format("%8.3f",r_aby) % ',' math_format("%8.3f",r_abz) % ')'
* rotate I
tmpx = _ix * math_cos(-theta_z) - _iy * math_sin(-theta_z)
tmpy = _ix * math_sin(-theta_z) + _iy * math_cos(-theta_z)
tmpz = _iz
r_iz = tmpz * math_cos(-theta_y) - tmpx * math_sin(-theta_y)
r_ix = tmpz * math_sin(-theta_y) + tmpx * math_cos(-theta_y)
r_iy = tmpy
* say ' (r_ix,r_iy,r_iz) = (' % math_format("%8.3f",r_ix) % ',' % math_format("%8.3f",r_iy) % ',' math_format("%8.3f",r_iz) % ')'
* 'set line 5' ; 'arrow 3 2 '3+r_abx' '2+r_aby
* 'set line 6' ; 'arrow 3 2 '3+r_ix' '2+r_iy
* fold with z-axis to obtain reflection vector R
r_rx = -r_ix ; r_ry = -r_iy ; r_rz = r_iz
r_rx = -r_rx ; r_ry = -r_ry ; r_rz = -r_rz
* reversely rotate AxB (for check)
* tmpz = r_abz * math_cos(theta_y) - r_abx * math_sin(theta_y)
* tmpx = r_abz * math_sin(theta_y) + r_abx * math_cos(theta_y)
* tmpy = r_aby
* testx = tmpx * math_cos(theta_z) - tmpy * math_sin(theta_z)
* testy = tmpx * math_sin(theta_z) + tmpy * math_cos(theta_z)
* testz = tmpz
* 'set line 7' ; 'arrow 3 2 '3+testx' '2+testy
* reversely rotate R
tmpz = r_rz * math_cos(theta_y) - r_rx * math_sin(theta_y)
tmpx = r_rz * math_sin(theta_y) + r_rx * math_cos(theta_y)
tmpy = r_ry
rx = tmpx * math_cos(theta_z) - tmpy * math_sin(theta_z)
ry = tmpx * math_sin(theta_z) + tmpy * math_cos(theta_z)
rz = tmpz
* 'set line 7' ; 'arrow 3 4 '3+rx' '4+ry
* say ' (rx,ry,rz) = (' % math_format("%8.3f",rx) % ',' % math_format("%8.3f",ry) % ',' math_format("%8.3f",rz) % ')'
* obtain angle between R and E
theta = ( rx*ex + ry*ey + rz*ez ) / ( math_sqrt( rx*rx + ry*ry + rz*rz ) * math_sqrt( ex*ex + ey*ey + ez*ez) )
theta = math_acos(theta)
if( r_abz * r_iz > 0 )
theta = -999
* say ' -> not reflected'
endif
return theta
function alpha2bri( alpha )
cr_alpha = _pi * 1.0 / 2.0
* cr_alpha = _pi * 3.0 / 7.0
* cr_alpha = _pi * 2.0 / 5.0
* cr_alpha = _pi * 1.0 / 3.0
bmin = 100
bmax = 225
if( alpha = -999 )
* no reflection
b = bmin
else
* brightest
if( alpha < cr_alpha )
b = bmax
else
* medium brightness
* b = 135
b = bmax - (bmax-bmin) * (alpha-cr_alpha)/(135*_d2r-cr_alpha)
* b = bmax - (bmax-bmin) * (alpha-cr_alpha)/(180*_d2r-cr_alpha)
if( b > bmax ) ; b = bmax ; endif
endif
endif
return b
*************************************************
*
* rotate (_x.n, _y.n, _z.n)
* angle in degree
*
function rotate( rot_p, rot_q, rot_r )
_rotfinx = _rotfinx + rot_p
_rotfiny = _rotfiny + rot_q
_rotfinz = _rotfinz + rot_r
say "rotating..."
rot_p = rot_p * _d2r
rot_q = rot_q * _d2r
rot_r = rot_r * _d2r
* rotation with respect to r (x-y plane)
i = 1
tmpsin = math_sin(rot_r)
tmpcos = math_cos(rot_r)
while( i <= _xn )
x_org = _x.i
y_org = _y.i
z_org = _z.i
_x.i = x_org * tmpcos - y_org * tmpsin
_y.i = x_org * tmpsin + y_org * tmpcos
_z.i = z_org
i = i + 1
endwhile
* rotation with respect to q (z-x plane)
i = 1
tmpsin = math_sin(rot_q)
tmpcos = math_cos(rot_q)
while( i <= _xn )
x_org = _x.i
y_org = _y.i
z_org = _z.i
_z.i = z_org * tmpcos - x_org * tmpsin
_x.i = z_org * tmpsin + x_org * tmpcos
_y.i = y_org
i = i + 1
endwhile
* rotation with respect to p (y-z plane)
i = 1
tmpsin = math_sin(rot_p)
tmpcos = math_cos(rot_p)
while( i <= _xn )
x_org = _x.i
y_org = _y.i
z_org = _z.i
_y.i = y_org * tmpcos - z_org * tmpsin
_z.i = y_org * tmpsin + z_org * tmpcos
_x.i = x_org
i = i + 1
endwhile
return
*************************************************
function get_lsmask( x, y, z )
rot_p = -_rotfinx * _d2r
rot_q = -_rotfiny * _d2r
rot_r = -_rotfinz * _d2r
* rotation with respect to p (y-z plane)
tmpsin = math_sin(rot_p)
tmpcos = math_cos(rot_p)
x_org = x
y_org = y
z_org = z
y = y_org * tmpcos - z_org * tmpsin
z = y_org * tmpsin + z_org * tmpcos
x = x_org
* rotation with respect to q (z-x plane)
tmpsin = math_sin(rot_q)
tmpcos = math_cos(rot_q)
x_org = x
y_org = y
z_org = z
z = z_org * tmpcos - x_org * tmpsin
x = z_org * tmpsin + x_org * tmpcos
y = y_org
* rotation with respect to r (x-y plane)
tmpsin = math_sin(rot_r)
tmpcos = math_cos(rot_r)