% for inclusion in 3d graphics programs

/RUN {} def
RUN (../ps/mkpath.inc) run

% [...] /parametrization t0 ti N 

% [x y z] -> [x/z y/z]

/perspective-0-render {
1 dict begin
/x exch def
[
x 0 get x 2 get div
x 1 get x 2 get div
]
end
} def

% [[x y z] [x' y' z']] -> [[x/z y/z][(x/z)' (y/z)']]

/perspective-1-render {
2 dict begin
aload pop
/v exch def
/x exch def
[
[
x 0 get x 2 get div
x 1 get x 2 get div
]
[
v 0 get x 2 get mul 		
x 0 get v 2 get mul sub
x 2 get dup mul div

v 1 get x 2 get mul 		
x 1 get v 2 get mul sub
x 2 get dup mul div
]
]
end
} def

% [x y z] -> [x y]

/projection-0-render {
1 dict begin
/x exch def
[
x 0 get
x 1 get
]
end
} def

% [[x y z] [x' y' z']] -> [[x y][x' y']]

/projection-1-render {
% dup ==
2 dict begin
aload pop
/v exch def
/x exch def
[
[
x 0 get
x 1 get 
]
[
v 0 get 		
v 1 get
]
]
end
} def

% -------------------------------------------------------------

% M v

/3Daffine {
3 dict begin
/3Dv exch def
aload pop
/3DT exch def
/3DM exch def
[
3DM 0 get 0 get 3Dv 0 get mul
3DM 0 get 1 get 3Dv 1 get mul
add
3DM 0 get 2 get 3Dv 2 get mul
add
3DT 0 get add

3DM 1 get 0 get 3Dv 0 get mul
3DM 1 get 1 get 3Dv 1 get mul
add
3DM 1 get 2 get 3Dv 2 get mul
add
3DT 1 get add

3DM 2 get 0 get 3Dv 0 get mul
3DM 2 get 1 get 3Dv 1 get mul
add
3DM 2 get 2 get 3Dv 2 get mul
add
3DT 2 get add
]
end
} def

% M v

/3Dmatrixvector {
2 dict begin
/3Dv exch def
/3DM exch def
[
3DM 0 get 0 get 3Dv 0 get mul
3DM 0 get 1 get 3Dv 1 get mul
add
3DM 0 get 2 get 3Dv 2 get mul
add

3DM 1 get 0 get 3Dv 0 get mul
3DM 1 get 1 get 3Dv 1 get mul
add
3DM 1 get 2 get 3Dv 2 get mul
add

3DM 2 get 0 get 3Dv 0 get mul
3DM 2 get 1 get 3Dv 1 get mul
add
3DM 2 get 2 get 3Dv 2 get mul
add
]
end
} def

% -------------------------------------------------------------

% args: [location matrix + pars to drawing call + the parametrization] + t
% output = [[X(t) Y(t)][X'(t) Y'(t)]]

/projection-convert {
10 dict begin
/t exch def
/pars exch def
/f pars 2 get cvx def
/newpars pars 1 get def
/locmat pars 0 get exch def
/position newpars t f 0 get def
/velocity newpars t f 1 get def
/position locmat position 3Daffine def
/velocity locmat 0 get velocity 3Dmatrixvector def
[position velocity]
projection-1-render
end
} def

/perspective-convert {
10 dict begin
/t exch def
/pars exch def
/f pars 2 get cvx def
/newpars pars 1 get def
/locmat pars 0 get exch def
/position newpars t f 0 get def
/velocity newpars t f 1 get def
/position locmat position 3Daffine def
/velocity locmat 0 get velocity 3Dmatrixvector def
[position velocity] 
perspective-1-render
end
} def

% 

/mkpolypath3d {
10 dict begin
/N exch def
/tf exch def
/ti exch def
/f exch def
/pars exch def
/locmat exch def
[locmat pars f] convert ti tf N mkpolypath
end
} def

/mkpath3d {
10 dict begin
/N exch def
/tf exch def
/ti exch def
/f exch def
/pars exch def
/locmat exch def
[locmat pars f] convert ti tf N mkpath
end
} def

% takes in an array of N 3D points

/mkpolygon3d {
10 dict begin
/p exch def
/locmat exch def
/N p length def
N 2 lt 
{
	% no path
} 

{
	% there is a path to be drawn
	thereisacurrentpoint 
	{
		locmat
		p 0 get  
		3Daffine 
		polygon3d-render
		aload pop
		lineto 
	}
	{
		locmat  
		p 0 get 
		3Daffine 
		polygon3d-render
		aload pop
		moveto 
	} ifelse
	1 1 N 1 sub { 
		/i exch def
		locmat  
		p i get
		3Daffine 
		polygon3d-render
		aload pop
		lineto 
	} for
} 
ifelse
end
} def

% -------------------------------------------------------

/use-perspective {
/polygon3d-render /perspective-0-render cvx def
/convert /perspective-convert def
} def

/use-projection {
/polygon3d-render /projection-0-render cvx def
/convert /projection-convert def
} def

% -------------------------------------------------------