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%D \module
%D [ file=mp-tres.mpiv,
%D version=2017.11.08,
%D title=\CONTEXT\ \METAPOST\ graphics,
%D subtitle=Pseudo 3D,
%D author=Alan Braslau,
%D date=\currentdate,
%D copyright={PRAGMA ADE \& \CONTEXT\ Development Team}]
%C
%C This module is part of the \CONTEXT\ macro||package and is
%C therefore copyrighted by \PRAGMA. See licen-en.pdf for
%C details.
%D This module provides simple 3D->2D projections. The code is an adaption of code
%D by Urs Oswald, Dr.sc.math.\ ETH as presented in:
%D
%D \starttyping
%D http://www.ursoswald.ch/metapost/tutorial.html.
%D \stoptyping
%D
%D We need a bit more so it got extended.
if known context_three : endinput ; fi ;
boolean context_three ; context_three := true ;
pair mfun_three_xy ; % this avoids the costly save and allocate
pair mfun_three_yz ;
pair mfun_three_zx ;
transform Txy ;
def setTxy(expr ori, ang) =
begingroup
save P, t ;
pair P[] ;
transform t ;
P0 = ori ; % origin in MetaPost coordinates (bp)
P1 = (left rotated ang) scaled (cosd ang) ; % x axis (in mathematical coordinates)
% A sort of "cavalier projection".
% t: maps mathematical 2D coordinates onto MetaPost coordinates.
t := identity shifted P0 ; % Note: no shift when P0 = origin!
% Txy: maps the x-y plane of 3D space onto MetaPost coordinates,
% z is the vertical (MetaPost y).
% Txy:=identity
% reflectedabout((0,0), (1,1))
% yscaled ypart P1
% slanted (xpart P1/ypart P1)
% transformed t ;
% Alternatively, defined via Pxy:
% Pxy is the projection of the 3D plane z=0 onto the mathematical 2D coordinates.
% Pxy is determined by 3 e q u a t i o n s describing
% how (1,0), (0,1), and (0,0) are mapped
save Pxy ;
transform Pxy ;
P1 = (1,0) transformed Pxy ; % Pxy: (1,0) --> P1
(1,0) = (0,1) transformed Pxy ; % (0,1) --> (1,0)
(0,0) = (0,0) transformed Pxy ; % (0,0) --> (0,0)
% mathematical 2D coordinates --> MetaPost coordinates
Txy := Pxy transformed t ;
endgroup
enddef ;
setTxy(origin,60) ;
%D We already define triplet (as rgbcolor synonym) in in \type {mp-tool.mpiv}:
let Xpart = redpart ;
let Ypart = greenpart ;
let Zpart = bluepart ;
primarydef p Xscaled q =
(q*Xpart p, Ypart p, Zpart p)
enddef ;
primarydef p Yscaled q =
(Xpart p, q*Ypart p, Zpart p)
enddef ;
primarydef p Zscaled q =
(Xpart p, Ypart p, q*Zpart p)
enddef ;
primarydef p XYZscaled q =
(q*Xpart p,q*Ypart p,q*Zpart p)
enddef ;
vardef projection expr t =
if triplet t :
(Xpart t, Ypart t) transformed Txy shifted (0,Zpart t)
elseif pair t :
t transformed Txy
else :
origin transformed Txy
fi
enddef ;
%D This overloads the plain macro \type {abs} (being \type {length}):
vardef abs primary p =
if triplet p :
sqrt((Xpart p)**2+(Ypart p)**2+(Zpart p)**2)
else :
length p
fi
enddef ;
primarydef p dotproduct q =
((Xpart p)*(Xpart q) + (Ypart p)*(Ypart q) + (Zpart p)*(Zpart q))
enddef ;
primarydef p crossproduct q =
(
(Ypart p)*(Zpart q) - (Zpart p)*(Ypart q),
(Zpart p)*(Xpart q) - (Xpart p)*(Zpart q),
(Xpart p)*(Ypart q) - (Ypart p)*(Xpart q)
)
enddef ;
primarydef p rotatedaboutX q =
hide (
mfun_three_yz := (Ypart p, Zpart p) ;
mfun_three_yz := mfun_three_yz rotated q ;
)
(Xpart p, xpart mfun_three_yz, ypart mfun_three_yz)
enddef ;
primarydef p rotatedaboutY q =
hide(
mfun_three_zx := (Zpart p, Xpart p) ;
mfun_three_zx := mfun_three_zx rotated q ;
)
(ypart mfun_three_zx, Ypart p, xpart mfun_three_zx)
enddef ;
primarydef p rotatedaboutZ q =
hide (
mfun_three_xy := (Xpart p, Ypart p) ;
mfun_three_xy := mfun_three_xy rotated q ;
)
(xpart mfun_three_xy, ypart mfun_three_xy, Zpart p)
enddef ;
%D We can use a rotation about an arbitrary direction t ... (easy)
% primarydef p rotatedabout(expr t, a) =
% enddef ;
vardef draw_vector@# (expr v, s) text t =
if triplet v :
drawarrow projection(Origin) -- projection(v) t ;
if string s :
label@#(s, projection(v)) t ;
fi
fi
enddef ;
%D Some constants...
triplet Origin, Xunitvector, Yunitvector, Zunitvector ;
Origin := (0,0,0) ;
Xunitvector := (1,0,0) ;
Yunitvector := (0,1,0) ;
Zunitvector := (0,0,1) ;
%D We could do but don't:
% let normalxpart = xpart ;
% let normalypart = ypart ;
% vardef xpart expr p = if triplet p : redpart else : normalxpart fi p enddef ;
% vardef ypart expr p = if triplet p : greenpart else : normalypart fi p enddef ;
% vardef zpart expr p = bluepart p enddef ;
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