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Diffstat (limited to 'metapost/context/base/mpiv/mp-tres.mpiv')
| -rw-r--r-- | metapost/context/base/mpiv/mp-tres.mpiv | 186 |
1 files changed, 186 insertions, 0 deletions
diff --git a/metapost/context/base/mpiv/mp-tres.mpiv b/metapost/context/base/mpiv/mp-tres.mpiv new file mode 100644 index 000000000..335670a98 --- /dev/null +++ b/metapost/context/base/mpiv/mp-tres.mpiv @@ -0,0 +1,186 @@ +%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 ; + |