perm filename VIEWER[G,BGB]2 blob
sn#049883 filedate 1973-06-26 generic text, type C, neo UTF8
COMMENT ⊗ VALID 00028 PAGES
C REC PAGE DESCRIPTION
C00001 00001
C00004 00002 TITLE VIEWER - IMAGE FORMING SUBROUTINES - JULY 1972.
C00005 00003 SUBR(SHOW1)WINDOW,GLASS -----------------------------------------
C00007 00004 SUBR(SHOW2)WINDOW,GLASS ------------------------------------------
C00009 00005 SUBR(CROP)WINDOW -------------------------------------------------
C00011 00006 SUBR(PPROJ)CAMERA,WORLD---------------------------------------
C00013 00007 ----(PPROJ) TRANSLATE TO CAMERA LOCUS.
C00014 00008 ----(PPROJ) DO Z-CLIP MARKING WRT CAMERA CENTERED COORDINATES.
C00016 00009 SUBR(VPROJ,VERTEX)TRANSLATE VERTEX TO CAMERA LOCUS.
C00018 00010 SUBR(EMRKALL)WORLD-----------------------------------------------
C00019 00011 SUBR(UNPROJECT)VERTEX---------------------------------------------
C00021 00012 SUBR(FACOEF)BODY OR FACE,FLAG-------------------------------------
C00024 00013 SUBR(ENORM)BODY---------------------------------------------------
C00026 00014 SUBR(ZCLIPF)FACE--------------------------------------------------
C00028 00015 SUBR(FMRK)WORLD--------------------------------------------------
C00030 00016 SUBR(EMRK)WORLD--------------------------------------------------
C00033 00017 SUBR(VMARK)WINDOW,WORLD - MARK THE NSEW BIT OF ALL THE VERTICES.
C00036 00018 SUBR(ZCLIP)V1,U,V2------------------------------------------------
C00038 00019 XY-CLIPPER, SKIPS WHEN PORTION IS VISIBLE.
C00040 00020 XY-CLIPPER continued.
C00042 00021 SUBR(CLIPER)WINDOW -----------------------------------------------
C00044 00022 MAKE CURVY EDGED OBJECTS.
C00046 00023 CROSS I-VECTOR INTO J-VECTOR TO GET K-VECTOR RIGHT-HANDED.
C00048 00024 CREATE A VERTEX ON THE CUBIC EDGE.
C00050 00025 SUBR EXTARW,NODE
C00053 00026 ---- EXTARW continued.
C00055 00027 Arrow Extension Mandala
C00057 00028 END
C00058 ENDMK
C⊗;
TITLE VIEWER - IMAGE FORMING SUBROUTINES - JULY 1972.
EXTERN OTHER,VCW,VCCW,ECCW
EXTERN KLJUTS,KLJOTS,KLTMPS
EXTERN IIIDPY
;VARIABLES GLOBAL TO VIEWER SUBROUTINES.
DECLARE{XL,XH,YL,YH}
DECLARE{FOCAL,LDZ}
DECLARE{SCALEX,SCALEY,SCALEZ}
DECLARE{SOX,SOY,MAG}
DECLARE{CAMFRAME}
DECLARE{ZCCMIN}
DECLARE{FOLDCNT,EDGECNT}
DECLARE{CAMERA,WINDOW,WORLD,GLASS}
DECLARE{ALLSHARP}
SUBR(SHOW1)WINDOW,GLASS -----------------------------------------
BEGIN SHOW1; SHOW THRU WINDOW, TYPE 1 - DISPLAY ALL EDGES IN VIEW.
LACM ARG1↔ANDI 17↔DAC GLASS
SETOM ALLSHARP
LAC 1,ARG2↔DAC 1,WINDOW
ALT2 2,1↔DAC 2,WORLD↔JUMPE 2,POP2J.
$TYPE 0,2↔CAIE 0,$WORLD↔GO .+4
ALT 0,1↔DAC CAMERA↔JUMPE POP2J.
CALL(PPROJ,CAMERA,WORLD)
CALL(EMRKALL,WORLD)
CALL(CLIPER,WINDOW)
CALL(IIIDPY,WINDOW,GLASS)
POP2J
BEND SHOW1; BGB 16 MARCH 1973 ------------------------------------
SUBR(SHOW3)WINDOW,GLASS -----------------------------------------
BEGIN SHOW3; SHOW THUR WINDOW, TYPE 3 - BACKSIDED FACES REMOVED.
LACM ARG1↔ANDI 17↔DAC GLASS
SETZM ALLSHARP
LAC 1,ARG2↔DAC 1,WINDOW
ALT 0,1↔DAC CAMERA↔JUMPE POP2J.
ALT2 0,1↔DAC WORLD↔JUMPE POP2J.
CALL(PPROJ,CAMERA,WORLD)
CALL(FMRK,WORLD)
CALL(EMRK,WORLD)
CALL(CLIPER,WINDOW)
CALL(IIIDPY,WINDOW,GLASS)
POP2J
BEND SHOW3; BGB 16 MARCH 1973 ------------------------------------
SUBR(SHOW2)WINDOW,GLASS ------------------------------------------
BEGIN SHOW2; SHOW WINDOW TYPE 2 - VECTOR HIDDEN LINE IMAGE.
EXTERN OCCULT
LACM ARG1↔ANDI 17↔DAC GLASS
SETZM ALLSHARP
LAC 1,ARG2↔DAC 1,WINDOW
ALT 0,1↔DAC CAMERA↔JUMPE POP2J.
ALT2 0,1↔DAC WORLD↔JUMPE POP2J.
CALL(PPROJ,CAMERA,WORLD)
CALL(FMRK,WORLD)
CALL(EMRK,WORLD)
CALL(OCCULT,WORLD)
CALL(KLJOTS,WORLD)
CALL(CLIPER,WINDOW)
CALL(IIIDPY,WINDOW,GLASS)
CALL(KLTMPS,WORLD)
POP2J
BEND SHOW2; 16 MARCH 1973 ----------------------------------------
SUBR(SHOW4)WINDOW,GLASS ------------------------------------------
BEGIN SHOW3; SHOW WINDOW TYPE 3B - RUN OCCULT DIAGONOSTICS.
EXTERN OCCULT
LACM ARG1↔ANDI 17↔DAC GLASS
SETZM ALLSHARP
LAC 1,ARG2↔DAC 1,WINDOW
ALT 0,1↔DAC CAMERA↔JUMPE POP2J.
ALT2 0,1↔DAC WORLD↔JUMPE POP2J.
CALL(PPROJ,CAMERA,WORLD)
CALL(FMRK,WORLD)
CALL(EMRK,WORLD)
CALL({OCCULT+1},WORLD)
CALL(KLJOTS,WORLD)
CALL(CLIPER,WINDOW)
CALL(IIIDPY,WINDOW,GLASS)
CALL(KLTMPS,WORLD)
POP2J
BEND;2/12/73------------------------------------------------------
SUBR(CROP)WINDOW -------------------------------------------------
BEGIN CROP
; XL ← (OX - MAG*LDX) MAX -511.
; XH ← (OX + MAG*LDX) MIN +511.
; YL ← (OY - MAG*LDY) MAX -384.
; YH ← (OY + MAG*LDY) MIN +384.
ACCUMULATORS{WND,C,OX,OY,LDX,LDY,MAG}
LAC WND,ARG1
ALT C,WND↔JUMPE C,POP1J.
LAC MAG,-1(WND)
NIP OX,-2(WND)↔FLOAT OX,
NAP OY,-2(WND)↔FLOAT OY,
NAP LDX,1(C)↔FLOAT LDX,
NAP LDY,2(C)↔FLOAT LDY,
LAC LDX↔FMPR MAG↔DAC OX,1
FSBR 1,0↔FADR 0,OX↔FIXX 0,↔FIXX 1,
CAMGE 1,[-=511]↔LAC 1,[-=511]↔DIP 1,1(WND)
CAMLE 0,[ =511]↔LAC 0,[ =511]↔DAP 0,1(WND)
LAC LDY↔FMPR MAG↔DAC OY,1
FSBR 1,0↔FADR 0,OY↔FIXX 0,↔FIXX 1,
CAMGE 1,[-=384]↔LAC 1,[-=384]↔DIP 1,2(WND)
CAMLE 0,[ =384]↔LAC 0,[ =384]↔DAP 0,2(WND)
POP1J
BEND CROP; 13 MARCH 1973 -----------------------------------------
SUBR(PPROJ)CAMERA,WORLD---------------------------------------
BEGIN PPROJ
ACCUMULATORS{B,F,E,V,CAM,E0,X,XX,Y,YY,Z,ZZ}
LAC B,ARG1↔$TYPE 0,B↔CAIE $WORLD↔POP2J
;CLEAR FACE PZZ & NZZ BITS.
LAC B,ARG1
I0: CCW B,B↔TESTZ B,BBIT↔GO[LAC F,B
I1: PFACE F,F↔TEST F,FBIT↔GO I0↔MARKZ F,PZZ∨NZZ↔GO I1]
;GET CAMERA SCALES AND FOCAL.
LAC CAM,ARG2
LAC -3(CAM)↔DAC SCALEX
LAC -2(CAM)↔DAC SCALEY
LAC -1(CAM)↔DAC SCALEZ
HLLZ 3(CAM)↔DAC FOCAL
CDR 3(CAM)↔FLOAT↔DAC LDZ
;GET THE CAMERA'S FRAME.
LAC CAM,ARG2
FRAME CAM,CAM
DAC CAM,CAMFRAME
;FOR ALL THE BODIES OF THE WORLD.
LAC B,ARG1
L1: CCW B,B
TEST B,BBIT↔POP2J
MARKZ B,VISIBLE
;FOR ALL THE VERTICES OF EACH BODY.
LAC V,B
L2: PVT V,V
TEST V,VBIT↔GO L1
ZIP 7(V); CLEAR POTENT VALENCE.
CALL(VPROJ+1,V)
COMMENT⊗;----(PPROJ) TRANSLATE TO CAMERA LOCUS.
LAC X,XWC(V)↔FSBR X,XWC(CAM)
LAC Y,YWC(V)↔FSBR Y,YWC(CAM)
LAC Z,ZWC(V)↔FSBR Z,ZWC(CAM)
;ROTATE TO CAMERA ORIENTATION.
DEFINE ROTATE $(QQ,Q){
LAC QQ,X↔ FMPR QQ,Q$X(CAM)
LAC Y↔FMPR Q$Y(CAM)↔FADR QQ,
LAC Z↔FMPR Q$Z(CAM)↔FADR QQ,}
ROTATE(XX,I);
ROTATE(YY,J);
ROTATE(ZZ,K);
;PERSPECTIVE TRANSFORMATION.
FMPR XX,SCALEX↔FDVR XX,ZZ↔DAC XX,XPP(V)
FMPR YY,SCALEY↔FDVR YY,ZZ↔DAC YY,YPP(V)
MOVN Z,SCALEZ↔FDVR Z,ZZ↔DAC Z,ZPP(V)
⊗;
;----(PPROJ) DO Z-CLIP MARKING WRT CAMERA CENTERED COORDINATES.
LAC X,[JUTBIT+JOTBIT+PZZ+NZZ+FOLDED+VISIBLE+POTENT+TBIT1]
ANDCAM X,(V) ;TURN 'EM ALL OFF.
SLACI X,(PZZ) ; + HALFSPACE, BEHIND THE CAMERA.
MOVN FOCAL
CAMGE ZZ,0 ;SKIP WHEN Zcc ≥ -FOCAL.
SLACI X,(NZZ) ; - HALFSPACE, INVIEW.
IORM X,(V)
PED E,V↔DAC E,E0↔JUMPE E,[
PFACE F,B↔IORM X,(F)↔GO L1] ;VERTEX BODY CASE.
L3: PVT 1,E↔CAME 1,V↔GO .+3↔PCW 1,E↔GO .+5
NVT 1,E↔CAME 1,V↔GO L2 ↔NCW 1,E
IORM X,(E)
PFACE F,E↔IORM X,(F)
NFACE F,E↔IORM X,(F)
LAC E,1↔CAME E,E0↔GO L3↔GO L2
BEND;1/14/73------------------------------------------------------
SUBR(VPROJ,VERTEX);TRANSLATE VERTEX TO CAMERA LOCUS.
BEGIN VPROJ
ACCUMULATORS{B,F,E,V,CAM,E0,X,XX,Y,YY,Z,ZZ}
LAC CAM,CAMFRAME↔LAC V,ARG1
LAC X,XWC(V)↔FSBR X,XWC(CAM)
LAC Y,YWC(V)↔FSBR Y,YWC(CAM)
LAC Z,ZWC(V)↔FSBR Z,ZWC(CAM)
APROJ2:
;ROTATE TO CAMERA ORIENTATION.
DEFINE ROTATE $(QQ,Q){
LAC QQ,X↔ FMPR QQ,Q$X(CAM)
LAC Y↔FMPR Q$Y(CAM)↔FADR QQ,
LAC Z↔FMPR Q$Z(CAM)↔FADR QQ,}
ROTATE(XX,I);
ROTATE(YY,J);
ROTATE(ZZ,K);
;PERSPECTIVE TRANSFORMATION.
FMPR XX,SCALEX↔FDVR XX,ZZ↔DAC XX,XPP(V)
FMPR YY,SCALEY↔FDVR YY,ZZ↔DAC YY,YPP(V)
MOVN Z,SCALEZ↔FDVR Z,ZZ↔DAC Z,ZPP(V)
POP1J
↑APROJ: LAC CAM,CAMFRAME↔LAC V,ARG1
LAC X,XPP(V)↔FSBR X,XWC(CAM)
LAC Y,YPP(V)↔FSBR Y,YWC(CAM)
LAC Z,ZPP(V)↔FSBR Z,ZWC(CAM)
GO APROJ2
BEND VPROJ
SUBR(EMRKALL)WORLD-----------------------------------------------
BEGIN EMRKALL;MARK ALL EDGE AS POTENT.
ACCUMULATORS{B,E}
;FOR ALL THE BODIES OF THE WORLD.
LAC B,ARG1
L1: CCW B,B
TEST B,BBIT↔POP1J
;FOR ALL THE EDGES OF EACH BODY.
LAC E,B
L2: PED E,E
TEST E,EBIT↔GO L1
MARK E,POTENT↔GO L2
BEND;1/14/73------------------------------------------------------
SUBR(UNPROJECT)VERTEX---------------------------------------------
BEGIN UNPROJ
ACCUMULATORS{V,C,X,Y,Z,XX,YY,ZZ}
LAC V,ARG1
LAC C,CAMFRAME
;UNDO PERSPECTIVE.
LACN Z,SCALEZ↔FDVR Z,ZPP(V)
LAC Y,YPP(V)↔FMPR Y,Z↔FDVR Y,SCALEY
LAC X,XPP(V)↔FMPR X,Z↔FDVR X,SCALEX
;ROTATE BY TRANSPOSE OF CAMERA ORIENTATION.
LAC XX,X↔FMPR XX,IX(C)
LAC Y↔FMPR JX(C)↔FADR XX,
LAC Z↔FMPR KX(C)↔FADR XX,
LAC YY,Y↔FMPR YY,IY(C)
LAC Y↔FMPR JY(C)↔FADR YY,
LAC Z↔FMPR KY(C)↔FADR YY,
LAC ZZ,Z↔FMPR ZZ,IZ(C)
LAC Y↔FMPR JZ(C)↔FADR ZZ,
LAC Z↔FMPR KZ(C)↔FADR ZZ,
;TRANSLATE TO CAMERA LOCUS.
FADR XX,XWC(C)↔DAC XX,XWC(V)
FADR YY,YWC(C)↔DAC YY,YWC(V)
FADR ZZ,ZWC(C)↔DAC ZZ,ZWC(V)
POP1J
BEND;1/14/73------------------------------------------------------
SUBR(FACOEF)BODY OR FACE,FLAG-------------------------------------
BEGIN FACOEF;FACE COEFFICIENTS - FLAG=0 FOR WC, FLAG=-1 FOR PP.
ACCUMULATORS {Q,E,V1,V2,V3,ABC,F,ARG}
FOR @% Qε{XYZ}{FOR @$ N←1,3{
DEFINE Q%$N<Q%WC(V$N)>↔}}
;FOREACH F|BF⊗B≡F.
LAC F,ARG2
LAC ARG,(F) ;ORIGINAL ARG TYPE.
TLNN ARG,(BBIT)↔GO L2
L1: PFACE F,F
TEST F,FBIT↔POP2J
;FIRST THREE VERTICES CCW ABOUT THE FACE.
L2: PED E,F↔ZIP 6(F) ;CLEAR ALT LINK.
SETQ(V1,{VCW,E,F})
SETQ(V2,{VCCW,E,F})
SETQ(E,{ECCW,E,F})
SETQ(V3,{VCCW,E,F})
;FLG TRUE FOR PERSPECTIVE PROJECTED FACOEF.
SKIPE ARG1
GO[ADDI V1,7↔ADDI V2,7↔ADDI V3,7↔GO .+1]
;KK(F) ← X1*(Z2*Y3-Y2*Z3) + Y1*(X2*Z3-Z2*X3) + Z1*(Y2*X3-X2*Y3).
LAC 1,Z2↔FMPR 1,Y3↔LAC Y2↔FMPR Z3↔FSBR 1,0↔FMPR 1,X1
LAC 2,X2↔FMPR 2,Z3
LAC Z2↔FMPR X3↔FSBR 2,0↔FMPR 2,Y1↔FADR 1,2
LAC 3,Y2↔FMPR 3,X3
LAC X2↔FMPR Y3↔FSBR 3,0↔FMPR 3,Z1↔FADR 1,3
DAC 1,KK(F)
;AA(F) ← (Z1*(Y2-Y3) + Z2*(Y3-Y1) + Z3*(Y1-Y2)).
LAC 1,Y2↔FSBR 1,Y3↔FMPR 1,Z1↔LAC 0,1
LAC 1,Y3↔FSBR 1,Y1↔FMPR 1,Z2↔FADR 0,1
LAC 1,Y1↔FSBR 1,Y2↔FMPR 1,Z3↔FADR 0,1
DAC AA(F)↔FMPR↔DAC ABC
;BB(F) ← (X1*(Z2-Z3) + X2*(Z3-Z1) + X3*(Z1-Z2)).
LAC 1,Z2↔FSBR 1,Z3↔FMPR 1,X1↔LAC 0,1
LAC 1,Z3↔FSBR 1,Z1↔FMPR 1,X2↔FADR 0,1
LAC 1,Z1↔FSBR 1,Z2↔FMPR 1,X3↔FADR 0,1
DAC BB(F)↔FMPR↔FADRM ABC
;CC(F) ← (X1*(Y3-Y2) + X2*(Y1-Y3) + X3*(Y2-Y1)).
LAC 1,Y3↔FSBR 1,Y2↔FMPR 1,X1↔LAC 0,1
LAC 1,Y1↔FSBR 1,Y3↔FMPR 1,X2↔FADR 0,1
LAC 1,Y2↔FSBR 1,Y1↔FMPR 1,X3↔FADR 0,1
DAC CC(F)↔FMPR↔FADRM ABC
;NORMALIZE.
EXTERN SQRT↔CALL(SQRT,ABC)↔SLACI(<1.0>)↔FDVR 1
FMPRM AA(F)↔FMPRM BB(F)↔FMPRM CC(F)↔FMPRM KK(F)
TLNN ARG,(BBIT)↔POP2J↔GO L1
BEND;1/14/73------------------------------------------------------
SUBR(ENORM)BODY---------------------------------------------------
BEGIN ENORM;COMPUTE EDGE NORMALS FROM FACE NORMALS.
ACCUMULATORS{E,F1,F2}
LAC E,ARG1
PED E,E↔TEST E,EBIT↔POP1J
PFACE F1,E↔NFACE F2,E
LAC AA(F1)↔FAD AA(F2)↔FSC -1↔DACN AA(E)
LAC BB(F1)↔FAD BB(F2)↔FSC -1↔DACN BB(E)
LAC CC(F1)↔FAD CC(F2)↔FSC -1↔DACN CC(E)
GO ENORM+1
BEND;1/14/73------------------------------------------------------
SUBR(VNORM)BODY---------------------------------------------------
BEGIN VNORM;COMPUTE VERTEX NORMALS FROM EDGE NROMALS.
ACCUMULATORS{V,E,E0,A,B,C}
LAC V,ARG1
L1: PVT V,V↔TEST V,VBIT↔POP1J
PED E,V↔SKIPN E0,E↔POP1J ;VERTEX BODY CASE.
SETZB 0,A↔SETZB B,C
L2: FAD A,AA(E)↔FAD B,BB(E)↔FAD C,CC(E)
PVT 1,E↔CAME 1,V↔GO .+3↔PCW E,E↔GO .+5
NVT 1,E↔CAME 1,V↔AOJA .+5↔NCW E,E
CAME E,E0↔AOJA L2↔AOS
FSC 233↔FDV A,↔FDV B,↔FDV C,
DAC A,XPP(V)↔DAC B,YPP(V)↔DAC C,ZPP(V)
GO L1
BEND;1/14/73------------------------------------------------------
SUBR(ZCLIPF)FACE--------------------------------------------------
BEGIN ZCLIPF
GO L0
DECLARE{F,E,V,V1,V2,U0,U1,U2,ENEW,F0}
EXTERN MKFE,ESPLIT
;GET A PZZ VERTEX OF F0
L0: LAC 1,ARG1
DAC 1,F0↔DAC 1,U1↔DAC 1,F
PED 0,1↔DAC E
L1: SETQ(E,{ECCW,E,F})
SETQ(V,{VCCW,E,F})
TEST 1,PZZ↔GO L1
;GET FIRST NZZ VERTEX CCW AROUND F FROM E.
L2: SETQ(E,{ECCW,E,F})
SETQ(V,{VCCW,E,F})
TEST 1,NZZ↔GO L2
;MAKE Z-CLIP VERTEX.
LAC 1,E↔PVT 0,1↔CAMN 0,V↔GO .+3↔CALL INVERT,E
PVT 0,1↔DAC V1
NVT 0,1↔DAC V2
SETQ(U2,{ESPLIT,E})
LAC 1,U2↔MARK 1,TMPBIT
LAC 1,E↔TEST 1,DARKEN↔GO[
LAC 1,U2↔MARK 1,DARKEN↔GO .+1]
CALL ZCLIP,V1,U2,V2
CALL UNPROJECT,U2
LAC 1,U2↔MARK 1,NZZ
;MAKE Z-CLIP EDGE.
L3: LAC 1,U1↔TEST 1,VBIT↔GO L4
SETQ(ENEW,{MKFE,U1,F,U2})
LAC 2,ENEW↔NFACE 1,2
MARK 1,PZZ
MARK 2,TMPBIT
LAC 1,F↔MARKZ 1,PZZ
MARK 1,NZZ
CAMN 1,F0↔POP1J; .......EXIT.
NFACE 1,2↔DAC 1,F
MARK 1,PZZ
GO .+3
L4: LAC U2↔DAC U0
;ADVANCE INTO THE NEXT FACE.
LAC U2↔DAC U1
SETQ(F,{OTHER,E,F})
CAME 1,F0↔GO L2
LAC U0↔DAC U2↔GO L3
BEND;1/14/73------------------------------------------------------
SUBR(FMRK)WORLD--------------------------------------------------
BEGIN FMRK; MARK POTENT FACES.
ACCUMULATORS{W,B,F,Q,R}
;INITIALIZE THE WORLD'S POTENTIALLY VISIBLE FACE AND EDGE LISTS.
LAC 1,ARG1↔SETZ
PFACE. 0,1↔PED. 0,1↔NED. 0,1
;FOR ALL THE BODIES OF THE WORLD.
LAC B,ARG1↔DAC B,BODY#
L1: LAC B,BODY↔CCW B,B↔DAC B,BODY
TEST B,BBIT↔POP1J
PED 1,B↔TEST 1,EBIT↔POP1J ;DON'T LOOK AT SINGLE POINTS
;FOR ALL THE FACES OF EACH BODY.
LAC F,B
L2: PFACE F,F↔DAC F,FACE#
TEST F,FBIT↔GO L1
HIDE F
TEST F,NZZ↔GO L2 ;FACE IS FULLY BEHIND THE CAMERA.
TEST F,PZZ↔GO L3 ;FACE IS PARTIALLY IN VIEW.
CALL ZCLIPF,F ;DO Z-CLIPPING.
LAC F,FACE
L3: SETOM↔CALL(FACOEF,F,0)
LAC F,FACE
LAC CC(F)↔FMPR LDZ
CAML KK(F)↔GO L2 ;FACE HAS BACKSIDE TOWARDS CAMERA.
;POTENTIALLY VISIBLE FACE.
L4: MARK F,POTENT
LAC 1,ARG1↔PFACE 0,1
POTEN. 0,F↔PFACE. F,1
GO L2
BEND;1/14/73------------------------------------------------------
SUBR(EMRK)WORLD--------------------------------------------------
BEGIN EMRK; MARK POTENT EDGES FOR OCCULT.
ACCUMULATORS{Q,R,S,B,F1,F2,E,A,FLG}
ACCUMULATORS{V1,V2}
EXTERN INVERT,SQRT
SETZM FOLDCNT↔SETZM EDGECNT
;FOR ALL THE BODIES OF THE WORLD.
LAC B,ARG1
L1: CCW B,B↔TEST B,BBIT↔POP1J
;FOR ALL THE EDGES OF EACH BODY.
LAC E,B
L2: PED E,E↔TEST E,EBIT↔GO L1
DZM↔POTEN. 0,(E)
MARKZ E,7B13
PFACE F1,E
NFACE F2,E
;WHEN EITHER FACE IS POTENT THEN THE EDGE IS POTENT.
LAC(F1)↔IOR(F2)↔TLNN(POTENT)↔GO L2
MARK E,POTENT
;CONS THE EGDE INTO THE WORLD'S POTENTIALLY VISIBLE EDGE LIST.
LAC 1,ARG1↔PED 0,1↔SKIPN↔NED. E,1
PED. E,1↔POTEN. 0,E↔ZIP 7(E)
; AOSA FLG,EDGECNT
AOS FLG,EDGECNT
JRST ECOEF+1 ;PLEASE DON'T FALL THRU
;COMPUTE NORMALIZED EDGE COEFFICIENTS.
SUBR(ECOEF)
GO[SETZ FLG,↔LAC E,ARG1↔GO .+1]
NVT V1,E↔PVT V2,E
LAC YPP(V2)↔FSBR YPP(V1)↔DAC AA(E)↔FMPR↔DAC 1
LAC XPP(V1)↔FSBR XPP(V2)↔DAC BB(E)↔FMPR↔FADR 1,0
LAC XPP(V2)↔FMPR YPP(V1)
LAC S,XPP(V1)↔FMPR S,YPP(V2)
FSBR S↔DAC CC(E)
CALL(SQRT,1)
SLACI(<1.0>)↔FDVR 0,1
FMPRM AA(E)↔FMPRM BB(E)↔FMPRM CC(E)
JUMPE FLG,POP1J.
MARK V1,POTENT↔IORM(V2)
CAR 7(V1)↔AOS↔DIP 7(V1) ;VALENCE.
CAR 7(V2)↔AOS↔DIP 7(V2) ;VALENCE.
;WHEN ONLY ONE FACE IS POTENT THEN EDGE IS FOLDED.
LAC(F1)↔XOR(F2)↔TLNN(POTENT)↔GO L2
TEST F1,POTENT↔GO[CALL INVERT,E↔GO .+1];NOTA BENE !
MARK E,FOLDED↔IORM(V1)↔IORM(V2)
GO L2
BEND;1/14/73------------------------------------------------------
;SUBR(VMARK)WINDOW,WORLD - MARK THE NSEW BIT OF ALL THE VERTICES.
VMARK: 0
BEGIN VMARK;BGB - 4 FEB 1973.
ACCUMULATORS{B,E,V,X,Y}
;GET THE 2D CLIP WINDOW FRAME.
LAC 1,ARG1
NIP 1(1)↔FLOAT↔DAC XL
NAP 1(1)↔FLOAT↔DAC XH
NIP 2(1)↔FLOAT↔DAC YL
NAP 2(1)↔FLOAT↔DAC YH
;SOURCE-OBJECT MAPPING.
LAC -1(1)↔DAC MAG
NIP 2,-3(1)↔FLOAT 2,↔FMPR 2,MAG
NIP 0,-2(1)↔FLOAT↔FSB 2↔DAC SOX
NAP 2,-3(1)↔FLOAT 2,↔FMPR 2,MAG
NAP 0,-2(1)↔FLOAT↔FSB 2↔DAC SOY
;FOR ALL THE BODIES OF THE WORLD.
LAC B,ARG1↔ALT2 B,B
L1: CCW B,B
TEST B,BBIT↔GO @VMARK
;FOR ALL THE VERTICES OF EACH BODY.
LAC V,B
L2: PVT V,V
TEST V,VBIT↔GO L1
TESTZ V,POTENT↔ZAP 7(V)
COMMENT ⊗
;COMPUTE DISPLAY COORDINATES OF THE VERTEX.
LAC X,XPP(V)↔FMPR X,MAG↔FADR X,SOX↔XDC. X,V↔HLLES X
LAC Y,YPP(V)↔FMPR Y,MAG↔FADR Y,SOY↔YDC. Y,V↔HLLES Y
;DO XY-CLIP MARKING.
TYPE 0,V↔TRZ(NSEW);NSEW RESET.
CAMLE Y,YH↔TRO(NORTH)
CAMGE Y,YL↔TRO(SOUTH)
CAMLE X,XH↔TRO(EAST)
CAMGE X,XL↔TRO(WEST)
TYPE. 0,V
⊗;
; GO L2
;THE FOLLOWING IS JUST A TEST... (TVR)
CALL VMARK2
PY 1,V
JUMPE 1,L2
PUSH P,V
PUSH P,B
YLOOP: YCODE 0,1
CAIN 0,$TEXTHD
GO [ MARKZ 1,TBIT1↔CALL(VPROJ,1)↔LAC V,1(P)
CALL VMARK2↔LAC 1,V↔GO YCONT ]
CAIN 0,$ARROW
GO [ CALL(EXTARW,1)↔LAC 1,1(P)↔GO YCONT]
YCONT: PY 1,1
JUMPN 1,YLOOP
POP P,B
POP P,V
GO L2
;COMPUTE DISPLAY COORDINATES OF THE VERTEX.
VMARK2: LAC X,XPP(V)↔FMPR X,MAG↔FADR X,SOX↔XDC. X,V↔HLLES X
LAC Y,YPP(V)↔FMPR Y,MAG↔FADR Y,SOY↔YDC. Y,V↔HLLES Y
;DO XY-CLIP MARKING.
TYPE 0,V↔TRZ(NSEW);NSEW RESET.
CAMLE Y,YH↔TRO(NORTH)
CAMGE Y,YL↔TRO(SOUTH)
CAMLE X,XH↔TRO(EAST)
CAMGE X,XL↔TRO(WEST)
TYPE. 0,V
POP0J
BEND;1/14/73------------------------------------------------------
SUBR(ZCLIP)V1,U,V2------------------------------------------------
BEGIN ZCLIP
F←0 ↔ U←1
ACCUMULATORS{V1,V2,X1,Y1,Z1,X2,Y2,Z2}
SAVAC(11)
;V1 BEHIND CAMERA PLANE, V2 VEFORE CAMERA PLANE.
CDR V1,ARG3
CDR U,ARG2
CDR V2,ARG1
LAC F,FOCAL
;UNPROJECT TO CAMERA CENTERED COORDINATES.
FOR @$ I←1,2{
MOVN Z$I,SCALEZ↔ FDVR Z$I,ZPP(V$I)
LAC Y$I,Z$I↔ FMPR Y$I,YPP(V$I)↔ FDVR Y$I,SCALEY
LAC X$I,Z$I↔ FMPR X$I,XPP(V$I)↔ FDVR X$I,SCALEX}
;PIERCE Z=-FOCAL PLANE BY SIMILAR TRIANGLES & REPROJECT.
FSBR X1,X2↔ FSBR Y1,Y2↔ FSBR Z1,Z2
FADR Z2,F↔MOVNS Z2
FMPR X1,Z2↔FDVR X1,Z1↔FADR X1,X2
FMPR X1,SCALEX↔FDVR X1,F↔DACN X1,XPP(U)
FMPR Y1,Z2↔FDVR Y1,Z1↔FADR Y1,Y2
FMPR Y1,SCALEY↔FDVR Y1,F↔DACN Y1,YPP(U)
LAC 2,SCALEZ↔FDVR 2,F↔DAC 2,ZPP(U)
;MARK U'S NSEW BITS.
ACCUMULATORS{XX,YY}
LAC XX,XPP(U)↔FMPR XX,MAG↔FADR XX,SOX↔XDC. XX,U↔HLLES
LAC YY,YPP(U)↔FMPR YY,MAG↔FADR YY,SOY↔YDC. YY,U↔HLLES
TYPE 0,U↔TRZ(NSEW);NSEW RESET.
CAMLE YY,YH↔TRO(NORTH)
CAMGE YY,YL↔TRO(SOUTH)
CAMLE XX,XH↔TRO(EAST)
CAMGE XX,XL↔TRO(WEST)
TRZ(PZZ)↔TRO(NZZ)
TYPE. 0,U
GETAC(11)
POP3J
BEND;1/14/73------------------------------------------------------
;XY-CLIPPER, SKIPS WHEN PORTION IS VISIBLE.
;EXPECTS ACCUMULATORS TO BE INITIALIZED.
BEGIN XYCLIP
ACCUMULATORS{E,V1,V2,X1,Y1,X2,Y2,PTR}
DECLARE{A,B,C,FLGO,FLGZ,AXH,AXL,BYH,BYL,QNE,QNW,QSW,QSE}
↑XYCLIP: 0
;GET NSEW BITS.
LDB 0,[POINT 4,(V1),8];
LDB 1,[POINT 4,(V2),8];
;EASY OUTSIDER EDGE.
TRNE 0,(1)↔GO @XYCLIP
;GET ENDS' LOCII.
XDC X1,V1↔YDC Y1,V1
XDC X2,V2↔YDC Y2,V2
;EASY INSIDER VERTICES.
JUMPE 0,[LAC X1↔FIXX↔DIP(PTR)↔
LAC Y1↔FIXX↔DAP(PTR)↔AOBJN PTR,.+1]
JUMPE 1,[LAC X2↔FIXX↔DIP(PTR)↔
LAC Y2↔FIXX↔DAP(PTR)↔AOBJN PTR,.+1↔GO L]
;COMPUTE EDGE COEFFICIENTS.
LAC Y1↔FSBR Y2↔DAC A
LAC X2↔FSBR X1↔DAC B
LAC X2↔FMPR Y1↔MOVNM C
LAC X1↔FMPR Y2↔FADRM C
;PARTIAL PRODUCTS.
LAC A↔FMPR XH↔DAC AXH
LAC A↔FMPR XL↔DAC AXL
LAC B↔FMPR YH↔DAC BYH
LAC B↔FMPR YL↔DAC BYL
;CORNER Q'S.
SETOM FLGO↔SETZM FLGZ
LAC AXH↔FADR BYH↔FADR C↔DAC QNE↔ANDM FLGO↔IORM FLGZ
LAC AXL↔FADR BYH↔FADR C↔DAC QNW↔ANDM FLGO↔IORM FLGZ
LAC AXL↔FADR BYL↔FADR C↔DAC QSW↔ANDM FLGO↔IORM FLGZ
LAC AXH↔FADR BYL↔FADR C↔DAC QSE↔ANDM FLGO↔IORM FLGZ
;HARD OUTSIDER CASES.
SKIPGE FLGO↔GO @XYCLIP
SKIPL FLGZ↔GO @XYCLIP
;XY-CLIPPER continued.
;NORTH BORDER CROSSING.
LAC QNE↔XOR QNW↔SKIPL↔GO L2
LAC Y1↔CAMGE Y2↔LAC Y2↔CAMG YH↔GO L2
LAC BYH↔FADR C↔MOVNS↔FDVR A↔FIXX↔DIP(PTR)
LAC YH↔FIXX↔DAP(PTR)
AOBJN PTR,.+2↔GO L
;SOUTH BORDER CROSSING.
L2: LAC QSE↔XOR QSW↔SKIPL↔GO L3
LAC Y1↔CAMLE Y2↔LAC Y2↔CAML YL↔GO L3
LAC BYL↔FADR C↔MOVNS↔FDVR A↔FIXX↔DIP(PTR)
LAC YL↔FIXX↔DAP(PTR)
AOBJN PTR,.+2↔GO L
;EAST BORDER CROSSING.
L3: LAC QSE↔XOR QNE↔SKIPL↔GO L4
LAC X1↔CAMGE X2↔LAC X2↔CAMG XH↔GO L4
LAC XH↔FIXX↔DIP(PTR)
LAC AXH↔FADR C↔MOVNS↔FDVR B↔FIXX↔DAP(PTR)
AOBJN PTR,.+2↔GO L
;WEST BORDER CROSSING.
L4: LAC QSW↔XOR QNW↔SKIPL↔GO L5
LAC X1↔CAMLE X2↔LAC X2↔CAML XL↔GO L5
LAC XL↔FIXX↔DIP(PTR)
LAC AXL↔FADR C↔MOVNS↔FDVR B↔FIXX↔DAP(PTR)
AOBJN PTR,.+2↔GO L
;STRANGE EXIT - VMARK & ECOEF ARE INCONSISTENT.
L5: OUTSTR[ASCIZ/XY-CLIPPER FALL THRU !
/]↔ GO @XYCLIP
;VISIBLE PORTION EXIT.
L: AOS XYCLIP
GO @XYCLIP
LIT
BEND;1/14/73------------------------------------------------------
;END OF XY-CLIPPER.
SUBR(CLIPER)WINDOW -----------------------------------------------
BEGIN CLIPER
ACCUMULATORS{E,V1,V2,X1,Y1,X2,Y2,PTR,B,LINK}
JSR VMARK
SETZM CNT#↔SETZ LINK,;NIL OF THE LIST.
;FOR ALL THE BODIES OF THE WORLD.
LAC B,ARG1↔ALT2 B,B
L1: CCW B,B
TEST B,BBIT↔GO[PED. LINK,B↔POP1J] ;EXIT.
;FOR ALL THE EDGES OF EACH BODY.
LAC E,B
L2: PED E,E
TEST E,EBIT↔GO L1
TEST E,FOLDED↔SKIPE ALLSHARP↔GO L2A ;If it's a fold, ignore NSHARP bit (TVR)
TESTZ E,NSHARP↔GO L2
L2A: TESTZ E,DARKEN↔GO L2
TEST E,VISIBLE∨POTENT↔GO L2
;DOES EDGE NEED Z-CLIPPING.
PVT V1,E↔NVT V2,E↔LACI PTR,U
LDB 1,[POINT 2,(E),10] ;PICKUP PZZ/NZZ.
SLACI(PZZ∨NZZ)↔ANDCAM(E) ;CLEAR 'EM.
GO .+1(1) ;PZZ,NZZ
JFCL ;0,0 - EDGE AIN'T MARKED.
GO L3 ;0,1 - INVIEW HALFSPACE.
GO L4 ;1,0 - OUT'A'SIGHT.
TEST V2,NZZ ;1,1 - NEEDS Z-CLIPPING.
EXCH V1,V2 ;GET V2 INVIEW.
;CALL SUB-CLIPPER-ROUTINES.
SETQ(V1,{ZCLIP,V1,PTR,V2})
L3: SLACI PTR,-2↔LAPI PTR,-3(E)
JSR XYCLIP
GO [L4: MARKZ E,VISIBLE↔GO L2]
;CONS EDGE INTO VISIBLE EDGE LIST.
AOS CNT#
MARK E,VISIBLE
ALT2. LINK,E
LAC LINK,E
GO L2
;PSEUDO VERTEX FOR Z-CLIPPER.
LIT↔VAR
0↔0↔0↔U: BLOCK 9
BEND;2/5/73-------------------------------------------------------
COMMENT⊗;MAKE CURVY EDGED OBJECTS.
SUBR(MKCURV)------------------------------------------------------
BEGIN MKCURV
EXTERN ESPLIT,NORM
ACCUMULATORS{V,V1,V2,E}
BDY←15
;PUT NORMAL VECTORS ON EVERYTHING.
DAC 12,TMP12#
; LAC BDY,WORLD
;L1: CCW BDY,BDY
; TEST BDY,BBIT↔GO L2
LAC BDY,ARG1
SETZ↔CALL(FACOEF,BDY,0) ;WORLD COORDINATES FACE COEF.
CALL(ENORM,BDY)
CALL(VNORM,BDY)
; GO L1
L2: CCW BDY,BDY
; TESTZ BDY,BBIT↔GO .+3↔LAC 12,TMP12↔POP0J
LAC E,ARG1
L3: PED E,E↔TEST E,EBIT↔GO L2
MOVSI AA(E)↔HRRI J↔BLT J+2 ;EDGE NORMAL AS Y-AXIS.
PVT V1,E↔NVT V2,E
TESTZ V1,TMPBIT↔GO L2
TESTZ V2,TMPBIT↔GO L2
;EDGE FRAME ORIGIN IS THE EDGE'S MIDPOINT.
LAC XWC(V1)↔FAD XWC(V2)↔FSC -1↔DAC L+0 ;ORIGIN AT EDGE MIDPOINT.
LAC YWC(V1)↔FAD YWC(V2)↔FSC -1↔DAC L+1
LAC ZWC(V1)↔FAD ZWC(V2)↔FSC -1↔DAC L+2
;EDGE LINE IS THE X-AXIS.
LAC XWC(V1)↔FSB XWC(V2)↔DAC I+0
LAC YWC(V1)↔FSB YWC(V2)↔DAC I+1
LAC ZWC(V1)↔FSB ZWC(V2)↔DAC I+2
;HALF EDGE LENGTH IS UNIT.
LAC 0,I+0↔FMP
LAC 1,I+1↔FMP 1,I+1↔FAD 1
LAC 1,I+2↔FMP 1,I+2↔FAD 1
CALL(SQRT,0)↔LAC 1 ;EDGE'S LENGTH.
FSC 1,-1↔DAC 1,S ;SCALE UNIT.
FDVR [0.30]↔FIXX↔DAC CNT# ;NUMBER OF SPACES.
FSC 233↔MOVSI 1,(1.0)↔DAC 1,X# ;INITIAL X=+1.
FDVR 1,0↔FSC 1,1↔DACN 1,DX#↔SOS CNT
;CROSS I-VECTOR INTO J-VECTOR TO GET K-VECTOR RIGHT-HANDED.
K1: LAC 0,I+1↔FMPR 0,J+2
LAC 1,J+1↔FMPR 1,I+2↔FSBR 0,1↔DAC 0,K+0
LAC 0,J+0↔FMPR 0,I+2
LAC 1,I+0↔FMPR 1,J+2↔FSBR 0,1↔DAC 0,K+1
LAC 0,I+0↔FMPR 0,J+1
LAC 1,J+0↔FMPR 1,I+1↔FSBR 0,1↔DAC 0,K+2
MOVEI I↔CALL(NORM,0)
;COMPUTE SLOPE M EDGE'S PVT.
K2: PVT V,E
LAC [XWD I,7]↔BLT 14 ;PICKUP I&J VECTORS.
FMP 7,XPP(V)↔FMP 12,XPP(V) ;DOT WITH VERTEX NORMAL.
FMP 10,YPP(V)↔FMP 13,YPP(V)
FMP 11,ZPP(V)↔FMP 14,ZPP(V)
FAD 7,10↔FAD 7,11↔FAD 12,13↔FAD 12,14
FDVR 7,12↔DACN 7,M# ;SLOPE DY/DX AT PVT.
;COMPUTE SLOPE N EDGE'S NVT.
K3: NVT V,E
LAC [XWD I,7]↔BLT 14 ;PICKUP I&J VECTORS.
FMP 7,XPP(V)↔FMP 12,XPP(V) ;DOT WITH VERTEX NORMAL.
FMP 10,YPP(V)↔FMP 13,YPP(V)
FMP 11,ZPP(V)↔FMP 14,ZPP(V)
FAD 7,10↔FAD 7,11↔FAD 12,13↔FAD 12,14
FDVR 7,12↔DACN 7,N# ;SLOPE DY/DX AT NVT.
;SETUP CUBIC COEFFICIENTS.
K4: LAC M↔FAD N↔FSC -2
DAC A#↔DACN C#
LAC M↔FSB N↔FSC -2
DAC B#↔DACN D#
;CREATE A VERTEX ON THE CUBIC EDGE.
L4: LAC X↔FAD DX↔DAC X
SETQ(V,{ESPLIT,E})
MARK V,TMPBIT
;LOCUS IN Y = ((A*X+B)*X+C)*X+D).
LAC A↔FMP X↔FAD B↔FMP X↔FAD C↔FMP X↔FAD D
FMP S↔DAC 7↔DAC 8↔DAC 9
;EDGE FRAME TO WORLD FRAME.
FMP 7,J↔FMP 8,J+1↔FMP 9,J+2
LAC 1,X↔FMP 1,S
LAC I+0↔FMP 1↔FAD 7,
LAC I+1↔FMP 1↔FAD 8,
LAC I+2↔FMP 1↔FAD 9,
FAD 7,L+0↔FAD 8,L+1↔FAD 9,L+2 ;TRANSLATE.
DAC 7,XWC(V)↔DAC 8,YWC(V)↔DAC 9,ZWC(V)
SOSLE CNT↔GO L4↔GO L3
;EDGE FRAME OF REFERENCE.
L: 0 ↔ 0 ↔ 0 ;ORIGIN.
I: 0 ↔ 0 ↔ 0
J: 0 ↔ 0 ↔ 0
K: 0 ↔ 0 ↔ 0
S: 0 ;SCALE.
;L2: LAC 12,TMP12↔POP1J
BEND;1/14/73------------------------------------------------------
⊗;
SUBR EXTARW,NODE
BEGIN EXTARW
ACCUMULATORS{N,T1,T2,X1,Y1,Z1,X2,Y2,Z2,X3,Y3,Z3}
LAC N,-1(P)
TESTZ N,TBIT1↔POP1J
LDB 0,[POINT 3,(N),12] ;Get type of extension
CAILE 0,3 ;If less than 3 then get face coefficients
GO NOFACE
TRNN 0,1 ;Is PFACE involved?
GO NOTPFA
YPF 0,N ;Face coefficients for PFACE
CALL(FACOEF,0,[0])
LAC N,-1(P)
LDB 0,[POINT 3,(N),12] ;Get type of extension
TRNN 0,2 ;Is NFACE involved?
GO NOFACE
NOTPFA: YNF 0,N ;Face coefficients for NFACE
CALL(FACOEF,0,[0])
LAC N,-1(P)
NOFACE: PVT T1,N ;Pointer to first vertex in T1
PARRW 1,N↔PVT T2,1 ;Pointer to second vertex - T2
MARK N,TBIT1
MARK 1,TBIT1
FOR @` I ε {XYZ} ;Fetch second vertex coordinates.
< LAC I`1,I`WC(T2)
> ; -→
FOR @` I ε {XYZ} ;Subtract the first to get E1
< FSBR I`1,I`WC(T1)
>
LDB T1,[POINT 3,(N),12] ;Get type of extension
XCT [ ;Fetch appropriate face
GO [ ILGEXT: FATAL(ILLEGAL EXTENSION TYPE) ]
YPF T2,N
YNF T2,N
YPF T2,N
GO ILGEXT
GO ILGEXT
GO ILGEXT
GO ILGEXT ](T1) ; -→
LAC X2,AA(T2) ;Copy normal into E2
LAC Y2,BB(T2)
LAC Z2,CC(T2)
CAIE T1,3 ;Is type 3?
GO L2 ;No
YNF T2,N ;Yes, make bisector of dihedral angle
FADR X2,AA(T2)
FADR Y2,BB(T2)
FADR Z2,CC(T2) ; -→ -→ -→ -→ -→
L2: DEFINE CROSS `(X,Y,Z) ;The extension, E3 = E1 x NF (NF is in E2)
< LAC X`3,Y`1
LAC T1,Z`1
FMPR X`3,Z`2
FMPR T1,Y`2
FSBR X`3,T1
>
CROSS X,Y,Z
CROSS Y,Z,X
CROSS Z,X,Y
;---- EXTARW continued.
CALL EXTONE ;Calculate world co-ordinates for each
PARRW N,N
CALL EXTONE
CALL APROJ,N ;Run each thru projector
CALL MAKDPY
PARRW N,N
CALL APROJ,N
CALL MAKDPY
POP1J
;EXTEND ONE VERTEX
EXTONE: PVT T1,N
FOR @` I ε {XYZ} ; -→
< LAC I`1,I`3 ;Copy E3
FADR I`1,I`WC(T1) ;Add to V1
DAC I`1,I`PP(N) ;Store into V1' (into incorrect place!)
>
POP0J
;COMPUTE DISPLAY COORDINATES OF THE VERTEX.
MAKDPY: PVT T1,N ;Fetch vertex
FOR @` I ε {XYZ}
< LAC I`1,I`PP(N)↔FSBR I`1,I`PP(T1)
>
LAC 0,X1↔FMPR 0,0↔LAC 1,X1↔FMPR 1,1↔FADR 0,1
CALL SQRT,1↔LAC 0,OFFSET(N)↔FDVR 0,1
FOR @` I ε {XYZ}
< FMPR I`1,0↔FADR I`1,I`PP(T1)↔DAC I`1,I`PP(N)
>
LAC 0,XPP(N)↔FMPR 0,MAG↔FADR 0,SOX↔XDC. 0,N
LAC 0,YPP(N)↔FMPR 0,MAG↔FADR 0,SOY↔YDC. 0,N
POP0J
;Arrow Extension Mandala
COMMENT $
The dimensioning in GEOMED is done semi-automatically, by the the
command XX. It positions the arrow in terms of the offset from the
two points and a face which determines the direction of the
extension lines. This direction is calculated as follows.
V1' V2'
⊗-----------------------⊗
| |
|-→ |
|E2 -→ |
| E1 |
V1⊗-----------------------⊗V2
| __ \
| -→ /| \
| NF / \
| F1 / \
| / \
| ⊗ \
| \
⊗-------------------------------⊗
The face, F1 is defined as Ax+By+Cz+K=0
-→
The normal to F1 is: NF = (A,B,C)
-→
The endpoint of the extension, V1' is to be perpendicular to edge E1
defined by the two points, V1 and V2, and parallel to the face F1.
V1' may be defined as
-→ -→ -→ -→
V1' = V1 + k E2 where E2 = E1 X NF
-→
and similarly V2' = V2 + k E2.
The constant, k, is chosen automatically according to the distance
from the camera and focal length.
$;
BEND EXTARW;6-JUN-73(TVR)
END
VIEWER.FAI - EOF.