十進BASIC第2掲示板過去ログ

3次元図形表示

投稿者：しばっち投稿日：2019年 3月30日(土)20時04分8秒

外積を使って3次元図形表示をします。まず、座標系として上向きをY軸(Z軸ではありません)とし、奥行きを手前に向かってZ軸とする右手系を使用します。　y 　│ 　・─ x ／ z 簡単にするため光源は平行光源とし、平行投影(Z座標を無視)で描写して、拡大縮小はWINDOW文で行います。ワイヤーフレームではなく、隠面処理したサーフェスモデルでレンダリング(描画)を行います。それには頂点データ(座標値 X,Y,Z)とメッシュデータ(どの頂点と頂点をどう繋いでいくか)を用意します。この方法はデータさえ揃えればいろいろと描画させることができます。頂点データとは単に座標値のことで、頂点には順に番号が振られます。座標値を配列変数でX(n),Y(n),Z(n)とするならば添え字のnが頂点番号となります。 Meshデータとはどの頂点とを結んでいくかで、頂点にふられた頂点番号(添え字)を使って3角形、又は 4角形以上(※全ての頂点が同一平面上にあること)で構成します。また、4角形以上は3角形に分割できます。ややこしいのですがメッシュデータには「裏・表」があり、頂点(1,2,3)とする3角形が「表」向きとするなら頂点(3,2,1)では「裏」向きとなります。裏・表の判断には法線ベクトルを使い、外積によってそれを求めます。そして表向きとなる面だけを描画していけばオブジェクトの表示ができます。 3角形等はPLOT AREA文で描画できます。十進BASICのPLOT AREA文は描画が非常に高速なので、アニメーション表示が可能です。スライドバーで動かせます。 2進モードで実行してください。 ※外積を使った方法は、オブジェクトに凹み等があると正しく描画できません。 4面体を表示します(外積) OPTION ANGLE DEGREES FOR I=0 TO 7 SET COLOR MIX(I) BITAND(I,2)/2,BITAND(I,4)/4,BITAND(I,1) NEXT I CLEAR DIM X0(4),Y0(4),Z0(4),X1(4),Y1(4),Z1(4),X2(4),Y2(4),Z2(4) DIM P0(4),P1(4),P2(4) DIM L(4),M(4),N(3),CPOS(3) DIM Q(4,4),ROTX(4,4),ROTY(4,4) MAT READ CPOS !'視線ベクトル DATA 0,0,1 CALL TETRAHEDRON(0,0,0,2) LOCATE VALUE NOWAIT(1),RANGE 1 TO 10,AT 3:SCALE LOCATE VALUE NOWAIT(2),RANGE -360 TO 360,AT 0:XTH LOCATE VALUE NOWAIT(3),RANGE -360 TO 360,AT 0:YTH LOCATE VALUE NOWAIT(4),RANGE -360 TO 360,AT 0:ZTH DO LOCATE VALUE NOWAIT(1):SCALE LOCATE VALUE NOWAIT(2):XTH LOCATE VALUE NOWAIT(3):YTH LOCATE VALUE NOWAIT(4):ZTH SET WINDOW -SCALE,SCALE,-SCALE,SCALE MAT ROTX=IDN ! x軸のまわりの回転 LET ROTX(2,2)=COS(XTH) LET ROTX(2,3)=SIN(XTH) LET ROTX(3,2)=-SIN(XTH) LET ROTX(3,3)=COS(XTH) MAT ROTY=IDN ! y軸のまわりの回転 LET ROTY(1,1)=COS(YTH) LET ROTY(1,3)=-SIN(YTH) LET ROTY(3,1)=SIN(YTH) LET ROTY(3,3)=COS(YTH) MAT Q=ROTATE(ZTH) MAT Q=Q*ROTY*ROTX SET DRAW MODE HIDDEN CLEAR FOR I=1 TO NUM LET P0(1)=X0(I) LET P0(2)=Y0(I) LET P0(3)=Z0(I) LET P1(1)=X1(I) LET P1(2)=Y1(I) LET P1(3)=Z1(I) LET P2(1)=X2(I) LET P2(2)=Y2(I) LET P2(3)=Z2(I) LET P0(4),P1(4),P2(4)=1 MAT P0=P0*Q MAT P1=P1*Q MAT P2=P2*Q MAT L=P2-P1 MAT M=P1-P0 CALL OUTER(N,L,M) LET S=DOT(CPOS,N) !'内積 COS(TH) -90<TH<90...表 IF S>0 THEN !'表向きなら CALL SETBRIGHTNESS(N) CALL PLOT3(P0,P1,P2) END IF NEXT I SET DRAW MODE EXPLICIT LOOP SUB TETRAHEDRON(X,Y,Z,L) !'4面体 LET XX1=X+L*COS(0) LET ZZ1=Z+L*SIN(0) LET YY1=Y LET XX2=X+L*COS(120) LET ZZ2=Z+L*SIN(120) LET YY2=Y LET XX3=X+L*COS(240) LET ZZ3=Z+L*SIN(240) LET YY3=Y LET XX4=X LET ZZ4=Z LET YY4=Y+L*SQR(2) LET NUM=NUM+1 LET X0(NUM)=XX4 LET Y0(NUM)=YY4 LET Z0(NUM)=ZZ4 LET X1(NUM)=XX1 LET Y1(NUM)=YY1 LET Z1(NUM)=ZZ1 LET X2(NUM)=XX2 LET Y2(NUM)=YY2 LET Z2(NUM)=ZZ2 LET NUM=NUM+1 LET X0(NUM)=XX3 LET Y0(NUM)=YY3 LET Z0(NUM)=ZZ3 LET X1(NUM)=XX2 LET Y1(NUM)=YY2 LET Z1(NUM)=ZZ2 LET X2(NUM)=XX1 LET Y2(NUM)=YY1 LET Z2(NUM)=ZZ1 LET NUM=NUM+1 LET X0(NUM)=XX4 LET Y0(NUM)=YY4 LET Z0(NUM)=ZZ4 LET X1(NUM)=XX3 LET Y1(NUM)=YY3 LET Z1(NUM)=ZZ3 LET X2(NUM)=XX1 LET Y2(NUM)=YY1 LET Z2(NUM)=ZZ1 LET NUM=NUM+1 LET X0(NUM)=XX4 LET Y0(NUM)=YY4 LET Z0(NUM)=ZZ4 LET X1(NUM)=XX2 LET Y1(NUM)=YY2 LET Z1(NUM)=ZZ2 LET X2(NUM)=XX3 LET Y2(NUM)=YY3 LET Z2(NUM)=ZZ3 END SUB END EXTERNAL SUB PLOT3(P0(),P1(),P2()) !'3角形描画 PLOT AREA :P0(1),P0(2);P1(1),P1(2);P2(1),P2(2) END SUB EXTERNAL SUB SETBRIGHTNESS(N()) DIM A(3) MAT READ A ! 光源の向き DATA 1,1,1 LET S=DOT(A,N)/(SQR(DOT(A,A))*SQR(DOT(N,N))) LET S=(S+1)/2 SET COLOR MIX(8) S,S,S SET AREA COLOR 8 END SUB EXTERNAL SUB OUTER(C(),A(),B()) !'外積 LET C(1)=A(2)*B(3)-A(3)*B(2) LET C(2)=A(3)*B(1)-A(1)*B(3) LET C(3)=A(1)*B(2)-A(2)*B(1) END SUB

3次元図形表示

投稿者：しばっち投稿日：2019年 3月30日(土)20時04分40秒

6面体を表示します(外積) OPTION ANGLE DEGREES FOR I=0 TO 7 SET COLOR MIX(I) BITAND(I,2)/2,BITAND(I,4)/4,BITAND(I,1) NEXT I CLEAR DIM X0(6),Y0(6),Z0(6),X1(6),Y1(6),Z1(6),X2(6),Y2(6),Z2(6),X3(6),Y3(6),Z3(6) DIM P0(4),P1(4),P2(4),P3(4) DIM L(4),M(4),N(3),CPOS(3) DIM Q(4,4),ROTX(4,4),ROTY(4,4) MAT READ CPOS !'視線ベクトル DATA 0,0,1 CALL CUBE(0,0,0,2) LOCATE VALUE NOWAIT(1),RANGE 1 TO 10,AT 3:SCALE LOCATE VALUE NOWAIT(2),RANGE -360 TO 360,AT 0:XTH LOCATE VALUE NOWAIT(3),RANGE -360 TO 360,AT 0:YTH LOCATE VALUE NOWAIT(4),RANGE -360 TO 360,AT 0:ZTH DO LOCATE VALUE NOWAIT(1):SCALE LOCATE VALUE NOWAIT(2):XTH LOCATE VALUE NOWAIT(3):YTH LOCATE VALUE NOWAIT(4):ZTH SET WINDOW -SCALE,SCALE,-SCALE,SCALE MAT ROTX=IDN ! x軸のまわりの回転 LET ROTX(2,2)=COS(XTH) LET ROTX(2,3)=SIN(XTH) LET ROTX(3,2)=-SIN(XTH) LET ROTX(3,3)=COS(XTH) MAT ROTY=IDN ! y軸のまわりの回転 LET ROTY(1,1)=COS(YTH) LET ROTY(1,3)=-SIN(YTH) LET ROTY(3,1)=SIN(YTH) LET ROTY(3,3)=COS(YTH) MAT Q=ROTATE(ZTH) MAT Q=Q*ROTY*ROTX SET DRAW MODE HIDDEN CLEAR FOR I=1 TO NUM LET P0(1)=X0(I) LET P0(2)=Y0(I) LET P0(3)=Z0(I) LET P1(1)=X1(I) LET P1(2)=Y1(I) LET P1(3)=Z1(I) LET P2(1)=X2(I) LET P2(2)=Y2(I) LET P2(3)=Z2(I) LET P3(1)=X3(I) LET P3(2)=Y3(I) LET P3(3)=Z3(I) LET P0(4),P1(4),P2(4),P3(4)=1 MAT P0=P0*Q MAT P1=P1*Q MAT P2=P2*Q MAT P3=P3*Q MAT L=P2-P1 MAT M=P1-P0 CALL OUTER(N,L,M) LET S=DOT(CPOS,N) !'内積 COS(TH) -90<TH<90...表 IF S>0 THEN CALL SETBRIGHTNESS(N) CALL PLOT3(P0,P1,P2) END IF MAT L=P3-P2 MAT M=P2-P0 CALL OUTER(N,L,M) LET S=DOT(CPOS,N) !'内積 COS(TH) -90<TH<90...表 IF S>0 THEN CALL SETBRIGHTNESS(N) CALL PLOT3(P0,P2,P3) END IF NEXT I SET DRAW MODE EXPLICIT LOOP SUB CUBE(X,Y,Z,L) !'立方体 LET NUM=NUM+1 LET X0(NUM)=X-L/2 LET Y0(NUM)=Y+L/2 LET Z0(NUM)=Z-L/2 LET X1(NUM)=X+L/2 LET Y1(NUM)=Y+L/2 LET Z1(NUM)=Z-L/2 LET X2(NUM)=X+L/2 LET Y2(NUM)=Y+L/2 LET Z2(NUM)=Z+L/2 LET X3(NUM)=X-L/2 LET Y3(NUM)=Y+L/2 LET Z3(NUM)=Z+L/2 LET NUM=NUM+1 LET X0(NUM)=X-L/2 LET Y0(NUM)=Y+L/2 LET Z0(NUM)=Z+L/2 LET X1(NUM)=X+L/2 LET Y1(NUM)=Y+L/2 LET Z1(NUM)=Z+L/2 LET X2(NUM)=X+L/2 LET Y2(NUM)=Y-L/2 LET Z2(NUM)=Z+L/2 LET X3(NUM)=X-L/2 LET Y3(NUM)=Y-L/2 LET Z3(NUM)=Z+L/2 LET NUM=NUM+1 LET X0(NUM)=X-L/2 LET Y0(NUM)=Y-L/2 LET Z0(NUM)=Z+L/2 LET X1(NUM)=X+L/2 LET Y1(NUM)=Y-L/2 LET Z1(NUM)=Z+L/2 LET X2(NUM)=X+L/2 LET Y2(NUM)=Y-L/2 LET Z2(NUM)=Z-L/2 LET X3(NUM)=X-L/2 LET Y3(NUM)=Y-L/2 LET Z3(NUM)=Z-L/2 LET NUM=NUM+1 LET X0(NUM)=X-L/2 LET Y0(NUM)=Y-L/2 LET Z0(NUM)=Z-L/2 LET X1(NUM)=X+L/2 LET Y1(NUM)=Y-L/2 LET Z1(NUM)=Z-L/2 LET X2(NUM)=X+L/2 LET Y2(NUM)=Y+L/2 LET Z2(NUM)=Z-L/2 LET X3(NUM)=X-L/2 LET Y3(NUM)=Y+L/2 LET Z3(NUM)=Z-L/2 LET NUM=NUM+1 LET X0(NUM)=X+L/2 LET Y0(NUM)=Y+L/2 LET Z0(NUM)=Z-L/2 LET X1(NUM)=X+L/2 LET Y1(NUM)=Y-L/2 LET Z1(NUM)=Z-L/2 LET X2(NUM)=X+L/2 LET Y2(NUM)=Y-L/2 LET Z2(NUM)=Z+L/2 LET X3(NUM)=X+L/2 LET Y3(NUM)=Y+L/2 LET Z3(NUM)=Z+L/2 LET NUM=NUM+1 LET X0(NUM)=X-L/2 LET Y0(NUM)=Y-L/2 LET Z0(NUM)=Z-L/2 LET X1(NUM)=X-L/2 LET Y1(NUM)=Y+L/2 LET Z1(NUM)=Z-L/2 LET X2(NUM)=X-L/2 LET Y2(NUM)=Y+L/2 LET Z2(NUM)=Z+L/2 LET X3(NUM)=X-L/2 LET Y3(NUM)=Y-L/2 LET Z3(NUM)=Z+L/2 END SUB END EXTERNAL SUB PLOT3(P0(),P1(),P2()) !'3角形描画 PLOT AREA :P0(1),P0(2);P1(1),P1(2);P2(1),P2(2) END SUB EXTERNAL SUB SETBRIGHTNESS(N()) DIM A(3) MAT READ A ! 光源の向き DATA 1,1,1 LET S=DOT(A,N)/(SQR(DOT(A,A))*SQR(DOT(N,N))) LET S=(S+1)/2 SET COLOR MIX(8) S,S,S SET AREA COLOR 8 END SUB EXTERNAL SUB OUTER(C(),A(),B()) !'外積 LET C(1)=A(2)*B(3)-A(3)*B(2) LET C(2)=A(3)*B(1)-A(1)*B(3) LET C(3)=A(1)*B(2)-A(2)*B(1) END SUB

3次元図形表示

投稿者：しばっち投稿日：2019年 3月30日(土)20時05分18秒

8面体を表示します(外積) OPTION ANGLE DEGREES FOR I=0 TO 7 SET COLOR MIX(I) BITAND(I,2)/2,BITAND(I,4)/4,BITAND(I,1) NEXT I CLEAR DIM X0(8),Y0(8),Z0(8),X1(8),Y1(8),Z1(8),X2(8),Y2(8),Z2(8) DIM P0(4),P1(4),P2(4) DIM L(4),M(4),N(3),CPOS(3) DIM Q(4,4),ROTX(4,4),ROTY(4,4) MAT READ CPOS !'視線ベクトル DATA 0,0,1 CALL OCTAH(0,0,0,2,2,2) LOCATE VALUE NOWAIT(1),RANGE 1 TO 10,AT 3:SCALE LOCATE VALUE NOWAIT(2),RANGE -360 TO 360,AT 0:XTH LOCATE VALUE NOWAIT(3),RANGE -360 TO 360,AT 0:YTH LOCATE VALUE NOWAIT(4),RANGE -360 TO 360,AT 0:ZTH DO LOCATE VALUE NOWAIT(1):SCALE LOCATE VALUE NOWAIT(2):XTH LOCATE VALUE NOWAIT(3):YTH LOCATE VALUE NOWAIT(4):ZTH SET WINDOW -SCALE,SCALE,-SCALE,SCALE MAT ROTX=IDN ! x軸のまわりの回転 LET ROTX(2,2)=COS(XTH) LET ROTX(2,3)=SIN(XTH) LET ROTX(3,2)=-SIN(XTH) LET ROTX(3,3)=COS(XTH) MAT ROTY=IDN ! y軸のまわりの回転 LET ROTY(1,1)=COS(YTH) LET ROTY(1,3)=-SIN(YTH) LET ROTY(3,1)=SIN(YTH) LET ROTY(3,3)=COS(YTH) MAT Q=ROTATE(ZTH) MAT Q=Q*ROTY*ROTX SET DRAW MODE HIDDEN CLEAR FOR I=1 TO NUM LET P0(1)=X0(I) LET P0(2)=Y0(I) LET P0(3)=Z0(I) LET P1(1)=X1(I) LET P1(2)=Y1(I) LET P1(3)=Z1(I) LET P2(1)=X2(I) LET P2(2)=Y2(I) LET P2(3)=Z2(I) LET P0(4),P1(4),P2(4)=1 MAT P0=P0*Q MAT P1=P1*Q MAT P2=P2*Q MAT L=P2-P1 MAT M=P1-P0 CALL OUTER(N,L,M) LET S=DOT(CPOS,N) !'内積 COS(TH) -90<TH<90...表 IF S>0 THEN CALL SETBRIGHTNESS(N) CALL PLOT3(P0,P1,P2) END IF NEXT I SET DRAW MODE EXPLICIT LOOP SUB OCTAH(X,Y,Z,XL,YL,ZL) !'8面体 LET XX0=X LET YY0=Y+YL/2 LET ZZ0=Z LET XX1=X+XL/2 LET YY1=Y LET ZZ1=Z LET XX2=X LET YY2=Y LET ZZ2=Z+ZL/2 LET XX3=X-XL/2 LET YY3=Y LET ZZ3=Z LET XX4=X LET YY4=Y LET ZZ4=Z-ZL/2 LET XX5=X LET YY5=Y-YL/2 LET ZZ5=Z LET NUM=NUM+1 LET X0(NUM)=XX0 LET Y0(NUM)=YY0 LET Z0(NUM)=ZZ0 LET X1(NUM)=XX1 LET Y1(NUM)=YY1 LET Z1(NUM)=ZZ1 LET X2(NUM)=XX2 LET Y2(NUM)=YY2 LET Z2(NUM)=ZZ2 LET NUM=NUM+1 LET X0(NUM)=XX0 LET Y0(NUM)=YY0 LET Z0(NUM)=ZZ0 LET X1(NUM)=XX2 LET Y1(NUM)=YY2 LET Z1(NUM)=ZZ2 LET X2(NUM)=XX3 LET Y2(NUM)=YY3 LET Z2(NUM)=ZZ3 LET NUM=NUM+1 LET X0(NUM)=XX0 LET Y0(NUM)=YY0 LET Z0(NUM)=ZZ0 LET X1(NUM)=XX3 LET Y1(NUM)=YY3 LET Z1(NUM)=ZZ3 LET X2(NUM)=XX4 LET Y2(NUM)=YY4 LET Z2(NUM)=ZZ4 LET NUM=NUM+1 LET X0(NUM)=XX0 LET Y0(NUM)=YY0 LET Z0(NUM)=ZZ0 LET X1(NUM)=XX4 LET Y1(NUM)=YY4 LET Z1(NUM)=ZZ4 LET X2(NUM)=XX1 LET Y2(NUM)=YY1 LET Z2(NUM)=ZZ1 LET NUM=NUM+1 LET X0(NUM)=XX5 LET Y0(NUM)=YY5 LET Z0(NUM)=ZZ5 LET X1(NUM)=XX2 LET Y1(NUM)=YY2 LET Z1(NUM)=ZZ2 LET X2(NUM)=XX1 LET Y2(NUM)=YY1 LET Z2(NUM)=ZZ1 LET NUM=NUM+1 LET X0(NUM)=XX5 LET Y0(NUM)=YY5 LET Z0(NUM)=ZZ5 LET X1(NUM)=XX3 LET Y1(NUM)=YY3 LET Z1(NUM)=ZZ3 LET X2(NUM)=XX2 LET Y2(NUM)=YY2 LET Z2(NUM)=ZZ2 LET NUM=NUM+1 LET X0(NUM)=XX5 LET Y0(NUM)=YY5 LET Z0(NUM)=ZZ5 LET X1(NUM)=XX4 LET Y1(NUM)=YY4 LET Z1(NUM)=ZZ4 LET X2(NUM)=XX3 LET Y2(NUM)=YY3 LET Z2(NUM)=ZZ3 LET NUM=NUM+1 LET X0(NUM)=XX5 LET Y0(NUM)=YY5 LET Z0(NUM)=ZZ5 LET X1(NUM)=XX1 LET Y1(NUM)=YY1 LET Z1(NUM)=ZZ1 LET X2(NUM)=XX4 LET Y2(NUM)=YY4 LET Z2(NUM)=ZZ4 END SUB END EXTERNAL SUB PLOT3(P0(),P1(),P2()) !'3角形描画 PLOT AREA :P0(1),P0(2);P1(1),P1(2);P2(1),P2(2) END SUB EXTERNAL SUB SETBRIGHTNESS(N()) DIM A(3) MAT READ A ! 光源の向き DATA 1,1,1 LET S=DOT(A,N)/(SQR(DOT(A,A))*SQR(DOT(N,N))) LET S=(S+1)/2 SET COLOR MIX(8) S,S,S SET AREA COLOR 8 END SUB EXTERNAL SUB OUTER(C(),A(),B()) !'外積 LET C(1)=A(2)*B(3)-A(3)*B(2) LET C(2)=A(3)*B(1)-A(1)*B(3) LET C(3)=A(1)*B(2)-A(2)*B(1) END SUB

3次元図形表示

投稿者：しばっち投稿日：2019年 3月30日(土)20時05分59秒

12面体を表示します(外積) OPTION ANGLE DEGREES FOR I=0 TO 7 SET COLOR MIX(I) BITAND(I,2)/2,BITAND(I,4)/4,BITAND(I,1) NEXT I CLEAR DIM X0(36),Y0(36),Z0(36),X1(36),Y1(36),Z1(36),X2(36),Y2(36),Z2(36) DIM P0(4),P1(4),P2(4),P3(4) DIM L(4),M(4),N(3),CPOS(3) DIM Q(4,4),ROTX(4,4),ROTY(4,4) DIM XX(20),YY(20),ZZ(20) LET LL=1 FOR TH=0 TO 359 STEP 72 LET K=K+1 LET XX(K)=LL*COS((TH+18)) LET ZZ(K)=LL*SIN((TH+18)) LET YY(K)=LL*(SQR(5)+3)/4 NEXT TH FOR TH=0 TO 359 STEP 72 LET K=K+1 LET XX(K)=LL*(SQR(5)+1)/2*COS((TH+18)) LET ZZ(K)=LL*(SQR(5)+1)/2*SIN((TH+18)) LET YY(K)=LL*(SQR(5)-1)/4 NEXT TH FOR TH=0 TO 359 STEP 72 LET K=K+1 LET XX(K)=LL*(SQR(5)+1)/2*COS((TH+54)) LET ZZ(K)=LL*(SQR(5)+1)/2*SIN((TH+54)) LET YY(K)=-LL*(SQR(5)-1)/4 NEXT TH FOR TH=0 TO 359 STEP 72 LET K=K+1 LET XX(K)=LL*COS((TH+54)) LET ZZ(K)=LL*SIN((TH+54)) LET YY(K)=-LL*(SQR(5)+3)/4 NEXT TH FOR I=1 TO 36 READ A,B,C LET X0(I)=XX(A+1) LET Y0(I)=YY(A+1) LET Z0(I)=ZZ(A+1) LET X1(I)=XX(B+1) LET Y1(I)=YY(B+1) LET Z1(I)=ZZ(B+1) LET X2(I)=XX(C+1) LET Y2(I)=YY(C+1) LET Z2(I)=ZZ(C+1) NEXT I DATA 0,1,2 !'メッシュデータ DATA 0,2,3 DATA 0,3,4 DATA 5,10,6 DATA 5,6,1 DATA 5,1,0 DATA 6,11,7 DATA 6,7,2 DATA 6,2,1 DATA 7,12,8 DATA 7,8,3 DATA 7,3,2 DATA 8,13,9 DATA 8,9,4 DATA 8,4,3 DATA 9,14,5 DATA 9,5,0 DATA 9,0,4 DATA 15,16,11 DATA 15,11,6 DATA 15,6,10 DATA 16,17,12 DATA 16,12,7 DATA 16,7,11 DATA 17,18,13 DATA 17,13,8 DATA 17,8,12 DATA 18,19,14 DATA 18,14,9 DATA 18,9,13 DATA 19,15,10 DATA 19,10,5 DATA 19,5,14 DATA 19,18,17 DATA 19,17,16 DATA 19,16,15 MAT READ CPOS !'視線ベクトル DATA 0,0,1 LOCATE VALUE NOWAIT(1),RANGE 1 TO 10,AT 3:SCALE LOCATE VALUE NOWAIT(2),RANGE -360 TO 360,AT 0:XTH LOCATE VALUE NOWAIT(3),RANGE -360 TO 360,AT 0:YTH LOCATE VALUE NOWAIT(4),RANGE -360 TO 360,AT 0:ZTH DO LOCATE VALUE NOWAIT(1):SCALE LOCATE VALUE NOWAIT(2):XTH LOCATE VALUE NOWAIT(3):YTH LOCATE VALUE NOWAIT(4):ZTH SET WINDOW -SCALE,SCALE,-SCALE,SCALE MAT ROTX=IDN ! x軸のまわりの回転 LET ROTX(2,2)=COS(XTH) LET ROTX(2,3)=SIN(XTH) LET ROTX(3,2)=-SIN(XTH) LET ROTX(3,3)=COS(XTH) MAT ROTY=IDN ! y軸のまわりの回転 LET ROTY(1,1)=COS(YTH) LET ROTY(1,3)=-SIN(YTH) LET ROTY(3,1)=SIN(YTH) LET ROTY(3,3)=COS(YTH) MAT Q=ROTATE(ZTH) MAT Q=Q*ROTY*ROTX SET DRAW MODE HIDDEN CLEAR FOR I=1 TO 36 LET P0(1)=X0(I) LET P0(2)=Y0(I) LET P0(3)=Z0(I) LET P1(1)=X1(I) LET P1(2)=Y1(I) LET P1(3)=Z1(I) LET P2(1)=X2(I) LET P2(2)=Y2(I) LET P2(3)=Z2(I) LET P0(4),P1(4),P2(4)=1 MAT P0=P0*Q MAT P1=P1*Q MAT P2=P2*Q MAT L=P2-P1 MAT M=P1-P0 CALL OUTER(N,L,M) LET S=DOT(CPOS,N) !'内積 COS(TH) -90<TH<90...表 IF S>0 THEN CALL SETBRIGHTNESS(N) CALL PLOT3(P0,P1,P2) END IF NEXT I SET DRAW MODE EXPLICIT LOOP END EXTERNAL SUB PLOT3(P0(),P1(),P2()) !'3角形描画 PLOT AREA :P0(1),P0(2);P1(1),P1(2);P2(1),P2(2) END SUB EXTERNAL SUB SETBRIGHTNESS(N()) DIM A(3) MAT READ A ! 光源の向き DATA 1,1,1 LET S=DOT(A,N)/(SQR(DOT(A,A))*SQR(DOT(N,N))) LET S=(S+1)/2 SET COLOR MIX(8) S,S,S SET AREA COLOR 8 END SUB EXTERNAL SUB OUTER(C(),A(),B()) !'外積 LET C(1)=A(2)*B(3)-A(3)*B(2) LET C(2)=A(3)*B(1)-A(1)*B(3) LET C(3)=A(1)*B(2)-A(2)*B(1) END SUB

3次元図形表示

投稿者：しばっち投稿日：2019年 3月30日(土)20時06分41秒

4角錐を表示します(外積) OPTION ANGLE DEGREES FOR I=0 TO 7 SET COLOR MIX(I) BITAND(I,2)/2,BITAND(I,4)/4,BITAND(I,1) NEXT I DIM X0(100),Y0(100),Z0(100),X1(100),Y1(100),Z1(100),X2(100),Y2(100),Z2(100) DIM P0(4),P1(4),P2(4) DIM L(4),M(4),N(3),CPOS(3) DIM Q(4,4),ROTX(4,4),ROTY(4,4) DIM XX(15),YY(15),ZZ(15) LOCATE VALUE NOWAIT(1),RANGE 1 TO 10,AT 3:SCALE LOCATE VALUE NOWAIT(2),RANGE -360 TO 360,AT 0:XTH LOCATE VALUE NOWAIT(3),RANGE -360 TO 360,AT 0:YTH LOCATE VALUE NOWAIT(4),RANGE -360 TO 360,AT 0:ZTH LOCATE VALUE NOWAIT(5),RANGE .1 TO 5,AT 2:LL DO LOCATE VALUE NOWAIT(1):SCALE LOCATE VALUE NOWAIT(2):XTH LOCATE VALUE NOWAIT(3):YTH LOCATE VALUE NOWAIT(4):ZTH LOCATE VALUE NOWAIT(5):LL SET WINDOW -SCALE,SCALE,-SCALE,SCALE LET XX(1)=X LET YY(1)=Y LET ZZ(1)=Z LET XX(2)=X-LL/2 LET YY(2)=Y-LL*SQR(3)/2 LET ZZ(2)=Z+LL/2 LET XX(3)=X+LL/2 LET YY(3)=Y-LL*SQR(3)/2 LET ZZ(3)=Z+LL/2 LET XX(4)=X+LL/2 LET YY(4)=Y-LL*SQR(3)/2 LET ZZ(4)=Z-LL/2 LET XX(5)=X-LL/2 LET YY(5)=Y-LL*SQR(3)/2 LET ZZ(5)=Z-LL/2 RESTORE FOR I=1 TO 6 READ A,B,C LET X0(I)=XX(A+1) LET Y0(I)=YY(A+1) LET Z0(I)=ZZ(A+1) LET X1(I)=XX(B+1) LET Y1(I)=YY(B+1) LET Z1(I)=ZZ(B+1) LET X2(I)=XX(C+1) LET Y2(I)=YY(C+1) LET Z2(I)=ZZ(C+1) NEXT I DATA 0,2,1 !'メッシュデータ DATA 0,3,2 DATA 0,4,3 DATA 0,1,4 DATA 1,2,3 DATA 1,3,4 MAT ROTX=IDN ! x軸のまわりの回転 LET ROTX(2,2)=COS(XTH) LET ROTX(2,3)=SIN(XTH) LET ROTX(3,2)=-SIN(XTH) LET ROTX(3,3)=COS(XTH) MAT ROTY=IDN ! y軸のまわりの回転 LET ROTY(1,1)=COS(YTH) LET ROTY(1,3)=-SIN(YTH) LET ROTY(3,1)=SIN(YTH) LET ROTY(3,3)=COS(YTH) MAT Q=ROTATE(ZTH) MAT Q=Q*ROTY*ROTX MAT READ CPOS !'視線ベクトル DATA 0,0,1 SET DRAW MODE HIDDEN CLEAR FOR I=1 TO 6 LET P0(1)=X0(I) LET P0(2)=Y0(I) LET P0(3)=Z0(I) LET P1(1)=X1(I) LET P1(2)=Y1(I) LET P1(3)=Z1(I) LET P2(1)=X2(I) LET P2(2)=Y2(I) LET P2(3)=Z2(I) LET P0(4),P1(4),P2(4)=1 MAT P0=P0*Q MAT P1=P1*Q MAT P2=P2*Q MAT L=P2-P1 MAT M=P1-P0 CALL OUTER(N,L,M) LET S=DOT(CPOS,N) !'内積 COS(TH) -90<TH<90...表 IF S>0 THEN CALL SETBRIGHTNESS(N) CALL PLOT3(P0,P1,P2) END IF NEXT I SET DRAW MODE EXPLICIT LOOP END EXTERNAL SUB PLOT3(P0(),P1(),P2()) !'3角形描画 PLOT AREA :P0(1),P0(2);P1(1),P1(2);P2(1),P2(2) END SUB EXTERNAL SUB SETBRIGHTNESS(N()) DIM A(3) MAT READ A ! 光源の向き DATA 1,1,1 LET S=DOT(A,N)/(SQR(DOT(A,A))*SQR(DOT(N,N))) LET S=(S+1)/2 SET COLOR MIX(8) S,S,S SET AREA COLOR 8 END SUB EXTERNAL SUB OUTER(C(),A(),B()) !'外積 LET C(1)=A(2)*B(3)-A(3)*B(2) LET C(2)=A(3)*B(1)-A(1)*B(3) LET C(3)=A(1)*B(2)-A(2)*B(1) END SUB

3次元図形表示

投稿者：しばっち投稿日：2019年 3月30日(土)20時07分30秒

N角柱を表示します(外積) OPTION ANGLE DEGREES FOR I=0 TO 7 SET COLOR MIX(I) BITAND(I,2)/2,BITAND(I,4)/4,BITAND(I,1) NEXT I DIM X0(100),Y0(100),Z0(100),X1(100),Y1(100),Z1(100),X2(100),Y2(100),Z2(100) DIM P0(4),P1(4),P2(4) DIM L(4),M(4),N(3),CPOS(3) DIM Q(4,4),ROTX(4,4),ROTY(4,4) DIM XX(15),YY(15),ZZ(15) MAT READ CPOS !'視線ベクトル DATA 0,0,1 LOCATE VALUE NOWAIT(1),RANGE 1 TO 10,AT 3:SCALE LOCATE VALUE NOWAIT(2),RANGE -360 TO 360,AT 0:XTH LOCATE VALUE NOWAIT(3),RANGE -360 TO 360,AT 0:YTH LOCATE VALUE NOWAIT(4),RANGE -360 TO 360,AT 0:ZTH LOCATE VALUE NOWAIT(5),RANGE .1 TO 5,AT 2:LL LOCATE VALUE NOWAIT(6),RANGE .1 TO 5,AT 1:H LOCATE VALUE NOWAIT(7),RANGE 3 TO 7,AT 3:NN DO LOCATE VALUE NOWAIT(1):SCALE LOCATE VALUE NOWAIT(2):XTH LOCATE VALUE NOWAIT(3):YTH LOCATE VALUE NOWAIT(4):ZTH LOCATE VALUE NOWAIT(5):LL LOCATE VALUE NOWAIT(6):H LOCATE VALUE NOWAIT(7):NN LET NN=INT(NN) SET WINDOW -SCALE,SCALE,-SCALE,SCALE LET NUM=0 FOR TH=0 TO 359 STEP 360/NN LET NUM=NUM+1 LET XX(NUM)=LL*COS(TH) LET ZZ(NUM)=LL*SIN(TH) LET YY(NUM)=0 NEXT TH FOR TH=0 TO 359 STEP 360/NN LET NUM=NUM+1 LET XX(NUM)=LL*COS(TH) LET ZZ(NUM)=LL*SIN(TH) LET YY(NUM)=H NEXT TH LET NUM=0 FOR I=1 TO NN-2 LET NUM=NUM+1 LET X0(NUM)=XX(1) LET Y0(NUM)=YY(1) LET Z0(NUM)=ZZ(1) LET X1(NUM)=XX(I+2) LET Y1(NUM)=YY(I+2) LET Z1(NUM)=ZZ(I+2) LET X2(NUM)=XX(I+1) LET Y2(NUM)=YY(I+1) LET Z2(NUM)=ZZ(I+1) NEXT I FOR I=NN+1 TO 2*NN-2 LET NUM=NUM+1 LET X0(NUM)=XX(NN+1) LET Y0(NUM)=YY(NN+1) LET Z0(NUM)=ZZ(NN+1) LET X1(NUM)=XX(I+1) LET Y1(NUM)=YY(I+1) LET Z1(NUM)=ZZ(I+1) LET X2(NUM)=XX(I+2) LET Y2(NUM)=YY(I+2) LET Z2(NUM)=ZZ(I+2) NEXT I FOR I=0 TO NN-2 LET NUM=NUM+1 LET X0(NUM)=XX(I+1) LET Y0(NUM)=YY(I+1) LET Z0(NUM)=ZZ(I+1) LET X1(NUM)=XX(I+2) LET Y1(NUM)=YY(I+2) LET Z1(NUM)=ZZ(I+2) LET X2(NUM)=XX(I+NN+2) LET Y2(NUM)=YY(I+NN+2) LET Z2(NUM)=ZZ(I+NN+2) LET NUM=NUM+1 LET X0(NUM)=XX(I+1) LET Y0(NUM)=YY(I+1) LET Z0(NUM)=ZZ(I+1) LET X1(NUM)=XX(I+NN+2) LET Y1(NUM)=YY(I+NN+2) LET Z1(NUM)=ZZ(I+NN+2) LET X2(NUM)=XX(I+NN+1) LET Y2(NUM)=YY(I+NN+1) LET Z2(NUM)=ZZ(I+NN+1) NEXT I LET NUM=NUM+1 LET X0(NUM)=XX(NN) LET Y0(NUM)=YY(NN) LET Z0(NUM)=ZZ(NN) LET X1(NUM)=XX(1) LET Y1(NUM)=YY(1) LET Z1(NUM)=ZZ(1) LET X2(NUM)=XX(NN+1) LET Y2(NUM)=YY(NN+1) LET Z2(NUM)=ZZ(NN+1) LET NUM=NUM+1 LET X0(NUM)=XX(NN) LET Y0(NUM)=YY(NN) LET Z0(NUM)=ZZ(NN) LET X1(NUM)=XX(NN+1) LET Y1(NUM)=YY(NN+1) LET Z1(NUM)=ZZ(NN+1) LET X2(NUM)=XX(2*NN) LET Y2(NUM)=YY(2*NN) LET Z2(NUM)=ZZ(2*NN) MAT ROTX=IDN ! x軸のまわりの回転 LET ROTX(2,2)=COS(XTH) LET ROTX(2,3)=SIN(XTH) LET ROTX(3,2)=-SIN(XTH) LET ROTX(3,3)=COS(XTH) MAT ROTY=IDN ! y軸のまわりの回転 LET ROTY(1,1)=COS(YTH) LET ROTY(1,3)=-SIN(YTH) LET ROTY(3,1)=SIN(YTH) LET ROTY(3,3)=COS(YTH) MAT Q=ROTATE(ZTH) MAT Q=Q*ROTY*ROTX SET DRAW MODE HIDDEN CLEAR FOR I=1 TO NUM LET P0(1)=X0(I) LET P0(2)=Y0(I) LET P0(3)=Z0(I) LET P1(1)=X1(I) LET P1(2)=Y1(I) LET P1(3)=Z1(I) LET P2(1)=X2(I) LET P2(2)=Y2(I) LET P2(3)=Z2(I) LET P0(4),P1(4),P2(4)=1 MAT P0=P0*Q MAT P1=P1*Q MAT P2=P2*Q MAT L=P2-P1 MAT M=P1-P0 CALL OUTER(N,L,M) LET S=DOT(CPOS,N) !'内積 COS(TH) -90<TH<90...表 IF S>0 THEN CALL SETBRIGHTNESS(N) CALL PLOT3(P0,P1,P2) END IF NEXT I SET DRAW MODE EXPLICIT LOOP END EXTERNAL SUB PLOT3(P0(),P1(),P2()) !'3角形描画 PLOT AREA :P0(1),P0(2);P1(1),P1(2);P2(1),P2(2) END SUB EXTERNAL SUB SETBRIGHTNESS(N()) DIM A(3) MAT READ A ! 光源の向き DATA 1,1,1 LET S=DOT(A,N)/(SQR(DOT(A,A))*SQR(DOT(N,N))) LET S=(S+1)/2 SET COLOR MIX(8) S,S,S SET AREA COLOR 8 END SUB EXTERNAL SUB OUTER(C(),A(),B()) !'外積 LET C(1)=A(2)*B(3)-A(3)*B(2) LET C(2)=A(3)*B(1)-A(1)*B(3) LET C(3)=A(1)*B(2)-A(2)*B(1) END SUB

3次元図形表示

投稿者：しばっち投稿日：2019年 3月30日(土)20時08分21秒

多角形体を表示します(外積) OPTION ANGLE DEGREES LET NN=30 FOR I=0 TO 7 SET COLOR MIX(I) BITAND(I,2)/2,BITAND(I,4)/4,BITAND(I,1) NEXT I CLEAR DIM X0(2*NN*NN),Y0(2*NN*NN),Z0(2*NN*NN),X1(2*NN*NN),Y1(2*NN*NN),Z1(2*NN*NN),X2(2*NN*NN),Y2(2*NN*NN),Z2(2*NN*NN) DIM P0(4),P1(4),P2(4),P3(4),CPOS(3) DIM L(4),M(4),N(3) DIM Q(4,4),ROTX(4,4),ROTY(4,4) MAT READ CPOS DATA 0,0,1 !'視線ベクトル DEF A(N)=360/N DEF S1(X)=FP(X) DEF CNP(N,T)=COS(A(N)*S1(T/A(N))-A(N)/2) DEF PC(N,T)=COS(T)*COS(A(N)/2)/CNP(N,T) DEF PS(N,T)=SIN(T)*COS(A(N)/2)/CNP(N,T) DEF P3X(N,U,V)=PS(N,U)*PC(N,V) DEF P3Y(N,U,V)=PS(N,U)*PS(N,V) DEF P3Z(N,U)=PC(N,U) LOCATE VALUE NOWAIT(1),RANGE 1 TO 5,AT 3:SCALE LOCATE VALUE NOWAIT(2),RANGE -360 TO 360,AT 0:XTH LOCATE VALUE NOWAIT(3),RANGE -360 TO 360,AT 0:YTH LOCATE VALUE NOWAIT(4),RANGE -360 TO 360,AT 0:ZTH LOCATE VALUE NOWAIT(5),RANGE 3 TO 10,AT 3:N0 DO LOCATE VALUE NOWAIT(1):SCALE LOCATE VALUE NOWAIT(2):XTH LOCATE VALUE NOWAIT(3):YTH LOCATE VALUE NOWAIT(4):ZTH LOCATE VALUE NOWAIT(5):N0 LET N0=INT(N0) SET WINDOW -SCALE,SCALE,-SCALE,SCALE LET NUM=0 FOR I=0 TO NN-1 FOR J=0 TO NN-1 LET NUM=NUM+1 LET XX0=P3X(N0,I*180/NN,J*360/NN) LET YY0=P3Y(N0,I*180/NN,J*360/NN) LET ZZ0=P3Z(N0,I*180/NN) LET XX1=P3X(N0,I*180/NN,(J+1)*360/NN) LET YY1=P3Y(N0,I*180/NN,(J+1)*360/NN) LET ZZ1=P3Z(N0,I*180/NN) LET XX2=P3X(N0,(I+1)*180/NN,(J+1)*360/NN) LET YY2=P3Y(N0,(I+1)*180/NN,(J+1)*360/NN) LET ZZ2=P3Z(N0,(I+1)*180/NN) LET XX3=P3X(N0,(I+1)*180/NN,J*360/NN) LET YY3=P3Y(N0,(I+1)*180/NN,J*360/NN) LET ZZ3=P3Z(N0,(I+1)*180/NN) LET X0(NUM)=XX0 LET Y0(NUM)=YY0 LET Z0(NUM)=ZZ0 LET X1(NUM)=XX1 LET Y1(NUM)=YY1 LET Z1(NUM)=ZZ1 LET X2(NUM)=XX2 LET Y2(NUM)=YY2 LET Z2(NUM)=ZZ2 LET NUM=NUM+1 LET X0(NUM)=XX0 LET Y0(NUM)=YY0 LET Z0(NUM)=ZZ0 LET X1(NUM)=XX2 LET Y1(NUM)=YY2 LET Z1(NUM)=ZZ2 LET X2(NUM)=XX3 LET Y2(NUM)=YY3 LET Z2(NUM)=ZZ3 NEXT J NEXT I MAT ROTX=IDN ! x軸のまわりの回転 LET ROTX(2,2)=COS(XTH) LET ROTX(2,3)=SIN(XTH) LET ROTX(3,2)=-SIN(XTH) LET ROTX(3,3)=COS(XTH) MAT ROTY=IDN ! y軸のまわりの回転 LET ROTY(1,1)=COS(YTH) LET ROTY(1,3)=-SIN(YTH) LET ROTY(3,1)=SIN(YTH) LET ROTY(3,3)=COS(YTH) MAT Q=ROTATE(ZTH) MAT Q=Q*ROTY*ROTX SET DRAW MODE HIDDEN CLEAR FOR I=1 TO NUM LET P0(1)=X0(I) LET P0(2)=Y0(I) LET P0(3)=Z0(I) LET P1(1)=X1(I) LET P1(2)=Y1(I) LET P1(3)=Z1(I) LET P2(1)=X2(I) LET P2(2)=Y2(I) LET P2(3)=Z2(I) LET P0(4),P1(4),P2(4)=1 MAT P0=P0*Q MAT P1=P1*Q MAT P2=P2*Q MAT L=P2-P1 MAT M=P1-P0 CALL OUTER(N,L,M) LET S=DOT(CPOS,N) !'内積 COS(TH) -90<TH<90...表 IF S>0 THEN CALL SETBRIGHTNESS(N) CALL PLOT3(P0,P1,P2) END IF NEXT I SET DRAW MODE EXPLICIT LOOP END EXTERNAL SUB PLOT3(P0(),P1(),P2()) !'3角形描画 PLOT AREA :P0(1),P0(2);P1(1),P1(2);P2(1),P2(2) END SUB EXTERNAL SUB SETBRIGHTNESS(N()) DIM LA(3),LIGHT(3) MAT READ LA DATA .8,.7,.1 MAT READ LIGHT DATA 1,1,1 LET S=DOT(LIGHT,N)/(SQR(DOT(LIGHT,LIGHT))*SQR(DOT(N,N))) MAT LA=((S+1)/2)*LA SET COLOR MIX(8) LA(1),LA(2),LA(3) SET AREA COLOR 8 END SUB EXTERNAL SUB OUTER(C(),A(),B()) !'外積 LET C(1)=A(2)*B(3)-A(3)*B(2) LET C(2)=A(3)*B(1)-A(1)*B(3) LET C(3)=A(1)*B(2)-A(2)*B(1) END SUB

3次元図形表示

投稿者：しばっち投稿日：2019年 3月30日(土)20時10分38秒

Zソートと呼ばれる方法で3次元図形表示します。 ZソートとはZ値でソートを行い、奥から手前に向かって描画していくことにより表示する方法で、一見するとムダに見えますが奥にあるオブジェクトを手前にあるオブジェクトで塗り潰していくことで陰面処理を行います。 Zソートも描画が速くアニメーション表示が可能です。スライドバーで動かせます。2進モードを使用してください ※オブジェクトが貫通している、三すくみ等があると正しく描画できません。切頭6面体を表示します(Zソート) OPTION ANGLE DEGREES FOR I=0 TO 7 SET COLOR MIX(I) BITAND(I,2)/2,BITAND(I,4)/4,BITAND(I,1) NEXT I DIM X0(100),Y0(100),Z0(100),X1(100),Y1(100),Z1(100),X2(100),Y2(100),Z2(100),KEY(100),INDEX(100) DIM P0(4),P1(4),P2(4) DIM L(4),M(4),N(3) DIM Q(4,4),ROTX(4,4),ROTY(4,4) DIM XX(50),YY(50),ZZ(50) LOCATE VALUE NOWAIT(1),RANGE 1 TO 10,AT 3:SCALE LOCATE VALUE NOWAIT(2),RANGE -360 TO 360,AT 0:XTH LOCATE VALUE NOWAIT(3),RANGE -360 TO 360,AT 0:YTH LOCATE VALUE NOWAIT(4),RANGE -360 TO 360,AT 0:ZTH DO LOCATE VALUE NOWAIT(1):SCALE LOCATE VALUE NOWAIT(2):XTH LOCATE VALUE NOWAIT(3):YTH LOCATE VALUE NOWAIT(4):ZTH SET WINDOW -SCALE,SCALE,-SCALE,SCALE LET NUM=0 FOR TH=22.5 TO 359+22.5 STEP 45 LET NUM=NUM+1 LET XX(NUM)=COS(TH) LET YY(NUM)=COS(22.5) LET ZZ(NUM)=SIN(TH) NEXT TH FOR TH=22.5 TO 359+22.5 STEP 45 LET NUM=NUM+1 LET XX(NUM)=-COS(22.5) LET YY(NUM)=COS(TH) LET ZZ(NUM)=SIN(TH) NEXT TH FOR TH=22.5 TO 359+22.5 STEP 45 LET NUM=NUM+1 LET XX(NUM)=COS(TH) LET YY(NUM)=-COS(22.5) LET ZZ(NUM)=SIN(TH) NEXT TH FOR TH=22.5 TO 359+22.5 STEP 45 LET NUM=NUM+1 LET XX(NUM)=COS(22.5) LET YY(NUM)=COS(TH) LET ZZ(NUM)=SIN(TH) NEXT TH FOR TH=22.5 TO 359+22.5 STEP 45 LET NUM=NUM+1 LET XX(NUM)=COS(TH) LET YY(NUM)=SIN(TH) LET ZZ(NUM)=-COS(22.5) NEXT TH FOR TH=22.5 TO 359+22.5 STEP 45 LET NUM=NUM+1 LET XX(NUM)=COS(TH) LET YY(NUM)=SIN(TH) LET ZZ(NUM)=COS(22.5) NEXT TH RESTORE FOR I=1 TO 44 READ A,B,C LET X0(I)=XX(A+1) LET Y0(I)=YY(A+1) LET Z0(I)=ZZ(A+1) LET X1(I)=XX(B+1) LET Y1(I)=YY(B+1) LET Z1(I)=ZZ(B+1) LET X2(I)=XX(C+1) LET Y2(I)=YY(C+1) LET Z2(I)=ZZ(C+1) NEXT I DATA 0,1,2 !'メッシュデータ DATA 0,2,3 DATA 0,3,4 DATA 0,4,5 DATA 0,5,6 DATA 0,6,7 DATA 8,9,10 DATA 8,10,11 DATA 8,11,12 DATA 8,12,13 DATA 8,13,14 DATA 8,14,15 DATA 16,18,17 DATA 16,19,18 DATA 16,20,19 DATA 16,21,20 DATA 16,22,21 DATA 16,23,22 DATA 24,26,25 DATA 24,27,26 DATA 24,28,27 DATA 24,29,28 DATA 24,30,29 DATA 24,31,30 DATA 32,33,34 DATA 32,34,35 DATA 32,35,36 DATA 32,36,37 DATA 32,37,38 DATA 32,38,39 DATA 40,42,41 DATA 40,43,42 DATA 40,44,43 DATA 40,45,44 DATA 40,46,45 DATA 40,47,46 DATA 0,25,1 DATA 8,2,9 DATA 10,18,11 DATA 16,17,26 DATA 30,31,6 DATA 14,5,15 DATA 28,29,22 DATA 20,21,13 MAT ROTX=IDN ! x軸のまわりの回転 LET ROTX(2,2)=COS(XTH) LET ROTX(2,3)=SIN(XTH) LET ROTX(3,2)=-SIN(XTH) LET ROTX(3,3)=COS(XTH) MAT ROTY=IDN ! y軸のまわりの回転 LET ROTY(1,1)=COS(YTH) LET ROTY(1,3)=-SIN(YTH) LET ROTY(3,1)=SIN(YTH) LET ROTY(3,3)=COS(YTH) MAT Q=ROTATE(ZTH) MAT Q=Q*ROTY*ROTX FOR I=1 TO 44 LET P0(1)=X0(I) LET P0(2)=Y0(I) LET P0(3)=Z0(I) LET P1(1)=X1(I) LET P1(2)=Y1(I) LET P1(3)=Z1(I) LET P2(1)=X2(I) LET P2(2)=Y2(I) LET P2(3)=Z2(I) LET P0(4),P1(4),P2(4)=1 MAT P0=P0*Q MAT P1=P1*Q MAT P2=P2*Q LET X0(I)=P0(1) LET Y0(I)=P0(2) LET Z0(I)=P0(3) LET X1(I)=P1(1) LET Y1(I)=P1(2) LET Z1(I)=P1(3) LET X2(I)=P2(1) LET Y2(I)=P2(2) LET Z2(I)=P2(3) LET KEY(I)=(Z0(I)+Z1(I)+Z2(I))/3 !'各頂点のZ座標値の平均 LET INDEX(I)=I NEXT I CALL QUICKSORT(1,44,KEY,INDEX) !'Zソート SET DRAW MODE HIDDEN CLEAR FOR I=1 TO 44 LET P0(1)=X0(INDEX(I)) LET P0(2)=Y0(INDEX(I)) LET P0(3)=Z0(INDEX(I)) LET P1(1)=X1(INDEX(I)) LET P1(2)=Y1(INDEX(I)) LET P1(3)=Z1(INDEX(I)) LET P2(1)=X2(INDEX(I)) LET P2(2)=Y2(INDEX(I)) LET P2(3)=Z2(INDEX(I)) MAT L=P2-P1 MAT M=P1-P0 CALL OUTER(N,L,M) CALL SETBRIGHTNESS(N) CALL PLOT3(P0,P1,P2) NEXT I SET DRAW MODE EXPLICIT LOOP END EXTERNAL SUB PLOT3(P0(),P1(),P2()) !'3角形描画 PLOT AREA :P0(1),P0(2);P1(1),P1(2);P2(1),P2(2) END SUB EXTERNAL SUB SETBRIGHTNESS(N()) DIM A(3) MAT READ A ! 光源の向き DATA 1,1,1 LET S=DOT(A,N)/(SQR(DOT(A,A))*SQR(DOT(N,N))) LET S=(S*.7+1)/2 SET COLOR MIX(8) S,S,S SET AREA COLOR 8 END SUB EXTERNAL SUB OUTER(C(),A(),B()) !'外積 LET C(1)=A(2)*B(3)-A(3)*B(2) LET C(2)=A(3)*B(1)-A(1)*B(3) LET C(3)=A(1)*B(2)-A(2)*B(1) END SUB EXTERNAL SUB QUICKSORT(FI,LA,A(),INDEX()) LET X=A(INDEX((FI+LA)/2)) LET I=FI LET J=LA DO DO WHILE A(INDEX(I))<X LET I=I+1 LOOP DO WHILE X<A(INDEX(J)) LET J=J-1 LOOP IF I>=J THEN EXIT DO SWAP INDEX(I),INDEX(J) LET I=I+1 LET J=J-1 LOOP IF FI<I-1 THEN CALL QUICKSORT(FI,I-1,A,INDEX) IF J+1<LA THEN CALL QUICKSORT(J+1,LA,A,INDEX) END SUB

3次元図形表示

投稿者：しばっち投稿日：2019年 3月30日(土)20時11分15秒

切頭12面体を表示します(Zソート) OPTION ANGLE DEGREES FOR I=0 TO 7 SET COLOR MIX(I) BITAND(I,2)/2,BITAND(I,4)/4,BITAND(I,1) NEXT I DIM X0(200),Y0(200),Z0(200),X1(200),Y1(200),Z1(200),X2(200),Y2(200),Z2(200),KEY(200),INDEX(200) DIM P0(4),P1(4),P2(4) DIM L(4),M(4),N(3) DIM Q(4,4),ROTX(4,4),ROTY(4,4) DIM XX(100),YY(100),ZZ(100) LOCATE VALUE NOWAIT(1),RANGE 1 TO 10,AT 5:SCALE LOCATE VALUE NOWAIT(2),RANGE -360 TO 360,AT 0:XTH LOCATE VALUE NOWAIT(3),RANGE -360 TO 360,AT 0:YTH LOCATE VALUE NOWAIT(4),RANGE -360 TO 360,AT 0:ZTH DO LOCATE VALUE NOWAIT(1):SCALE LOCATE VALUE NOWAIT(2):XTH LOCATE VALUE NOWAIT(3):YTH LOCATE VALUE NOWAIT(4):ZTH SET WINDOW -SCALE,SCALE,-SCALE,SCALE RESTORE FOR I=1 TO 60 READ XX(I),YY(I),ZZ(I) NEXT I DATA -.16838141 , .83850515 ,-.51822468 !'座標データ DATA -.44082824 , .83850515 ,-.32028047 DATA -.54489368 , .83850515 , 0 DATA -.44082824 , .83850515 , .32028047 DATA -.16838141 , .83850515 , .51822468 DATA .16838141 , .83850515 , .51822468 DATA .44082824 , .83850515 , .32028047 DATA .54489368 , .83850515 , 0 DATA .44082824 , .83850515 ,-.32028047 DATA .16838141 , .83850515 ,-.51822468 DATA 0 , .66145846 ,-.7499818 DATA 0 , .3749909 ,-.92702849 DATA .16838141 , .08852334 ,-.98173893 DATA .44082824 ,-.08852334 ,-.89321558 DATA .71327508 ,-.08852334 ,-.69527137 DATA .88165649 , .08852334 ,-.46351425 DATA .88165649 , .3749909 ,-.28646756 DATA .71327508 , .66145846 ,-.23175712 DATA -.16838141 , .08852334 ,-.98173893 DATA -.44082824 ,-.08852334 ,-.89321558 DATA -.71327508 ,-.08852334 ,-.69527137 DATA -.88165649 , .08852334 ,-.46351425 DATA -.88165649 , .3749909 ,-.28646756 DATA -.71327508 , .66145846 ,-.23175712 DATA -.98572192 , .08852334 ,-.14323378 DATA -.98572192 ,-.08852334 , .14323378 DATA -.88165649 ,-.08852334 , .46351425 DATA -.71327508 , .08852334 , .69527137 DATA -.54489368 , .3749909 , .7499818 DATA -.44082824 , .66145846 , .60674802 DATA -.44082824 , .08852334 , .89321558 DATA -.16838141 ,-.08852334 , .98173893 DATA .16838141 ,-.08852334 , .98173893 DATA .44082824 , .08852334 , .89321558 DATA .54489368 , .3749909 , .7499818 DATA .44082824 , .66145846 , .60674802 DATA .71327508 , .08852334 , .69527137 DATA .88165649 ,-.08852334 , .46351425 DATA .98572192 ,-.08852334 , .14323378 DATA .98572192 , .08852334 ,-.14323378 DATA .54489368 ,-.3749909 ,-.7499818 DATA .44082824 ,-.66145846 ,-.60674802 DATA .16838141 ,-.83850515 ,-.51822468 DATA -.16838141 ,-.83850515 ,-.51822468 DATA -.44082824 ,-.66145846 ,-.60674802 DATA -.54489368 ,-.3749909 ,-.7499818 DATA -.44082824 ,-.83850515 ,-.32028047 DATA -.54489367 ,-.83850515 , 0 DATA -.71327508 ,-.66145846 , .23175712 DATA -.88165649 ,-.3749909 , .28646756 DATA -.44082824 ,-.83850515 , .32028047 DATA -.16838141 ,-.83850515 , .51822468 DATA 0 ,-.66145846 , .7499818 DATA 0 ,-.3749909 , .92702849 DATA .16838141 ,-.83850515 , .51822468 DATA .44082824 ,-.83850515 , .32028047 DATA .71327508 ,-.66145846 , .23175712 DATA .88165649 ,-.3749909 , .28646756 DATA .54489368 ,-.83850515 , 0 DATA .44082824 ,-.83850515 ,-.32028047 FOR I=1 TO 116 READ A,B,C LET X0(I)=XX(A) LET Y0(I)=YY(A) LET Z0(I)=ZZ(A) LET X1(I)=XX(B) LET Y1(I)=YY(B) LET Z1(I)=ZZ(B) LET X2(I)=XX(C) LET Y2(I)=YY(C) LET Z2(I)=ZZ(C) NEXT I DATA 1,2,24 !'メッシュデータ DATA 1,24,23 DATA 1,23,22 DATA 1,22,21 DATA 1,21,20 DATA 1,20,19 DATA 1,19,12 DATA 1,12,11 DATA 1,11,10 DATA 1,10,9 DATA 1,9,8 DATA 1,8,7 DATA 1,7,6 DATA 1,6,5 DATA 1,5,4 DATA 1,4,3 DATA 1,3,2 DATA 2,3,24 DATA 3,4,30 DATA 3,30,29 DATA 3,29,28 DATA 3,28,27 DATA 3,27,26 DATA 3,26,25 DATA 3,25,23 DATA 3,23,24 DATA 4,5,30 DATA 5,6,36 DATA 5,36,35 DATA 5,35,34 DATA 5,34,33 DATA 5,33,32 DATA 5,32,31 DATA 5,31,29 DATA 5,29,30 DATA 6,7,36 DATA 7,8,18 DATA 7,18,17 DATA 7,17,40 DATA 7,40,39 DATA 7,39,38 DATA 7,38,37 DATA 7,37,35 DATA 7,35,36 DATA 8,9,18 DATA 9,10,11 DATA 9,11,12 DATA 9,12,13 DATA 9,13,14 DATA 9,14,15 DATA 9,15,16 DATA 9,16,17 DATA 9,17,18 DATA 12,19,13 DATA 13,19,20 DATA 13,20,46 DATA 13,46,45 DATA 13,45,44 DATA 13,44,43 DATA 13,43,42 DATA 13,42,41 DATA 13,41,14 DATA 14,41,15 DATA 15,41,42 DATA 15,42,60 DATA 15,60,59 DATA 15,59,57 DATA 15,57,58 DATA 15,58,39 DATA 15,39,40 DATA 15,40,16 DATA 16,40,17 DATA 20,21,46 DATA 21,22,25 DATA 21,25,26 DATA 21,26,50 DATA 21,50,49 DATA 21,49,48 DATA 21,48,47 DATA 21,47,45 DATA 21,45,46 DATA 22,23,25 DATA 26,27,50 DATA 27,28,31 DATA 27,31,32 DATA 27,32,54 DATA 27,54,53 DATA 27,53,52 DATA 27,52,51 DATA 27,51,49 DATA 27,49,50 DATA 28,29,31 DATA 32,33,54 DATA 33,34,37 DATA 33,37,38 DATA 33,38,58 DATA 33,58,57 DATA 33,57,56 DATA 33,56,55 DATA 33,55,53 DATA 33,53,54 DATA 34,35,37 DATA 38,39,58 DATA 42,43,60 DATA 43,44,47 DATA 43,47,48 DATA 43,48,51 DATA 43,51,52 DATA 43,52,55 DATA 43,55,56 DATA 43,56,59 DATA 43,59,60 DATA 44,45,47 DATA 48,49,51 DATA 52,53,55 DATA 56,57,59 MAT ROTX=IDN ! x軸のまわりの回転 LET ROTX(2,2)=COS(XTH) LET ROTX(2,3)=SIN(XTH) LET ROTX(3,2)=-SIN(XTH) LET ROTX(3,3)=COS(XTH) MAT ROTY=IDN ! y軸のまわりの回転 LET ROTY(1,1)=COS(YTH) LET ROTY(1,3)=-SIN(YTH) LET ROTY(3,1)=SIN(YTH) LET ROTY(3,3)=COS(YTH) MAT Q=ROTATE(ZTH) MAT Q=Q*ROTY*ROTX SET DRAW MODE HIDDEN CLEAR FOR I=1 TO 116 LET P0(1)=X0(I) LET P0(2)=Y0(I) LET P0(3)=Z0(I) LET P1(1)=X1(I) LET P1(2)=Y1(I) LET P1(3)=Z1(I) LET P2(1)=X2(I) LET P2(2)=Y2(I) LET P2(3)=Z2(I) LET P0(4),P1(4),P2(4)=1 MAT P0=P0*Q MAT P1=P1*Q MAT P2=P2*Q MAT L=P2-P1 MAT M=P1-P0 LET X0(I)=P0(1) LET Y0(I)=P0(2) LET Z0(I)=P0(3) LET X1(I)=P1(1) LET Y1(I)=P1(2) LET Z1(I)=P1(3) LET X2(I)=P2(1) LET Y2(I)=P2(2) LET Z2(I)=P2(3) LET KEY(I)=(Z0(I)+Z1(I)+Z2(I))/3 !'各頂点のZ座標値の平均 LET INDEX(I)=I NEXT I CALL QUICKSORT(1,116,KEY,INDEX) !'Zソート SET DRAW MODE HIDDEN CLEAR FOR I=1 TO 116 LET P0(1)=X0(INDEX(I)) LET P0(2)=Y0(INDEX(I)) LET P0(3)=Z0(INDEX(I)) LET P1(1)=X1(INDEX(I)) LET P1(2)=Y1(INDEX(I)) LET P1(3)=Z1(INDEX(I)) LET P2(1)=X2(INDEX(I)) LET P2(2)=Y2(INDEX(I)) LET P2(3)=Z2(INDEX(I)) MAT L=P2-P1 MAT M=P1-P0 CALL OUTER(N,L,M) CALL SETBRIGHTNESS(N) CALL PLOT3(P0,P1,P2) NEXT I SET DRAW MODE EXPLICIT LOOP END EXTERNAL SUB PLOT3(P0(),P1(),P2()) !'3角形描画 PLOT AREA :P0(1),P0(2);P1(1),P1(2);P2(1),P2(2) END SUB EXTERNAL SUB SETBRIGHTNESS(N()) DIM LIGHT(3) MAT READ LIGHT ! 光源の向き DATA 1,1,1 LET S=DOT(LIGHT,N)/(SQR(DOT(LIGHT,LIGHT))*SQR(DOT(N,N))) LET S=(S+1)/2 SET COLOR MIX(8) S,S,S SET AREA COLOR 8 END SUB EXTERNAL SUB OUTER(C(),A(),B()) !'外積 LET C(1)=A(2)*B(3)-A(3)*B(2) LET C(2)=A(3)*B(1)-A(1)*B(3) LET C(3)=A(1)*B(2)-A(2)*B(1) END SUB EXTERNAL SUB QUICKSORT(FI,LA,A(),INDEX()) LET X=A(INDEX((FI+LA)/2)) LET I=FI LET J=LA DO DO WHILE A(INDEX(I))<X LET I=I+1 LOOP DO WHILE X<A(INDEX(J)) LET J=J-1 LOOP IF I>=J THEN EXIT DO SWAP INDEX(I),INDEX(J) LET I=I+1 LET J=J-1 LOOP IF FI<I-1 THEN CALL QUICKSORT(FI,I-1,A,INDEX) IF J+1<LA THEN CALL QUICKSORT(J+1,LA,A,INDEX) END SUB

3次元図形表示

投稿者：しばっち投稿日：2019年 3月30日(土)20時11分53秒

切頭20面体を表示します(Zソート) OPTION ANGLE DEGREES FOR I=0 TO 7 SET COLOR MIX(I) BITAND(I,2)/2,BITAND(I,4)/4,BITAND(I,1) NEXT I DIM X0(200),Y0(200),Z0(200),X1(200),Y1(200),Z1(200),X2(200),Y2(200),Z2(200),KEY(200),INDEX(200) DIM P0(4),P1(4),P2(4) DIM L(4),M(4),N(3) DIM Q(4,4),ROTX(4,4),ROTY(4,4) DIM XX(100),YY(100),ZZ(100) LOCATE VALUE NOWAIT(1),RANGE 1 TO 10,AT 5:SCALE LOCATE VALUE NOWAIT(2),RANGE -360 TO 360,AT 0:XTH LOCATE VALUE NOWAIT(3),RANGE -360 TO 360,AT 0:YTH LOCATE VALUE NOWAIT(4),RANGE -360 TO 360,AT 0:ZTH DO LOCATE VALUE NOWAIT(1):SCALE LOCATE VALUE NOWAIT(2):XTH LOCATE VALUE NOWAIT(3):YTH LOCATE VALUE NOWAIT(4):ZTH SET WINDOW -SCALE,SCALE,-SCALE,SCALE RESTORE FOR I=1 TO 60 READ XX(I),YY(I),ZZ(I) NEXT I DATA -.20177411 , .93923362 ,-.27771823 !'座標データ DATA -.40354821 , .72707577 ,-.55543646 DATA -.20177411 , .51491792 ,-.8331547 DATA .20177411 , .51491792 ,-.8331547 DATA .40354821 , .72707577 ,-.55543646 DATA .20177411 , .93923362 ,-.27771823 DATA -.32647736 , .93923362 , .10607893 DATA -.65295472 , .72707577 , .21215785 DATA -.85472883 , .51491792 ,-.06556038 DATA -.73002557 , .51491792 ,-.44935754 DATA -.73002557 , .17163931 ,-.66151539 DATA -.40354821 , .17163931 ,-.89871508 DATA -.20177411 ,-.17163931 ,-.96427546 DATA .20177411 ,-.17163931 ,-.96427546 DATA .40354821 , .17163931 ,-.89871508 DATA .73002557 , .17163931 ,-.66151539 DATA .73002557 , .51491792 ,-.44935754 DATA .85472883 , .51491792 ,-.06556038 DATA .65295472 , .72707577 , .21215785 DATA .32647736 , .93923362 , .10607893 DATA 0 , .93923362 , .34327861 DATA -.65295472 , .51491792 , .55543646 DATA -.85472883 , .17163931 , .48987608 DATA -.97943209 , .17163931 , .10607893 DATA -.97943209 ,-.17163931 ,-.10607892 DATA -.85472883 ,-.17163931 ,-.48987608 DATA -.65295472 ,-.51491792 ,-.55543646 DATA -.32647736 ,-.51491792 ,-.79263615 DATA 0 ,-.72707577 ,-.68655723 DATA .32647736 ,-.51491792 ,-.79263615 DATA .65295472 ,-.51491792 ,-.55543646 DATA .85472883 ,-.17163931 ,-.48987608 DATA .97943209 ,-.17163931 ,-.10607893 DATA .97943209 , .17163931 , .10607893 DATA .85472883 , .17163931 , .48987608 DATA .65295472 , .51491792 , .55543646 DATA .32647736 , .51491792 , .79263615 DATA 0 , .72707577 , .68655723 DATA -.32647736 , .51491792 , .79263615 DATA -.73002557 ,-.17163931 , .66151539 DATA -.73002557 ,-.51491792 , .44935754 DATA -.85472883 ,-.51491792 , .06556038 DATA -.65295472 ,-.72707577 ,-.21215785 DATA -.32647736 ,-.93923362 ,-.10607892 DATA 0 ,-.93923362 ,-.34327861 DATA .32647736 ,-.93923362 ,-.10607892 DATA .65295472 ,-.72707577 ,-.21215785 DATA .85472883 ,-.51491792 , .06556038 DATA .73002557 ,-.51491792 , .44935754 DATA .73002557 ,-.17163931 , .66151539 DATA .40354821 ,-.17163931 , .89871508 DATA .20177411 , .17163931 , .96427546 DATA -.20177411 , .17163931 , .96427546 DATA -.40354821 ,-.17163931 , .89871508 DATA -.20177411 ,-.51491792 , .83315469 DATA -.40354821 ,-.72707577 , .55543646 DATA -.20177411 ,-.93923362 , .27771823 DATA .2017741 ,-.93923362 , .27771823 DATA .40354821 ,-.72707577 , .55543646 DATA .20177411 ,-.51491792 , .83315469 FOR I=1 TO 116 READ A,B,C LET X0(I)=XX(A) LET Y0(I)=YY(A) LET Z0(I)=ZZ(A) LET X1(I)=XX(B) LET Y1(I)=YY(B) LET Z1(I)=ZZ(B) LET X2(I)=XX(C) LET Y2(I)=YY(C) LET Z2(I)=ZZ(C) NEXT I DATA 1,6,20 !'メッシュデータ DATA 1,20,21 DATA 1,21,7 DATA 1,7,8 DATA 1,8,9 DATA 1,9,10 DATA 1,10,2 DATA 1,2,3 DATA 1,3,4 DATA 1,4,5 DATA 1,5,6 DATA 2,10,11 DATA 2,11,12 DATA 2,12,3 DATA 3,12,13 DATA 3,13,14 DATA 3,14,15 DATA 3,15,4 DATA 4,15,16 DATA 4,16,17 DATA 4,17,5 DATA 5,17,18 DATA 5,18,19 DATA 5,19,20 DATA 5,20,6 DATA 7,21,38 DATA 7,38,39 DATA 7,39,22 DATA 7,22,8 DATA 8,22,23 DATA 8,23,24 DATA 8,24,9 DATA 9,24,25 DATA 9,25,26 DATA 9,26,11 DATA 9,11,10 DATA 11,26,27 DATA 11,27,28 DATA 11,28,13 DATA 11,13,12 DATA 13,28,29 DATA 13,29,30 DATA 13,30,14 DATA 14,30,31 DATA 14,31,32 DATA 14,32,16 DATA 14,16,15 DATA 16,32,33 DATA 16,33,34 DATA 16,34,18 DATA 16,18,17 DATA 18,34,35 DATA 18,35,36 DATA 18,36,19 DATA 19,36,37 DATA 19,37,38 DATA 19,38,21 DATA 19,21,20 DATA 22,39,53 DATA 22,53,54 DATA 22,54,40 DATA 22,40,23 DATA 23,40,41 DATA 23,41,42 DATA 23,42,25 DATA 23,25,24 DATA 25,42,43 DATA 25,43,27 DATA 25,27,26 DATA 27,43,44 DATA 27,44,45 DATA 27,45,29 DATA 27,29,28 DATA 29,45,46 DATA 29,46,47 DATA 29,47,31 DATA 29,31,30 DATA 31,47,48 DATA 31,48,33 DATA 31,33,32 DATA 33,48,49 DATA 33,49,50 DATA 33,50,35 DATA 33,35,34 DATA 35,50,51 DATA 35,51,52 DATA 35,52,37 DATA 35,37,36 DATA 37,52,53 DATA 37,53,39 DATA 37,39,38 DATA 40,54,55 DATA 40,55,56 DATA 40,56,41 DATA 41,56,57 DATA 41,57,44 DATA 41,44,43 DATA 41,43,42 DATA 44,57,58 DATA 44,58,46 DATA 44,46,45 DATA 46,58,59 DATA 46,59,49 DATA 46,49,48 DATA 46,48,47 DATA 49,59,60 DATA 49,60,51 DATA 49,51,50 DATA 51,60,55 DATA 51,55,54 DATA 51,54,53 DATA 51,53,52 DATA 55,60,59 DATA 55,59,58 DATA 55,58,57 DATA 55,57,56 MAT ROTX=IDN ! x軸のまわりの回転 LET ROTX(2,2)=COS(XTH) LET ROTX(2,3)=SIN(XTH) LET ROTX(3,2)=-SIN(XTH) LET ROTX(3,3)=COS(XTH) MAT ROTY=IDN ! y軸のまわりの回転 LET ROTY(1,1)=COS(YTH) LET ROTY(1,3)=-SIN(YTH) LET ROTY(3,1)=SIN(YTH) LET ROTY(3,3)=COS(YTH) MAT Q=ROTATE(ZTH) MAT Q=Q*ROTY*ROTX SET DRAW MODE HIDDEN CLEAR FOR I=1 TO 116 LET P0(1)=X0(I) LET P0(2)=Y0(I) LET P0(3)=Z0(I) LET P1(1)=X1(I) LET P1(2)=Y1(I) LET P1(3)=Z1(I) LET P2(1)=X2(I) LET P2(2)=Y2(I) LET P2(3)=Z2(I) LET P0(4),P1(4),P2(4)=1 MAT P0=P0*Q MAT P1=P1*Q MAT P2=P2*Q MAT L=P2-P1 MAT M=P1-P0 LET X0(I)=P0(1) LET Y0(I)=P0(2) LET Z0(I)=P0(3) LET X1(I)=P1(1) LET Y1(I)=P1(2) LET Z1(I)=P1(3) LET X2(I)=P2(1) LET Y2(I)=P2(2) LET Z2(I)=P2(3) LET KEY(I)=(Z0(I)+Z1(I)+Z2(I))/3 !'各頂点のZ座標値の平均 LET INDEX(I)=I NEXT I CALL QUICKSORT(1,116,KEY,INDEX) !'Zソート SET DRAW MODE HIDDEN CLEAR FOR I=1 TO 116 LET P0(1)=X0(INDEX(I)) LET P0(2)=Y0(INDEX(I)) LET P0(3)=Z0(INDEX(I)) LET P1(1)=X1(INDEX(I)) LET P1(2)=Y1(INDEX(I)) LET P1(3)=Z1(INDEX(I)) LET P2(1)=X2(INDEX(I)) LET P2(2)=Y2(INDEX(I)) LET P2(3)=Z2(INDEX(I)) MAT L=P2-P1 MAT M=P1-P0 CALL OUTER(N,L,M) CALL SETBRIGHTNESS(N) CALL PLOT3(P0,P1,P2) NEXT I SET DRAW MODE EXPLICIT LOOP END EXTERNAL SUB PLOT3(P0(),P1(),P2()) !'3角形描画 PLOT AREA :P0(1),P0(2);P1(1),P1(2);P2(1),P2(2) END SUB EXTERNAL SUB SETBRIGHTNESS(N()) DIM LIGHT(3) MAT READ LIGHT ! 光源の向き DATA 1,1,1 LET S=DOT(LIGHT,N)/(SQR(DOT(LIGHT,LIGHT))*SQR(DOT(N,N))) LET S=(S+1)/2 SET COLOR MIX(8) S,S,S SET AREA COLOR 8 END SUB EXTERNAL SUB OUTER(C(),A(),B()) !'外積 LET C(1)=A(2)*B(3)-A(3)*B(2) LET C(2)=A(3)*B(1)-A(1)*B(3) LET C(3)=A(1)*B(2)-A(2)*B(1) END SUB EXTERNAL SUB QUICKSORT(FI,LA,A(),INDEX()) LET X=A(INDEX((FI+LA)/2)) LET I=FI LET J=LA DO DO WHILE A(INDEX(I))<X LET I=I+1 LOOP DO WHILE X<A(INDEX(J)) LET J=J-1 LOOP IF I>=J THEN EXIT DO SWAP INDEX(I),INDEX(J) LET I=I+1 LET J=J-1 LOOP IF FI<I-1 THEN CALL QUICKSORT(FI,I-1,A,INDEX) IF J+1<LA THEN CALL QUICKSORT(J+1,LA,A,INDEX) END SUB

3次元図形表示

投稿者：しばっち投稿日：2019年 3月30日(土)20時12分38秒

12・20面体を表示します(Zソート) OPTION ANGLE DEGREES FOR I=0 TO 7 SET COLOR MIX(I) BITAND(I,2)/2,BITAND(I,4)/4,BITAND(I,1) NEXT I DIM X0(200),Y0(200),Z0(200),X1(200),Y1(200),Z1(200),X2(200),Y2(200),Z2(200),KEY(200),INDEX(200) DIM P0(4),P1(4),P2(4) DIM L(4),M(4),N(3) DIM Q(4,4),ROTX(4,4),ROTY(4,4) DIM XX(100),YY(100),ZZ(100) LOCATE VALUE NOWAIT(1),RANGE 1 TO 10,AT 5:SCALE LOCATE VALUE NOWAIT(2),RANGE -360 TO 360,AT 0:XTH LOCATE VALUE NOWAIT(3),RANGE -360 TO 360,AT 0:YTH LOCATE VALUE NOWAIT(4),RANGE -360 TO 360,AT 0:ZTH DO LOCATE VALUE NOWAIT(1):SCALE LOCATE VALUE NOWAIT(2):XTH LOCATE VALUE NOWAIT(3):YTH LOCATE VALUE NOWAIT(4):ZTH SET WINDOW -SCALE,SCALE,-SCALE,SCALE RESTORE FOR I=1 TO 30 READ XX(I),YY(I),ZZ(I) NEXT I DATA -.30901699 , 0 ,-.95105652 !'座標データ DATA -.80901699 , 0 ,-.58778525 DATA -1 , 0 , 0 DATA -.80901699 , 0 , .58778525 DATA -.309017 , 0 , .95105652 DATA .30901699 , 0 , .95105652 DATA .80901699 , 0 , .58778525 DATA 1 , 0 , 0 DATA .80901699 , 0 ,-.58778525 DATA .30901699 , 0 ,-.95105652 DATA 0 ,-.52573111 ,-.85065081 DATA -.80901699 ,-.52573111 ,-.26286556 DATA -.5 ,-.52573111 , .68819096 DATA .5 ,-.52573111 , .68819096 DATA .80901699 ,-.52573111 ,-.26286556 DATA -.30901699 ,-.85065081 ,-.4253254 DATA -.5 ,-.85065081 , .16245985 DATA 0 ,-.85065081 , .52573111 DATA .5 ,-.85065081 , .16245985 DATA .30901699 ,-.85065081 ,-.4253254 DATA -.5 , .52573111 ,-.68819096 DATA .5 , .52573111 ,-.68819096 DATA .80901699 , .52573111 , .26286556 DATA 0 , .52573111 , .85065081 DATA -.80901699 , .52573111 , .26286556 DATA 0 , .85065081 ,-.52573111 DATA .5 , .85065081 ,-.16245985 DATA .30901699 , .85065081 , .4253254 DATA -.30901699 , .85065081 , .4253254 DATA -.5 , .85065081 ,-.16245985 FOR I=1 TO 56 READ A,B,C LET X0(I)=XX(A) LET Y0(I)=YY(A) LET Z0(I)=ZZ(A) LET X1(I)=XX(B) LET Y1(I)=YY(B) LET Z1(I)=ZZ(B) LET X2(I)=XX(C) LET Y2(I)=YY(C) LET Z2(I)=ZZ(C) NEXT I DATA 1,2,12 !'メッシュデータ DATA 1,12,16 DATA 1,16,11 DATA 1,11,10 DATA 1,10,22 DATA 1,22,26 DATA 1,26,21 DATA 1,21,2 DATA 2,3,12 DATA 2,21,30 DATA 2,30,25 DATA 2,25,3 DATA 3,4,13 DATA 3,13,17 DATA 3,17,12 DATA 3,25,4 DATA 4,5,13 DATA 4,25,29 DATA 4,29,24 DATA 4,24,5 DATA 5,6,14 DATA 5,14,18 DATA 5,18,13 DATA 5,24,6 DATA 6,7,14 DATA 6,24,28 DATA 6,28,23 DATA 6,23,7 DATA 7,8,15 DATA 7,15,19 DATA 7,19,14 DATA 7,23,8 DATA 8,9,15 DATA 8,23,27 DATA 8,27,22 DATA 8,22,9 DATA 9,10,11 DATA 9,11,20 DATA 9,20,15 DATA 9,22,10 DATA 11,16,20 DATA 12,17,16 DATA 13,18,17 DATA 14,19,18 DATA 15,20,19 DATA 16,17,18 DATA 16,18,19 DATA 16,19,20 DATA 21,26,30 DATA 22,27,26 DATA 23,28,27 DATA 24,29,28 DATA 25,30,29 DATA 26,27,28 DATA 26,28,29 DATA 26,29,30 MAT ROTX=IDN ! x軸のまわりの回転 LET ROTX(2,2)=COS(XTH) LET ROTX(2,3)=SIN(XTH) LET ROTX(3,2)=-SIN(XTH) LET ROTX(3,3)=COS(XTH) MAT ROTY=IDN ! y軸のまわりの回転 LET ROTY(1,1)=COS(YTH) LET ROTY(1,3)=-SIN(YTH) LET ROTY(3,1)=SIN(YTH) LET ROTY(3,3)=COS(YTH) MAT Q=ROTATE(ZTH) MAT Q=Q*ROTY*ROTX SET DRAW MODE HIDDEN CLEAR FOR I=1 TO 56 LET P0(1)=X0(I) LET P0(2)=Y0(I) LET P0(3)=Z0(I) LET P1(1)=X1(I) LET P1(2)=Y1(I) LET P1(3)=Z1(I) LET P2(1)=X2(I) LET P2(2)=Y2(I) LET P2(3)=Z2(I) LET P0(4),P1(4),P2(4)=1 MAT P0=P0*Q MAT P1=P1*Q MAT P2=P2*Q MAT L=P2-P1 MAT M=P1-P0 LET X0(I)=P0(1) LET Y0(I)=P0(2) LET Z0(I)=P0(3) LET X1(I)=P1(1) LET Y1(I)=P1(2) LET Z1(I)=P1(3) LET X2(I)=P2(1) LET Y2(I)=P2(2) LET Z2(I)=P2(3) LET KEY(I)=(Z0(I)+Z1(I)+Z2(I))/3 !'各頂点のZ座標値の平均 LET INDEX(I)=I NEXT I CALL QUICKSORT(1,56,KEY,INDEX) !'Zソート SET DRAW MODE HIDDEN CLEAR FOR I=1 TO 56 LET P0(1)=X0(INDEX(I)) LET P0(2)=Y0(INDEX(I)) LET P0(3)=Z0(INDEX(I)) LET P1(1)=X1(INDEX(I)) LET P1(2)=Y1(INDEX(I)) LET P1(3)=Z1(INDEX(I)) LET P2(1)=X2(INDEX(I)) LET P2(2)=Y2(INDEX(I)) LET P2(3)=Z2(INDEX(I)) MAT L=P2-P1 MAT M=P1-P0 CALL OUTER(N,L,M) CALL SETBRIGHTNESS(N) CALL PLOT3(P0,P1,P2) NEXT I SET DRAW MODE EXPLICIT LOOP END EXTERNAL SUB PLOT3(P0(),P1(),P2()) !'3角形描画 PLOT AREA :P0(1),P0(2);P1(1),P1(2);P2(1),P2(2) END SUB EXTERNAL SUB SETBRIGHTNESS(N()) DIM LIGHT(3) MAT READ LIGHT ! 光源の向き DATA 1,1,1 LET S=DOT(LIGHT,N)/(SQR(DOT(LIGHT,LIGHT))*SQR(DOT(N,N))) LET S=(S+1)/2 SET COLOR MIX(8) S,S,S SET AREA COLOR 8 END SUB EXTERNAL SUB OUTER(C(),A(),B()) !'外積 LET C(1)=A(2)*B(3)-A(3)*B(2) LET C(2)=A(3)*B(1)-A(1)*B(3) LET C(3)=A(1)*B(2)-A(2)*B(1) END SUB EXTERNAL SUB QUICKSORT(FI,LA,A(),INDEX()) LET X=A(INDEX((FI+LA)/2)) LET I=FI LET J=LA DO DO WHILE A(INDEX(I))<X LET I=I+1 LOOP DO WHILE X<A(INDEX(J)) LET J=J-1 LOOP IF I>=J THEN EXIT DO SWAP INDEX(I),INDEX(J) LET I=I+1 LET J=J-1 LOOP IF FI<I-1 THEN CALL QUICKSORT(FI,I-1,A,INDEX) IF J+1<LA THEN CALL QUICKSORT(J+1,LA,A,INDEX) END SUB

3次元図形表示

投稿者：しばっち投稿日：2019年 3月30日(土)20時13分21秒

トーラスを表示します(Zソート) OPTION ANGLE DEGREES LET NN=30 FOR I=0 TO 7 SET COLOR MIX(I) BITAND(I,2)/2,BITAND(I,4)/4,BITAND(I,1) NEXT I DIM X0(2*NN*NN),Y0(2*NN*NN),Z0(2*NN*NN),X1(2*NN*NN),Y1(2*NN*NN),Z1(2*NN*NN),X2(2*NN*NN),Y2(2*NN*NN),Z2(2*NN*NN),KEY(2*NN*NN),INDEX(2*NN*NN) DIM P0(4),P1(4),P2(4),P3(4) DIM N(3),L(4),M(4) DIM Q(4,4),ROTX(4,4),ROTY(4,4) LOCATE VALUE NOWAIT(1),RANGE 1 TO 30,AT 5 : SCALE LOCATE VALUE NOWAIT(2),RANGE -360 TO 360,AT 0:XTH LOCATE VALUE NOWAIT(3),RANGE -360 TO 360,AT 0:YTH LOCATE VALUE NOWAIT(4),RANGE -360 TO 360,AT 0:ZTH LOCATE VALUE NOWAIT(5),RANGE 0 TO 10,AT 0 : K LOCATE VALUE NOWAIT(6),RANGE 0 TO 8,AT 1 : RR LOCATE VALUE NOWAIT(7),RANGE 0 TO 8,AT .5 : R0 LOCATE VALUE NOWAIT(8),RANGE 0 TO 8,AT 1 : R1 LOCATE VALUE NOWAIT(9),RANGE 0 TO 8,AT 1 : R2 DO LOCATE VALUE NOWAIT(1):SCALE LOCATE VALUE NOWAIT(2):XTH LOCATE VALUE NOWAIT(3):YTH LOCATE VALUE NOWAIT(4):ZTH LOCATE VALUE NOWAIT(5):K LOCATE VALUE NOWAIT(6):RR LOCATE VALUE NOWAIT(7):R0 LOCATE VALUE NOWAIT(8):R1 LOCATE VALUE NOWAIT(9):R2 LET K=INT(K) SET WINDOW -SCALE,SCALE,-SCALE,SCALE LET NUM=0 FOR I=0 TO NN-1 FOR J=0 TO NN-1 LET NUM=NUM+1 LET ALPHA=I*360/NN LET BETA=J*360/NN LET XX0=(R1+R0*COS(ALPHA))*(R2+RR*COS(K*BETA))*COS(BETA) LET ZZ0=(R1+R0*COS(ALPHA))*(R2+RR*COS(K*BETA))*SIN(BETA) LET YY0=R0*SIN(ALPHA)*(R2+RR*COS(K*BETA)) LET ALPHA=I*360/NN LET BETA=(J+1)*360/NN LET XX1=(R1+R0*COS(ALPHA))*(R2+RR*COS(K*BETA))*COS(BETA) LET ZZ1=(R1+R0*COS(ALPHA))*(R2+RR*COS(K*BETA))*SIN(BETA) LET YY1=R0*SIN(ALPHA)*(R2+RR*COS(K*BETA)) LET ALPHA=(I+1)*360/NN LET BETA=(J+1)*360/NN LET XX2=(R1+R0*COS(ALPHA))*(R2+RR*COS(K*BETA))*COS(BETA) LET ZZ2=(R1+R0*COS(ALPHA))*(R2+RR*COS(K*BETA))*SIN(BETA) LET YY2=R0*SIN(ALPHA)*(R2+RR*COS(K*BETA)) LET ALPHA=(I+1)*360/NN LET BETA=J*360/NN LET XX3=(R1+R0*COS(ALPHA))*(R2+RR*COS(K*BETA))*COS(BETA) LET ZZ3=(R1+R0*COS(ALPHA))*(R2+RR*COS(K*BETA))*SIN(BETA) LET YY3=R0*SIN(ALPHA)*(R2+RR*COS(K*BETA)) LET X0(NUM)=XX0 LET Y0(NUM)=YY0 LET Z0(NUM)=ZZ0 LET X1(NUM)=XX1 LET Y1(NUM)=YY1 LET Z1(NUM)=ZZ1 LET X2(NUM)=XX2 LET Y2(NUM)=YY2 LET Z2(NUM)=ZZ2 LET NUM=NUM+1 LET X0(NUM)=XX0 LET Y0(NUM)=YY0 LET Z0(NUM)=ZZ0 LET X1(NUM)=XX2 LET Y1(NUM)=YY2 LET Z1(NUM)=ZZ2 LET X2(NUM)=XX3 LET Y2(NUM)=YY3 LET Z2(NUM)=ZZ3 NEXT J NEXT I MAT ROTX=IDN ! x軸のまわりの回転 LET ROTX(2,2)=COS(XTH) LET ROTX(2,3)=SIN(XTH) LET ROTX(3,2)=-SIN(XTH) LET ROTX(3,3)=COS(XTH) MAT ROTY=IDN ! y軸のまわりの回転 LET ROTY(1,1)=COS(YTH) LET ROTY(1,3)=-SIN(YTH) LET ROTY(3,1)=SIN(YTH) LET ROTY(3,3)=COS(YTH) MAT Q=ROTATE(ZTH) MAT Q=Q*ROTY*ROTX FOR I=1 TO NUM LET P0(1)=X0(I) LET P0(2)=Y0(I) LET P0(3)=Z0(I) LET P1(1)=X1(I) LET P1(2)=Y1(I) LET P1(3)=Z1(I) LET P2(1)=X2(I) LET P2(2)=Y2(I) LET P2(3)=Z2(I) MAT P0=P0*Q MAT P1=P1*Q MAT P2=P2*Q LET X0(I)=P0(1) LET Y0(I)=P0(2) LET Z0(I)=P0(3) LET X1(I)=P1(1) LET Y1(I)=P1(2) LET Z1(I)=P1(3) LET X2(I)=P2(1) LET Y2(I)=P2(2) LET Z2(I)=P2(3) LET KEY(I)=(Z0(I)+Z1(I)+Z2(I))/3 !'各頂点のZ座標値の平均 LET INDEX(I)=I NEXT I CALL QUICKSORT(1,NUM,KEY,INDEX) !'Zソート SET DRAW MODE HIDDEN CLEAR FOR I=1 TO NUM LET P0(1)=X0(INDEX(I)) LET P0(2)=Y0(INDEX(I)) LET P0(3)=Z0(INDEX(I)) LET P1(1)=X1(INDEX(I)) LET P1(2)=Y1(INDEX(I)) LET P1(3)=Z1(INDEX(I)) LET P2(1)=X2(INDEX(I)) LET P2(2)=Y2(INDEX(I)) LET P2(3)=Z2(INDEX(I)) MAT L=P2-P1 MAT M=P1-P0 CALL OUTER(N,L,M) IF DOT(N,N)<>0 THEN CALL SETBRIGHTNESS(N) CALL PLOT3(P0,P1,P2) END IF NEXT I SET DRAW MODE EXPLICIT LOOP END EXTERNAL SUB PLOT3(P0(),P1(),P2()) !'3角形描画 PLOT AREA :P0(1),P0(2);P1(1),P1(2);P2(1),P2(2) END SUB EXTERNAL SUB SETBRIGHTNESS(N()) DIM LA(3),LIGHT(3) MAT READ LA DATA .8,.6,.3 MAT READ LIGHT DATA 1,1,1 LET S=DOT(LIGHT,N)/(SQR(DOT(LIGHT,LIGHT))*SQR(DOT(N,N))) LET S=ABS(S) MAT LA=((S+1)/2)*LA SET COLOR MIX(8) LA(1),LA(2),LA(3) SET AREA COLOR 8 END SUB EXTERNAL SUB OUTER(C(),A(),B()) !'外積 LET C(1)=A(2)*B(3)-A(3)*B(2) LET C(2)=A(3)*B(1)-A(1)*B(3) LET C(3)=A(1)*B(2)-A(2)*B(1) END SUB EXTERNAL SUB QUICKSORT(FI,LA,A(),INDEX()) LET X=A(INDEX((FI+LA)/2)) LET I=FI LET J=LA DO DO WHILE A(INDEX(I))<X LET I=I+1 LOOP DO WHILE X<A(INDEX(J)) LET J=J-1 LOOP IF I>=J THEN EXIT DO SWAP INDEX(I),INDEX(J) LET I=I+1 LET J=J-1 LOOP IF FI<I-1 THEN CALL QUICKSORT(FI,I-1,A,INDEX) IF J+1<LA THEN CALL QUICKSORT(J+1,LA,A,INDEX) END SUB

3次元図形表示

投稿者：しばっち投稿日：2019年 3月30日(土)20時14分2秒

花型球体を表示します(Zソート) OPTION ANGLE DEGREES LET NN=30 FOR I=0 TO 7 SET COLOR MIX(I) BITAND(I,2)/2,BITAND(I,4)/4,BITAND(I,1) NEXT I DIM X0(2*NN*NN),Y0(2*NN*NN),Z0(2*NN*NN),X1(2*NN*NN),Y1(2*NN*NN),Z1(2*NN*NN),X2(2*NN*NN),Y2(2*NN*NN),Z2(2*NN*NN),KEY(2*NN*NN),INDEX(2*NN*NN) DIM P0(4),P1(4),P2(4),P3(4) DIM N(3),L(4),M(4) DIM Q(4,4),ROTX(4,4),ROTY(4,4) LOCATE VALUE NOWAIT(1),RANGE 1 TO 5,AT 3:SCALE LOCATE VALUE NOWAIT(2),RANGE -360 TO 360,AT 0:XTH LOCATE VALUE NOWAIT(3),RANGE -360 TO 360,AT 0:YTH LOCATE VALUE NOWAIT(4),RANGE -360 TO 360,AT 0:ZTH LOCATE VALUE NOWAIT(5),RANGE 1 TO 10,AT 1:A LOCATE VALUE NOWAIT(6),RANGE 1 TO 10,AT 1:B LOCATE VALUE NOWAIT(7),RANGE 1 TO 10,AT 1:N1 LOCATE VALUE NOWAIT(8),RANGE 1 TO 10,AT 1:M1 LOCATE VALUE NOWAIT(9),RANGE 1 TO 10,AT 1:RR DO LOCATE VALUE NOWAIT(1):SCALE LOCATE VALUE NOWAIT(2):XTH LOCATE VALUE NOWAIT(3):YTH LOCATE VALUE NOWAIT(4):ZTH LOCATE VALUE NOWAIT(5):A LOCATE VALUE NOWAIT(6):B LOCATE VALUE NOWAIT(7):N1 LOCATE VALUE NOWAIT(8):M1 LOCATE VALUE NOWAIT(9):RR LET N1=INT(N1) LET M1=INT(M1) SET WINDOW -SCALE,SCALE,-SCALE,SCALE LET NUM=0 FOR I=0 TO NN-1 FOR J=0 TO NN-1 LET NUM=NUM+1 LET R0=FUNC(1,A/20,B/20,N1,M1,RR/10,I*180/NN,J*360/NN) LET XX0=-R0*SIN(I*180/NN)*COS(J*360/NN) LET YY0=R0*COS(I*180/NN) LET ZZ0=R0*SIN(I*180/NN)*SIN(J*360/NN) LET R0=FUNC(1,A/20,B/20,N1,M1,RR/10,I*180/NN,(J+1)*360/NN) LET XX1=-R0*SIN(I*180/NN)*COS((J+1)*360/NN) LET YY1=R0*COS(I*180/NN) LET ZZ1=R0*SIN(I*180/NN)*SIN((J+1)*360/NN) LET R0=FUNC(1,A/20,B/20,N1,M1,RR/10,(I+1)*180/NN,(J+1)*360/NN) LET XX2=-R0*SIN((I+1)*180/NN)*COS((J+1)*360/NN) LET YY2=R0*COS((I+1)*180/NN) LET ZZ2=R0*SIN((I+1)*180/NN)*SIN((J+1)*360/NN) LET R0=FUNC(1,A/20,B/20,N1,M1,RR/10,(I+1)*180/NN,J*360/NN) LET XX3=-R0*SIN((I+1)*180/NN)*COS(J*360/NN) LET YY3=R0*COS((I+1)*180/NN) LET ZZ3=R0*SIN((I+1)*180/NN)*SIN(J*360/NN) LET X0(NUM)=XX0 LET Y0(NUM)=YY0 LET Z0(NUM)=ZZ0 LET X1(NUM)=XX1 LET Y1(NUM)=YY1 LET Z1(NUM)=ZZ1 LET X2(NUM)=XX2 LET Y2(NUM)=YY2 LET Z2(NUM)=ZZ2 LET NUM=NUM+1 LET X0(NUM)=XX0 LET Y0(NUM)=YY0 LET Z0(NUM)=ZZ0 LET X1(NUM)=XX2 LET Y1(NUM)=YY2 LET Z1(NUM)=ZZ2 LET X2(NUM)=XX3 LET Y2(NUM)=YY3 LET Z2(NUM)=ZZ3 NEXT J NEXT I MAT ROTX=IDN ! x軸のまわりの回転 LET ROTX(2,2)=COS(XTH) LET ROTX(2,3)=SIN(XTH) LET ROTX(3,2)=-SIN(XTH) LET ROTX(3,3)=COS(XTH) MAT ROTY=IDN ! y軸のまわりの回転 LET ROTY(1,1)=COS(YTH) LET ROTY(1,3)=-SIN(YTH) LET ROTY(3,1)=SIN(YTH) LET ROTY(3,3)=COS(YTH) MAT Q=ROTATE(ZTH) MAT Q=Q*ROTY*ROTX FOR I=1 TO NUM LET P0(1)=X0(I) LET P0(2)=Y0(I) LET P0(3)=Z0(I) LET P1(1)=X1(I) LET P1(2)=Y1(I) LET P1(3)=Z1(I) LET P2(1)=X2(I) LET P2(2)=Y2(I) LET P2(3)=Z2(I) MAT P0=P0*Q MAT P1=P1*Q MAT P2=P2*Q LET X0(I)=P0(1) LET Y0(I)=P0(2) LET Z0(I)=P0(3) LET X1(I)=P1(1) LET Y1(I)=P1(2) LET Z1(I)=P1(3) LET X2(I)=P2(1) LET Y2(I)=P2(2) LET Z2(I)=P2(3) LET KEY(I)=(Z0(I)+Z1(I)+Z2(I))/3 !'各頂点のZ座標値の平均 LET INDEX(I)=I NEXT I CALL QUICKSORT(1,NUM,KEY,INDEX) !'Zソート SET DRAW MODE HIDDEN CLEAR FOR I=1 TO NUM LET P0(1)=X0(INDEX(I)) LET P0(2)=Y0(INDEX(I)) LET P0(3)=Z0(INDEX(I)) LET P1(1)=X1(INDEX(I)) LET P1(2)=Y1(INDEX(I)) LET P1(3)=Z1(INDEX(I)) LET P2(1)=X2(INDEX(I)) LET P2(2)=Y2(INDEX(I)) LET P2(3)=Z2(INDEX(I)) MAT L=P2-P1 MAT M=P1-P0 CALL OUTER(N,L,M) IF DOT(N,N)<>0 THEN CALL SETBRIGHTNESS(N) CALL PLOT3(P0,P1,P2) END IF NEXT I SET DRAW MODE EXPLICIT LOOP END EXTERNAL FUNCTION FUNC(R,A,B,N,M,RR,ALPHA,BETA) !'バラ曲線 OPTION ANGLE DEGREES LET FUNC=ABS(R*(1+A*SIN(ALPHA*N)*(1+B*SIN(BETA*M)+RR))) END FUNCTION EXTERNAL SUB PLOT3(P0(),P1(),P2()) !'3角形描画 PLOT AREA :P0(1),P0(2);P1(1),P1(2);P2(1),P2(2) END SUB EXTERNAL SUB SETBRIGHTNESS(N()) DIM LA(3),LIGHT(3) MAT READ LA DATA .8,.8,.1 MAT READ LIGHT DATA 1,1,1 LET S=DOT(LIGHT,N)/(SQR(DOT(LIGHT,LIGHT))*SQR(DOT(N,N))) MAT LA=((S+1)/2)*LA SET COLOR MIX(8) LA(1),LA(2),LA(3) SET AREA COLOR 8 END SUB EXTERNAL SUB OUTER(C(),A(),B()) !'外積 LET C(1)=A(2)*B(3)-A(3)*B(2) LET C(2)=A(3)*B(1)-A(1)*B(3) LET C(3)=A(1)*B(2)-A(2)*B(1) END SUB EXTERNAL SUB QUICKSORT(FI,LA,A(),INDEX()) LET X=A(INDEX((FI+LA)/2)) LET I=FI LET J=LA DO DO WHILE A(INDEX(I))<X LET I=I+1 LOOP DO WHILE X<A(INDEX(J)) LET J=J-1 LOOP IF I>=J THEN EXIT DO SWAP INDEX(I),INDEX(J) LET I=I+1 LET J=J-1 LOOP IF FI<I-1 THEN CALL QUICKSORT(FI,I-1,A,INDEX) IF J+1<LA THEN CALL QUICKSORT(J+1,LA,A,INDEX) END SUB

3次元図形表示

投稿者：しばっち投稿日：2019年 3月30日(土)20時14分45秒

超楕円体を表示します(Zソート) OPTION ANGLE DEGREES LET NN=30 FOR I=0 TO 7 SET COLOR MIX(I) BITAND(I,2)/2,BITAND(I,4)/4,BITAND(I,1) NEXT I DIM X0(2*NN*NN),Y0(2*NN*NN),Z0(2*NN*NN),X1(2*NN*NN),Y1(2*NN*NN),Z1(2*NN*NN),X2(2*NN*NN),Y2(2*NN*NN),Z2(2*NN*NN),KEY(2*NN*NN),INDEX(2*NN*NN) DIM P0(4),P1(4),P2(4),P3(4) DIM N(3),L(4),M(4) DIM Q(4,4),ROTX(4,4),ROTY(4,4) LOCATE VALUE NOWAIT(1),RANGE 1 TO 5,AT 3:SCALE LOCATE VALUE NOWAIT(2),RANGE -360 TO 360,AT 0:XTH LOCATE VALUE NOWAIT(3),RANGE -360 TO 360,AT 0:YTH LOCATE VALUE NOWAIT(4),RANGE -360 TO 360,AT 0:ZTH LOCATE VALUE NOWAIT(5),RANGE 0 TO 4,AT 1:N0 LOCATE VALUE NOWAIT(6),RANGE 0 TO 4,AT 1:M0 LOCATE VALUE NOWAIT(7),RANGE .1 TO 4,AT 1:R1 LOCATE VALUE NOWAIT(8),RANGE .1 TO 4,AT 1:R2 LOCATE VALUE NOWAIT(9),RANGE .1 TO 4,AT 1:R3 DO LOCATE VALUE NOWAIT(1):SCALE LOCATE VALUE NOWAIT(2):XTH LOCATE VALUE NOWAIT(3):YTH LOCATE VALUE NOWAIT(4):ZTH LOCATE VALUE NOWAIT(5):N0 LOCATE VALUE NOWAIT(6):M0 LOCATE VALUE NOWAIT(7):R1 LOCATE VALUE NOWAIT(8):R2 LOCATE VALUE NOWAIT(9):R3 SET WINDOW -SCALE,SCALE,-SCALE,SCALE LET NUM=0 FOR I=0 TO NN-1 FOR J=0 TO NN-1 LET NUM=NUM+1 LET XX0=-R1*SGN(SIN(I*180/NN))*ABS(SIN(I*180/NN))^N0*SGN(COS(J*360/NN))*ABS(COS(J*360/NN))^M0 LET YY0=R2*SGN(COS(I*180/NN))*ABS(COS(I*180/NN))^N0 LET ZZ0=R3*SGN(SIN(I*180/NN))*ABS(SIN(I*180/NN))^N0*SGN(SIN(J*360/NN))*ABS(SIN(J*360/NN))^M0 LET XX1=-R1*SGN(SIN(I*180/NN))*ABS(SIN(I*180/NN))^N0*SGN(COS((J+1)*360/NN))*ABS(COS((J+1)*360/NN))^M0 LET YY1=R2*SGN(COS(I*180/NN))*ABS(COS(I*180/NN))^N0 LET ZZ1=R3*SGN(SIN(I*180/NN))*ABS(SIN(I*180/NN))^N0*SGN(SIN((J+1)*360/NN))*ABS(SIN((J+1)*360/NN))^M0 LET XX2=-R1*SGN(SIN((I+1)*180/NN))*ABS(SIN((I+1)*180/NN))^N0*SGN(COS((J+1)*360/NN))*ABS(COS((J+1)*360/NN))^M0 LET YY2=R2*SGN(COS((I+1)*180/NN))*ABS(COS((I+1)*180/NN))^N0 LET ZZ2=R3*SGN(SIN((I+1)*180/NN))*ABS(SIN((I+1)*180/NN))^N0*SGN(SIN((J+1)*360/NN))*ABS(SIN((J+1)*360/NN))^M0 LET XX3=-R1*SGN(SIN((I+1)*180/NN))*ABS(SIN((I+1)*180/NN))^N0*SGN(COS(J*360/NN))*ABS(COS(J*360/NN))^M0 LET YY3=R2*SGN(COS((I+1)*180/NN))*ABS(COS((I+1)*180/NN))^N0 LET ZZ3=R3*SGN(SIN((I+1)*180/NN))*ABS(SIN((I+1)*180/NN))^N0*SGN(SIN(J*360/NN))*ABS(SIN(J*360/NN))^M0 LET X0(NUM)=XX0 LET Y0(NUM)=YY0 LET Z0(NUM)=ZZ0 LET X1(NUM)=XX1 LET Y1(NUM)=YY1 LET Z1(NUM)=ZZ1 LET X2(NUM)=XX2 LET Y2(NUM)=YY2 LET Z2(NUM)=ZZ2 LET NUM=NUM+1 LET X0(NUM)=XX0 LET Y0(NUM)=YY0 LET Z0(NUM)=ZZ0 LET X1(NUM)=XX2 LET Y1(NUM)=YY2 LET Z1(NUM)=ZZ2 LET X2(NUM)=XX3 LET Y2(NUM)=YY3 LET Z2(NUM)=ZZ3 NEXT J NEXT I MAT ROTX=IDN ! x軸のまわりの回転 LET ROTX(2,2)=COS(XTH) LET ROTX(2,3)=SIN(XTH) LET ROTX(3,2)=-SIN(XTH) LET ROTX(3,3)=COS(XTH) MAT ROTY=IDN ! y軸のまわりの回転 LET ROTY(1,1)=COS(YTH) LET ROTY(1,3)=-SIN(YTH) LET ROTY(3,1)=SIN(YTH) LET ROTY(3,3)=COS(YTH) MAT Q=ROTATE(ZTH) MAT Q=Q*ROTY*ROTX FOR I=1 TO NUM LET P0(1)=X0(I) LET P0(2)=Y0(I) LET P0(3)=Z0(I) LET P1(1)=X1(I) LET P1(2)=Y1(I) LET P1(3)=Z1(I) LET P2(1)=X2(I) LET P2(2)=Y2(I) LET P2(3)=Z2(I) MAT P0=P0*Q MAT P1=P1*Q MAT P2=P2*Q LET X0(I)=P0(1) LET Y0(I)=P0(2) LET Z0(I)=P0(3) LET X1(I)=P1(1) LET Y1(I)=P1(2) LET Z1(I)=P1(3) LET X2(I)=P2(1) LET Y2(I)=P2(2) LET Z2(I)=P2(3) LET KEY(I)=(Z0(I)+Z1(I)+Z2(I))/3 !'各頂点のZ座標値の平均 LET INDEX(I)=I NEXT I CALL QUICKSORT(1,NUM,KEY,INDEX) !'Zソート SET DRAW MODE HIDDEN CLEAR FOR I=1 TO NUM LET P0(1)=X0(INDEX(I)) LET P0(2)=Y0(INDEX(I)) LET P0(3)=Z0(INDEX(I)) LET P1(1)=X1(INDEX(I)) LET P1(2)=Y1(INDEX(I)) LET P1(3)=Z1(INDEX(I)) LET P2(1)=X2(INDEX(I)) LET P2(2)=Y2(INDEX(I)) LET P2(3)=Z2(INDEX(I)) MAT L=P2-P1 MAT M=P1-P0 CALL OUTER(N,L,M) IF DOT(N,N)<>0 THEN CALL SETBRIGHTNESS(N) CALL PLOT3(P0,P1,P2) END IF NEXT I SET DRAW MODE EXPLICIT LOOP END EXTERNAL SUB PLOT3(P0(),P1(),P2()) !'3角形描画 PLOT AREA :P0(1),P0(2);P1(1),P1(2);P2(1),P2(2) END SUB EXTERNAL SUB SETBRIGHTNESS(N()) DIM LA(3),LIGHT(3) MAT READ LA DATA .8,.8,.1 MAT READ LIGHT DATA 1,1,1 LET S=DOT(LIGHT,N)/(SQR(DOT(LIGHT,LIGHT))*SQR(DOT(N,N))) LET S=ABS(S) MAT LA=((S+1)/2)*LA SET COLOR MIX(8) LA(1),LA(2),LA(3) SET AREA COLOR 8 END SUB EXTERNAL SUB OUTER(C(),A(),B()) !'外積 LET C(1)=A(2)*B(3)-A(3)*B(2) LET C(2)=A(3)*B(1)-A(1)*B(3) LET C(3)=A(1)*B(2)-A(2)*B(1) END SUB EXTERNAL SUB QUICKSORT(FI,LA,A(),INDEX()) LET X=A(INDEX((FI+LA)/2)) LET I=FI LET J=LA DO DO WHILE A(INDEX(I))<X LET I=I+1 LOOP DO WHILE X<A(INDEX(J)) LET J=J-1 LOOP IF I>=J THEN EXIT DO SWAP INDEX(I),INDEX(J) LET I=I+1 LET J=J-1 LOOP IF FI<I-1 THEN CALL QUICKSORT(FI,I-1,A,INDEX) IF J+1<LA THEN CALL QUICKSORT(J+1,LA,A,INDEX) END SUB

3次元図形表示

投稿者：しばっち投稿日：2019年 3月30日(土)20時15分35秒

シェルピンスキーの三角形を表示します(Zソート) https://ja.wikipedia.org/wiki/シェルピンスキーのギャスケット 4面体を使用し、シェルピンスキーの三角形を表示します OPTION ANGLE DEGREES FOR I=0 TO 7 SET COLOR MIX(I) BITAND(I,2)/2,BITAND(I,4)/4,BITAND(I,1) NEXT I CLEAR INPUT PROMPT "LEVEL (1-4)=":LEV DIM X0(4^(LEV+1)),Y0(4^(LEV+1)),Z0(4^(LEV+1)),X1(4^(LEV+1)),Y1(4^(LEV+1)),Z1(4^(LEV+1)),X2(4^(LEV+1)),Y2(4^(LEV+1)),Z2(4^(LEV+1)),KEY(4^(LEV+1)),INDEX(4^(LEV+1)) DIM P0(4),P1(4),P2(4) DIM L(4),M(4),N(3) DIM Q(4,4),ROTX(4,4),ROTY(4,4) LOCATE VALUE NOWAIT(1),RANGE 1 TO 10,AT 3:SCALE LOCATE VALUE NOWAIT(2),RANGE -360 TO 360,AT 0:XTH LOCATE VALUE NOWAIT(3),RANGE -360 TO 360,AT 0:YTH LOCATE VALUE NOWAIT(4),RANGE -360 TO 360,AT 0:ZTH DO LOCATE VALUE NOWAIT(1):SCALE LOCATE VALUE NOWAIT(2):XTH LOCATE VALUE NOWAIT(3):YTH LOCATE VALUE NOWAIT(4):ZTH SET WINDOW -SCALE,SCALE,-SCALE,SCALE MAT ROTX=IDN ! x軸のまわりの回転 LET ROTX(2,2)=COS(XTH) LET ROTX(2,3)=SIN(XTH) LET ROTX(3,2)=-SIN(XTH) LET ROTX(3,3)=COS(XTH) MAT ROTY=IDN ! y軸のまわりの回転 LET ROTY(1,1)=COS(YTH) LET ROTY(1,3)=-SIN(YTH) LET ROTY(3,1)=SIN(YTH) LET ROTY(3,3)=COS(YTH) MAT Q=ROTATE(ZTH) MAT Q=Q*ROTY*ROTX LET NUM=0 CALL RECURSIVE(LEV,0,0,0,1) LET MX=0 LET MY=0 LET MZ=0 FOR I=1 TO NUM !'重心を求める LET MX=MX+X0(I) LET MY=MY+Y0(I) LET MZ=MZ+Z0(I) LET MX=MX+X1(I) LET MY=MY+Y1(I) LET MZ=MZ+Z1(I) LET MX=MX+X2(I) LET MY=MY+Y2(I) LET MZ=MZ+Z2(I) NEXT I LET MX=MX/3/NUM LET MY=MY/3/NUM LET MZ=MZ/3/NUM FOR I=1 TO NUM LET P0(1)=X0(I)-MX LET P0(2)=Y0(I)-MY LET P0(3)=Z0(I)-MZ LET P1(1)=X1(I)-MX LET P1(2)=Y1(I)-MY LET P1(3)=Z1(I)-MZ LET P2(1)=X2(I)-MX LET P2(2)=Y2(I)-MY LET P2(3)=Z2(I)-MZ LET P0(4),P1(4),P2(4)=1 MAT P0=P0*Q MAT P1=P1*Q MAT P2=P2*Q LET X0(I)=P0(1) LET Y0(I)=P0(2) LET Z0(I)=P0(3) LET X1(I)=P1(1) LET Y1(I)=P1(2) LET Z1(I)=P1(3) LET X2(I)=P2(1) LET Y2(I)=P2(2) LET Z2(I)=P2(3) LET KEY(I)=(Z0(I)+Z1(I)+Z2(I))/3 !'各頂点のZ座標値の平均 LET INDEX(I)=I NEXT I CALL QUICKSORT(1,NUM,KEY,INDEX) !'Zソート SET DRAW MODE HIDDEN CLEAR FOR I=1 TO NUM LET P0(1)=X0(INDEX(I)) LET P0(2)=Y0(INDEX(I)) LET P0(3)=Z0(INDEX(I)) LET P1(1)=X1(INDEX(I)) LET P1(2)=Y1(INDEX(I)) LET P1(3)=Z1(INDEX(I)) LET P2(1)=X2(INDEX(I)) LET P2(2)=Y2(INDEX(I)) LET P2(3)=Z2(INDEX(I)) MAT L=P2-P1 MAT M=P1-P0 CALL OUTER(N,L,M) CALL SETBRIGHTNESS(N) CALL PLOT3(P0,P1,P2) NEXT I SET DRAW MODE EXPLICIT LOOP SUB TETRAHEDRON(X,Y,Z,L) !'4面体 LET XX1=X+L*COS(0) LET ZZ1=Z+L*SIN(0) LET YY1=Y LET XX2=X+L*COS(120) LET ZZ2=Z+L*SIN(120) LET YY2=Y LET XX3=X+L*COS(240) LET ZZ3=Z+L*SIN(240) LET YY3=Y LET XX4=X LET ZZ4=Z LET YY4=Y+L*SQR(2) LET NUM=NUM+1 LET X0(NUM)=XX4 LET Y0(NUM)=YY4 LET Z0(NUM)=ZZ4 LET X1(NUM)=XX1 LET Y1(NUM)=YY1 LET Z1(NUM)=ZZ1 LET X2(NUM)=XX2 LET Y2(NUM)=YY2 LET Z2(NUM)=ZZ2 LET NUM=NUM+1 LET X0(NUM)=XX3 LET Y0(NUM)=YY3 LET Z0(NUM)=ZZ3 LET X1(NUM)=XX2 LET Y1(NUM)=YY2 LET Z1(NUM)=ZZ2 LET X2(NUM)=XX1 LET Y2(NUM)=YY1 LET Z2(NUM)=ZZ1 LET NUM=NUM+1 LET X0(NUM)=XX4 LET Y0(NUM)=YY4 LET Z0(NUM)=ZZ4 LET X1(NUM)=XX3 LET Y1(NUM)=YY3 LET Z1(NUM)=ZZ3 LET X2(NUM)=XX1 LET Y2(NUM)=YY1 LET Z2(NUM)=ZZ1 LET NUM=NUM+1 LET X0(NUM)=XX4 LET Y0(NUM)=YY4 LET Z0(NUM)=ZZ4 LET X1(NUM)=XX2 LET Y1(NUM)=YY2 LET Z1(NUM)=ZZ2 LET X2(NUM)=XX3 LET Y2(NUM)=YY3 LET Z2(NUM)=ZZ3 END SUB SUB RECURSIVE(LEV,X,Y,Z,L) !'シェルピンスキー IF LEV=0 THEN CALL TETRAHEDRON(X,Y,Z,L*2) ELSE CALL RECURSIVE(LEV-1,X,Y+L*SQR(2),Z,L/2) CALL RECURSIVE(LEV-1,X+L*COS(0),Y,Z+L*SIN(0),L/2) CALL RECURSIVE(LEV-1,X+L*COS(120),Y,Z+L*SIN(120),L/2) CALL RECURSIVE(LEV-1,X+L*COS(240),Y,Z+L*SIN(240),L/2) END IF END SUB END EXTERNAL SUB PLOT3(P0(),P1(),P2()) !'3角形描画 PLOT AREA :P0(1),P0(2);P1(1),P1(2);P2(1),P2(2) END SUB EXTERNAL SUB SETBRIGHTNESS(N()) DIM A(3) MAT READ A ! 光源の向き DATA 1,1,1 LET S=DOT(A,N)/(SQR(DOT(A,A))*SQR(DOT(N,N))) LET S=(S+1)/2 SET COLOR MIX(8) S,S,S SET AREA COLOR 8 END SUB EXTERNAL SUB OUTER(C(),A(),B()) !'外積 LET C(1)=A(2)*B(3)-A(3)*B(2) LET C(2)=A(3)*B(1)-A(1)*B(3) LET C(3)=A(1)*B(2)-A(2)*B(1) END SUB EXTERNAL SUB QUICKSORT(FI,LA,A(),INDEX()) LET X=A(INDEX((FI+LA)/2)) LET I=FI LET J=LA DO DO WHILE A(INDEX(I))<X LET I=I+1 LOOP DO WHILE X<A(INDEX(J)) LET J=J-1 LOOP IF I>=J THEN EXIT DO SWAP INDEX(I),INDEX(J) LET I=I+1 LET J=J-1 LOOP IF FI<I-1 THEN CALL QUICKSORT(FI,I-1,A,INDEX) IF J+1<LA THEN CALL QUICKSORT(J+1,LA,A,INDEX) END SUB

3次元図形表示

投稿者：しばっち投稿日：2019年 3月30日(土)20時16分18秒

メンガースポンジを表示します(Zソート) https://ja.wikipedia.org/wiki/メンガーのスポンジ立方体を大量に使用して、レベル4のメンガーを表示します。表示が速いZソートですが、データ量が非常に多く処理が重いため表示のみです。 OPTION ANGLE DEGREES LET ZTH=0 ! z軸のまわりの回転角 LET XTH=20 ! x軸のまわりの回転角初期値 LET YTH=10 ! y軸のまわりの回転角初期値 FOR I=0 TO 7 SET COLOR MIX(I) BITAND(I,2)/2,BITAND(I,4)/4,BITAND(I,1) NEXT I LET LEV=4 DIM X0(6*20^LEV),Y0(6*20^LEV),Z0(6*20^LEV),X1(6*20^LEV),Y1(6*20^LEV),Z1(6*20^LEV),X2(6*20^LEV),Y2(6*20^LEV),Z2(6*20^LEV) DIM X3(6*20^LEV),Y3(6*20^LEV),Z3(6*20^LEV),KEY(6*20^LEV),INDEX(6*20^LEV) DIM P0(4),P1(4),P2(4),P3(4) DIM L(4),M(4),N(3) DIM Q(4,4),ROTX(4,4),ROTY(4,4) CALL RECURSIVE(LEV,0,0,0,2) SET WINDOW -1.5,1.5,-1.5,1.5 MAT ROTX=IDN ! x軸のまわりの回転 LET ROTX(2,2)=COS(XTH) LET ROTX(2,3)=SIN(XTH) LET ROTX(3,2)=-SIN(XTH) LET ROTX(3,3)=COS(XTH) MAT ROTY=IDN ! y軸のまわりの回転 LET ROTY(1,1)=COS(YTH) LET ROTY(1,3)=-SIN(YTH) LET ROTY(3,1)=SIN(YTH) LET ROTY(3,3)=COS(YTH) MAT Q=ROTATE(ZTH) MAT Q=Q*ROTY*ROTX FOR I=1 TO NUM LET P0(1)=X0(I) LET P0(2)=Y0(I) LET P0(3)=Z0(I) LET P1(1)=X1(I) LET P1(2)=Y1(I) LET P1(3)=Z1(I) LET P2(1)=X2(I) LET P2(2)=Y2(I) LET P2(3)=Z2(I) LET P3(1)=X3(I) LET P3(2)=Y3(I) LET P3(3)=Z3(I) LET P0(4),P1(4),P2(4),P3(4)=1 MAT P0=P0*Q MAT P1=P1*Q MAT P2=P2*Q MAT P3=P3*Q LET X0(I)=P0(1) LET Y0(I)=P0(2) LET Z0(I)=P0(3) LET X1(I)=P1(1) LET Y1(I)=P1(2) LET Z1(I)=P1(3) LET X2(I)=P2(1) LET Y2(I)=P2(2) LET Z2(I)=P2(3) LET X3(I)=P3(1) LET Y3(I)=P3(2) LET Z3(I)=P3(3) LET KEY(I)=(Z0(I)+Z1(I)+Z2(I)+Z3(I))/4 !'各頂点のZ座標値の平均 LET INDEX(I)=I NEXT I CALL QUICKSORT(1,NUM,KEY,INDEX) !'Zソート SET DRAW MODE HIDDEN CLEAR FOR I=1 TO NUM LET P0(1)=X0(INDEX(I)) LET P0(2)=Y0(INDEX(I)) LET P0(3)=Z0(INDEX(I)) LET P1(1)=X1(INDEX(I)) LET P1(2)=Y1(INDEX(I)) LET P1(3)=Z1(INDEX(I)) LET P2(1)=X2(INDEX(I)) LET P2(2)=Y2(INDEX(I)) LET P2(3)=Z2(INDEX(I)) LET P3(1)=X3(INDEX(I)) LET P3(2)=Y3(INDEX(I)) LET P3(3)=Z3(INDEX(I)) MAT L=P3-P1 MAT M=P1-P0 CALL OUTER(N,L,M) CALL SETBRIGHTNESS(N) CALL PLOT4(P0,P1,P2,P3) NEXT I SET DRAW MODE EXPLICIT SUB CUBE(X,Y,Z,L) !'立方体 LET NUM=NUM+1 LET X0(NUM)=X-L/2 LET Y0(NUM)=Y+L/2 LET Z0(NUM)=Z-L/2 LET X1(NUM)=X+L/2 LET Y1(NUM)=Y+L/2 LET Z1(NUM)=Z-L/2 LET X2(NUM)=X+L/2 LET Y2(NUM)=Y+L/2 LET Z2(NUM)=Z+L/2 LET X3(NUM)=X-L/2 LET Y3(NUM)=Y+L/2 LET Z3(NUM)=Z+L/2 LET NUM=NUM+1 LET X0(NUM)=X-L/2 LET Y0(NUM)=Y+L/2 LET Z0(NUM)=Z+L/2 LET X1(NUM)=X+L/2 LET Y1(NUM)=Y+L/2 LET Z1(NUM)=Z+L/2 LET X2(NUM)=X+L/2 LET Y2(NUM)=Y-L/2 LET Z2(NUM)=Z+L/2 LET X3(NUM)=X-L/2 LET Y3(NUM)=Y-L/2 LET Z3(NUM)=Z+L/2 LET NUM=NUM+1 LET X0(NUM)=X-L/2 LET Y0(NUM)=Y-L/2 LET Z0(NUM)=Z+L/2 LET X1(NUM)=X+L/2 LET Y1(NUM)=Y-L/2 LET Z1(NUM)=Z+L/2 LET X2(NUM)=X+L/2 LET Y2(NUM)=Y-L/2 LET Z2(NUM)=Z-L/2 LET X3(NUM)=X-L/2 LET Y3(NUM)=Y-L/2 LET Z3(NUM)=Z-L/2 LET NUM=NUM+1 LET X0(NUM)=X-L/2 LET Y0(NUM)=Y-L/2 LET Z0(NUM)=Z-L/2 LET X1(NUM)=X+L/2 LET Y1(NUM)=Y-L/2 LET Z1(NUM)=Z-L/2 LET X2(NUM)=X+L/2 LET Y2(NUM)=Y+L/2 LET Z2(NUM)=Z-L/2 LET X3(NUM)=X-L/2 LET Y3(NUM)=Y+L/2 LET Z3(NUM)=Z-L/2 LET NUM=NUM+1 LET X0(NUM)=X+L/2 LET Y0(NUM)=Y+L/2 LET Z0(NUM)=Z-L/2 LET X1(NUM)=X+L/2 LET Y1(NUM)=Y-L/2 LET Z1(NUM)=Z-L/2 LET X2(NUM)=X+L/2 LET Y2(NUM)=Y-L/2 LET Z2(NUM)=Z+L/2 LET X3(NUM)=X+L/2 LET Y3(NUM)=Y+L/2 LET Z3(NUM)=Z+L/2 LET NUM=NUM+1 LET X0(NUM)=X-L/2 LET Y0(NUM)=Y-L/2 LET Z0(NUM)=Z-L/2 LET X1(NUM)=X-L/2 LET Y1(NUM)=Y+L/2 LET Z1(NUM)=Z-L/2 LET X2(NUM)=X-L/2 LET Y2(NUM)=Y+L/2 LET Z2(NUM)=Z+L/2 LET X3(NUM)=X-L/2 LET Y3(NUM)=Y-L/2 LET Z3(NUM)=Z+L/2 END SUB SUB RECURSIVE(N,X,Y,Z,L) !'メンガー IF N=0 THEN CALL CUBE(X,Y,Z,L) ELSE CALL RECURSIVE(N-1,X-L/3,Y+L/3,Z+L/3,L/3) CALL RECURSIVE(N-1,X,Y+L/3,Z+L/3,L/3) CALL RECURSIVE(N-1,X+L/3,Y+L/3,Z+L/3,L/3) CALL RECURSIVE(N-1,X-L/3,Y,Z+L/3,L/3) CALL RECURSIVE(N-1,X+L/3,Y,Z+L/3,L/3) CALL RECURSIVE(N-1,X-L/3,Y-L/3,Z+L/3,L/3) CALL RECURSIVE(N-1,X,Y-L/3,Z+L/3,L/3) CALL RECURSIVE(N-1,X+L/3,Y-L/3,Z+L/3,L/3) CALL RECURSIVE(N-1,X-L/3,Y+L/3,Z-L/3,L/3) CALL RECURSIVE(N-1,X,Y+L/3,Z-L/3,L/3) CALL RECURSIVE(N-1,X+L/3,Y+L/3,Z-L/3,L/3) CALL RECURSIVE(N-1,X-L/3,Y,Z-L/3,L/3) CALL RECURSIVE(N-1,X+L/3,Y,Z-L/3,L/3) CALL RECURSIVE(N-1,X-L/3,Y-L/3,Z-L/3,L/3) CALL RECURSIVE(N-1,X,Y-L/3,Z-L/3,L/3) CALL RECURSIVE(N-1,X+L/3,Y-L/3,Z-L/3,L/3) CALL RECURSIVE(N-1,X-L/3,Y+L/3,Z,L/3) CALL RECURSIVE(N-1,X+L/3,Y+L/3,Z,L/3) CALL RECURSIVE(N-1,X-L/3,Y-L/3,Z,L/3) CALL RECURSIVE(N-1,X+L/3,Y-L/3,Z,L/3) END IF END SUB END EXTERNAL SUB PLOT4(P0(),P1(),P2(),P3()) !'4角形描画 PLOT AREA :P0(1),P0(2);P1(1),P1(2);P2(1),P2(2);P3(1),P3(2) END SUB EXTERNAL SUB SETBRIGHTNESS(N()) DIM A(3) MAT READ A ! 光源の向き DATA 1,1,1 LET S=DOT(A,N)/(SQR(DOT(A,A))*SQR(DOT(N,N))) LET S=(S+1)/2 SET COLOR MIX(8) S,S,S SET AREA COLOR 8 END SUB EXTERNAL SUB OUTER(C(),A(),B()) !'外積 LET C(1)=A(2)*B(3)-A(3)*B(2) LET C(2)=A(3)*B(1)-A(1)*B(3) LET C(3)=A(1)*B(2)-A(2)*B(1) END SUB EXTERNAL SUB QUICKSORT(FI,LA,A(),INDEX()) LET X=A(INDEX((FI+LA)/2)) LET I=FI LET J=LA DO DO WHILE A(INDEX(I))<X LET I=I+1 LOOP DO WHILE X<A(INDEX(J)) LET J=J-1 LOOP IF I>=J THEN EXIT DO SWAP INDEX(I),INDEX(J) LET I=I+1 LET J=J-1 LOOP IF FI<I-1 THEN CALL QUICKSORT(FI,I-1,A,INDEX) IF J+1<LA THEN CALL QUICKSORT(J+1,LA,A,INDEX) END SUB

3次元図形表示

投稿者：しばっち投稿日：2019年 3月30日(土)20時20分41秒

Zバッファと呼ばれる方法で3次元図形表示をします。現在では主流な方法のようです。 Zバッファとは、Zバッファと呼ばれるメモリーを用意し Z値を比較しながら、より手前にある場合にZ値を更新しながら描画していく方法です。このプログラムでは、オブジェクト内を走査する必要があり座標値は3D陽関数によって与えられている必要があります。メインループにおいてステップ数が1/8となっていますがこれは隙間ができないようにするためで、計算量は増大しますが手抜き処理なのでご了承下さい。 ※本来はもっと複雑なアルゴリズムを用いてオブジェクト内を走査する必要があります。ドット単位の描画のため処理に時間がかかります。 2進モードで実行してください。プログラムが簡単な割に比較的高品位な画像が得られました。下記のサンプル画像はY値を用いて青から赤へのグラデーションをかけています。 ※Zバッファでは半透明(ガラス等)などは正しく描画できません。 3D陽関数を表示します(Zバッファ) OPTION ANGLE DEGREES LET ZTH=0 ! z軸のまわりの回転角 LET XTH=30 ! x軸のまわりの回転角初期値 LET YTH=0 ! y軸のまわりの回転角初期値 SET COLOR MIX(0) 0,0,0 CLEAR SET COLOR MODE "NATIVE" LET XS,YS,ZS=-5 LET XE,YE,ZE=5 SET WINDOW XS,XE,YS,YE ASK BITMAP SIZE XSIZE,YSIZE DIM ZBUFF(0 TO XSIZE,0 TO YSIZE),COLORMAP(0 TO XSIZE,0 TO YSIZE) MAT ZBUFF=(-1000000000)*CON !' Zバッファー無限遠 ∞ DIM P0(4),P1(4),P2(4) DIM L(4),M(4),N(3) DIM Q(4,4),ROTX(4,4),ROTY(4,4) MAT ROTX=IDN ! x軸のまわりの回転 LET ROTX(2,2)=COS(XTH) LET ROTX(2,3)=SIN(XTH) LET ROTX(3,2)=-SIN(XTH) LET ROTX(3,3)=COS(XTH) MAT ROTY=IDN ! y軸のまわりの回転 LET ROTY(1,1)=COS(YTH) LET ROTY(1,3)=-SIN(YTH) LET ROTY(3,1)=SIN(YTH) LET ROTY(3,3)=COS(YTH) MAT Q=ROTATE(ZTH) MAT Q=Q*ROTY*ROTX SET TEXT HEIGHT (YE-YS)/10 SET TEXT BACKGROUND "OPAQUE" SET COLOR COLORINDEX(1,1,1) LET YMIN=-1 LET YMAX=1 LET RMIN=0 LET RMAX=1 LET GMIN,GMAX=0 LET BMIN=1 LET BMAX=0 FOR I=0 TO YSIZE STEP 1/8 PLOT TEXT ,AT XS,YS:USING$("###.##",I/YSIZE*100)&"%" FOR J=0 TO XSIZE STEP 1/8 LET P0(1)=XS+(XE-XS)/XSIZE*J LET P0(3)=ZS+(ZE-ZS)/YSIZE*I LET P0(2)=FUNC(P0(1),P0(3)) LET P1(1)=XS+(XE-XS)/XSIZE*(J+1) LET P1(3)=ZS+(ZE-ZS)/YSIZE*I LET P1(2)=FUNC(P1(1),P1(3)) LET P2(1)=XS+(XE-XS)/XSIZE*(J+1) LET P2(3)=ZS+(ZE-ZS)/YSIZE*(I+1) LET P2(2)=FUNC(P2(1),P2(3)) LET P0(4),P1(4),P2(4)=1 LET Y0=P0(2) MAT P0=P0*Q MAT P1=P1*Q MAT P2=P2*Q LET XX=PIXELX(P0(1)) LET YY=PIXELY(P0(2)) LET ZZ=P0(3) IF XX>=0 AND XX<=XSIZE AND YY>=0 AND YY<=YSIZE THEN IF ZBUFF(XX,YY)<ZZ THEN !'手前なら LET ZBUFF(XX,YY)=ZZ !'Zバッファー値更新 MAT L=P2-P1 MAT M=P1-P0 CALL OUTER(N,L,M) CALL SHADE(N,COLORMAP(XX,YY)) !'CALL GRADATION(Y0,YMIN,YMAX,RMIN,RMAX,GMIN,GMAX,BMIN,BMAX,COLORMAP(XX,YY)) END IF END IF NEXT J NEXT I MAT PLOT CELLS, IN XS,YS ; XE,YE : COLORMAP END EXTERNAL FUNCTION FUNC(X,Z) !'3D陽関数 OPTION ANGLE RADIANS LET FUNC=COS(3*SQR(X*X+Z*Z)) END FUNCTION EXTERNAL SUB GRADATION(X,SMIN,SMAX,RMIN,RMAX,GMIN,GMAX,BMIN,BMAX,COL) LET T=(X-SMIN)/(SMAX-SMIN) LET R=RMIN+T*(RMAX-RMIN) LET G=GMIN+T*(GMAX-GMIN) LET B=BMIN+T*(BMAX-BMIN) LET COL=COLORINDEX(R,G,B) END SUB EXTERNAL SUB SHADE(N(),COL) DIM LIGHT(3),CPOS(3),LA(3),KD(3),KS(3),KA(3),LC(3) DIM VR(3),BR(3) MAT READ CPOS !'視線ベクトル DATA 0,0,1 MAT READ LA !'背景の色 DATA .2,.5,.8 MAT READ KD !'拡散反射係数 DATA 0.6,0.3,0.4 MAT READ KS !'鏡面反射係数 DATA 0.8,0.7,0.6 MAT READ KA !'環境光係数 DATA 0.3,0.2,0.1 MAT READ LC !'光源の色 DATA 1,.8,.7 MAT READ LIGHT !'光線ベクトル DATA 1,1,1 LET NS=16 IF DOT(N,N)<>0 THEN MAT N=(1/SQR(DOT(N,N)))*N MAT LIGHT=(1/SQR(DOT(LIGHT,LIGHT)))*LIGHT LET COSTHETA=DOT(N,LIGHT) IF COSTHETA<0 THEN IF BACK<>0 THEN LET COSTHETA=-COSTHETA ELSE LET COSTHETA=0 END IF FOR I=1 TO 3 LET VR(I)=2*COSTHETA*N(I)-LIGHT(I) NEXT I MAT CPOS=(1/SQR(DOT(CPOS,CPOS)))*CPOS MAT VR=(1/SQR(DOT(VR,VR)))*VR LET COSALPHA=DOT(CPOS,VR) IF COSALPHA>0 THEN LET EA=COSALPHA^NS ELSE LET EA=0 FOR I=1 TO 3 LET BR(I)=LC(I)*KD(I)*COSTHETA+LA(I)*KA(I)+LC(I)*KS(I)*EA LET BR(I)=MIN(1,MAX(0,BR(I))) NEXT I LET COL=COLORINDEX(BR(1),BR(2),BR(3)) END SUB EXTERNAL SUB OUTER(C(),A(),B()) !'外積 LET C(1)=A(2)*B(3)-A(3)*B(2) LET C(2)=A(3)*B(1)-A(1)*B(3) LET C(3)=A(1)*B(2)-A(2)*B(1) END SUB

3次元図形表示

投稿者：しばっち投稿日：2019年 3月30日(土)20時22分23秒

メインループ内で球を(螺旋状に)移動させます。すると、残像として描かれます。(※描いて消してないだけです) 移動させるためにループを追加しています。実行時間にご注意ください。このプログラムはBASIC Acc 又は Paract BASICの2進モードで実行してください。 ※但し、最新のパワーマシン(ハイスペックPC)を除く(笑) https://hp.vector.co.jp/authors/VA008683/BASICAccJa.htm https://hp.vector.co.jp/authors/VA008683/BASICAcc2Ja.htm 最新鋭のモンスターマシンをお持ちの方は、更にループを加えて 2重、3重、4重螺旋等にしてみるのもおもしろいかと思います。 (計算時間が更に2倍、3倍、4倍になります) 螺旋を表示します(Zバッファ) (球を360個表示しているだけです) OPTION ANGLE DEGREES LET ZTH=10 ! z軸のまわりの回転角 LET XTH=20 ! x軸のまわりの回転角初期値 LET YTH=0 ! y軸のまわりの回転角初期値 SET COLOR MIX(0) 0,0,0 CLEAR SET COLOR MODE "NATIVE" LET XS,YS=-5 LET XE,YE=5 SET WINDOW XS,XE,YS,YE ASK BITMAP SIZE XSIZE,YSIZE DIM ZBUFF(0 TO XSIZE,0 TO YSIZE),COLORMAP(0 TO XSIZE,0 TO YSIZE) MAT ZBUFF=(-1000000000)*CON !' Zバッファー無限遠 ∞ DIM P0(4) DIM L(4),M(4),N(3) DIM Q(4,4),Q0(4),ROTX(4,4),ROTY(4,4) MAT ROTX=IDN ! x軸のまわりの回転 LET ROTX(2,2)=COS(XTH) LET ROTX(2,3)=SIN(XTH) LET ROTX(3,2)=-SIN(XTH) LET ROTX(3,3)=COS(XTH) MAT ROTY=IDN ! y軸のまわりの回転 LET ROTY(1,1)=COS(YTH) LET ROTY(1,3)=-SIN(YTH) LET ROTY(3,1)=SIN(YTH) LET ROTY(3,3)=COS(YTH) MAT Q=ROTATE(ZTH) MAT Q=Q*ROTY*ROTX SET TEXT HEIGHT (YE-YS)/10 SET TEXT BACKGROUND "OPAQUE" SET COLOR COLORINDEX(1,1,1) LET YMIN=-.5 LET YMAX=.5 LET RMIN=0 LET RMAX=1 LET GMIN=0 LET GMAX=0 LET BMIN=1 LET BMAX=0 FOR I=0 TO 180 STEP 1/8 PLOT TEXT ,AT XS,YS:USING$("###.##",I/180*100)&"%" FOR J=0 TO 360 STEP 1/8 FOR K=0 TO 359 !'オブジェクトを移動させる LET X=COS(3*K)*RAD(K)/1.5 LET Z=SIN(3*K)*RAD(K)/1.5 LET Y=RAD(360-K)/2 LET P0(1)=-.5*SIN(I)*COS(J)+X LET P0(2)=.5*COS(I)+Y LET P0(3)=.5*SIN(I)*SIN(J)+Z LET P0(4)=1 LET Y0=P0(2)-Y MAT Q0=P0*Q LET XX=PIXELX(Q0(1)) LET YY=PIXELY(Q0(2)) LET ZZ=Q0(3) IF XX>=0 AND XX<=XSIZE AND YY>=0 AND YY<=YSIZE THEN IF ZBUFF(XX,YY)<ZZ THEN !'手前なら LET ZBUFF(XX,YY)=ZZ !'Zバッファー値更新 CALL GRADATION(Y0,YMIN,YMAX,RMIN,RMAX,GMIN,GMAX,BMIN,BMAX,COLORMAP(XX,YY)) END IF END IF NEXT K NEXT J NEXT I MAT PLOT CELLS, IN XS,YS ; XE,YE : COLORMAP END EXTERNAL SUB GRADATION(X,SMIN,SMAX,RMIN,RMAX,GMIN,GMAX,BMIN,BMAX,COL) LET T=(X-SMIN)/(SMAX-SMIN) LET R=RMIN+T*(RMAX-RMIN) LET G=GMIN+T*(GMAX-GMIN) LET B=BMIN+T*(BMAX-BMIN) LET COL=COLORINDEX(R,G,B) END SUB

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十進BASIC 第2掲示板 過去ログ

十進BASIC 第2掲示板過去ログ