Решение метрических задач по начертательной геометрии на ЭВМ: Методические указания к практическим занятиям по начертательной геометрии

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<ul><li><p> , </p><p>.. , .. , .. , .. </p><p> - </p><p> 2003 </p></li><li><p> 22.151.3 7 47 514.18:618.3 (07) , .. , .. </p><p> .., .., .., .. </p><p> 47 : . : , 2003.- 66 . </p><p> . </p><p> 22.151.3 7 </p><p>98961602050000</p><p> .., .., .., .., 2003 , 2003 </p><p> 2</p></li><li><p>1 </p><p>1.1 </p><p> . </p><p> 1.2 </p><p> "", IBM, </p><p> MS-DOS . : </p><p>- ; - . , </p><p> , , (. ). </p><p> 1.3 </p><p>IBM 286 MS DOS. "KOMG4", 3- : </p><p>- ; - ; - . . </p><p> , - "Enter". </p><p>1.4 </p><p> . </p><p> 3</p></li><li><p> 2 </p><p> "KOMG4.EXE" , "Enter". . , "Enter". , "Page Up" "Page Down". , "". </p><p>1 .., - .. . - .: , 1969. -368. </p><p> 4</p></li><li><p> () </p><p> ("") . , f () f , f , . </p><p> f , . . f . . </p><p> PgUp PgDn Esc </p><p> 5</p></li><li><p> 1. () , , [], </p><p>{ } </p><p> PgUp PgDn Esc </p><p> 6</p></li><li><p> 1. , , [], </p><p>{ } </p><p> , . 2 , .. 12 11 , </p><p>{ } </p><p> PgUp PgDn Esc </p><p> 7</p></li><li><p>1. () , , [], </p><p>{ } </p><p> . 2 , .. 12 11 , </p><p>{ } 22 2 </p><p> 22 , , . : </p><p> () . </p><p>{ } </p><p> PgUp PgDn Esc </p><p> 8</p></li><li><p>1. () , , [], </p><p>{ } </p><p> . 2 , .. 12 11 , </p><p>{ } 22 2 </p><p> 22 , , . : </p><p> () . </p><p>{ } </p><p>, 11 . 21 12 = 22 . </p><p> 11, , : () . </p><p> PgUp PgDn Esc </p><p> 9</p></li><li><p> . : </p><p>b += bz +=(1) 11 , 22 </p><p> 2</p><p>2 , . 2 : </p><p> = 11 </p><p>(2) 21</p><p>1</p><p>1sin</p><p>+</p><p>= ; </p><p>(3) 21</p><p>1</p><p>1cos</p><p>+</p><p>= , </p><p> . , </p><p> . </p><p> 1 1 : = aza sin*cos* + , y = y , z aza cos*sin* += ; </p><p> PgUp PgDn Esc </p><p> 10</p></li><li><p>2</p><p>2 : = aza sin*cos* + , y aya cos*sin* += ; z z= , </p><p> (2) (3) (4) , , z : </p><p>21</p><p>1</p><p>21 11 </p><p>y</p><p>+</p><p>+= ; </p><p>(5) 21</p><p>21</p><p>1</p><p>11 y</p><p>y+</p><p>+</p><p>= ; </p><p>zz = . </p><p> , y, z (5) (1), : </p><p>b )( yky2</p><p>1</p><p>1</p><p>1 k+= ; y 22</p><p>1</p><p>12</p><p>1b</p><p>k</p><p>k+</p><p>+</p><p>= . </p><p>PgUp PgDn Esc </p><p> 11</p></li><li><p> 2. () </p><p> . { } </p><p> PgUp PgDn Esc </p><p> 12</p></li><li><p> 2. () </p><p> . { } . </p><p> )( f </p><p>22</p><p>21 , (. 1) { } </p><p> PgUp PgDn Esc </p><p> 13</p></li><li><p> 2. () </p><p> . { } . </p><p> )( f </p><p>22</p><p>21 , (. 1) { } )( 11 f , </p><p> 1 )( 2122 , 21 , </p><p>. </p><p> PgUp PgDn Esc </p><p> 14</p></li><li><p> 3. </p><p>. { } </p><p> PgUp PgDn Esc </p><p> 15</p></li><li><p> 3. </p><p>. { } </p><p> (111, 222). , 2 2 1 1 . </p><p>1</p><p>1 . 1 , )( ff . 2211</p><p>{ } </p><p> PgUp PgDn Esc </p><p> 16</p></li><li><p>3. . </p><p>{ } </p><p> (111, 222). , 2 2 1 1 . </p><p>1</p><p>1 . 1 , )( ff . 2211</p><p>{ } 1 , 1 , 1 1, </p><p>1, 1 . </p><p> PgUp PgDn Esc </p><p> 17</p></li><li><p> 4. </p><p>(, , ) , .., . </p><p>{ } </p><p> PgUp PgDn Esc </p><p> 18</p></li><li><p> 4. </p><p>(, , ) , .., . </p><p>{ } , </p><p> ( ), , , . 1 2</p><p>( )11 f , 2 1 (. 3) </p><p>{ } </p><p> PgUp PgDn Esc </p><p> 19</p></li><li><p> 4. </p><p>(, , ) , .., . </p><p>{ } , </p><p> ( ), , , . 1 2</p><p>( )11 f , 2 1 (. 3) </p><p>{ } </p><p> ( )22 f , ||, 2 1 , 2 . PgUp PgDn Esc </p><p> 20</p></li><li><p> , </p><p> . 1: </p><p> , , . </p><p> 2: </p><p> , , . </p><p> PgUp PgDn Esc </p><p> 21</p></li><li><p> 1. </p><p> . { } </p><p> PgUp PgDn Esc </p><p> 22</p></li><li><p> 1. </p><p> . { } </p><p> . </p><p> , 11 . , 11 11 [] [ ] . </p><p>{ } PgUp PgDn Esc </p><p> 23</p></li><li><p> 1. </p><p> . { } </p><p> . , 11</p><p>1</p><p> . , 1 11 [] [ ] . </p><p>{ } , , 2, W2 </p><p> , W , . </p><p>(||= 22 ) q . PgUp PgDn Esc </p><p> 24</p></li><li><p> 2. () </p><p> . { } </p><p> PgUp PgDn Esc </p><p> 25</p></li><li><p> 2. () </p><p> . { } </p><p>. 1 (. 1) </p><p>{ } PgUp PgDn Esc </p><p> 26</p></li><li><p> 2. () </p><p> . { } </p><p> . 1 </p><p> (. 1) { } 2 </p><p> . | 22 |=| 22 |, 1 , 1 , S1 S, , . </p><p> PgUp PgDn Esc </p><p> 27</p></li><li><p> 3. , </p><p> . { } </p><p> PgUp PgDn Esc </p><p> 28</p></li><li><p> 3. , </p><p> . { } </p><p> , . </p><p> . </p><p> : . 1</p><p> u . 222 B , ),( fff . |</p><p>21</p><p>222|=| 222 B |, 1, 1, 1 , , 1, W1, 1 , . </p><p> PgUp PgDn Esc </p><p> 29</p></li><li><p> u 1 , </p><p> . 11 , 11 , . 222 B . </p><p>{ } PgUp PgDn Esc </p><p> 30</p></li><li><p> u 1 , </p><p> . 11 , 11 , . 222 B . </p><p>{ } 2 , </p><p> 1 . 11</p><p>,</p><p>uu 1, 2 . </p><p> PgUp PgDn Esc </p><p> 31</p></li><li><p>uses crt,graph; var c:char; GD,GM,kod,ukaz,s:integer; i:longint; procedure setka; begin for i:=0 to 19 do line(20*i,26,20*i,26+14*22); for i:=0 to 22 do line(0,26+14*i,20*19,26+14*i); end; procedure ent(n{,t}:integer); begin repeat { if t=1 then repeat outtextxy(315,80,' '); for i:=1 to 300000 do begin end; bar(315,80,600,90); for i:=1 to 300000 do begin end; until keypressed;} c:=readkey; kod:=ord(c); if kod=73 then begin s:=s-1; if s=0 then begin s:=1; kod:=33; end else exit; end; if kod=81 then begin s:=s+1; if s&gt;n then begin s:=n; kod:=33; end else exit; </p><p> 32</p></li><li><p> end; if kod=27 then exit; until kod=13; end; procedure niz; begin setcolor(8); setbkcolor(15); outtextxy(10,340,' PgUp - PgDn - Esc - '); end; procedure otkr_gr; begin Gd:=0; InitGraph(GD,GM,''); setfillstyle(1,0); setcolor(black); bar(0,0,getmaxx,getmaxy); end; procedure nazv1; begin settextstyle(0,0,1); setcolor(8); setbkcolor(15); outtextxy(80,14,' '); Line(79,24,546,24); end; procedure nazv2; begin settextstyle(0,0,1); setcolor(8); setbkcolor(15); outtextxy(70,14,' '); Line(69,24,556,24); end; procedure t_ka(x,y:integer); begin </p><p> 33</p></li><li><p> setfillstyle(1,0); circle(x,y,3); { floodfill(x,y,0);} end; procedure ris1; begin setcolor(8); setbkcolor(15); Line(2*20,26+14*6,12*20,26+14*6); {x12} Line(2*20+1,27+14*6,12*20,27+14*6); Line(2*20,26+14*6,2*20+10,30+14*6); {} Line(2*20,26+14*6,2*20+10,22+14*6); Line(5*20,25+14*2,11*20,25+14*4); {A2B2} Line(5*20,26+14*2,11*20,26+14*4); Line(5*20,27+14*2,11*20,27+14*4); Line(20*5,25+11*14,11*20,25+14*7); {A1B1} Line(20*5,26+11*14,11*20,26+14*7); Line(20*5,27+11*14,11*20,27+14*7); Line(20*5,26+14*2,20*5,26+14*11); {A1A2} Line(11*20,26+14*4,11*20,26+14*7); {B1B2} t_ka(5*20,26+14*2); {A2} t_ka(11*20,26+14*4); {B2} t_ka(5*20,26+14*11); {A1} t_ka(11*20,26+14*7); {B1} outtextxy(10,26+14*6-4,'X'); outtextxy(20,26+14*6-1,'12'); outtextxy(20*2+10,26+14*5,''); outtextxy(20*3,26+14*5+3,'2'); outtextxy(20*2+12,26+14*6+6,''); outtextxy(20*3,26+14*6+9,'1'); outtextxy(20*4+10,26+14*1,'A'); outtextxy(20*5,26+14*1+3,'2'); outtextxy(11*20,26+14*3,'B'); outtextxy(11*20+10,26+14*3+3,'2'); outtextxy(20*4,26+14*11-10,'A'); outtextxy(20*4+8,26+14*11-7,'1'); outtextxy(20*11+5,26+14*7-10,'B'); outtextxy(20*11+13,26+14*7-7,'1'); end; procedure ris2; begin setcolor(8); setbkcolor(15); Line(20*4,26+14*14,20*13,26+14*8); {x_12} Line(20*4+1,25+14*14,20*13,25+14*8); Line(20*4,26+14*14,20*4+10,26+14*14-8); {} Line(20*4,26+14*14,20*4+15,26+14*14-3); outtextxy(20*3-10,26+14*14-4,'X'); outtextxy(20*3-11,26+14*14-10,'-'); outtextxy(20*3,26+14*14-1,'12'); outtextxy(20*4+3,26+14*13-7,''); outtextxy(20*4+11,26+14*13-4,'1'); outtextxy(20*5-12,26+14*14+5,''); outtextxy(20*5-13,26+14*14-1,'-'); outtextxy(20*5-2,26+14*14+8,'2'); </p><p> 34</p></li><li><p>end; procedure ris3; begin setcolor(8); setbkcolor(15); Line(11*20,26+14*7,20*13-2,26+14*10+4); {B1B_2} Line(20*5,26+14*11,20*8-3,26+14*16); {A1A_2} Line(20*13-2,25+14*10+4,20*8-3,25+14*16); {A_2B_2} Line(20*13-2,26+14*10+4,20*8-3,26+14*16); Line(20*13-2,27+14*10+4,20*8-3,27+14*16); arc(20*12+1,26+14*9-5,124,209,15); {} putpixel(20*12-8,26+14*9-6,14); {} circle(20*12-8,26+14*9-6,1); Line(20*7-10,26+14*14+5,20*8-10,26+14*14+7); {} Line(20*12-1,26+14*9+4,20*13-3,26+14*9+6); Line(20*12+3,26+14*9+8,20*13-1,26+14*9+10); Line(20*5-4,26+14*4-4,20*5+4,26+14*4+4); {} Line(11*20-4,26+14*5-5,11*20+4,26+14*5-1); Line(11*20-4,26+14*5+1,11*20+4,26+14*5+5); t_ka(5*20,26+14*11); {A1} t_ka(11*20,26+14*7); {B1} t_ka(8*20-3,26+14*16); {A_2} t_ka(13*20-2,26+14*10+4); {B_2} outtextxy(20*9-12,26+14*16-8,'-'); outtextxy(20*9-11,26+14*16-2,'A'); outtextxy(20*8+19,26+14*16+1,'2'); outtextxy(20*13+5,26+14*10-6,'-'); outtextxy(13*20+6,26+14*10,'B'); outtextxy(14*20-4,26+14*10+3,'2'); end; procedure ris4; begin setcolor(8); setbkcolor(15); Line(13*20-2,26+14*10+4,20*5+4,26+14*19); {B_2A__1} t_ka(8*20-3,26+14*16); {A_2} t_ka(13*20-2,26+14*10+4); {B_2} t_ka(5*20+4,26+14*19); {A__1} Line(20*4+14,26+14*16,20*9-10,26+14*20-3); {X__21} Line(20*4+15,26+14*16,20*9-9,26+14*20-3); Line(20*4+14,26+14*16,20*5+6,26+14*16+12); {} Line(20*4+14,26+14*16,20*5+14,26+14*16+8); arc(20*6+8,26+14*18-4,318,50,15); {} putpixel(20*6+17,26+14*18-5,14); {} circle(20*6+17,26+14*18-5,1); Line(20*6,26+14*12-1,20*5+5,26+14*12+1); {} Line(20*5+5,26+14*12+1,20*6-4,26+14*12-6); Line(20*6-6,26+14*18-1,20*6-1,26+14*18+10); {} Line(20*6-6,26+14*18-1,20*6+5,26+14*18+7); </p><p> 35</p></li><li><p> outtextxy(20*3+5,26+14*16-6,'X'); outtextxy(20*3+4,26+14*16-13,'-'); outtextxy(20*3+4,26+14*16-15,'-'); outtextxy(20*3+15,26+14*16-3,'12'); outtextxy(20*4+10,26+14*17-6,'-'); outtextxy(20*4+10,26+14*17-9,'-'); outtextxy(20*4+10,26+14*17,''); outtextxy(20*4+17,26+14*17+3,'1'); outtextxy(20*5+10,26+14*16-1,''); outtextxy(20*5+10,26+14*16-8,'-'); outtextxy(20*5+20,26+14*16+2,'2'); outtextxy(20*4,26+14*20-7,'A = B'); outtextxy(20*4,26+14*20-4,' 1 1'); outtextxy(20*4-1,26+14*19-3,'_ _'); outtextxy(20*4-1,26+14*19-6,'_ _'); end; procedure ris31; begin setcolor(8); setbkcolor(15); Line(2*20,26+14*11,7*20+10,26+14*11); {x12} Line(2*20+1,27+14*11,7*20+10,27+14*11); Line(2*20,26+14*11,2*20+10,30+14*11); {} Line(2*20,26+14*11,2*20+10,22+14*11); Line(20*3,25+14*17,7*20,25+14*13); {A1B1} Line(20*3,26+14*17,7*20,26+14*13); Line(20*3,27+14*17,7*20,27+14*13); Line(20*3,25+14*17,6*20,25+14*21); {A1C1} Line(20*3,26+14*17,6*20,26+14*21); Line(20*3,27+14*17,6*20,27+14*21); Line(20*7-1,26+14*13,6*20-1,26+14*21); {B1C1} Line(20*7,26+14*13,6*20,26+14*21); Line(20*7+1,26+14*13,6*20+1,26+14*21); Line(3*20,25+14*3,7*20,25+14*3+3); {A2B2} Line(3*20,26+14*3,7*20,26+14*3+3); Line(3*20,27+14*3,7*20,27+14*3+3); Line(3*20,25+14*3,6*20,25+14*6+4); {A22} Line(3*20,26+14*3,6*20,26+14*6+4); Line(3*20,27+14*3,6*20,27+14*6+4); Line(20*7-1,26+14*3+3,6*20-1,26+14*6+4); {B2C2} Line(20*7,26+14*3+3,6*20,26+14*6+4); Line(20*7+1,26+14*3+3,6*20+1,26+14*6+4); Line(20*3,26+14*17,20*3,26+14*3); {A1A2} Line(7*20,26+14*3+3,7*20,26+14*13); {B1B2} Line(6*20,26+14*21,6*20,26+14*6+4); {B1B2} t_ka(3*20,26+14*17); {A1} t_ka(7*20,26+14*13); {B1} t_ka(6*20,26+14*21); {C1} t_ka(6*20,26+14*6+4); {C2} t_ka(3*20,26+14*3); {A2} t_ka(7*20,26+14*3+3); {B2} outtextxy(10,26+14*11-4,'X'); outtextxy(20,26+14*11-1,'12'); </p><p> 36</p></li><li><p> outtextxy(20*2,26+14*10-1,''); outtextxy(20*3-10,26+14*10+2,'2'); outtextxy(20*2+3,26+14*11+6,''); outtextxy(20*3-10,26+14*11+9,'1'); outtextxy(20*2,26+14*3,'A'); outtextxy(20*2+10,26+14*3+3,'2'); outtextxy(7*20-5,26+14*2+3,'B'); outtextxy(7*20+5,26+14*2+6,'2'); outtextxy(5*20,26+14*6+3,'C'); outtextxy(5*20+10,26+14*6+6,'2'); outtextxy(20*2+5,26+14*17+5,'A'); outtextxy(20*2+13,26+14*17+8,'1'); outtextxy(20*7+5,26+14*13-10,'B'); outtextxy(20*7+13,26+14*13-7,'1'); outtextxy(20*6+6,26+14*21-2,'C'); outtextxy(20*6+12,26+14*21+1,'1'); end; procedure ris32; begin setcolor(8); setbkcolor(15); Line(20*2,26+14*17,20*8,26+14*17); {f1} Line(20*6+10,26+14*16+5,20*6+10,26+14*5-4); {1112} Line(20*2,26+14*2+7,20*8,26+14*5+7); {f2} Line(20*10+10,26+14*2,20*8-3,26+14*8); {x_21} Line(20*10+9,26+14*2,20*8-4,26+14*8); Line(20*10+10,26+14*2,20*10+7,26+14*2+12); {} Line(20*10+10,26+14*2,20*10-2,26+14*2+10); t_ka(3*20,26+14*17); {A1} t_ka(20*6+10,26+14*17); {11} t_ka(20*6+10,26+14*5-4); {12} t_ka(3*20,26+14*3); {A2} outtextxy(20*2-5,26+14*16+2,'f'); outtextxy(20*2+3,26+14*16+5,'1'); outtextxy(20*7-6,26+14*17+3,'1'); outtextxy(20*7+2,26+14*17+6,'1'); outtextxy(20*7+1,26+14*4+6,'1'); outtextxy(20*7+11,26+14*4+8,'2'); outtextxy(20*10,26+14*1+3,'X'); outtextxy(20*10,26+14*1-6,'_'); outtextxy(20*10+10,26+14*1+6,'21'); outtextxy(20*11-8,26+14*2+7,''); outtextxy(20*11,26+14*2+10,'1'); outtextxy(20*9-1,26+14*2+3,''); outtextxy(20*11-9,26+14*2+1,'-'); outtextxy(20*9+9,26+14*2+5,'2'); end; procedure ris33; begin setcolor(8); setbkcolor(15); Line(20*8,26+14*5+7,20*14-3,26+14*8+6); {A2A_1} Line(20*7,26+14*3+3,20*11+2,26+14*5+4); {B2B_1} Line(20*6,26+14*6+4,20*17-6,26+14*12-5); {C2C_1} Line(20*10-4,26+14*5-1,20*10+4,26+14*5-6); {} Line(20*7+3,26+14*12-4,20*7-3,26+14*12+4); Line(20*3+3,26+14*14-4,20*3-3,26+14*14+4); Line(20*3+3,26+14*14+1,20*3-3,26+14*14+9); Line(20*6+3,26+15*14,20*6-3,26+14*15+8); Line(20*6+3,26+15*14+5,20*6-3,26+14*15+13); </p><p> 37</p></li><li><p> Line(20*6+3,26+15*14...</p></li></ul>

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