Warning: Use of undefined constant memo - assumed 'memo' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 278
홍차넷
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/outlogin_toby.php on line 34
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/outlogin_toby.php on line 45
Warning: Use of undefined constant r - assumed 'r' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/outlogin_toby.php on line 47
Warning: Use of undefined constant r - assumed 'r' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/outlogin_toby.php on line 51
Warning: Use of undefined constant memo - assumed 'memo' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 237
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/outlogin_toby.php on line 34
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/outlogin_toby.php on line 45
Warning: Use of undefined constant r - assumed 'r' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/outlogin_toby.php on line 47
Warning: Use of undefined constant r - assumed 'r' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/outlogin_toby.php on line 51
Warning: Use of undefined constant memo - assumed 'memo' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 237
Warning: Use of undefined constant is_admin - assumed 'is_admin' (this will throw an Error in a future version of PHP) in /home/redtea/html/zero_header.php on line 269
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/zero_header.php on line 300
Warning: Use of undefined constant title - assumed 'title' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/bbs_title.php on line 16
티타임
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/bbs_title.php on line 21
Warning: Use of undefined constant header - assumed 'header' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/bbs_title.php on line 31
- 다양한 주제에 대해 자유롭게 글을 작성하는 게시판입니다.
Warning: Use of undefined constant use_formmail - assumed 'use_formmail' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 519
Warning: Use of undefined constant use_category - assumed 'use_category' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/include/print_category.php on line 9
전체기타일상/생각꿀팁/강좌방송/연예도서/문학영화의료/건강문화/예술경제생활체육과학/기술철학/종교정치요리/음식역사여행육아/가정IT/컴퓨터음악창작게임스포츠사회오프모임
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/setup.php on line 29
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/setup.php on line 41
Warning: Use of undefined constant memo - assumed 'memo' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 389
Warning: Use of undefined constant memo - assumed 'memo' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 389
Warning: Use of undefined constant memo - assumed 'memo' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 389
Warning: Use of undefined constant memo - assumed 'memo' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 389
Warning: Use of undefined constant memo - assumed 'memo' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 389
Warning: Use of undefined constant memo - assumed 'memo' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 389
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 398
Warning: Use of undefined constant subject - assumed 'subject' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 402
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 403
Warning: Use of undefined constant reg_date - assumed 'reg_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 405
Warning: Use of undefined constant total_comment - assumed 'total_comment' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 406
Warning: Use of undefined constant subject - assumed 'subject' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 402
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 403
Warning: Use of undefined constant reg_date - assumed 'reg_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 405
Warning: Use of undefined constant total_comment - assumed 'total_comment' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 406
Warning: Use of undefined constant subject - assumed 'subject' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 402
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 403
Warning: Use of undefined constant reg_date - assumed 'reg_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 405
Warning: Use of undefined constant total_comment - assumed 'total_comment' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 406
Warning: Use of undefined constant subject - assumed 'subject' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 402
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 403
Warning: Use of undefined constant reg_date - assumed 'reg_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 405
Warning: Use of undefined constant total_comment - assumed 'total_comment' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 406
Warning: Use of undefined constant name - assumed 'name' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 2
Warning: Use of undefined constant HTTP_HOST - assumed 'HTTP_HOST' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/memo_replace.php on line 3
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 10
Warning: Use of undefined constant use_category - assumed 'use_category' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 40
| Date |
Warning: Use of undefined constant reg_date - assumed 'reg_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 53 21/07/29 20:13:20 Warning: Use of undefined constant mod_date - assumed 'mod_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 56 |
| Name | 그런데 |
| Subject | MSX 시절에 동그라미 그리던 이야기 |
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아주 오래 전 이야기입니다. 컴퓨터가 8 bit 시절인 이야기니까요. 요즘 PC는 보통 64 bit CPU를 씁니다. 이 숫자는 CPU라고 하는 중앙 처리 장치가 한 번에 들고 다니는 변수의 크기를 뜻하는데 8 bit면 0 ~ 255의 숫자를 한 번에 들고 다니는 거죠. 하여튼 이런 시절 이야기입니다. 이 8 bit 컴퓨터 중에는 MSX라는 물건이 있었는데 컴퓨터를 사 달라고 해서 사 줬더니 하루 종일 게임만 하더라.. 의 국내 첫번째 제품이라고 생각하시면 됩니다. 컬러 그래픽 게임이 보급된 사실상 첫 번째 기종이지요. 요즘은 emulator가 잘 나와서 https://bluemsx.com 같은 곳에서 온라인으로 실행해 볼 수도 있습니다. 이 글을 쓰게 된 이유도 이 emulator가 타임라인에 올라와서 생각이 나서입니다. 여기에는 basic이라고 하는 컴퓨터 언어를 기본 내장하고 있었는데 이 이용법을 가르쳐 주는 컴퓨터 학원이 동네마다 생겼고 저는 중학교 때 이 학원을 다녔습니다. 당시 문제 중, sin/cos 을 이용하여 원을 그리는 문제가 있었습니다. 원을 그리는 별도의 명령어가 있는 경우도 있었지만 그렇지 않은 경우 원을 그리려면 삼각함수를 동원해야 합니다. 원 위의 한 점은 해당 원의 x축으로부터의 각도에 따라 삼각함수로 표시되는데 중심을 기준으로 x 축 offset은 cos (각도) 의 값이 되고, y축은 sin (각도)가 됩니다. 이는 중학교 처음 삼각함수를 배울 때 그림으로 알게 됩니다. 이런 그림을 보면 쉽지요.  따라서 원 위의 각 점은 다음과 같이 되지요. x = (중심의 x좌표) + (원의 반지름) * cos (각도) y = (중심의 y좌표) - (원의 반지름) * sin (각도) y에서 - 인 이유는 좌표계의 원점이 왼쪽 위가 (0, 0)이고 아래로 내려올 수록 값이 커지는 좌표계이기 때문입니다. 이를 이용하면 다음과 같이 원을 그릴 수 있지요. 값을 0에서 360도까지 하나씩 증가시키면서 각각의 sin, cos 값을 구한 후 해당 값으로 (x, y) 좌표를 계산해서 점을 하나씩 찍으면 이들이 연결되어 원이 됩니다. 다음과 같이 소스를 입력하면  실행 결과(run)은 다음처럼 됩니다.  그런데, 이렇게 하면 상당히 그리는데 오래 걸립니다. 예전 컴퓨터는 아주 느렸거든요. 현재 emul로도 대략 2분쯤 걸리네요. 특히 sin, cos 등 실수연산을 하는 건 한 줄 출력하는 것이 보일만큼 느립니다. 당시 기억에 apple II+에서 그림 하나 그리려면 10분 이상 걸렸습니다. 좀 빨리 하면 어떨까 생각하다가 원은 중심을 기준으로 선대칭인 것에 착안해서 다음처럼 그리기로 바꾸었습니다.  그러면 sin 함수 계산을 하는 횟수가 4분의 1로 줄어드니 훨씬 빨라지지요. 그 당시에는 중학생이라 sin ^2 + cos ^ 2 = 1 등의 공식을 모를 때라서 보다 더 최적화하지는 못했던 것이 지금 와서는 아쉽군요. 당시 이처럼 속도를 올릴 꼼수를 왜 생각했느냐 하면 그날의 과제를 끝내고 나면 나머지 시간 동안 게임을 할 수 있었기 때문이었습니다. 뭐든 동기가 부여되어야 더 잘하려 한다. 는 이야기입니다. ps. 그림 포함된 글은 처음 써 보는데 link가 제대로 되는지 모르겠군요. 잘 안되면 link를 다른 곳으로 옮겨 보겠습니다. Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 133 Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 146 Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 161 6
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Warning: Use of undefined constant memo - assumed 'memo' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 185
Warning: Use of undefined constant use_comment - assumed 'use_comment' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 540
Warning: Use of undefined constant name - assumed 'name' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 542
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 543
Warning: Use of undefined constant memo - assumed 'memo' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 545
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 576
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 577
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 577
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 577
Warning: Use of undefined constant grant_delete - assumed 'grant_delete' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 577
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 429
Warning: Use of undefined constant use_formmail - assumed 'use_formmail' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 605
Warning: Use of undefined constant name - assumed 'name' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 599
Warning: Use of undefined constant name - assumed 'name' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 599
Warning: Use of undefined constant name - assumed 'name' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 600
Warning: Use of undefined constant name - assumed 'name' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 600
Warning: Use of undefined constant is_admin - assumed 'is_admin' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 605
Warning: Use of undefined constant is_admin - assumed 'is_admin' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 605
Warning: Use of undefined constant is_admin - assumed 'is_admin' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 609
Warning: Use of undefined constant is_admin - assumed 'is_admin' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 609
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 614
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 616
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 618
Warning: Use of undefined constant name - assumed 'name' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 618
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 612
Warning: Use of undefined constant name - assumed 'name' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 612
Warning: Use of undefined constant reg_date - assumed 'reg_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 620
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 628
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 628
Warning: Use of undefined constant HTTP_HOST - assumed 'HTTP_HOST' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 640
Warning: Use of undefined constant name - assumed 'name' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 644
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 646
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 646
Warning: Use of undefined constant HTTP_HOST - assumed 'HTTP_HOST' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/cmt_replace.php on line 3
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 6
Warning: Use of undefined constant file_name - assumed 'file_name' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 28
Warning: Use of undefined constant file_name - assumed 'file_name' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 29
Warning: Use of undefined constant file_name - assumed 'file_name' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 29
Warning: Use of undefined constant file_name - assumed 'file_name' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 29
Warning: Use of undefined constant file_name - assumed 'file_name' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 29
Warning: Use of undefined constant file_name - assumed 'file_name' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 48
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 65
160744 class="iamcmt" style="display:none;"> Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 66
160744 class='vcm '>
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 70
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 71
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 76
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 117
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 118
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 119
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 120
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 121
160744'> 그런데
Warning: Use of undefined constant mod_date - assumed 'mod_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 133
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 140
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 140
Warning: Use of undefined constant reg_date - assumed 'reg_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 142
21/07/29 20:16
160744>삭제 주소복사
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 150
아래 소스로 열심히 그림을 그리고 있는 도중에 캡쳐하였습니다.
제 느린 손으로도 캡쳐될 만큼 느려텨졌습니다.
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 158
Warning: Use of undefined constant password - assumed 'password' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 166
Warning: Use of undefined constant password - assumed 'password' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 168
Warning: Use of undefined constant password - assumed 'password' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 168
Warning: Use of undefined constant password - assumed 'password' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 168
Warning: Use of undefined constant password - assumed 'password' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 168
Warning: Use of undefined constant password - assumed 'password' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 168
Warning: Use of undefined constant password - assumed 'password' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 168
Warning: Use of undefined constant password - assumed 'password' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 168
Warning: Use of undefined constant password - assumed 'password' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 168
Warning: Use of undefined constant password - assumed 'password' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 168
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 172
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
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