Circle Drawing

From KBase

1 Introduction
2 Writing Test Application
3 Analysis
4 Filling a Circle
- 4.1 Source Code
- 4.2 Output

[edit] Introduction

Azydream 님께서 http://azydream.tistory.com/51 에 PA_Lib 에 있는 원 그리기 함수를 소개해 주셨다. 처음에 이 함수를 보았을 때는 저걸로 어떻게 원을 그리지? 하는 생각이 문득 들었다. 그래서 과연 원을 그려줄 것인지 보려고 간단한 프로그램을 만들어 보았다.

[edit] Writing Test Application

원 소스에 있는 PA_DrawCircle() 은 고치지 않은 채로 결과를 Terminal 에서 확인할 수 있도록 했다.

[edit] Source Code

#include <stdio.h>
#include <stdlib.h>

#define CX_CANVAS 60
#define CY_CANVAS 60
#define DEFAULT_X 30
#define DEFAULT_Y 30
#define DEFAULT_R 10

static int count = 0;
static int occurrences[CY_CANVAS][CY_CANVAS];

void PA_DrawPixel(int x, int y, int color)
{
   printf("(%2d,%2d) ", x, y);
   if ((++count % 8) == 0) {
       printf("\n");
   }
   if (x >= 0 && x < CX_CANVAS &&
       y >= 0 && y < CY_CANVAS)
   {
       occurrences[y][x]++;
   }
}

void PA_DrawCircle(int xCenter, int yCenter, int radius, int color)
{
 int x = 0;
 int y = radius;
 int p = 3 - 2 * radius;

  while (x <= y){
     PA_DrawPixel(xCenter + x, yCenter + y, color);
     PA_DrawPixel(xCenter - x, yCenter + y, color);
     PA_DrawPixel(xCenter + x, yCenter - y, color);
     PA_DrawPixel(xCenter - x, yCenter - y, color);
     PA_DrawPixel(xCenter + y, yCenter + x, color);
     PA_DrawPixel(xCenter - y, yCenter + x, color);
     PA_DrawPixel(xCenter + y, yCenter - x, color);
     PA_DrawPixel(xCenter - y, yCenter - x, color);
     if (p < 0) p += 4 * x++ + 6;
     else p += 4 * (x++ - y--) + 10;
  }
}

void printOccurrences(int w, int h)
{
   for (int y = 0; y < w; y++) {
       for (int x = 0; x < h; x++) {
           if (occurrences[y][x]) {
               putchar('0' + occurrences[y][x]);
           } else {
               putchar(' ');
           }
       }
       printf("\n");
   }
}

int main(int argc, char *argv[])
{
   int r = DEFAULT_R;
   if (argc > 1) {
       r = atoi(argv[1]);
   }

   if (r <= 0 || (r >= CX_CANVAS / 2) || (r >= CY_CANVAS / 2)) {
       return 1;
   }

   PA_DrawCircle(r, r, r, 0);

   int maxx = 2 * r + 1;
   int maxy = 2 * r + 1;
   printOccurrences(maxx, maxy);

   return 0;
}

[edit] Explanation

main()
- 반지름을 인자로 받아 원을 그린 뒤 출력한다
PA_DrawPixel()
- PA_DrawCircle() 이 이 함수를 이용하므로, 가상으로 만들어 준다. 점을 찍는 위치를 순서대로 표시해 주고, 해당 첨이 몇 번 출력되는지 확인하기 위해 occurrence 라는 이름의 이차원 배열을 사용한다
printOccurrences()
- 저장해 둔 occurrence 를 출력한다.

[edit] Output

/cygdrive/c/Temp $ ./a.exe
(10,20) (10,20) (10, 0) (10, 0) (20,10) ( 0,10) (20,10) ( 0,10)
(11,20) ( 9,20) (11, 0) ( 9, 0) (20,11) ( 0,11) (20, 9) ( 0, 9)
(12,20) ( 8,20) (12, 0) ( 8, 0) (20,12) ( 0,12) (20, 8) ( 0, 8)
(13,20) ( 7,20) (13, 0) ( 7, 0) (20,13) ( 0,13) (20, 7) ( 0, 7)
(14,19) ( 6,19) (14, 1) ( 6, 1) (19,14) ( 1,14) (19, 6) ( 1, 6)
(15,19) ( 5,19) (15, 1) ( 5, 1) (19,15) ( 1,15) (19, 5) ( 1, 5)
(16,18) ( 4,18) (16, 2) ( 4, 2) (18,16) ( 2,16) (18, 4) ( 2, 4)
(17,17) ( 3,17) (17, 3) ( 3, 3) (17,17) ( 3,17) (17, 3) ( 3, 3)
       1112111
     11       11
    1           1
   2             2
  1               1
 1                 1
 1                 1
1                   1
1                   1
1                   1
2                   2
1                   1
1                   1
1                   1
 1                 1
 1                 1
  1               1
   2             2
    1           1
     11       11
       1112111

/cygdrive/c/Temp $ ./a.exe 2
( 2, 4) ( 2, 4) ( 2, 0) ( 2, 0) ( 4, 2) ( 0, 2) ( 4, 2) ( 0, 2)
( 3, 4) ( 1, 4) ( 3, 0) ( 1, 0) ( 4, 3) ( 0, 3) ( 4, 1) ( 0, 1)
 121
1   1
2   2
1   1
 121

/cygdrive/c/Temp $ ./a.exe 3
( 3, 6) ( 3, 6) ( 3, 0) ( 3, 0) ( 6, 3) ( 0, 3) ( 6, 3) ( 0, 3)
( 4, 6) ( 2, 6) ( 4, 0) ( 2, 0) ( 6, 4) ( 0, 4) ( 6, 2) ( 0, 2)
( 5, 5) ( 1, 5) ( 5, 1) ( 1, 1) ( 5, 5) ( 1, 5) ( 5, 1) ( 1, 1)
  121
 2   2
1     1
2     2
1     1
 2   2
  121

/cygdrive/c/Temp $ ./a.exe 4
( 4, 8) ( 4, 8) ( 4, 0) ( 4, 0) ( 8, 4) ( 0, 4) ( 8, 4) ( 0, 4)
( 5, 8) ( 3, 8) ( 5, 0) ( 3, 0) ( 8, 5) ( 0, 5) ( 8, 3) ( 0, 3)
( 6, 7) ( 2, 7) ( 6, 1) ( 2, 1) ( 7, 6) ( 1, 6) ( 7, 2) ( 1, 2)
( 7, 7) ( 1, 7) ( 7, 1) ( 1, 1) ( 7, 7) ( 1, 7) ( 7, 1) ( 1, 1)
   121
 21   12
 1     1
1       1
2       2
1       1
 1     1
 21   12
   121

/cygdrive/c/Temp $ ./a.exe 5
( 5,10) ( 5,10) ( 5, 0) ( 5, 0) (10, 5) ( 0, 5) (10, 5) ( 0, 5)
( 6,10) ( 4,10) ( 6, 0) ( 4, 0) (10, 6) ( 0, 6) (10, 4) ( 0, 4)
( 7,10) ( 3,10) ( 7, 0) ( 3, 0) (10, 7) ( 0, 7) (10, 3) ( 0, 3)
( 8, 9) ( 2, 9) ( 8, 1) ( 2, 1) ( 9, 8) ( 1, 8) ( 9, 2) ( 1, 2)
   11211
  1     1
 1       1
1         1
1         1
2         2
1         1
1         1
 1       1
  1     1
   11211

/cygdrive/c/Temp $ ./a.exe 6
( 6,12) ( 6,12) ( 6, 0) ( 6, 0) (12, 6) ( 0, 6) (12, 6) ( 0, 6)
( 7,12) ( 5,12) ( 7, 0) ( 5, 0) (12, 7) ( 0, 7) (12, 5) ( 0, 5)
( 8,12) ( 4,12) ( 8, 0) ( 4, 0) (12, 8) ( 0, 8) (12, 4) ( 0, 4)
( 9,11) ( 3,11) ( 9, 1) ( 3, 1) (11, 9) ( 1, 9) (11, 3) ( 1, 3)
(10,10) ( 2,10) (10, 2) ( 2, 2) (10,10) ( 2,10) (10, 2) ( 2, 2)
    11211
   1     1
  2       2
 1         1
1           1
1           1
2           2
1           1
1           1
 1         1
  2       2
   1     1
    11211

[edit] Analysis

일단 신기하다 ^^ 좀 더 두고 보자. : )

http://helloktk.tistory.com/archive/20080603 등에서 Circle Drawing Algorithm 을 소개하고 있다.

[edit] Filling a Circle

안을 채우는 것을 간단히 고쳐 보았습니다. 점 여덟 개를 찍는 대신 각각을 가로 선으로 잇기만 하면 되며, 가로 선은 가장 싼 값(cost) 에 그릴 수 있습니다. Clipping 역시 선그리기에서 합니다.

[edit] Source Code

#include <stdio.h>
#include <stdlib.h>

#define CX_CANVAS 24
#define CY_CANVAS 24
#define DEFAULT_X 10
#define DEFAULT_Y 10
#define DEFAULT_R 10

static int occurrences[CY_CANVAS][CY_CANVAS];

void PA_DrawPixel(int x, int y, int color)
{
    if (x >= 0 && x < CX_CANVAS &&
        y >= 0 && y < CY_CANVAS)
    {
        occurrences[y][x]++;
    }
}

void PA_DrawHorzLine(int x1, int x2, int y, int color)
{
    if (y < 0 || y >= CY_CANVAS || x1 >= CX_CANVAS || x2 < 0)
        return;

    if (x1 < 0) x1 = 0;
    if (x2 >= CX_CANVAS) x2 = CX_CANVAS - 1;

    for (int x = x1; x <= x2; x++) {
        occurrences[y][x]++;
    }
}

void PA_DrawCircle(int xCenter, int yCenter, int radius, int color)
{
  int x = 0;
  int y = radius;
  int p = 3 - 2 * radius;

   while (x <= y){
      PA_DrawHorzLine(xCenter - x, xCenter + x, yCenter + y, color);
      PA_DrawHorzLine(xCenter - x, xCenter + x, yCenter - y, color);
      PA_DrawHorzLine(xCenter - y, xCenter + y, yCenter + x, color);
      PA_DrawHorzLine(xCenter - y, xCenter + y, yCenter - x, color);
      if (p < 0) p += 4 * x++ + 6;
      else p += 4 * (x++ - y--) + 10;
   }
}

void printOccurrences(int w, int h)
{
    for (int y = 0; y < w; y++) {
        for (int x = 0; x < h; x++) {
            if (occurrences[y][x]) {
                putchar('0' + occurrences[y][x]);
            } else {
                putchar(' ');
            }
        }
        printf("\n");
    }
}

int main(int argc, char *argv[])
{
    int r = DEFAULT_R;
    if (argc > 1) {
        r = atoi(argv[1]);
    }

    // if (r <= 0 || (r >= CX_CANVAS / 2) || (r >= CY_CANVAS / 2)) {
    //  return 1;
    // }

    PA_DrawCircle(r, r, r, 0);

    int maxx = 2 * r + 1;
    int maxy = 2 * r + 1;
    if (maxx > CX_CANVAS)
        maxx = CX_CANVAS;
    if (maxy > CY_CANVAS)
        maxy = CY_CANVAS;
    printOccurrences(maxx, maxy);

    return 0;
}

[edit] Output

소스에서 Canvas 크기를 24로 해 두었기 때문에, 반지름을 15 로 하면 clipping 이 일어나는 것을 볼 수 있다.

/cygdrive/c/Temp$ ./a.exe 2
 121
11111
22222
11111
 121

/cygdrive/c/Temp$ ./a.exe 3
  121
 22222
1111111
2222222
1111111
 22222
  121

/cygdrive/c/Temp$ ./a.exe 4
   121
 2333332
 1111111
111111111
222222222
111111111
 1111111
 2333332
   121

/cygdrive/c/Temp$ ./a.exe 10
       1234321
     12222222221
    1111111111111
   222222222222222
  11111111111111111
 1111111111111111111
 1111111111111111111
111111111111111111111
111111111111111111111
111111111111111111111
222222222222222222222
111111111111111111111
111111111111111111111
111111111111111111111
 1111111111111111111
 1111111111111111111
  11111111111111111
   222222222222222
    1111111111111
     12222222221
       1234321

/cygdrive/c/Temp$ ./a.exe 15
            1234321
         1233333333321
       12222222222222221
      111111111111111111
     1111111111111111111
    11111111111111111111
   111111111111111111111
  1111111111111111111111
  1111111111111111111111
 11111111111111111111111
 11111111111111111111111
 11111111111111111111111
111111111111111111111111
111111111111111111111111
111111111111111111111111
222222222222222222222222
111111111111111111111111
111111111111111111111111
111111111111111111111111
 11111111111111111111111
 11111111111111111111111
 11111111111111111111111
  1111111111111111111111
  1111111111111111111111

Retrieved from "http://scgyong.net/wiki/index.php/Circle_Drawing"

Circle Drawing

From KBase

Contents

[edit] Introduction

[edit] Writing Test Application

[edit] Source Code

[edit] Explanation

[edit] Output

[edit] Analysis

[edit] Filling a Circle

[edit] Source Code

[edit] Output

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