OpenGL学习进程（13）第十课：基本图形的底层实现及算法原理

1)当A点x坐标值大于B点坐标值时，即A点在B点的右侧时，交换A、B点的坐标。保证A点在B的左侧。
2)考虑特殊情况，当直线AB的斜率不存在时，做近似处理，设置斜率为-(y0-y1)*100，即近似无穷大。
3)当斜率m满足0<=m<=1时，按书本上的中点画线算法进行处理。
4)当m>1时和m<0时，以y为步进选择对象，计算x基于y的斜率，再重复中点画线的过程。

 1 #include<GL/glut.h>
 2 #pragma comment(linker,"/subsystem:\"windows\" /entry:\"mainCRTStartup\"")
 3 
 4 void myInit(){
 5     glMatrixMode(GL_MODELVIEW);
 6     glLoadIdentity();
 7     gluOrtho2D(0.0, 480, 0.0, 480);
 8 }
 9 void Drawpixel(int x, int y){
10     glPointSize(1.0);
11     glColor3f(1.0f, 0.0f, 0.0f);//设置颜色为红色
12     glVertex2i((int)(x), (int)(y));
13 }
14 void MidpointLine(int x0, int y0, int x1, int y1)
15 {
16     int a, b, d1, d2, d, x, y; float m;
17     if (x1<x0){
18         d = x0, x0 = x1, x1 = d;
19         d = y0, y0 = y1, y1 = d;
20     }
21     a = y0 - y1, b = x1 - x0;
22     if (b == 0)
23         m = -1 * a * 100;
24     else
25         m = (float)a / (x0 - x1); x = x0, y = y0;
26     Drawpixel(x, y);
27     if (m >= 0 && m <= 1){
28         d = 2 * a + b; d1 = 2 * a, d2 = 2 * (a + b);
29         while (x<x1){
30             if (d <= 0){
31                 x++, y++, d += d2;
32             }
33             else{
34                 x++, d += d1;
35             }
36             Drawpixel(x, y);
37         }
38     }
39     else if (m <= 0 && m >= -1){
40         d = 2 * a - b; d1 = 2 * a - 2 * b, d2 = 2 * a;
41         while (x<x1){
42             if (d>0){ x++, y--, d += d1; }
43             else{
44                 x++, d += d2;
45             }
46             Drawpixel(x, y);
47         }
48     }
49     else if (m>1){
50         d = a + 2 * b; d1 = 2 * (a + b), d2 = 2 * b;
51         while (y<y1){
52             if (d>0){
53                 x++, y++, d += d1;
54             }
55             else{
56                 y++, d += d2;
57             }
58             Drawpixel(x, y);
59         }
60     }
61     else{
62         d = a - 2 * b; d1 = -2 * b, d2 = 2 * (a - b);
63         while (y>y1){
64             if (d <= 0){
65                 x++, y--, d += d2;
66             }
67             else{
68                 y--, d += d1;
69             }
70             Drawpixel(x, y);
71         }
72     }
73 }
74 void myDisplay(){
75     glClearColor(0, 0, 0, 0);
76     glClear(GL_COLOR_BUFFER_BIT);
77     glBegin(GL_POINTS);
78     MidpointLine(100, 100, 400, 400);
79     MidpointLine(400, 100, 100, 400);
80     glEnd();
81     glFlush();
82 }
83 int main(int argc, char **argv)
84 {
85     glutInit(&argc, argv);
86     glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
87     glutInitWindowSize(480, 480);
88     glutInitWindowPosition(200, 200);
89     glutCreateWindow("中点画线法");
90     myInit();
91     glutDisplayFunc(myDisplay);
92     glutMainLoop();
93     return 0;
94 }

1)类似中点画线法，保证A(x0,y0)点在B(x1,y1)的左侧。
2)斜率为无穷大时单独画线；
3)其余情况分为4种情况:
一、斜率大于0小于1，按书本上的算法进行画线;
二、斜率大于1则交换横纵坐标;
三、斜率大于-1小于1的情况可先以y=y0作B点的对称点B‘，将AB’(此时斜率转化到情况二)画出之后，转化增量到相反的方向，画出直线AB；
四、当斜率小于-1时，先交换横纵坐标值转化为情况三，再利用情况三的算法转化为情况二进行画线。
总结:由于用的是转化法，无论斜率属于那种情况，计算增量的方式都转化到情况一上计算，因此我在这里将情况一抽象为一个函数，仅仅在画点时仅对不同情况做相应的坐标变换。

 1 #include<GL/glut.h>
 2 #pragma comment(linker,"/subsystem:\"windows\" /entry:\"mainCRTStartup\"")
 3 
 4 void myInit(){
 5     glMatrixMode(GL_MODELVIEW);
 6     glLoadIdentity();
 7     gluOrtho2D(0.0, 480, 0.0, 480);
 8 }
 9 void Drawpixel(int x, int y){
10     glPointSize(1.0);
11     glColor3f(1.0f, 0.0f, 0.0f);//设置颜色为红色
12     glVertex2i((int)(x), (int)(y));
13 }
14 void drawOrdinayLine(int x0, int y0, int x1, int y1, int flag){
15     int i;
16     int x, y, dx, dy, e;
17     dx = x1 - x0;
18     dy = y1 - y0;
19     e = -dx;
20     x = x0; y = y0;
21     for (i = 0; i <= dx; i++){
22         switch (flag){
23         case 0:        Drawpixel(x, y);  break;
24         case 1:        Drawpixel(x, 2 * y0 - y); break;//增量为(y-y0)则，实际增量应取相反方向为y0-（y-y0）=2y0-y
25         case 2:        Drawpixel(y, x); break;//这里也要交换
26         case 3:        Drawpixel(2 * y0 - y, x); break;
27         }
28         x++;
29         e = e + 2 * dy;
30         if (e >= 0){
31             y++;
32             e = e - 2 * dx;
33         }
34     }
35 }
36 void BresenhamLine(int x0, int y0, int x1, int y1){
37     int d;
38     int i;
39     if (x0>x1){
40         d = x0, x0 = x1, x1 = d;
41         d = y0, y0 = y1, y1 = d;
42     }
43     if (x0 == x1){
44         if (y0>y1){//保证y0<y1;
45             d = y0, y0 = y1, y1 = d;
46         }
47         for (i = y0; i< y1; i++){
48             Drawpixel(x0, i);
49         }
50         return;
51     }
52     float k = (1.0*(y1 - y0)) / (x1 - x0);
53     if (0 <= k&&k <= 1){  //直接画
54         drawOrdinayLine(x0, y0, x1, y1, 0);
55     }
56     else if (-1 <= k&&k<0){//以y=y0作B点的对称点
57         drawOrdinayLine(x0, y0, x1, y1 + 2 * (y0 - y1), 1);
58     }
59     else if (k>1){//交换x,y的坐标值。
60         drawOrdinayLine(y0, x0, y1, x1, 2);
61     }
62     else if (k<-1){
63         //交换x0和y0,x1和y1;
64         d = x0; x0 = y0; y0 = d;
65         d = x1; x1 = y1; y1 = d;
66         //交换两个点
67         d = x0, x0 = x1, x1 = d;
68         d = y0, y0 = y1, y1 = d;
69         drawOrdinayLine(x0, y0, x1, y1 + 2 * (y0 - y1), 3);
70     }
71 }
72 void myDisplay(){
73     glClearColor(0, 0, 0, 0);
74     glClear(GL_COLOR_BUFFER_BIT);
75     glBegin(GL_POINTS);
76     int i;
77     BresenhamLine(200, 100, 300, 150);
78     BresenhamLine(200, 100, 300, 450);
79     BresenhamLine(125, 125, 400, 400);
80     BresenhamLine(125, 125, 75, 175);
81     glEnd();
82     glFlush();
83 }
84 int main(int argc, char **argv)
85 {
86     glutInit(&argc, argv);
87     glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
88     glutInitWindowSize(480, 480);
89     glutInitWindowPosition(200, 200);
90     glutCreateWindow("中点画线法");
91     myInit();
92     glutDisplayFunc(myDisplay);
93     glutMainLoop();
94     return 0;
95 }

1)先画椭圆上顶点，然后以上顶点为基础运用椭圆的坐标方程式和中点画线法计算步进值。
2)从上顶点开始，每两个像素点组成一组画一条直线，一个像素点可同时当开始点和结束点。
3)利用椭圆的轴对称性对称的画出其它三条线。任意坐标的指定利用像素点的平移操作来进行。

  1 #include <GL/glut.h>   
  2 #include <math.h>
  3 #pragma comment(linker,"/subsystem:\"windows\" /entry:\"mainCRTStartup\"")
  4 
  5 void Init()
  6 {
  7     glClearColor(0,0,0,0);
  8     glMatrixMode(GL_MODELVIEW);
  9     glLoadIdentity();
 10     gluOrtho2D(-400,400,-400,400);
 11 }
 12 void CirclePoint(int x0,int y0,int x,int y){
 13     //每画一个点对称的画出八个点，并按照中点坐标平移相同单位
 14     glVertex2d(x + x0, y + y0);
 15     glVertex2d(x + x0, -y + y0);
 16     glVertex2d(-x + x0, -y + y0);
 17     glVertex2d(-x + x0, y + y0);
 18     glVertex2d(y + x0, x + y0);
 19     glVertex2d(-y + x0, x + y0);
 20     glVertex2d(y + x0, -x + y0);
 21     glVertex2d(-y + x0, -x + y0);
 22 }
 23 void MidPointCircle(int x0,int y0,int r){//圆点和半径
 24     //画右上方1/8的圆
 25     int x, y;
 26     float d;
 27     x = 0; y = r;
 28     d = 1.25;
 29     CirclePoint(x0, y0,x,y);
 30     while (x <= y){
 31         if (d < 0)
 32             d += 2 * x + 3;
 33         else{
 34             d += 2 * (x - y) + 5;
 35             y--;
 36         }
 37         x++;
 38         CirclePoint(x0, y0, x, y);
 39     }
 40 }
 41 
 42 void Drawpixel(int x, int y){
 43     glPointSize(1.0);
 44     glColor3f(1.0f, 0.0f, 0.0f);//设置颜色为红色
 45     glVertex2i((int)(x), (int)(y));
 46 }
 47 void drawLine(int x0,int y0,int x1,int y1){
 48     int a, b, d1, d2, d, x, y; float m;
 49     if (x1<x0){
 50         d = x0, x0 = x1, x1 = d;
 51         d = y0, y0 = y1, y1 = d;
 52     }
 53     a = y0 - y1, b = x1 - x0;
 54     if (b == 0)
 55         m = -1 * a * 100;
 56     else
 57         m = (float)a / (x0 - x1); x = x0, y = y0;
 58     Drawpixel(x, y);
 59     if (m >= 0 && m <= 1){
 60         d = 2 * a + b; d1 = 2 * a, d2 = 2 * (a + b);
 61         while (x<x1){
 62             if (d <= 0){
 63                 x++, y++, d += d2;
 64             }
 65             else{
 66                 x++, d += d1;
 67             }
 68             Drawpixel(x, y);
 69         }
 70     }
 71     else if (m <= 0 && m >= -1){
 72         d = 2 * a - b; d1 = 2 * a - 2 * b, d2 = 2 * a;
 73         while (x<x1){
 74             if (d>0){ x++, y--, d += d1; }
 75             else{
 76                 x++, d += d2;
 77             }
 78             Drawpixel(x, y);
 79         }
 80     }
 81     else if (m>1){
 82         d = a + 2 * b; d1 = 2 * (a + b), d2 = 2 * b;
 83         while (y<y1){
 84             if (d>0){
 85                 x++, y++, d += d1;
 86             }
 87             else{
 88                 y++, d += d2;
 89             }
 90             Drawpixel(x, y);
 91         }
 92     }
 93     else{
 94         d = a - 2 * b; d1 = -2 * b, d2 = 2 * (a - b);
 95         while (y>y1){
 96             if (d <= 0){
 97                 x++, y--, d += d2;
 98             }
 99             else{
100                 y--, d += d1;
101             }
102             Drawpixel(x, y);
103         }
104     }
105 }
106 void drawOval(int x0,int y0,int a, int b){
107     int x, y;
108     int xx, yy;
109     double d1, d2;
110     x = 0; y = b;
111     d1 = b*b + a*a*(-b + 0.25);
112     drawLine(x0 + x, y0 + y, x0+ x, y0 + y);
113     drawLine(x0 - x, y0-y, x0 - x, y0-y);
114     drawLine(x0 + x, y0-y, x0 + x, y0-y);
115     drawLine(x0 - x, y0+y, x0 - x, y0+y);
116     xx = x; yy = y;
117     while (b*b*(x + 1)<a*a*(y - 0.5))
118     {
119         if (d1<0)
120         {
121             d1 += b*b*(2 * x + 3);
122             x++;
123         }
124         else
125         {
126             d1 += (b*b*(2 * x + 3) + a*a*(-2 * y + 2));
127             x++; y--;
128         }
129         drawLine(x0 + xx, y0+yy, x0 + x, y0+y);
130         drawLine(x0 - xx, y0-yy, x0 - x, y0-y);
131         drawLine(x0 + xx, y0-yy, x0 + x, y0-y);
132         drawLine(x0 - xx, y0+yy, x0 - x, y0+y);
133         xx = x; yy = y;
134     }
135     d2 = sqrt(b*(x + 0.5)) + sqrt(a*(y - 1)) - sqrt(a*b);
136     while (y>0)
137     {
138         if (d2<0)
139         {
140             d2 += b*b*(2 * x + 2) + a*a*(-2 * y + 3);
141             x++; y--;
142         }
143         else
144         {
145             d2 += a*a*(-2 * y + 3);
146             y--;
147         }
148         drawLine(x0 + xx, y0+yy, x0 + x, y0+y);
149         drawLine(x0 - xx, y0-yy, x0 - x, y0-y);
150         drawLine(x0 + xx, y0-yy, x0 + x, y0-y);
151         drawLine(x0 - xx, y0+yy, x0 - x, y0+y);
152         xx = x; yy = y;
153     }
154 }
155 void display(){
156     glClear(GL_COLOR_BUFFER_BIT);
157     glColor3f(1.0,1.0,0);
158     glBegin(GL_POINTS);
159     MidPointCircle(0, 50, 100);
160     MidPointCircle(0, -50, 100);
161     MidPointCircle(50, 0, 100);
162     MidPointCircle(-50, 0, 100);
163     //drawOval(100,0,200,100);
164     //drawOval(-100, 0, 200, 100);
165     //drawOval(0, 100, 200, 100);
166     //drawOval(0, -100, 200, 100);
167     glEnd();
168     glFlush();
169 }
170 int main(int argc, char * argv[])
171 {
172     glutInit(&argc, argv);
173     glutInitDisplayMode(GLUT_RGB | GLUT_SINGLE);
174     glutInitWindowPosition(300, 100);
175     glutInitWindowSize(400, 400);
176     glutCreateWindow("椭圆与圆的绘制");
177     Init();
178     glutDisplayFunc(display);
179     glutMainLoop();
180     return 0;
181 }

  1 #include <GL/glut.h>
  2 #include <stdio.h>
  3 //待填充多边形的点的个数或边的个数
  4 static int n;
  5 //待填充多边形的顶点最大纵坐标值
  6 static int max_y;
  7 static int min_y;
  8 struct POINT{
  9     int x;//多边形顶点横坐标
 10     int y;//多边形顶点纵坐标
 11 };
 12 typedef struct POINT Point;
 13 struct EDGE{
 14     struct POINT *point[2];//存指向一条直线的两个点的指针
 15     float k;//用来表示直线的斜率k=(x2-x1)/(y2-y1)
 16     int flag;//用来标识一条边是否有效，当直线水平时此边无效，flag置为0。否则flag置为1。
 17 };
 18 typedef struct EDGE Edge;
 19 //组成边表和活性边表的结点
 20 struct SHEETNODE{
 21     float x_cross;//扫描线与边交点的x坐标值
 22     float dx;//dx从当前扫描线到下一条扫描线间x的增量（(x2-x1)/(y2-y1)）;
 23     int y_max;//与当前扫描线相交的边的最大纵坐标y
 24     struct SHEETNODE *next;
 25 };
 26 typedef struct SHEETNODE SheetNode;
 27 typedef struct SHEETNODE *Sheet;
 28 Point *InitPoint(){
 29     n = 6;//六个点
 30     Point *pNumGroup = malloc(n*sizeof(struct POINT));
 31     pNumGroup[0].x = 2; pNumGroup[0].y = 2;
 32     pNumGroup[1].x = 5; pNumGroup[1].y = 1;
 33     pNumGroup[2].x = 10; pNumGroup[2].y =  3;
 34     pNumGroup[3].x =11; pNumGroup[3].y =  8;
 35     pNumGroup[4].x = 5; pNumGroup[4].y =  5;
 36     pNumGroup[5].x = 2; pNumGroup[5].y =7;
 37     return pNumGroup;
 38 }
 39 void printPoints(Point *p){
 40     int i;
 41     for (i = 0; i < n; i++){
 42         printf("第%d个顶点:x=%2d,y=%2d\n", i + 1, p[i].x, p[i].y);
 43     }
 44 }
 45 Edge *InitEdge(Point *p){
 46     Edge *eNumGroup = malloc(n*sizeof(struct EDGE));
 47     int i;
 48     for (i = 0; i < n; i++){
 49         eNumGroup[i].point[0] = &p[i];
 50         if (i != n - 1)//当当前边不是最后一条边时
 51             eNumGroup[i].point[1] = &p[i + 1];
 52         else//当当前边是最后一条边时
 53             eNumGroup[i].point[1] = &p[0];
 54     }
 55     //初始化EDGE中的k和flag
 56     for (i = 0; i < n; i++){
 57         //如果两个点的横坐标相同，代表斜率不存在，设为flag=1，边有效k=1
 58         if (eNumGroup[i].point[0]->x == eNumGroup[i].point[1]->x)
 59         {
 60             eNumGroup[i].flag = 1; eNumGroup[i].k = 0;
 61         }
 62         //如果两个点的纵坐标相同，代表斜率为1，属于无效边。flag=0;
 63         else if (eNumGroup[i].point[0]->y == eNumGroup[i].point[1]->y)
 64             eNumGroup[i].flag = 0;
 65         else{
 66             eNumGroup[i].flag = 1;
 67             eNumGroup[i].k = 1.0* (eNumGroup[i].point[0]->x - eNumGroup[i].point[1]->x) / (eNumGroup[i].point[0]->y - eNumGroup[i].point[1]->y);
 68         }
 69     }
 70     return eNumGroup;
 71 }
 72 int Min(int a, int b){
 73     return a > b ? b : a;
 74 }
 75 int Max(int a, int b){
 76     return a>b ? a : b;
 77 }
 78 void printEdge(Edge *edge){
 79     int i;
 80     for (i = 0; i < n; i++){
 81         if (edge[i].flag == 1)
 82             printf("边%d有效,斜率为%2.1f\n", i + 1, edge[i].k);
 83     }
 84 }
 85 //按x的递增顺序将结点插入边表
 86 void InsertIntoSheet(SheetNode *tempNode, Sheet sheet){
 87     SheetNode *ptr = sheet;
 88     while (ptr->next != NULL){
 89         if (tempNode->x_cross <= ptr->next->x_cross){
 90             tempNode->next = ptr->next;
 91             ptr->next = tempNode;
 92             return;
 93         }
 94         else{
 95             ptr = ptr->next;
 96         }
 97     }
 98     ptr->next = tempNode;
 99 }
100 Sheet InitNewEdgeSheet(Edge *e){
101     int i; int tempMax, tempMin;
102     max_y = e[0].point[0]->y;
103     min_y = e[0].point[0]->y;
104     for (i = 0; i < n; i++){
105         tempMax = Max(e[i].point[0]->y, e[i].point[1]->y);
106         tempMin = Min(e[i].point[0]->y, e[i].point[1]->y);
107         if (max_y < tempMax)
108             max_y = tempMax;
109         if (min_y>tempMin){
110             min_y = tempMin;
111         }
112     }
113     //新边表
114     int j;
115     //标记边是否被插入新边表的标志数组
116     int *EdgeIntoSheetFlag = malloc(n*sizeof(int));
117     for (i = 0; i < n; i++){
118         EdgeIntoSheetFlag[i] = 0;
119     }
120     Sheet s = malloc(max_y*sizeof(struct SHEETNODE));
121     for (i = 0; i <max_y; i++){
122         s[i].next = NULL;
123     }
124     for (i = 0; i <max_y; i++){
125         //讨论y=i这条扫描线与每条边的相交情况
126         for (j = 0; j < n; j++){
127             //如果这条边已经用过了，忽略这条边
128             if (EdgeIntoSheetFlag[j] == 1)
129                 continue;
130             //如果扫描线与边相交==>y=i在当前边的最大y值和最小y值之间
131             if ((i <= e[j].point[0]->y&&i >= e[j].point[1]->y) || (i <= e[j].point[1]->y) && (i >= e[j].point[0]->y)){
132                 EdgeIntoSheetFlag[j] = 1;
133                 SheetNode *tempNode = malloc(sizeof(struct SHEETNODE));
134                 tempNode->dx = e[j].k;
135                 tempNode->y_max = Max(e[j].point[0]->y, e[j].point[1]->y);
136                 //取一条直线的任意端点，这里使用第一个点。交点的横坐标为x=k(i-y0)+y0
137                 tempNode->x_cross = e[j].k*(i - e[j].point[0]->y) + e[j].point[0]->x;
138                 tempNode->next = NULL;
139                 //printf("插入 %.1f,%.1f,%d\n", tempNode->dx, tempNode->x_cross, tempNode->y_max);
140                 InsertIntoSheet(tempNode, &s[i]);
141             }
142         }
143     }
144     return s;
145 }
146 void printSheet(Sheet sheet){
147     int i;
148     for (i = 0; i <max_y; i++){
149         SheetNode *ptr = &sheet[i];
150         while (ptr->next != NULL){
151             printf("dx=%.1f x_cross=%.1f y_max=%d\n", ptr->next->dx, ptr->next->x_cross, ptr->next->y_max);
152             ptr = ptr->next;
153         }
154     }
155 }
156 Sheet InitDynamicEdgeSheet(Sheet sheet){
157     int i;
158     int j;
159     Sheet s_dynamic = malloc(max_y*sizeof(struct SHEETNODE));
160     for (i = 0; i <max_y; i++){
161         s_dynamic[i].next = NULL;
162     }
163     SheetNode *tempNode;
164     SheetNode *ptrNode;
165     for (i = 0; i <max_y; i++){
166         SheetNode *ptr = &sheet[i];
167         while (ptr->next != NULL){
168             tempNode = malloc(sizeof(struct SHEETNODE));
169             tempNode->next = NULL;
170             tempNode->dx = ptr->next->dx;
171             tempNode->x_cross = ptr->next->x_cross;
172             tempNode->y_max = ptr->next->y_max;
173             //printf("插入 %.1f,%.1f,%d\n", tempNode->dx, tempNode->x_cross, tempNode->y_max);
174             InsertIntoSheet(tempNode, &s_dynamic[i]);
175             if (tempNode->y_max>i){
176                 for (j = i + 1; j < tempNode->y_max; j++){
177                     ptrNode = malloc(sizeof(struct SHEETNODE));
178                     ptrNode->next = NULL;
179                     ptrNode->dx = tempNode->dx;
180                     ptrNode->y_max = tempNode->y_max;
181                     //printf("%f\n",tempNode->dx);
182                     ptrNode->x_cross = tempNode->x_cross + (j - i)*tempNode->dx;
183                     //printf("插入 %.1f,%.1f,%d\n", ptrNode->dx, ptrNode->x_cross, ptrNode->y_max);
184                     InsertIntoSheet(ptrNode, &s_dynamic[j]);
185                 }
186             }
187             ptr = ptr->next;
188         }
189     }
190     return s_dynamic;
191 }
192 void displayLine(Point A, Point B){
193     glColor3f(1.0, 0.0, 0);
194     glBegin(GL_LINES);
195     //printf("A.x=%d A.y=%d",A.x,A.y);
196     //printf("B.x=%d B.y=%d", B.x, B.y);
197     //printf("\n");
198     glVertex2i(A.x, A.y);
199     glVertex2i(B.x, B.y);
200     glEnd();
201 }
202 void paint(Sheet sheet){
203     int i; int minNum; int j;
204     SheetNode *ptrNode = NULL;
205     SheetNode *A_Node = NULL;
206     SheetNode *B_Node = NULL;
207     for (i = 0; i < max_y; i++){
208         ptrNode = &sheet[i];
209         while (ptrNode->next != NULL){
210             //结点总是成对出现
211             A_Node = ptrNode->next;
212             B_Node = ptrNode->next->next;
213             Point A, B;
214             A.y = i; B.y = i;
215             A.x = A_Node->x_cross;
216             B.x = B_Node->x_cross;
217             displayLine(A, B);
218             ptrNode = ptrNode->next->next;
219         }
220     }
221 }
222 Sheet ProcessBegin(){
223     //1.按顺序将多边形顶点输入数组
224     Point *p = NULL;
225     p = InitPoint();
226     printf("1.输出多边形的所有顶点坐标:\n"); printPoints(p);
227     //2.依据顶点初始化此多边形的各个边
228     Edge *e = NULL;
229     e = InitEdge(p);
230     printf("2.打印待扫描多边形所有的边\n"); printEdge(e);
231     //3.初始化新边表
232     Sheet newSheet = NULL;
233     newSheet = InitNewEdgeSheet(e);
234     printf("3.打印新边表:\n"); printSheet(newSheet);
235     //4.初始化活性边表
236     Sheet dynamicSheet = NULL;
237     dynamicSheet = InitDynamicEdgeSheet(newSheet);
238     printf("4.打印活性边表:\n"); printSheet(dynamicSheet);
239     //进行多边形扫描转化
240     return dynamicSheet;
241 }
242 void Init(){
243     glClearColor(0, 0, 0, 0);
244     glMatrixMode(GL_PROJECTION);
245     glLoadIdentity();
246     //定义裁剪区域
247     gluOrtho2D(0, 500, 0, 400);
248 }
249 
250 void display(void){
251     glClear(GL_COLOR_BUFFER_BIT);
252     glColor3d(1.0, 0, 0);
253     Sheet tempSheet = ProcessBegin();
254     paint(tempSheet);
255     glFlush();
256 }
257 int main(int argc, char *argv[]){
258     glutInit(&argc, argv);
259     glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
260     glutInitWindowPosition(400, 200);
261     glutInitWindowSize(500, 400);
262     glutCreateWindow("扫描线画多边形");
263     glutDisplayFunc(display);
264     Init();
265     glutMainLoop();
266     return 0;
267 }

Point *InitPoint(){
    n = 6;//六个点
    Point *pNumGroup = malloc(n*sizeof(struct POINT));
    pNumGroup[0].x = 4*20; pNumGroup[0].y = 4*20;
    pNumGroup[1].x = 4*50; pNumGroup[1].y = 4*10;
    pNumGroup[2].x = 4*100; pNumGroup[2].y = 4*30;
    pNumGroup[3].x = 4*110; pNumGroup[3].y = 4*80;
    pNumGroup[4].x = 4*50; pNumGroup[4].y = 4*50;
    pNumGroup[5].x = 4*20; pNumGroup[5].y = 4*70;
    return pNumGroup;
}

  1 /*
  2   ---------------------------------八连通多边形区域填充递归算法---------------------------------------------------
  3   1.初始化绘图区域的边界线的端点坐标(这里直线为例，不介绍曲线)
  4   2.依据顶点初始化边界线
  5   3.新建二维数组保存点阵的状态，数组值为1代表边界，0代表非边界
  6   4.利用中点画线法计算各条边界线经过的像素，并将点阵中的对应坐标的值置为1，表示边界
  7   上述过程意在完成图形的栅格化，并表示为点阵的形式，下面开始区域填充算法
  8   5.根据点阵和递归填充算法将栅格化的图形画在显示窗体上
  9 */
 10 //待填充多边形的点的个数或边的个数
 11 #include <stdio.h>
 12 #include <GL/glut.h>
 13 
 14 static int n;
 15 static int y_max; 
 16 static int x_max;
 17 struct POINT{
 18     int x;//多边形顶点横坐标
 19     int y;//多边形顶点纵坐标
 20 };
 21 typedef struct POINT Point;
 22 static Point seed;//种子坐标值
 23 Point *InitPoint(){
 24     n = 7;//六个点
 25     Point *pNumGroup = malloc(n*sizeof(struct POINT));
 26     pNumGroup[0].x = 4; pNumGroup[0].y = 0;
 27     pNumGroup[1].x = 7; pNumGroup[1].y = 2;
 28     pNumGroup[2].x = 8; pNumGroup[2].y = 6;
 29     pNumGroup[3].x = 12;pNumGroup[3].y = 14;
 30     pNumGroup[4].x = 4; pNumGroup[4].y = 12;
 31     pNumGroup[5].x = 7; pNumGroup[5].y = 7;
 32     pNumGroup[6].x = 2; pNumGroup[6].y = 9;
 33     seed.x = 5;seed.y = 5;
 34     return pNumGroup;
 35 }
 36 void setEdge(int x, int y, int **NumGroup){
 37     NumGroup[x][y] = 1;
 38     //printf("NumGroup[%d][%d]=1",x,y);
 39 }
 40 void MidpointLine(int x0, int y0, int x1, int y1, int **NumGroup)
 41 {
 42     int a, b, d1, d2, d, x, y; float m;
 43     if (x1<x0){
 44         d = x0, x0 = x1, x1 = d;
 45         d = y0, y0 = y1, y1 = d;
 46     }
 47     a = y0 - y1, b = x1 - x0;
 48     if (b == 0)
 49         m = -1 * a * 100;
 50     else
 51         m = (float)a / (x0 - x1); x = x0, y = y0;
 52     setEdge(x, y, NumGroup);
 53     if (m >= 0 && m <= 1){
 54         d = 2 * a + b; d1 = 2 * a, d2 = 2 * (a + b);
 55         while (x<x1){
 56             if (d <= 0){
 57                 x++, y++, d += d2;
 58             }
 59             else{
 60                 x++, d += d1;
 61             }
 62             setEdge(x, y, NumGroup);
 63         }
 64     }
 65     else if (m <= 0 && m >= -1){
 66         d = 2 * a - b; d1 = 2 * a - 2 * b, d2 = 2 * a;
 67         while (x<x1){
 68             if (d>0){ x++, y--, d += d1; }
 69             else{
 70                 x++, d += d2;
 71             }
 72             setEdge(x, y, NumGroup);
 73         }
 74     }
 75     else if (m>1){
 76         d = a + 2 * b; d1 = 2 * (a + b), d2 = 2 * b;
 77         while (y<y1){
 78             if (d>0){
 79                 x++, y++, d += d1;
 80             }
 81             else{
 82                 y++, d += d2;
 83             }
 84             setEdge(x, y, NumGroup);
 85         }
 86     }
 87     else{
 88         d = a - 2 * b; d1 = -2 * b, d2 = 2 * (a - b);
 89         while (y>y1){
 90             if (d <= 0){
 91                 x++, y--, d += d2;
 92             }
 93             else{
 94                 y--, d += d1;
 95             }
 96             setEdge(x, y, NumGroup);
 97         }
 98     }
 99 }
100 //在视窗上将此矩阵输出
101 void printEdgeMatrix(int **NumGroupMaxtrx, int x_num, int y_num){
102     int i;
103     int j;
104     for (i = 0; i < x_num; i++){
105         for (j = 0; j < y_num; j++){
106             //如果是边界点
107             if (NumGroupMaxtrx[i][j] == 1){
108                 glVertex2i(i, j);
109             }
110         }
111 
112     }
113 }
114 int **InitPointMatrixByPoint(Point *p){
115      int i;
116      y_max = p[0].x;
117      x_max = p[0].y;
118      for (i = 0; i < n;i++){
119          if (p[i].x>x_max)
120              x_max = p[i].x;
121          if (p[i].y > y_max)
122              y_max =p[i].y;
123      }
124      y_max++; x_max++;
125      int **NumGroup_Matrix = malloc(x_max*sizeof(int *));
126      for (i = 0; i < x_max;i++){
127          NumGroup_Matrix[i] = malloc(y_max*sizeof(int));
128      }
129      int j;
130      for (i = 0; i < x_max;i++){
131          for (j = 0; j < y_max;j++){
132             //取值有-1，0,1三种情况分别表示无效，内点和边界点
133              NumGroup_Matrix[i][j] = -1;
134          }
135      }
136      //printf("%d,%d",p[5].x,p[5].y);
137      for (i = 0; i < n; i++){
138          if (i != n - 1)
139              MidpointLine(p[i].x, p[i].y, p[i + 1].x, p[i + 1].y,NumGroup_Matrix);
140          else
141              MidpointLine(p[i].x, p[i].y, p[0].x, p[0].y,NumGroup_Matrix);
142      }
143      //这句话用来测试边界表示多边形边界是否正确
144      //printEdgeMatrix(NumGroup_Matrix,x_max,y_max);
145      return NumGroup_Matrix;
146 }
147 void fixPaint(int **numGroup,int x,int y){
148     if (x<0||y<0||x>=x_max||y>=y_max){
149         return;
150     }
151     //如果当前点是无效点，说明其在区域内部
152     if (numGroup[x][y] == -1){
153         glVertex2i(x,y);
154         numGroup[x][y] = 0;
155         fixPaint(numGroup, x, y + 1);
156         fixPaint(numGroup, x, y - 1);
157         fixPaint(numGroup, x+1, y);
158         fixPaint(numGroup, x-1, y);
159         fixPaint(numGroup, x + 1, y+1);
160         fixPaint(numGroup, x + 1, y-1);
161         fixPaint(numGroup, x - 1, y+1);
162         fixPaint(numGroup, x - 1, y-1);
163     }
164     else{
165         return;
166     }
167 }
168 void ProcessExcute(){
169     //1.初始化待填充区域的边界线段端点和种子坐标
170     Point *p=InitPoint();
171     //2.栅格化边界线段端点表示的待填充区域到像素阵列数组里
172     int **numGroupMatrix = InitPointMatrixByPoint(p);
173     //3.用递归法处理八连通区域的方法将栅格化的像素矩阵表示的区域填充
174     fixPaint(numGroupMatrix,seed.x,seed.y);
175 }
176 void display(){
177     glClear(GL_COLOR_BUFFER_BIT);
178     glColor3d(1.0, 0, 0);
179     glBegin(GL_POINTS);
180     ProcessExcute();
181     glEnd();
182     glFlush();;
183 }
184 //原画像素函数drawPixel改编而来
185 
186 void Init(){
187     glClearColor(0, 0, 0, 0);
188     glMatrixMode(GL_PROJECTION);
189     glLoadIdentity();
190     //定义裁剪区域
191     gluOrtho2D(0, 500, 0, 400);
192 }
193 int main(int argc, char *argv[]){
194     glutInit(&argc, argv);
195     glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
196     glutInitWindowPosition(400, 200);
197     glutInitWindowSize(500, 400);
198     glutCreateWindow("扫描线画多边形");
199     Init();
200     glutDisplayFunc(display);
201     glutMainLoop();
202     return 0;
203 }

Point *InitPoint(){
    n = 7;//六个点
    Point *pNumGroup = malloc(n*sizeof(struct POINT));
    pNumGroup[0].x = 40; pNumGroup[0].y = 00;
    pNumGroup[1].x = 70; pNumGroup[1].y = 20;
    pNumGroup[2].x = 80; pNumGroup[2].y = 60;
    pNumGroup[3].x = 120; pNumGroup[3].y = 140;
    pNumGroup[4].x = 40; pNumGroup[4].y = 120;
    pNumGroup[5].x = 70; pNumGroup[5].y = 70;
    pNumGroup[6].x = 20; pNumGroup[6].y = 90;
    seed.x = 50; seed.y = 50;
    return pNumGroup;
}
void fixPaint(int **numGroup, int x, int y){
    if (x<0 || y<0 || x>=x_max || y>=y_max){
        return;
    }
    //如果当前点是无效点，说明其在区域内部
    if (numGroup[x][y] == -1){
        glVertex2i(x, y);
        numGroup[x][y] = 0;
        fixPaint(numGroup, x, y + 1);
        fixPaint(numGroup, x, y - 1);
        fixPaint(numGroup, x + 1, y);
        fixPaint(numGroup, x - 1, y);
        //fixPaint(numGroup, x + 1, y + 1);
        //fixPaint(numGroup, x + 1, y - 1);
        //fixPaint(numGroup, x - 1, y + 1);
        //fixPaint(numGroup, x - 1, y - 1);
    }
    else{
        return;
    }
}

Point *InitPoint(){
    n = 8;//六个点
    Point *pNumGroup = malloc(n*sizeof(struct POINT));
    pNumGroup[0].x =6* 1; pNumGroup[0].y =6* 1;
    pNumGroup[1].x =6* 9; pNumGroup[1].y =6* 1;
    pNumGroup[2].x =6* 9; pNumGroup[2].y =6* 6;
    pNumGroup[3].x =6 *14; pNumGroup[3].y = 6 * 6;
    pNumGroup[4].x =6* 14; pNumGroup[4].y = 6*16;
    pNumGroup[5].x =6* 8; pNumGroup[5].y = 6*16;
    pNumGroup[6].x =6* 8; pNumGroup[6].y = 6*7;
    pNumGroup[7].x =6* 1; pNumGroup[7].y = 6*7;
    seed.x = 6*5; seed.y = 6*5;
    return pNumGroup;
}

1)初始化，堆栈置空，将种子结点入栈；
2)出栈，若栈空则结束；否则取栈顶元素，以栈顶元素的纵坐标y为当前扫描线；
3)填充并确定种子所在区段。从种子出发沿当前扫描线向左右两个方向填充直到边界。分别标记区段左右两端的坐标为left和right；
4)确定新的种子点。在区间[left,right]中检查与当前扫描线y上下相邻的两条扫描线上的像素。若存在非边界，未填充的像素，则把每一区间最右像素作为种子点压入堆栈。
5)返回第二步,直至栈为空。

  1 /*
  2 ---------------------------------区域填充扫描线算法---------------------------------------------------
  3 1.初始化绘图区域的边界线的端点坐标(这里直线为例，不介绍曲线)
  4 2.依据顶点初始化边界线
  5 3.新建二维数组保存点阵的状态，数组值为1代表边界，0代表非边界
  6 4.利用中点画线法计算各条边界线经过的像素，并将点阵中的对应坐标的值置为1，表示边界
  7 上述过程意在完成图形的栅格化，并表示为点阵的形式，下面开始区域填充算法
  8 5.根据点阵和扫描线算法将栅格化的图形画在显示窗体上
  9 */
 10 #include <stdio.h>
 11 #include <GL/glut.h>
 12 
 13 //待填充多边形的点的个数或边的个数
 14 static int n;
 15 static int y_max;
 16 static int x_max;
 17 struct POINT{
 18     int x;//多边形顶点横坐标
 19     int y;//多边形顶点纵坐标
 20 };
 21 typedef struct POINT Point;
 22 static Point seed;//种子坐标值
 23 Point *InitPoint(){
 24     n = 8;//六个点
 25     Point *pNumGroup = malloc(n*sizeof(struct POINT));
 26     pNumGroup[0].x = 1; pNumGroup[0].y = 1;
 27     pNumGroup[1].x = 9; pNumGroup[1].y = 1;
 28     pNumGroup[2].x = 9; pNumGroup[2].y = 6;
 29     pNumGroup[3].x = 14; pNumGroup[3].y = 6;
 30     pNumGroup[4].x = 14; pNumGroup[4].y = 16;
 31     pNumGroup[5].x = 8; pNumGroup[5].y = 16;
 32     pNumGroup[6].x = 8; pNumGroup[6].y = 7;
 33     pNumGroup[7].x = 1; pNumGroup[7].y = 7;
 34     seed.x =  5; seed.y = 5;
 35     return pNumGroup;
 36 }
 37 //原画像素函数drawPixel改编而来
 38 void setEdge(int x, int y, int **NumGroup){
 39     NumGroup[x][y] = 1;
 40 }
 41 void MidpointLine(int x0, int y0, int x1, int y1, int **NumGroup)
 42 {
 43     int a, b, d1, d2, d, x, y; float m;
 44     if (x1<x0){
 45         d = x0, x0 = x1, x1 = d;
 46         d = y0, y0 = y1, y1 = d;
 47     }
 48     a = y0 - y1, b = x1 - x0;
 49     if (b == 0)
 50         m = -1 * a * 100;
 51     else
 52         m = (float)a / (x0 - x1); x = x0, y = y0;
 53     setEdge(x, y, NumGroup);
 54     if (m >= 0 && m <= 1){
 55         d = 2 * a + b; d1 = 2 * a, d2 = 2 * (a + b);
 56         while (x<x1){
 57             if (d <= 0){
 58                 x++, y++, d += d2;
 59             }
 60             else{
 61                 x++, d += d1;
 62             }
 63             setEdge(x, y, NumGroup);
 64         }
 65     }
 66     else if (m <= 0 && m >= -1){
 67         d = 2 * a - b; d1 = 2 * a - 2 * b, d2 = 2 * a;
 68         while (x<x1){
 69             if (d>0){ x++, y--, d += d1; }
 70             else{
 71                 x++, d += d2;
 72             }
 73             setEdge(x, y, NumGroup);
 74         }
 75     }
 76     else if (m>1){
 77         d = a + 2 * b; d1 = 2 * (a + b), d2 = 2 * b;
 78         while (y<y1){
 79             if (d>0){
 80                 x++, y++, d += d1;
 81             }
 82             else{
 83                 y++, d += d2;
 84             }
 85             setEdge(x, y, NumGroup);
 86         }
 87     }
 88     else{
 89         d = a - 2 * b; d1 = -2 * b, d2 = 2 * (a - b);
 90         while (y>y1){
 91             if (d <= 0){
 92                 x++, y--, d += d2;
 93             }
 94             else{
 95                 y--, d += d1;
 96             }
 97             setEdge(x, y, NumGroup);
 98         }
 99     }
100 }
101 //在视窗上将此矩阵输出
102 void printEdgeMatrix(int **NumGroupMaxtrx, int x_num, int y_num){
103     int i;
104     int j;
105     for (i = 0; i < x_num; i++){
106         for (j = 0; j < y_num; j++){
107             //如果是边界点
108             if (NumGroupMaxtrx[i][j] == 1){
109                 glVertex2i(i, j);
110             }
111         }
112 
113     }
114 }
115 int **InitPointMatrixByPoint(Point *p){
116     int i;
117     y_max = p[0].x;
118     x_max = p[0].y;
119     for (i = 0; i < n; i++){
120         if (p[i].x>x_max)
121             x_max = p[i].x;
122         if (p[i].y > y_max)
123             y_max = p[i].y;
124     }
125     y_max++; x_max++;
126     int **NumGroup_Matrix = malloc(x_max*sizeof(int *));
127     for (i = 0; i < x_max; i++){
128         NumGroup_Matrix[i] = malloc(y_max*sizeof(int));
129     }
130     int j;
131     for (i = 0; i < x_max; i++){
132         for (j = 0; j < y_max; j++){
133             //取值有-1，0,1三种情况分别表示无效，内点和边界点
134             NumGroup_Matrix[i][j] = -1;
135         }
136     }
137     //printf("%d,%d",p[5].x,p[5].y);
138     for (i = 0; i < n; i++){
139         if (i != n - 1)
140             MidpointLine(p[i].x, p[i].y, p[i + 1].x, p[i + 1].y, NumGroup_Matrix);
141         else
142             MidpointLine(p[i].x, p[i].y, p[0].x, p[0].y, NumGroup_Matrix);
143     }
144     //这句话用来测试边界表示多边形边界是否正确
145     //printEdgeMatrix(NumGroup_Matrix,x_max,y_max);
146     return NumGroup_Matrix;
147 }
148 struct STACKNODE{
149     Point point;
150     struct STACKNODE *next;
151 };
152 typedef struct STACKNODE *PtrToNode;
153 typedef struct STACKNODE *Stack;
154 Stack createStack(){
155     Stack stack = malloc(sizeof(struct STACKNODE));
156     stack->next = NULL;
157     return stack;
158 }
159 void *Push(Stack stack,Point point){
160     PtrToNode tempNode = malloc(sizeof(struct STACKNODE));
161     tempNode->point.x = point.x;
162     tempNode->point.y = point.y;
163     tempNode->next = stack->next;
164     stack->next = tempNode;
165 }
166 Point *PopAndTop(Stack stack){
167     PtrToNode ptr = stack->next;
168     stack->next = stack->next->next;
169     return &ptr->point;
170 }
171 int IsNull(Stack s){
172     if (s->next == NULL)
173         return 1;
174     else
175         return 0;
176 }
177 void scanLineFixArea(int **numGroupMatrix){
178     Stack s = createStack();
179     Push(s,seed);
180     Point *tempPoint;
181     Point left, right;
182     int i;
183     while (!IsNull(s)){
184         tempPoint = PopAndTop(s);
185         glVertex2i(tempPoint->x, tempPoint->y); numGroupMatrix[tempPoint->x][tempPoint->y] = 0;
186         left.y = tempPoint->y;
187         right.y = tempPoint->y;
188         left.x = tempPoint->x;
189         right.x = tempPoint->x;
190         while (numGroupMatrix[left.x][left.y] != 1){
191             glVertex2i(left.x, left.y); numGroupMatrix[left.x][left.y]=0;
192             left.x--;
193         }
194         while (numGroupMatrix[right.x][right.y] != 1){
195             glVertex2i(right.x, right.y); numGroupMatrix[right.x][right.y] = 0;
196             right.x++;
197         }
198         for (i = right.x; i >= left.x;i--){
199             if (numGroupMatrix[i][right.y+1]==-1){
200                 right.y++;
201                 right.x = i;
202                 Push(s,right);
203                 break;
204             }
205         }
206         right.y = tempPoint->y;
207         for (i = right.x; i >= left.x; i--){
208             if (numGroupMatrix[i][right.y - 1] == -1){
209                 right.y--;
210                 right.x = i;
211                 Push(s, right);
212                 break;
213             }
214         
215         }
216     }
217 }
218 void ProcessExcute(){
219     //1.初始化待填充区域的边界线段端点和种子坐标
220     Point *p = InitPoint();
221     //2.栅格化边界线段端点表示的待填充区域到像素阵列数组里
222     int **numGroupMatrix = InitPointMatrixByPoint(p);
223     //3.用扫描线算法进行区域填充:
224     scanLineFixArea(numGroupMatrix);
225 }
226 void display(){
227     glClear(GL_COLOR_BUFFER_BIT);
228     glColor3d(1.0, 0, 0);
229     glBegin(GL_POINTS);
230     ProcessExcute();
231     glEnd();
232     glFlush();;
233 }
234 void Init(){
235     glClearColor(0, 0, 0, 0);
236     glMatrixMode(GL_PROJECTION);
237     glLoadIdentity();
238     //定义裁剪区域
239     gluOrtho2D(0, 500, 0, 400);
240 }
241 int main(int argc, char *argv[]){
242     glutInit(&argc, argv);
243     glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
244     glutInitWindowPosition(400, 200);
245     glutInitWindowSize(500, 400);
246     glutCreateWindow("扫描线区域填充算法");
247     Init();
248     glutDisplayFunc(display);
249     glutMainLoop();
250     return 0;
251 }