改进的Bresenham算法

这里不仔细讲原理，只是把我写的算法发出来，跟大家分享下，如果有错误的话，还请大家告诉我，如果写的不好，也请指出来，一起讨论进步。

算法步骤:

(1) 输入直线的两端点P0 (x0, y0)和P1 (x1, y1)。

(2) 计算初始值dx, dy, e = -dx, x = x0, y = y0。

(3) 绘制点 (x, y)。

(4) e更新为e+2 * dy。判断e的符号，若e > 0, 则(x, y)更新为(x+1, y+1)， 同时将e更新为e-2*dx；否则(x, y)更新为(x+1, y)。

(5) 当直线没有画完时，重复步骤(3)和(4)否则结束。

水平、垂直和|k| = 1的直线可以直接装入帧缓冲存储器面无须进行画线算法处理。下面是我的算法，如有错误请指出。

#include <GL/freeglut.h>
void init (void)
{
	glClearColor (0.0f, 0.0f, 0.0f, 1.0f);
}

void drawLine (int x1, int y1, int x2, int y2)
{
	int x, y, dx, dy, e;
	// k does not exist
	if (x1 == x2)
	{
		if (y1 < y2)
		{
			y = y1;
			glBegin (GL_POINTS);
			while (y <= y2)
			{
				glVertex2i (x1, y);
				++ y;
			}
			glEnd ();
		} // if (y1 < y2)
		else
		{
			y = y2;
			glBegin (GL_POINTS);
			while (y <= y1)
			{
				glVertex2i (x1, y);
				++ y;
			}
			glEnd ();
		}
	} // if (x1 == x2)
	else if (y1 == y2) // k = 0
	{
		if (x1 < x2)
		{
			x = x1;
			glBegin (GL_POINTS);
			while (x <= x2)
			{
				glVertex2i (x, y1);
				++ x;
			}
			glEnd ();
		} // if (x1 < x2)
		else
		{
			x = x2;
			glBegin (GL_POINTS);
			while (x <= x1)
			{
				glVertex2i (x, y1);
				++ x;
			}
			glEnd ();
		}
	}
	else
	{
		if (x1 > x2)
		{
			int temp = x1;
			x1 = x2;
			x2 = temp;
			temp = y1;
			y1 = y2;
			y2 = temp;
		}
		x = x1;
		y = y1;
		dx = x2 - x1;
		dy = y2 - y1;
		// k = 1
		if (dx == dy)
		{
			glBegin (GL_POINTS);
			while (x <= x2)
			{
				glVertex2i (x, y);
				++ x;
				++ y;
			}
			glEnd ();
		}
		else if (dx == -dy) // k = -1
		{
			glBegin (GL_POINTS);
			while (x <= x2)
			{
				glVertex2i (x, y);
				++ x;
				-- y;
			}
			glEnd ();
		}
		else if (dy > dx)	// k > 1
		{
			glBegin (GL_POINTS);
			dx <<= 1;
			e = - dy;
			dy <<= 1;
			y = y1 > y2 ? y2 : y1;
			int maxY = y1 > y2 ? y1 : y2;
			while (y <= maxY)
			{
				glVertex2i (x, y);
				++ y;
				e += dx;
				if (e > 0)
				{
					++ x;
					e -= dy;
				}
			}
			glEnd ();
		}
		else if (dy > 0)	// 0 < k < 1
		{
			e = -dx;
			dx <<= 1;
			dy <<= 1;
			glBegin (GL_POINTS);
			while (x <= x2)
			{
				glVertex2i (x, y);
				++ x;
				e += dy;
				if (e > 0)
				{
					e -= dx;
					++ y;
				}

			}
			glEnd ();
		}
		else if (-dy < dx)	// 0 > k > -1
		{
			e = -dx;
			dx <<= 1;
			dy <<= 1;
			glBegin (GL_POINTS);
			while (x <= x2)
			{
				glVertex2i (x, y);
				++ x;
				e += dy;
				if (e < 0)
				{
					-- y;
					e += dx;
				}
			}
			glEnd ();
		}
		else if (-dy > dx) // k < -1
		{
			e = dy;
			dx <<= 1;
			dy <<= 1;
			glBegin (GL_POINTS);
			y = y1 > y2 ? y1 : y2;
			int minY = y1 > y2 ? y2 : y1;
			while (y >= minY)
			{
				glVertex2i (x, y);
				-- y;
				e += dx;
				if (e > 0)
				{
					++ x;
					e += dy;
				}
			}
			glEnd ();
		}
	}
}

void display (void)
{
	glClear (GL_COLOR_BUFFER_BIT);
	glColor3f (1.0f, 0.0f, 0.0f);
	// Vertical line
	drawLine (0, -200, 0, 200);
	// Horizontal line
	drawLine (-200, 0, 200, 0);
	// k = 1 line
	drawLine (-200, -200, 200, 200);
	// k = -1 line
	drawLine (-200, 200, 200, -200);
	// k = 1/2 line
	drawLine (200, 100, -200, -100);
	// k = 2 line
	drawLine (-100, -200, 100, 200);
	// k = -1/2 line
	drawLine (-200, 100, 200, -100);
	// k = -2 line
	drawLine (-100, 200, 100, -200);

	drawLine (30, 120, 10, 70);

	drawLine (10, 70, 30, 10);

	drawLine (30, 10, 60, 50);

	drawLine (60, 50, 80, 10);

	drawLine (80, 10, 120, 80);

	drawLine (120, 80, 70, 80);

	drawLine (70, 80, 30, 120);

	glutSwapBuffers ();
}

void reshape (int w, int h)
{
	glViewport (0, 0, (GLsizei) w, (GLsizei) h);
	glMatrixMode (GL_PROJECTION);
	glLoadIdentity ();
	if (w <= h)
	{
		gluOrtho2D (-600.0, 600.0, -600.0 * (GLfloat) h / (GLfloat) w, 600.0 * (GLfloat) h / (GLfloat) w);
	}
	else
	{
		gluOrtho2D (-600.0 * (GLfloat) w / (GLfloat) h,600.0 * (GLfloat) w / (GLfloat) h, -600.0, 600.0);
	}
	glMatrixMode (GL_MODELVIEW);
	glLoadIdentity ();
}
void keyboard (unsigned char key, int x, int y)
{
	switch (key)
	{
	case 27: // 'VK_ESCAPE'
			exit (0);
			break;
	default:
		break;
	}
}
int main (int argc, char ** argv)
{
	glutInit (&argc, argv);
	glutInitDisplayMode (GLUT_DOUBLE | GLUT_RGB);
	glutInitWindowSize (600, 600);
	glutCreateWindow ("optimized Bresenham line");
	init ();
	glutReshapeFunc (reshape);
	glutDisplayFunc (display);
	glutKeyboardFunc (keyboard);
	glutMainLoop ();
	return 0;
}