计算机图形学实验（一） Bresenham画直线和中点画圆法画圆

末蓝、 2022-02-09 20:39 396阅读 0赞

图形学的第一个实验，

因为老师课上的讲解原因，所以这里将一个边长为1的正方形块作为一个像素，放大后可以看出来。

先上代码，画线的：

void drawLine(node * mnode)
    {
    	glClearColor(0.0f, 0.0f, 0.0f,0.0f);//绘图颜色为黑色   
    	glClear(GL_COLOR_BUFFER_BIT); 
    	glColor3f(1.0, 1.0, 1.0);
    	glBegin(GL_LINES);
    	//glViewport(0, 0, 400, 400);
    	for (int i = 0; i < 400; i++)
    	{
    		glVertex2i(i, 0);
    		glVertex2i(i, 400);
    	}
    	for (int i = 0; i < 400; i++)
    	{
    		glVertex2i(0, i);
    		glVertex2i(400,i);
    	}
    	glEnd();
    	//glClear(GL_COLOR_BUFFER_BIT);   //清空颜色缓冲池
    	glColor3f(1.0, 0.0, 0.0);
    	//glBegin(GL_POINTS);   
    	//glViewport(0, 0, 400, 400);
    	int x, y, dx, dy, e;
    	int x1 = mnode[0].x, y1 = mnode[0].y, x2 = mnode[1].x, y2 =mnode[1].y;  
    	dx = x2 - x1;
    	dy = y2 - y1;
    	e = -dx;
    	x = x1;
    	y = y1;
    	for (int i = 0; i <= dx; i++)
    	{
    		//glVertex2i(x, y);
    		glRectf(x,y, x+1, y+1);  //绘制矩形
    
    		x++;
    		e = e + 2 * dy;
    		if (e >= 0)
    		{
    			y++;
    			e = e - 2 * dx;
    		}
    	}
    	//glEnd();     
    	glFlush();
    }

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM4MjQ3NTQ0_size_16_color_FFFFFF_t_70][]

放大后的图像

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM4MjQ3NTQ0_size_16_color_FFFFFF_t_70 1][]

然后是画圆的代码：

void drawCircle()
    {
    	glClearColor(0.0f, 0.0f, 0.0f, 0.0f);//绘图颜色为黑色   
    	glClear(GL_COLOR_BUFFER_BIT);
    	glColor3f(1.0, 1.0, 1.0);
    	//glBegin(GL_POINTS);
    	glBegin(GL_LINES);
    	glViewport(0, 0, 400, 400);
    	for (int i = 0; i < 400; i++)
    	{
    		glVertex2i(i, 0);
    		glVertex2i(i, 400);
    	}
    	for (int i = 0; i < 400; i++)
    	{
    		glVertex2i(0, i);
    		glVertex2i(400, i);
    	}
    	glEnd();
    	//glViewport(0, 0, 400, 400);
    	glColor3f(1.0, 0.0, 0.0);
    	int x, y;
    	float d;
    	int r = 100;
    	x = 0, y = r;
    	d = 1.25 - r;
    	//glVertex2i(x+r,y+r);
    	//glVertex2i(y+r, x+r);
    	//glVertex2i(-x+r, y+r);
    	//glVertex2i(y+r, -x+r);
    	//glVertex2i(x+r, -y+r);
    	//glVertex2i(-y+r, x+r);
    	//glVertex2i(-x+r, -y+r);
    	//glVertex2i(-y+r, -x+r);
    	glRectf(x+r, y+r, x +r+1, y+r+1);  //绘制矩形
    	glRectf(y+r, x+r, y+r+ 1, x+r+1);  //绘制矩形	
    	glRectf(-x+r, y+r, -x+r+1, y +r+ 1);  //绘制矩形	
    	glRectf(y+r, -x+r, y+r+ 1, -x+r+ 1);  //绘制矩形	
    	glRectf(x+r, -y+r, x+r+ 1, -y+r+ 1);  //绘制矩形	
    	glRectf(-y+r, x+r, -y+r + 1, x+r+ 1);  //绘制矩形	
    	glRectf(-x+r, -y+r, -x+r + 1, -y+r + 1);  //绘制矩形	
    	glRectf(-y+r, -x+r, -y+r + 1, -x+r + 1);  //绘制矩形
    	while (x <= y)
    	{
    		if (d <= 0)
    		{
    			d += 2 * x + 3;
    		}
    		else
    		{
    			d += 2 * (x - y) + 5; 
    			y--;
    		}
    		x++;
    		//cout<< x <<" "<<y<< endl;
    		/*glVertex2i(x + r, y + r);
    		glVertex2i(y + r, x + r);
    		glVertex2i(-x + r, y + r);
    		glVertex2i(y + r, -x + r);
    		glVertex2i(x + r, -y + r);
    		glVertex2i(-y + r, x + r);
    		glVertex2i(-x + r, -y + r);
    		glVertex2i(-y + r, -x + r);*/
    		glRectf(x + r, y + r, x + r + 1, y + r + 1);  //绘制矩形
    		glRectf(y + r, x + r, y + r + 1, x + r + 1);  //绘制矩形	
    		glRectf(-x + r, y + r, -x + r + 1, y + r + 1);  //绘制矩形	
    		glRectf(y + r, -x + r, y + r + 1, -x + r + 1);  //绘制矩形	
    		glRectf(x + r, -y + r, x + r + 1, -y + r + 1);  //绘制矩形	
    		glRectf(-y + r, x + r, -y + r + 1, x + r + 1);  //绘制矩形	
    		glRectf(-x + r, -y + r, -x + r + 1, -y + r + 1);  //绘制矩形	
    		glRectf(-y + r, -x + r, -y + r + 1, -x + r + 1);  //绘制矩形
    	}
    	//glEnd();
    	glFlush();
    }

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM4MjQ3NTQ0_size_16_color_FFFFFF_t_70 2][]

放大后的代码：

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM4MjQ3NTQ0_size_16_color_FFFFFF_t_70 3][]

实现原理：

过各行各列像素中心构造一组网格线，按直线从起点到终点的顺序计算直线与各垂直网格线的交点，然后确定该列像素中与此交点最近的像素。该算法的巧妙之处在于采用增量计算，使得对于每一列，只要检查一个误差项的符号，就可以确定该列的所求的像素。

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM4MjQ3NTQ0_size_16_color_FFFFFF_t_70 4][]

简单来说就是如果在中点及以下则取y,中点以上则取y+1。

中点画圆法：

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM4MjQ3NTQ0_size_16_color_FFFFFF_t_70 5][]

完整的代码：

// ConsoleApplication2.cpp: 定义控制台应用程序的入口点。
    //
    #include "stdafx.h"
    #include<gl/GLUT.H>
    #include<cmath>
    #include<iostream>
    #include "node.h"
    using namespace std;
    node Line[2] = { node(0.0,0.0),node(0.0,0.0) };
    int nodeNumber = 0;
    bool finish = false;//已经画完
    void Initial(void)//初始化函数 
    {
    	glClearColor(1.0f, 1.0f, 1.0f, 1.0f);//白色背景，前3个是RGB，最后是Alpha值，用来控制透明，1.0表示完全不透明
    	glMatrixMode(GL_MODELVIEW);//OpenGL按照三维方式来处理图像，所以需要一个投影变换将三维图形投影到显示器的二维空间中
    	glLoadIdentity();
    	gluOrtho2D(0.0, 400, 0.0, 400.0);//指定使用正投影将一个x坐标在0~200，y坐标0~150范围内的矩形坐标区域投影到显示器窗口
    
    }
    void drawLine(node * mnode)
    {
    	glClearColor(0.0f, 0.0f, 0.0f,0.0f);//绘图颜色为黑色   
    	glClear(GL_COLOR_BUFFER_BIT); 
    	glColor3f(1.0, 1.0, 1.0);
    	glBegin(GL_LINES);
    	//glViewport(0, 0, 400, 400);
    	for (int i = 0; i < 400; i++)
    	{
    		glVertex2i(i, 0);
    		glVertex2i(i, 400);
    	}
    	for (int i = 0; i < 400; i++)
    	{
    		glVertex2i(0, i);
    		glVertex2i(400,i);
    	}
    	glEnd();
    	//glClear(GL_COLOR_BUFFER_BIT);   //清空颜色缓冲池
    	glColor3f(1.0, 0.0, 0.0);
    	//glBegin(GL_POINTS);   
    	//glViewport(0, 0, 400, 400);
    	int x, y, dx, dy, e;
    	int x1 = mnode[0].x, y1 = mnode[0].y, x2 = mnode[1].x, y2 =mnode[1].y;  
    	dx = x2 - x1;
    	dy = y2 - y1;
    	e = -dx;
    	x = x1;
    	y = y1;
    	for (int i = 0; i <= dx; i++)
    	{
    		//glVertex2i(x, y);
    		glRectf(x,y, x+1, y+1);  //绘制矩形
    
    		x++;
    		e = e + 2 * dy;
    		if (e >= 0)
    		{
    			y++;
    			e = e - 2 * dx;
    		}
    	}
    	//glEnd();     
    	glFlush();
    }
    void drawLine1()
    {
    	glClearColor(0.0f, 0.0f, 0.0f, 0.0f);//绘图颜色为黑色   
    	glClear(GL_COLOR_BUFFER_BIT);
    	glColor3f(1.0, 1.0, 1.0);
    	glBegin(GL_LINES);
    	//glViewport(0, 0, 400, 400);
    	for (int i = 0; i < 400; i++)
    	{
    		glVertex2i(i, 0);
    		glVertex2i(i, 400);
    	}
    	for (int i = 0; i < 400; i++)
    	{
    		glVertex2i(0, i);
    		glVertex2i(400, i);
    	}
    	glEnd();
    	//glClear(GL_COLOR_BUFFER_BIT);   //清空颜色缓冲池
    	glColor3f(1.0, 0.0, 0.0);
    	//glBegin(GL_POINTS);   
    	//glViewport(0, 0, 400, 400);
    	int x, y, dx, dy, e;
    	int x1 = 0, y1 = 8, x2 = 50, y2 = 100;
    	dx = x2 - x1;
    	dy = y2 - y1;
    	e = -dx;
    	x = x1;
    	y = y1;
    	for (int i = 0; i <= dx; i++)
    	{
    		//glVertex2i(x, y);
    		glRectf(x, y, x + 1, y + 1);  //绘制矩形
    
    		x++;
    		e = e + 2 * dy;
    		if (e >= 0)
    		{
    			y++;
    			e = e - 2 * dx;
    		}
    	}
    	//glEnd();     
    	glFlush();
    }
    void drawLine()
    {
    	if (finish)
    	{
    		drawLine(&Line[0]);
    		finish = false;
    	}
    }
    void drawCircle()
    {
    	glClearColor(0.0f, 0.0f, 0.0f, 0.0f);//绘图颜色为黑色   
    	glClear(GL_COLOR_BUFFER_BIT);
    	glColor3f(1.0, 1.0, 1.0);
    	//glBegin(GL_POINTS);
    	glBegin(GL_LINES);
    	glViewport(0, 0, 400, 400);
    	for (int i = 0; i < 400; i++)
    	{
    		glVertex2i(i, 0);
    		glVertex2i(i, 400);
    	}
    	for (int i = 0; i < 400; i++)
    	{
    		glVertex2i(0, i);
    		glVertex2i(400, i);
    	}
    	glEnd();
    	//glViewport(0, 0, 400, 400);
    	glColor3f(1.0, 0.0, 0.0);
    	int x, y;
    	float d;
    	int r = 100;
    	x = 0, y = r;
    	d = 1.25 - r;
    	//glVertex2i(x+r,y+r);
    	//glVertex2i(y+r, x+r);
    	//glVertex2i(-x+r, y+r);
    	//glVertex2i(y+r, -x+r);
    	//glVertex2i(x+r, -y+r);
    	//glVertex2i(-y+r, x+r);
    	//glVertex2i(-x+r, -y+r);
    	//glVertex2i(-y+r, -x+r);
    	glRectf(x+r, y+r, x +r+1, y+r+1);  //绘制矩形
    	glRectf(y+r, x+r, y+r+ 1, x+r+1);  //绘制矩形	
    	glRectf(-x+r, y+r, -x+r+1, y +r+ 1);  //绘制矩形	
    	glRectf(y+r, -x+r, y+r+ 1, -x+r+ 1);  //绘制矩形	
    	glRectf(x+r, -y+r, x+r+ 1, -y+r+ 1);  //绘制矩形	
    	glRectf(-y+r, x+r, -y+r + 1, x+r+ 1);  //绘制矩形	
    	glRectf(-x+r, -y+r, -x+r + 1, -y+r + 1);  //绘制矩形	
    	glRectf(-y+r, -x+r, -y+r + 1, -x+r + 1);  //绘制矩形
    	while (x <= y)
    	{
    		if (d <= 0)
    		{
    			d += 2 * x + 3;
    		}
    		else
    		{
    			d += 2 * (x - y) + 5; 
    			y--;
    		}
    		x++;
    		//cout<< x <<" "<<y<< endl;
    		/*glVertex2i(x + r, y + r);
    		glVertex2i(y + r, x + r);
    		glVertex2i(-x + r, y + r);
    		glVertex2i(y + r, -x + r);
    		glVertex2i(x + r, -y + r);
    		glVertex2i(-y + r, x + r);
    		glVertex2i(-x + r, -y + r);
    		glVertex2i(-y + r, -x + r);*/
    		glRectf(x + r, y + r, x + r + 1, y + r + 1);  //绘制矩形
    		glRectf(y + r, x + r, y + r + 1, x + r + 1);  //绘制矩形	
    		glRectf(-x + r, y + r, -x + r + 1, y + r + 1);  //绘制矩形	
    		glRectf(y + r, -x + r, y + r + 1, -x + r + 1);  //绘制矩形	
    		glRectf(x + r, -y + r, x + r + 1, -y + r + 1);  //绘制矩形	
    		glRectf(-y + r, x + r, -y + r + 1, x + r + 1);  //绘制矩形	
    		glRectf(-x + r, -y + r, -x + r + 1, -y + r + 1);  //绘制矩形	
    		glRectf(-y + r, -x + r, -y + r + 1, -x + r + 1);  //绘制矩形
    	}
    	//glEnd();
    	glFlush();
    }
    void mouseClick(int btn, int state, int x, int y)
    {
    	if (btn == GLUT_LEFT_BUTTON && state == GLUT_DOWN)//点击左键
    	{
    		y = 400 - y;
    		node temp(x, y);
    		if (nodeNumber<2)
    		{
              Line[nodeNumber] = temp;
    		  nodeNumber++;
    		  glColor3f(1.0, 0.0, 0.0);
    		 // glViewport(0, 0, 400, 400);
    		  glBegin(GL_POINTS);
    		  glVertex2d(x, y);
    		  glEnd();
    		  glFlush();
    		}
    		
    	}
    	if (btn == GLUT_RIGHT_BUTTON && state == GLUT_DOWN)//点击右键
    	{
    		//drawLine(&Line[0]);
    		finish = true;
    		nodeNumber = 0;
    	}
    }
    int main(int argc, char * argv[])//这是使用glut库函数进行窗口管理
    {
    	glutInit(&argc, argv);//使用glut库需要进行初始化
    	glutInitDisplayMode(GLUT_RGB | GLUT_SINGLE);//设定窗口显示模式，颜色模型和缓存，这里是RGB颜色模型和单缓存
    	glutInitWindowPosition(100, 100);//设定窗口的初始位置，屏幕左上角为原点，单位为像素
    	glutInitWindowSize(400, 400);//设定窗口的大小
    	glutCreateWindow("直线");//创建一个窗口，参数是窗口标题名 
    	Initial();
    	glutDisplayFunc(&drawLine1);//将myDisplay指定为当前窗口的显示内容函数*/
    	//glutMouseFunc(mouseClick);
    	glutCreateWindow("圆");//创建一个窗口，参数是窗口标题名 
    	Initial(); 
    	glutDisplayFunc(&drawCircle);//将myDisplay指定为当前窗口的显示内容函数							 
    	glutMainLoop();//使窗口框架运行起来，使显示回调函数开始工作
    	return 0;
    }

还有一个头文件：

#pragma once
    #pragma once
    struct node//点结构 
    {
    	double x;
    	double y;
    	node()
    	{
    		x = 0.0;
    		y = 0.0;
    	}
    	~node() {}
    	node(double xx, double yy)
    	{
    		x = xx;
    		y = yy;
    	}
    	/*node & operator=(const node& a)
       {
    		node m;
    		m.x = a.x;
    		m.y = a.y;
    		return m;
    	}*/
    };
    
    struct side//边结构
    {
    	node a;
    	node b;
    	side(node aa, node bb)
    	{
    		a.x = aa.x;
    		a.y = aa.y;
    		b.y = bb.y;
    		b.x = bb.x;
    	}
    	side(int n)
    	{
    		a.x = 0;
    		a.y = 0;
    		b.x = 0;
    		b.y = 0;
    	}
    	side()
    	{
    		a.x = 0;
    		a.y = 0;
    		b.x = 0;
    		b.y = 0;
    	}
    };

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