1. 程式人生 > >openGL一之直線DDA,正負法,Bresenham演算法,圓弧正負法,Bresenham演算法

openGL一之直線DDA,正負法,Bresenham演算法,圓弧正負法,Bresenham演算法

實驗目的:

1.  掌握OpenGL環境的配置方法。

2.  熟悉OpenGL應用程式基礎架構。

3.  熟練掌握簡單OpenGL應用程式的建立、除錯與執行。

4.  培養良好的程式設計習慣和風格,並且學習撰寫實驗報告。

實驗步驟與內容:

1. 實現直線的DDA演算法、正負法、Bresenham演算法。

實驗核心程式碼如下:

//直線DDA法
void dda(float x1, float y1,float  x2 ,float y2 ) {
	float k, i;
	float x, y, dx, dy;
	k = fabsf(x2 - x1);//這裡用fabsf,這裡可以取浮點數的絕對值
	if (fabsf(y2 - y1) > k)
		k =fabsf(y2 - y1);
	dx = float(x2 - x1) / k;
	dy = float(y2 - y1) / k;
	x = float(x1);
	y = float(y1);
	for (i = 0.0; i < k; i++) {
		glVertex2f(x, y);
		x = x + dx;//----q1
		y = y + dy;//----q2
	}
}

測試方法:

void Display1(void) {
	glClear(GL_COLOR_BUFFER_BIT);//注意這幾個glClear等函式放的位置
	glPointSize(2.0);
	glColor3f(1.0, 0.0, 0.0);/*用紅色繪製物件*/
	glBegin(GL_POINTS);
	dda(-250, 300, 300, 200);
	dda(-50, -100, 300, 250);
	dda(-500,0,0,-400);
	dda(-570, 0, 570, 0); //x軸
	dda(0, -570, 0, 570); //y軸
	glEnd();
	glFlush();
}

實驗結果:


1.2 正負法:

//直線正負法
void MidpointLine(float xs, float ys, float xe, float ye) {
	float a, b, dt1, dt2, d, x, y;
	float absY = ye - ys;
	float absX = xe - xs;
	//採用對稱的方法來繪畫其他象限的圖案
	if ((fabsf(absY) > fabsf(absX)) && absX>0 && absY>0) {//斜率大於1
		float  m = ys;
		ys = xs;
		xs = m;
		float n = ye;
		ye = xe;
		xe = n;
	}
	else if (absY<0 && absX>0 && (fabsf(absY) <= fabs(absX))) {//斜率-1到0
		ys = -ys;
		ye = -ye;
	}
	else if (absY<0 && absX>0 && (fabsf(absY)>fabs(absX))) {//斜率小於-1
		float  m = ys;
		ys = xs;
		xs = -m;
		float n = ye;
		ye = xe;
		xe = -n;
		/*printf("xs=%f\n", xs);
		printf("ys=%f\n", ys);
		printf("xe=%f\n", xe);
		printf("ye=%f\n", ye);*/

	}
	else {//斜率0到1
		  //do nothing 
	}
	a = ys - ye;
	b = xe - xs;
	d = 2 * a + b;
	dt1 = 2 * a;
	dt2 = 2 * (a + b);
	x = xs; y = ys;
	ManyGlVertex2f(absX, absY, x, y);
	while (x < xe) {
		if (d < 0) {
			x++;
			y++;
			d = d + dt2;
		}
		else {
			x++; d = d + dt1;
		}
		ManyGlVertex2f(absX, absY, x, y); //呼叫ManyGlVertex2f()函式
		
	}
	float maxY = getMax(ys, ye);
	float minY = getMin(ys, ye);
	//畫豎直的線
	if (xs == xe) {
		for (float i = minY; i <=maxY; i++) {
			glVertex2f(xs, i);
		}
	}
	
}

其中ManyGlVertex2f(absX,absY, x, y);函式程式碼如下:

void ManyGlVertex2f(float absX,float absY,float x,float y) {
	if ((fabsf(absY) > fabsf(absX)) && absX>0 && absY>0) {//斜率大於1
		glVertex2f(y, x);
	}
	else if (absY<0 && absX>0 && (fabsf(absY) <= fabs(absX))) {//斜率-1到0
		glVertex2f(x, -y);
	}
	else if (absY<0 && absX>0 && (fabsf(absY)>fabs(absX))) {//斜率小於-1
		//printf("到這了\n");
		glVertex2f(y, -x);
	}
	else {//斜率0到1
		glVertex2f(x, y);
	}
}

測試方法:

void Display1(void) {
	glClear(GL_COLOR_BUFFER_BIT);//注意這幾個glClear等函式放的位置
	glPointSize(2.0);
	glColor3f(1.0, 0.0, 0.0);/*用紅色繪製物件*/
	glBegin(GL_POINTS);
	MidpointLine(-250, 250, 350, 200);
	MidpointLine(50, -150, 350, 250);
	MidpointLine(-450,50,0,400);
	MidpointLine(-570, 0, 570, 0);//x軸
	MidpointLine(0, -570, 0, 570);//y軸
	glEnd();
	glFlush();
}

實驗結果:

1.3 Bresenham演算法:

//直線Bresenham法
void Bresenham(float xs, float ys, float xe, float ye) {
	float absY = ye - ys;
	float absX = xe - xs;
	//採用對稱的方法來繪畫其他象限的圖案
	if ((fabsf(absY) > fabsf(absX)) && absX>0 && absY>0) {//斜率大於1
		float  m = ys;
		ys = xs;
		xs = m;
		float n = ye;
		ye = xe;
		xe = n;
	}
	else if (absY<0 && absX>0 && (fabsf(absY) <= fabs(absX))) {//斜率-1到0
		ys = -ys;
		ye = -ye;
	}
	else if (absY<0 && absX>0 && (fabsf(absY)>fabs(absX))) {//斜率小於-1
		float  m = ys;
		ys = xs;
		xs = -m;
		float n = ye;
		ye = xe;
		xe = -n;
		/*printf("xs=%f\n", xs);
		printf("ys=%f\n", ys);
		printf("xe=%f\n", xe);
		printf("ye=%f\n", ye);*/

	}
	else {//斜率0到1
		  //do nothing 
	}
	float dx = xe - xs;
	float dy = ye - ys;
	float m = (double)dy / (double)dx;
	float e = m - 0.5;
	float x, y;
	x = xs;
	y = ys;
	for (int i = 0; i < dx; i++) {
		ManyGlVertex2f(absX, absY, x, y); //呼叫ManyGlVertex2f()函式
		if (e >= 0) {
			y = y + 1; e = e - 1;
		}
		x = x + 1; e = e + m;
	}
	
	//畫豎直的線
	if (xs == xe) {
		float maxY = getMax(ys, ye);
		float minY = getMin(ys, ye);
		for (float i = minY; i <= maxY; i++) {
			glVertex2f(xs, i);
		}
	}
}

其中呼叫的ManyGlVertex2f()的程式碼和直線正負法中呼叫的ManyGlVertex2f()的方法一樣。

測試方法:
void Display1(void) {
	glClear(GL_COLOR_BUFFER_BIT);//注意這幾個glClear等函式放的位置
	glPointSize(2.0);
	glColor3f(1.0, 0.0, 0.0);/*用紅色繪製物件*/
	glBegin(GL_POINTS);
	Bresenham(250, 250, 350, 200);
	Bresenham(50,150, 350, 250);
	Bresenham(-450,50,0,-400);
	Bresenham(-570, 0, 570, 0);//x軸
	Bresenham(0, -570, 0, 570);//y軸
	glEnd();
	glFlush();
}

實驗結果:

2. 實現圓弧的正負法和Bresenham演算法。

2.1圓弧正負法

//正負法
void pnarc(float radius,float m,float n) {
	float x, y, f;
	x = 0; y = 0 + radius; f = 0;
	while (y > 0) {
		glVertex2f(x+m, y+n);
		glVertex2f(-x+m, y+n);
		glVertex2f(-x+m,- y+n);
		glVertex2f(x+m, -y+n);
		if (f > 0) {
			f = f - 2 * y + 1; y = y - 1;
		}
		else {
			f = f + 2*x + 1; x = x + 1;
		}
	}
	if (y == 0) {
		glVertex2f(x + m, y + n);
		glVertex2f(-x + m, y + n);
		glVertex2f(-x + m, -y + n);
		glVertex2f(x + m, -y + n);

	}
}
測試方法:
void Display1(void) {
	glClear(GL_COLOR_BUFFER_BIT);//注意這幾個glClear等函式放的位置
	glPointSize(2.0);
	glColor3f(1.0, 0.0, 0.0);/*用紅色繪製物件*/
	glBegin(GL_POINTS);
	pnarc(150, -250, 250);
	pnarc(150, 250, 250);
	pnarc(150, 250, -250);
	pnarc(150, -250, -250);
	
	Bresenham(-570, 0, 570, 0);//x軸
	Bresenham(0, -570, 0, 570);//y軸
	glEnd();
	glColor3f(0, 1, 0);
	glBegin(GL_POINTS);
	pnarc(150, 0, 0);
	glEnd();

	glFlush();
}

實驗結果:


2.2圓弧Bresenham演算法

//Bresenham法
void bresenham_arc(float R,float m,float n) {
	float x, y, d;
	x = 0; y = R; d = 3 - 2 * R;
	while (x < y) {
		glVertex2f(x+m, y+n);
		glVertex2f(y+m, x+n);
		glVertex2f(y + m, -x + n);
		glVertex2f(x + m, -y + n);
		glVertex2f(-x + m, -y + n);
		glVertex2f(-y + m, -x + n);
		glVertex2f(-y + m, x + n);
		glVertex2f(-x + m, y + n);
		if (d < 0)
			d = d + 4 * x + 6;
		else {
			d = d + 4 * (x - y) + 10;
			y = y - 1;
		}
		x = x + 1;

	}
	if (x == y) {
		glVertex2f(x + m, y + n);
		glVertex2f(y + m, x + n);
		glVertex2f(y + m, -x + n);
		glVertex2f(x + m, -y + n);
		glVertex2f(-x + m, -y + n);
		glVertex2f(-y + m, -x + n);
		glVertex2f(-y + m, x + n);
		glVertex2f(-x + m, y + n);
	}
}

測試方法:

void Display1(void) {
	glClear(GL_COLOR_BUFFER_BIT);//注意這幾個glClear等函式放的位置
	glPointSize(2.0);
	glColor3f(1.0, 0.0, 0.0);/*用紅色繪製物件*/
	glBegin(GL_POINTS);
	bresenham_arc(150, -150, 100);
	bresenham_arc(150, 150, 100);
	bresenham_arc(150, 150, -100);
	bresenham_arc(150, -150, -100);
	
	Bresenham(-570, 0, 570, 0);//x軸
	Bresenham(0, -570, 0, 570);//y軸
	glEnd();
	glColor3f(0, 1, 0);
	glBegin(GL_POINTS);
	pnarc(150, 0, 0);
	glEnd();

	glFlush();
}

實驗結果:


3. 利用上述完成的演算法繪製中國象棋的棋盤和棋子。

//呼叫以上函式繪製中國象棋的棋盤和棋子
void Display(void) {
	glClear(GL_COLOR_BUFFER_BIT);//注意這幾個glClear等函式放的位置
	glPointSize(2.0);
	glColor3f(0.0, 0.0, 0.0);/*用紅色繪製物件*/
	glBegin(GL_POINTS);
	for (float i = -360; i <= 360; i += 80) {
		dda(-360, i, 360, i);
	}
	for (float i = -360; i <= 360; i += 90) {
		dda(i, 40, i, 360);
	}
	for (float i = -360; i <= 360; i += 90) {
		dda(i, -40, i, -360);
	}
	dda(-360, -40, -360, 40);
	dda(360, -40, 360, 40);
	float b = 90, c = 200, d = 360;
	dda(-b, c, b, d);
	dda(-b, d, b, c);
	dda(-b, -d, b, -c);
	dda(-b, -c, b, -d);
	glEnd();
	//畫象棋圖上的圓
	glColor3f(1.0, 0.0, 0.0);
	glBegin(GL_POINTS);
	float R = 28;
	for (float i = -360; i <= 360; i += 90) {
		pnarc(R, i, 360);
		pnarc(R, i, -360);
	}
	for (float i = -360; i <= 360; i += 180) {
		pnarc(R, i, 40);
		pnarc(R, i, -40);
	}
	for (float i = -270; i <= 320; i += 540) {
		pnarc(R, i, 200);
		pnarc(R, i, -200);
	}
	glEnd();
	//最外側直線
	glPointSize(3.0);
	glColor3f(0.0, 0.0, 0.0);
	glBegin(GL_POINTS);
	float a = 380;
	dda(-a, a, a, a);
	dda(a, a, a, -a);
	dda(a, -a, -a, -a);
	dda(-a, -a, -a, a);
	glEnd();
	glFlush();
}

結果:

4.以下是屬性設定函式和主函式main()

//設定屬性
void myinit(void) {
	/*設定屬性*/
	glClearColor(1.0, 1.0, 1.0, 1.0);/*白色背景*/
	/*建立檢視*/
	glMatrixMode(GL_PROJECTION);
	glLoadIdentity();
	gluOrtho2D(-570.0, 570.0, -570.0, 570.0);//二維檢視區域*
	glMatrixMode(GL_MODELVIEW);
}
int main(int argc, char * argv[])
 {
 glutInit(&argc, argv);
 glutInitDisplayMode(GLUT_RGB | GLUT_SINGLE);
 glutInitWindowPosition(20, 40);//設定位置
 glutInitWindowSize(680, 680);//設定高寬
 glutCreateWindow("第一個OpenGL程式");
 myinit();
 glutDisplayFunc(&Display);
 glutMainLoop();
 return 0;
 }

結論分析與體會:

  此次實驗著重獨立完成直線和圓弧的各種生成演算法,這也是我們學習計算機圖形學的目的,我們不僅要會使用openGL,更要懂得其內部實現演算法,通過此次的實驗課程,我們可以很清晰明瞭的瞭解具體實現。其實最有難度的還是前面的演算法,只要完成了前面的演算法,後面的棋盤繪畫就比較容易了。整體來說,此次實驗難度並不大,當然期間也遇到許多的小問題,不過最後問題都已解決。