【计算机图形学】Three-DimensionalScene Roaming_computer graphics with opengl fourth edition 源码

本博客基于课程"计算机图形学"，教材使用为计算机图形学（第4版） [Computer Graphics with OpenGL, Fourth Edition]，部分代码模板便来自于此教材，并且有所改动。大部分内容来自本人实验报告，有错误是难以避免的，若有表述错误或bug欢迎指出。

实验思路

代码思路

1. 变量介绍：CVector3D用于表示向量或者三维坐标，默认初始化为(0,0,0)；CViewFrame用于建立观察坐标系，其中数据成员包括每次移动的步长step、旋转角turn_a、仰角pitch_a、翻转角roll_a、观察原点P0，单位向量u,v,n，以及各个操作所对应的函数。
2. 在对应的各个函数中，根据实验报告册上所给的变量操作，对u,v,n各个变量进行变换。在gluLookAt()函数中，前三个参数表示相机在世界坐标系的位置，接着三个参数表示“相机”镜头对准的物体在世界坐标的位置，即教材中的Pref。，最后三个参数表示观察向上向量。在init()函数中，会对观察坐标系进行初始化，设置P0坐标和u,v,n三向量的初始值，并设定步长。在display()函数中，定义观察点，并将其和观察坐标系联系起来，所以P0若设置成(0,0,0)，那么观察初始点就是棋盘中心位置

问题及解决方法

1. view_frame需要设置成全局变量，因为此变量会在多个函数中进行更改，look_at则不需要，只在display()函数中进行更改，并且其初始值会随view_frame成员变量的值的更改而更改，所以每次对display()函数重复调用的时候，也不用担心其值发生未知错误。
2. 在编写各个变换函数时，需要多加注意修改的值，和所根据修改的变量，函数和所三角函数内参数角度需要严格对应，由于进行了坐标系类中包含了向量类，所以在访问成员函数时，需要多加注意

实现代码

核心代码及关键步骤注释

class CViewFrame {
public:
	float step; // step size每次移动的步长
	float turn_a; // turn angle旋转角
	float pitch_a; // pitch angle仰角
	float roll_a; // roll angle翻转角

	CVector3D P0; // View reference point
	CVector3D u; // unit vector in xv direction
	CVector3D v; // unit vector in yv direction
	CVector3D n; // unit vector in zv direction

	void move_up(void) {
		//Write your code here
		P0.x = P0.x + step * v.x;
		P0.y = P0.y + step * v.y;
		P0.z = P0.z + step * v.z;
	}
	void move_down(void) {
		//Write your code here
		P0.x = P0.x - step * v.x;
		P0.y = P0.y - step * v.y;
		P0.z = P0.z - step * v.z;
	}
	void move_left(void) {
		//Write your code here
		P0.x = P0.x - step * u.x;
		P0.y = P0.y - step * u.y;
		P0.z = P0.z - step * u.z;
	}
	void move_right(void) {
		//Write your code here
		P0.x = P0.x + step * u.x;
		P0.y = P0.y + step * u.y;
		P0.z = P0.z + step * u.z;
	}
	void move_forward(void) {
		//Write your code here
		P0.x = P0.x - step * n.x;
		P0.y = P0.y - step * n.y;
		P0.z = P0.z - step * n.z;
	}
	void move_backward(void) {
		//Write your code here
		P0.x = P0.x + step * n.x;
		P0.y = P0.y + step * n.y;
		P0.z = P0.z + step * n.z;
	}
	void turn_left(void) {
		//Write your code here
		u.x = u.x * cos(turn_a) - n.x * sin(turn_a);
		u.y = u.y * cos(turn_a) - n.y * sin(turn_a);
		u.z = u.z * cos(turn_a) - n.z * sin(turn_a);
		n.x = u.x * sin(turn_a) + n.x * cos(turn_a);
		n.y = u.y * sin(turn_a) + n.y * cos(turn_a);
		n.z = u.z * sin(turn_a) + n.z * cos(turn_a);
	}
	void turn_right(void) {
		//Write your code here
		u.x = u.x * cos(turn_a) + n.x * sin(turn_a);
		u.y = u.y * cos(turn_a) + n.y * sin(turn_a);
		u.z = u.z * cos(turn_a) + n.z * sin(turn_a);
		n.x = -u.x * sin(turn_a) + n.x * cos(turn_a);
		n.y = -u.y * sin(turn_a) + n.y * cos(turn_a);
		n.z = -u.z * sin(turn_a) + n.z * cos(turn_a);
	}
	void look_up(void) {
		//Write your code here
		v.x = v.x * cos(pitch_a) + n.x * sin(pitch_a);
		v.y = v.y * cos(pitch_a) + n.y * sin(pitch_a);
		v.z = v.z * cos(pitch_a) + n.z * sin(pitch_a);
		n.x = -v.x * sin(pitch_a) + n.x * cos(pitch_a);
		n.y = -v.y * sin(pitch_a) + n.y * cos(pitch_a);
		n.z = -v.z * sin(pitch_a) + n.z * cos(pitch_a);
	}
	void look_down(void) {
		//Write your code here
		v.x = v.x * cos(pitch_a) - n.x * sin(pitch_a);
		v.y = v.y * cos(pitch_a) - n.y * sin(pitch_a);
		v.z = v.z * cos(pitch_a) - n.z * sin(pitch_a);
		n.x = v.x * sin(pitch_a) + n.x * cos(pitch_a);
		n.y = v.y * sin(pitch_a) + n.y * cos(pitch_a);
		n.z = v.z * sin(pitch_a) + n.z * cos(pitch_a);
	}
	void roll_left(void) {
		//Write your code here
		u.x = u.x * cos(roll_a) + v.x * sin(roll_a);
		u.y = u.y * cos(roll_a) + v.y * sin(roll_a);
		u.z = u.z * cos(roll_a) + v.z * sin(roll_a);
		v.x = -u.x * sin(roll_a) + v.x * cos(roll_a);
		v.y = -u.y * sin(roll_a) + v.y * cos(roll_a);
		v.z = -u.z * sin(roll_a) + v.z * cos(roll_a);
	}
	void roll_right(void) {
		//Write your code here
		u.x = u.x * cos(roll_a) - v.x * sin(roll_a);
		u.y = u.y * cos(roll_a) - v.y * sin(roll_a);
		u.z = u.z * cos(roll_a) - v.z * sin(roll_a);
		v.x = u.x * sin(roll_a) + v.x * cos(roll_a);
		v.y = u.y * sin(roll_a) + v.y * cos(roll_a);
		v.z = u.z * sin(roll_a) + v.z * cos(roll_a);
	}
};

CViewFrame view_frame;

// Initialization function
void init(void) {
	static GLfloat light_ambient[] = { 0.01, 0.01, 0.01, 1.0 };
	static GLfloat light_diffuse[] = { 1.0, 1.0, 1.0, 1.0 };
	static GLfloat light_specular[] = { 1.0, 1.0, 1.0, 1.0 };

	glClearColor(0.0, 0.0, 0.0, 0.0);
	glShadeModel(GL_SMOOTH); // Set shading model

	// Set light source properties for light source #0
	glLightfv(GL_LIGHT0, GL_AMBIENT, light_ambient);
	glLightfv(GL_LIGHT0, GL_DIFFUSE, light_diffuse);
	glLightfv(GL_LIGHT0, GL_SPECULAR, light_specular);

	glEnable(GL_LIGHTING); // Enable lighting
	glEnable(GL_LIGHT0); // Enable light source #0
	glEnable(GL_DEPTH_TEST); // Enable depth buffer test
	glEnable(GL_NORMALIZE); // Enable auto normalization
	glEnable(GL_CULL_FACE); // Enable face culling

	// Set initial properties for view reference frame
	view_frame.P0 = CVector3D(700.0, 00.0, 100.0);
	view_frame.u = CVector3D(0.0, 1.0, 0.0);
	view_frame.v = CVector3D(0.0, 0.0, 1.0);
	view_frame.n = CVector3D(1.0, 0.0, 0.0);
	view_frame.step = 2;
	view_frame.turn_a = PI / 18;
	view_frame.pitch_a = PI / 18;
	view_frame.roll_a = PI / 18;
}

// Function to draw chess board on xy plane
void draw_chess_board(float sx, float sy, float sz, int nx, int ny)
// sx, sy, sz: size of the chess board
// nx, ny: Number of chess grids in x and y direction
{
	static GLfloat mat1_color[] = { 0.8, 0.8, 0.8, 1.0 };
	static GLfloat mat2_color[] = { 0.2, 0.2, 0.2, 1.0 };
	int i, j, iflag, jflag;
	float x, y, dx, dy;
	float* pcolor;

	dx = sx / (float)nx;
	dy = sy / (float)ny;

	for (i = 0; i < nx; ++i) {
		iflag = i % 2;
		x = (i + 0.5) * dx - 0.5 * sx;
		for (j = 0; j < ny; ++j) {
			jflag = j % 2;
			y = (j + 0.5) * dy - 0.5 * sy;
			if (iflag == jflag)
				pcolor = mat1_color;
			else
				pcolor = mat2_color;
			glMaterialfv(GL_FRONT_AND_BACK, GL_AMBIENT_AND_DIFFUSE, pcolor);
			glMaterialfv(GL_FRONT_AND_BACK, GL_SPECULAR, pcolor);
			glMaterialf(GL_FRONT_AND_BACK, GL_SHININESS, 64.0);
			glPushMatrix();
			glTranslatef(x, y, 0.0);
			glScalef(dx, dy, sz);
			glutSolidCube(1.0);
			glPopMatrix();
		}
	}
}
void keyboard(unsigned char key, int x, int y) {
	switch (key) {
	case 27:
		exit(0);
		break;
	case 'w':
		view_frame.move_forward();
		glutPostRedisplay();
		break;
	case 's': //move backward
		//Write your code here
		view_frame.move_backward();
		glutPostRedisplay();
		break;
	case 'a': //move left
		//Write your code here
		view_frame.move_left();
		glutPostRedisplay();
		break;
	case 'd': //move right
		//Write your code here
		view_frame.move_right();
		glutPostRedisplay();
		break;
	case 'q': //roll left
		//Write your code here
		view_frame.roll_left();
		glutPostRedisplay();
		break;
	case 'e': //roll right
		//Write your code here
		view_frame.roll_right();
		glutPostRedisplay();
		break;
	}
}

// Special key callback function
void special_key(int key, int x, int y) {
	switch (key) {
	case GLUT_KEY_LEFT:
		view_frame.turn_left();
		glutPostRedisplay();
		break;
	case GLUT_KEY_RIGHT: //turn right
		//Write your code here
		view_frame.turn_right();
		glutPostRedisplay();
		break;
	case GLUT_KEY_UP: //look up
		//Write your code here
		view_frame.look_up();
		glutPostRedisplay();
		break;
	case GLUT_KEY_DOWN: //look down
		//Write your code here
		view_frame.look_down();
		glutPostRedisplay();
		break;
	case GLUT_KEY_PAGE_UP: //move up
		//Write your code here
		view_frame.move_up();
		glutPostRedisplay();
		break;
	case GLUT_KEY_PAGE_DOWN: //move down
		//Write your code here
		view_frame.move_down();
		glutPostRedisplay();
		break;
	}
}
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全部代码

// ====== Computer Graphics Experiment #8 ======
// |             3D scene roaming              |
// =============================================
//
// Requirement:
// (1) Implement translation and rotation of view reference frame
// (2) Change smooth shading to flat shading and observe the effects
// (3) Carefully read and understand the rest of the source code

#include <GL/glut.h>
#include <math.h>
#include <windows.h>

#define PI 3.14159265

// 3D vector class
class CVector3D {
public:
	float x, y, z;

	// Constructors
	CVector3D(void) {
		x = 0.0;
		y = 0.0;
		z = 0.0;
	}
	CVector3D(float x0, float y0, float z0) {
		x = x0;
		y = y0;
		z = z0;
	}
};

// View reference frame class
class CViewFrame {
public:
	float step; // step size每次移动的步长
	float turn_a; // turn angle旋转角
	float pitch_a; // pitch angle仰角
	float roll_a; // roll angle翻转角

	CVector3D P0; // View reference point
	CVector3D u; // unit vector in xv direction
	CVector3D v; // unit vector in yv direction
	CVector3D n; // unit vector in zv direction

	void move_up(void) {
		//Write your code here
		P0.x = P0.x + step * v.x;
		P0.y = P0.y + step * v.y;
		P0.z = P0.z + step * v.z;
	}
	void move_down(void) {
		//Write your code here
		P0.x = P0.x - step * v.x;
		P0.y = P0.y - step * v.y;
		P0.z = P0.z - step * v.z;
	}
	void move_left(void) {
		//Write your code here
		P0.x = P0.x - step * u.x;
		P0.y = P0.y - step * u.y;
		P0.z = P0.z - step * u.z;
	}
	void move_right(void) {
		//Write your code here
		P0.x = P0.x + step * u.x;
		P0.y = P0.y + step * u.y;
		P0.z = P0.z + step * u.z;
	}
	void move_forward(void) {
		//Write your code here
		P0.x = P0.x - step * n.x;
		P0.y = P0.y - step * n.y;
		P0.z = P0.z - step * n.z;
	}
	void move_backward(void) {
		//Write your code here
		P0.x = P0.x + step * n.x;
		P0.y = P0.y + step * n.y;
		P0.z = P0.z + step * n.z;
	}
	void turn_left(void) {
		//Write your code here
		u.x = u.x * cos(turn_a) - n.x * sin(turn_a);
		u.y = u.y * cos(turn_a) - n.y * sin(turn_a);
		u.z = u.z * cos(turn_a) - n.z * sin(turn_a);
		n.x = u.x * sin(turn_a) + n.x * cos(turn_a);
		n.y = u.y * sin(turn_a) + n.y * cos(turn_a);
		n.z = u.z * sin(turn_a) + n.z * cos(turn_a);
	}
	void turn_right(void) {
		//Write your code here
		u.x = u.x * cos(turn_a) + n.x * sin(turn_a);
		u.y = u.y * cos(turn_a) + n.y * sin(turn_a);
		u.z = u.z * cos(turn_a) + n.z * sin(turn_a);
		n.x = -u.x * sin(turn_a) + n.x * cos(turn_a);
		n.y = -u.y * sin(turn_a) + n.y * cos(turn_a);
		n.z = -u.z * sin(turn_a) + n.z * cos(turn_a);
	}
	void look_up(void) {
		//Write your code here
		v.x = v.x * cos(pitch_a) + n.x * sin(pitch_a);
		v.y = v.y * cos(pitch_a) + n.y * sin(pitch_a);
		v.z = v.z * cos(pitch_a) + n.z * sin(pitch_a);
		n.x = -v.x * sin(pitch_a) + n.x * cos(pitch_a);
		n.y = -v.y * sin(pitch_a) + n.y * cos(pitch_a);
		n.z = -v.z * sin(pitch_a) + n.z * cos(pitch_a);
	}
	void look_down(void) {
		//Write your code here
		v.x = v.x * cos(pitch_a) - n.x * sin(pitch_a);
		v.y = v.y * cos(pitch_a) - n.y * sin(pitch_a);
		v.z = v.z * cos(pitch_a) - n.z * sin(pitch_a);
		n.x = v.x * sin(pitch_a) + n.x * cos(pitch_a);
		n.y = v.y * sin(pitch_a) + n.y * cos(pitch_a);
		n.z = v.z * sin(pitch_a) + n.z * cos(pitch_a);
	}
	void roll_left(void) {
		//Write your code here
		u.x = u.x * cos(roll_a) + v.x * sin(roll_a);
		u.y = u.y * cos(roll_a) + v.y * sin(roll_a);
		u.z = u.z * cos(roll_a) + v.z * sin(roll_a);
		v.x = -u.x * sin(roll_a) + v.x * cos(roll_a);
		v.y = -u.y * sin(roll_a) + v.y * cos(roll_a);
		v.z = -u.z * sin(roll_a) + v.z * cos(roll_a);
	}
	void roll_right(void) {
		//Write your code here
		u.x = u.x * cos(roll_a) - v.x * sin(roll_a);
		u.y = u.y * cos(roll_a) - v.y * sin(roll_a);
		u.z = u.z * cos(roll_a) - v.z * sin(roll_a);
		v.x = u.x * sin(roll_a) + v.x * cos(roll_a);
		v.y = u.y * sin(roll_a) + v.y * cos(roll_a);
		v.z = u.z * sin(roll_a) + v.z * cos(roll_a);
	}
};

CViewFrame view_frame;

// Initialization function
void init(void) {
	static GLfloat light_ambient[] = { 0.01, 0.01, 0.01, 1.0 };
	static GLfloat light_diffuse[] = { 1.0, 1.0, 1.0, 1.0 };
	static GLfloat light_specular[] = { 1.0, 1.0, 1.0, 1.0 };

	glClearColor(0.0, 0.0, 0.0, 0.0);
	glShadeModel(GL_SMOOTH); // Set shading model

	// Set light source properties for light source #0
	glLightfv(GL_LIGHT0, GL_AMBIENT, light_ambient);
	glLightfv(GL_LIGHT0, GL_DIFFUSE, light_diffuse);
	glLightfv(GL_LIGHT0, GL_SPECULAR, light_specular);

	glEnable(GL_LIGHTING); // Enable lighting
	glEnable(GL_LIGHT0); // Enable light source #0
	glEnable(GL_DEPTH_TEST); // Enable depth buffer test
	glEnable(GL_NORMALIZE); // Enable auto normalization
	glEnable(GL_CULL_FACE); // Enable face culling

	// Set initial properties for view reference frame
	view_frame.P0 = CVector3D(700.0, 00.0, 100.0);
	view_frame.u = CVector3D(0.0, 1.0, 0.0);
	view_frame.v = CVector3D(0.0, 0.0, 1.0);
	view_frame.n = CVector3D(1.0, 0.0, 0.0);
	view_frame.step = 2;
	view_frame.turn_a = PI / 18;
	view_frame.pitch_a = PI / 18;
	view_frame.roll_a = PI / 18;
}

// Function to draw chess board on xy plane
void draw_chess_board(float sx, float sy, float sz, int nx, int ny)
// sx, sy, sz: size of the chess board
// nx, ny: Number of chess grids in x and y direction
{
	static GLfloat mat1_color[] = { 0.8, 0.8, 0.8, 1.0 };
	static GLfloat mat2_color[] = { 0.2, 0.2, 0.2, 1.0 };
	int i, j, iflag, jflag;
	float x, y, dx, dy;
	float* pcolor;

	dx = sx / (float)nx;
	dy = sy / (float)ny;

	for (i = 0; i < nx; ++i) {
		iflag = i % 2;
		x = (i + 0.5) * dx - 0.5 * sx;
		for (j = 0; j < ny; ++j) {
			jflag = j % 2;
			y = (j + 0.5) * dy - 0.5 * sy;
			if (iflag == jflag)
				pcolor = mat1_color;
			else
				pcolor = mat2_color;
			glMaterialfv(GL_FRONT_AND_BACK, GL_AMBIENT_AND_DIFFUSE, pcolor);
			glMaterialfv(GL_FRONT_AND_BACK, GL_SPECULAR, pcolor);
			glMaterialf(GL_FRONT_AND_BACK, GL_SHININESS, 64.0);
			glPushMatrix();
			glTranslatef(x, y, 0.0);
			glScalef(dx, dy, sz);
			glutSolidCube(1.0);
			glPopMatrix();
		}
	}
}

// Function to draw chess pieces
void draw_chess_piece(float sx, float sy, float sz, int nx, int ny)
// sx, sy, sz: size of the chess board
// nx, ny: Number of chess grids in x and y direction
{
	static GLfloat mat_color[4][4] = {
		{ 1.0, 0.0, 0.0, 1.0 },
		{ 0.0, 1.0, 0.0, 1.0 },
		{ 0.0, 0.0, 1.0, 1.0 },
		{ 1.0, 1.0, 0.0, 1.0 }
	};
	float x, y, dx, dy, size;

	dx = sx / (float)nx;
	dy = sy / (float)ny;
	if (dx < dy)
		size = dx;
	else
		size = dy;

	//glPolygonMode(GL_FRONT_AND_BACK, GL_LINE);

	// Draw a sphere
	glMaterialfv(GL_FRONT_AND_BACK, GL_AMBIENT_AND_DIFFUSE, mat_color[0]);
	glMaterialfv(GL_FRONT_AND_BACK, GL_SPECULAR, mat_color[0]);
	glMaterialf(GL_FRONT_AND_BACK, GL_SHININESS, 64.0);
	x = (0 + 0.5) * dx - 0.5 * sx;
	y = (2 + 0.5) * dy - 0.5 * sy;
	glPushMatrix();
	glTranslatef(x, y, 0.5 * (sz + size));
	glutSolidSphere(0.5 * size, 10, 10);
	glPopMatrix();

	// Draw a torus
	glMaterialfv(GL_FRONT_AND_BACK, GL_AMBIENT_AND_DIFFUSE, mat_color[1]);
	glMaterialfv(GL_FRONT_AND_BACK, GL_SPECULAR, mat_color[1]);
	glMaterialf(GL_FRONT_AND_BACK, GL_SHININESS, 64.0);
	x = (1 + 0.5) * dx - 0.5 * sx;
	y = (0 + 0.5) * dy - 0.5 * sy;
	glPushMatrix();
	glTranslatef(x, y, 0.5 * (sz + size));
	glRotatef(-90, 1.0, 0.0, 0.0);
	glutSolidTorus(0.1 * size, 0.4 * size, 10, 20);
	glPopMatrix();

	// Draw a cone
	glMaterialfv(GL_FRONT_AND_BACK, GL_AMBIENT_AND_DIFFUSE, mat_color[2]);
	glMaterialfv(GL_FRONT_AND_BACK, GL_SPECULAR, mat_color[2]);
	glMaterialf(GL_FRONT_AND_BACK, GL_SHININESS, 64.0);
	x = (2 + 0.5) * dx - 0.5 * sx;
	y = (1 + 0.5) * dy - 0.5 * sy;
	glPushMatrix();
	glTranslatef(x, y, 0.5 * sz);
	glutSolidCone(0.4 * size, size, 10, 5);
	glPopMatrix();

	// Draw a rectangular solid
	glMaterialfv(GL_FRONT_AND_BACK, GL_AMBIENT_AND_DIFFUSE, mat_color[3]);
	glMaterialfv(GL_FRONT_AND_BACK, GL_SPECULAR, mat_color[3]);
	glMaterialf(GL_FRONT_AND_BACK, GL_SHININESS, 64.0);
	x = (3 + 0.5) * dx - 0.5 * sx;
	y = (3 + 0.5) * dy - 0.5 * sy;
	glPushMatrix();
	glTranslatef(x, y, 0.5 * (sz + 0.9 * size));
	glScalef(0.9 * dx, 0.9 * dy, 0.9 * size);
	glutSolidCube(1.0);
	glPopMatrix();

	//glPolygonMode(GL_FRONT_AND_BACK, GL_FILL);
}

// Display callback function
void display(void) {
	static GLfloat light_pos[4] = { 200.0, 200.0, 200.0, 1.0 };

	// Clear frame buffer and depth buffer
	glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

	glPushMatrix(); //Save current ModelView matrix

	// Set viewing transformation matrix
	CVector3D look_at;
	look_at.x = view_frame.P0.x - view_frame.n.x;
	look_at.y = view_frame.P0.y - view_frame.n.y;
	look_at.z = view_frame.P0.z - view_frame.n.z;
	gluLookAt(view_frame.P0.x, view_frame.P0.y, view_frame.P0.z,
		look_at.x, look_at.y, look_at.z,
		view_frame.v.x, view_frame.v.y, view_frame.v.z);

	// Set light source position
	glLightfv(GL_LIGHT0, GL_POSITION, light_pos);

	// Draw the scene
	draw_chess_board(400.0, 400.0, 40.0, 4, 4);
	draw_chess_piece(400.0, 400.0, 40.0, 4, 4);

	glPopMatrix(); //Restore ModelView matrix

	glutSwapBuffers(); // Swap front and back buffer
}

// Reshape callback function
void reshape(int w, int h) {
	// float wsize = 500.0;

	// Set viewport as the entire program window
	glViewport(0, 0, w, h);

	// Set symmetric perspective projection
	glMatrixMode(GL_PROJECTION);
	glLoadIdentity();
	gluPerspective(60.0, (float)w / (float)h, 10.0, 100000.0);

	// Reset modelview transformation matrix to identity
	glMatrixMode(GL_MODELVIEW);
	glLoadIdentity();
}

// Keyboard callback function
void keyboard(unsigned char key, int x, int y) {
	switch (key) {
	case 27:
		exit(0);
		break;
	case 'w':
		view_frame.move_forward();
		glutPostRedisplay();
		break;
	case 's': //move backward
		//Write your code here
		view_frame.move_backward();
		glutPostRedisplay();
		break;
	case 'a': //move left
		//Write your code here
		view_frame.move_left();
		glutPostRedisplay();
		break;
	case 'd': //move right
		//Write your code here
		view_frame.move_right();
		glutPostRedisplay();
		break;
	case 'q': //roll left
		//Write your code here
		view_frame.roll_left();
		glutPostRedisplay();
		break;
	case 'e': //roll right
		//Write your code here
		view_frame.roll_right();
		glutPostRedisplay();
		break;
	}
}

// Special key callback function
void special_key(int key, int x, int y) {
	switch (key) {
	case GLUT_KEY_LEFT:
		view_frame.turn_left();
		glutPostRedisplay();
		break;
	case GLUT_KEY_RIGHT: //turn right
		//Write your code here
		view_frame.turn_right();
		glutPostRedisplay();
		break;
	case GLUT_KEY_UP: //look up
		//Write your code here
		view_frame.look_up();
		glutPostRedisplay();
		break;
	case GLUT_KEY_DOWN: //look down
		//Write your code here
		view_frame.look_down();
		glutPostRedisplay();
		break;
	case GLUT_KEY_PAGE_UP: //move up
		//Write your code here
		view_frame.move_up();
		glutPostRedisplay();
		break;
	case GLUT_KEY_PAGE_DOWN: //move down
		//Write your code here
		view_frame.move_down();
		glutPostRedisplay();
		break;
	}
}

// Main program
int main(int argc, char* argv[]) {
	glutInit(&argc, argv);
	glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH);
	glutInitWindowSize(800, 800);
	glutInitWindowPosition(120, 120);
	glutCreateWindow("3D Scene Roaming");
	init();
	glutDisplayFunc(display);
	glutReshapeFunc(reshape);
	glutKeyboardFunc(keyboard);
	glutSpecialFunc(special_key);
	glutMainLoop();
	return 0;
}
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