实验六3D编程及Bezier曲线绘制

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1、文档供参考，可复制、编制，期待您的好评与关注！ 实验七 3D编程及Bezier曲线曲面绘制一、实验目的13D编程：熟悉视点观察函数的设置和使用；熟悉投影变换函数的设置和使用；熟悉基本3D图元的绘制2了解OpenGL绘制Bezier曲线的方法二、实验环境 硬件要求：PC机，主流配置，最好为独立显卡，显存512M以上。 软件环境：操作系统：Windows XP。语言开发工具：VC6.0。三、实验要求：按照实验内容做实验，保留所作步骤效果截图或演示程序，当场检查，现场计分四、实验内容1. 3D编程3D Cube.cpp 为一静止3D立方体，3D Cube2.cpp 为正交投影下的旋转3D立方体，按下

2、鼠标可实现不同方向的旋转。分析3D编程代码与程序结构。 图7-1 静止立方体效果图 图7-2 旋转立方体效果图 图7-3 旋转茶壶和圆环效果图 1让静止的立方体绕Z轴不停旋转2 修改视点，目标点不变，观看显示效果 3. 修改目标点，视点不动，观看显示效果4. 视点与目标点同时修改，观看显示效果5. 视点与目标点不变，修改观察体大小，观看显示效果6. 将正交投影观察体改为透视投影观察体，并设置其大小，观察显示效果7. 将立方体替换为茶壶，观看显示效果. 选做2. Bezier曲线绘制BezierCurve.cpp为绘制bezier曲线的源程序，仔细研读源程序，并作如下修改1) 改变控制点，观察曲

3、线和曲面形状的变化，控制点起什么作用？2) 改写bezier.cpp,增加控制点数目,修改控制点位置，使之成为空间封闭曲线，写出修改的关键代码及注释（TIPS：OpenGLBezier曲线绘制方法最多只能有8个控制点）3) 根据bezier曲线的性质，改写程序，使之成为两段曲线光滑连接。每段曲线用不同颜色表示，并画出控制点。 图7-2 Bezier曲线绘制效果五、函数参考（一）3D编程1 视点设置函数 void gluLookAt(GLdouble eyex, GLdouble eyey,GLdouble eyez,GLdouble atx,GLdouble aty,GLdouble atz,

4、GLdouble upx,GLdouble upy,GLdouble upz) 给出矩阵作用于当前矩阵，定义相机位置和方向 视点：eyex, eyey, eyez 目标点：atx,aty,atz 相机向上方向：upx,upy,upz 如果不引用该函数，则 eyex=0,eyey=0,eyez=0， atx=0,aty=0,atz=-1，Upx=0,upy=1,upz=0此函数放在display函数中调用 参考坐标系：世界坐标系2 正交投影变换设置函数 . void glOrtho(GLdouble left,GLdouble right,GLdouble bottom,GLdouble top

5、,GLdouble near,GLdouble far)，建立正交投影矩阵，定义一个正平行观察体。距离从相机位置处测量。rightleft,topbottom,farnearOpenGL中不提供对观察平面的选择功能。近裁减平面永远和观察平面重合。如果OpenGL不提供投影函数，默认调用为：glOrtho(-1.0,1.0,-1.0,1.0，-1.0，1.0) 3 透视投影变换设置函数void gluPerspective(GLdouble fov,GLdouble aspect, GLdouble near,GLdouble far)，定义一个透视矩阵作用于当前矩阵 fov-近裁剪平面与远裁剪

6、平面的连线与视点的角度,也称视场角(field-of-view angle) aspect-投影平面的宽与高之比 near,far-近裁剪平面和远裁剪平面离相机(视点)的距离4三维基本图形绘制函数1）立方体绘制函数void glutWireCube(GLdouble size) /线框模式void glutSolidCube(GLdouble size) /实体模式 功能：绘制一个边长为size的线框的或实心立方体，立方体的中心位于原点2）小球绘制函数void glutWireSphere(GLdouble Radius, Glint slices,Glint stacks) void glu

7、tSolidSphere(GLdouble Radius, Glint slices,Glint stacks); 功能：绘制一个半径为Radius的线框的的或实心小球，小球的中心点位于原点， slices: 为小球的经线数目，stacks为小球的纬线数目3）茶壶绘制函数void glutWireTeapot(GLdouble size); void glutSolidTeapot(GLdouble size); 功能：绘制一个半径为size的线框的或实心茶壶，茶壶的中心位于原点 参数说明：参数size为茶壶的近似半径，以size为半径的球体可完全包容这个茶壶。4）圆环绘制函数void glu

8、tWireTorus(GLdouble innerRadius, GLdouble outerRadius,Glint slices,Glint stacks);void glutWireTorus(GLdouble innerRadius, GLdouble outerRadius,Glint slices,Glint stacks); 功能：绘制一个半径为size的线框的的或实心圆环体，圆环体的中心位于原点，圆环的内径和外径由参数innerRadius, outerRadius指定 参数说明：innerRadius: 圆环体的内径outerRadius: 圆环体的外径 slices: 圆环

9、体的经线数目 stacks: 圆环体的纬线数目（二）Bezier曲线绘制1）Bezier曲线绘制步骤：1. Defining Bezier curvevoid glMap1fd (GLenum target, TYPE u1, TYPE u2, GLint stride, GLint order, const TYPE *points); l target: 指定控制点所描述的内容l u1, u2：曲线的参数范围(t)，一般u1=0,u2=1; l stride: 控制点之间的浮点数或双精度的个数l order: 次数+1， 即控制点的数目l points: 指向控制点的指针 2. Enabl

10、ing Bezier curve glEnable(GL_MAP1_VERTEX_3);3. Calculating data points4. Linking and drawingn 求出Bezier曲线上的详细点 void glEvalCoord1fd (TYPE u) void glEvalCoord1fdv (TYPE *u)n 画出Bezier曲线 glBegin(GL_LINE_STRIP); for (i = 0; i = 100; i+) glEvalCoord1f(GLfloat) i/100.0); glEnd();或n void glMapGridf,d (GLint

11、n,TYPE u1,TYPE u2);n void glEvalMesh1 (GLenum mode,GLint p1, GLint p2); Mode的取值可以是GL_POINT或GL_LINE n 相当于glBegin(GL_LINE_STRIP); for (i = p1; i = p2; i+) glEvalCoord1f(u1+i*(u2-u1)/n); glEnd(); 六、附属程序（一）3D编程1. 3D Cube.cpp 静止立方体程序#include void display() glClear(GL_COLOR_BUFFER_BIT); /清屏 glMatrixMode(G

12、L_MODELVIEW); /矩阵模式设置 glLoadIdentity(); /清空矩阵堆栈 gluLookAt(1.4,1.0,0.8,0.0,0.0,0.0,0.0,1.0,0.0); /设置视点 / gluLookAt(1,1.0,1.0,0.0,0.0,0.0,0.0,1.0,0.0); glColor3f(1,0,0); / glutWireCube(0.5); glutSolidCube(0.5); /绘制立方体，立方体中心在坐标原点 glColor3f(0,0,1); glutWireCube(0.5); /绘制线框立方体，体现边框效果 glutSwapBuffers(); v

13、oid reshape(int w,int h) glViewport(0,0,w,h); glMatrixMode(GL_PROJECTION); glLoadIdentity(); glOrtho(-1,1,-1,1,0.5,2.5); /定义三维观察体 glMatrixMode(GL_MODELVIEW); glLoadIdentity(); void init() glClearColor(0.0,0.0,0.0,0.0); glLineWidth(3); /glColor3f(1.0,1.0,1.0); int main(int argc, char* argv) glutInit(

14、&argc,argv); glutInitDisplayMode(GLUT_DOUBLE|GLUT_RGB); glutInitWindowSize(800,800); glutInitWindowPosition(0,0); glutCreateWindow(cube); glutReshapeFunc(reshape); glutDisplayFunc(display); init(); glutMainLoop();2. 3D Cube2.exe 旋转立方体参考程序#include math.h#include int flag=0;/GLfloat vertices3=-1.0,-1.

15、0,1.0,-1.0,1.0,1.0,1.0,1.0,1.0,1.0,-1.0,1.0,-1.0,-1.0,-1.0,/-1.0,1.0,-1.0,1.0,1.0,-1.0,1.0,-1.0,-1.0;GLfloat vertices3=-1.0,-1.0,-1.0,1.0,-1.0,-1.0,1.0,1.0,-1.0,-1.0,1.0,-1.0,-1.0,-1.0,1.0,1.0,-1.0,1.0,1.0,1.0,1.0,-1.0,1.0,1.0;GLfloat colors3=1.0,0.0,0.0,0.0,1.0,1.0,1.0,1.0,0.0,0.0,1.0,0.0,0.0,0.0,1

16、.0,1.0,0.0,1.0,0.0,1.0,1.0,1.0,1.0,1.0;void init()glPolygonMode(GL_FRONT_AND_BACK,GL_FILL);glEnable(GL_DEPTH_TEST);glLineWidth(3);void polygon(int a,int b,int c,int d)/* draw a polygon via list of vertices */if (flag=0)glBegin(GL_POLYGON); glColor3fv(colorsa); glVertex3fv(verticesa); glColor3fv(colo

17、rsb); glVertex3fv(verticesb); glColor3fv(colorsc); glVertex3fv(verticesc); glColor3fv(colorsd); glVertex3fv(verticesd); glEnd();elseglColor3f(0,0,0);glBegin(GL_POLYGON); glVertex3fv(verticesa); glVertex3fv(verticesb); glVertex3fv(verticesc); glVertex3fv(verticesd); glEnd();void colorcube(void) /* ma

18、p vertices to faces */ polygon(0,3,2,1); polygon(2,3,7,6); polygon(0,4,7,3); polygon(1,2,6,5); polygon(4,5,6,7); polygon(0,1,5,4);static GLfloat theta=0.0,0.0,0.0;static GLint axis=2; void display() / glClear(GL_COLOR_BUFFER_BIT); glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT); glLoadIdentity(); g

19、luLookAt(3,3,3,0,0,0,0,1,0); glRotatef(theta0,1.0,0.0,0.0); glRotatef(theta1,0.0,1.0,0.0); glRotatef(theta2,0.0,0.0,1.0);glPolygonMode(GL_FRONT_AND_BACK,GL_FILL);flag=0;colorcube(); /绘制彩色立方体 glPolygonMode(GL_FRONT_AND_BACK,GL_LINE);flag=1;colorcube(); /绘制彩色立方体 glutSwapBuffers(); void spinCube() thet

20、aaxis+=0.01; if (thetaaxis360.0) thetaaxis-=360.0; glutPostRedisplay(); void mouse(int btn, int state,int x, int y) if (btn=GLUT_LEFT_BUTTON & state=GLUT_DOWN) axis=0; if (btn=GLUT_MIDDLE_BUTTON & state=GLUT_DOWN) axis=1; if (btn=GLUT_RIGHT_BUTTON & state=GLUT_DOWN) axis=2; void reshape(int w,int h)

21、 glViewport(0,0,w,h); glMatrixMode(GL_PROJECTION); glLoadIdentity(); /定义正交投影观察体 if (w=h) glOrtho(-2.0,2.0,-2.0*(GLfloat)h/(GLfloat)w,2.0*(GLfloat)h/(GLfloat)w,1.0,20.0);else glOrtho(-2.0*(GLfloat)w/(GLfloat)h,2.0*(GLfloat)w/(GLfloat)h,-2.0,2.0,1.0,20.0); /gluPerspective(120,w/h,1,60); /定义透视投影投影观察体 g

22、lMatrixMode(GL_MODELVIEW); glLoadIdentity(); void main(int argc, char* argv) glutInit(&argc,argv); / glutInitDisplayMode(GLUT_DOUBLE|GLUT_RGB|GLUT_DETH); glutInitDisplayMode(GLUT_DOUBLE|GLUT_RGB|GLUT_DEPTH); glutInitWindowSize(800,800); glutCreateWindow(colorcube); init(); glutReshapeFunc(reshape);

23、glutDisplayFunc(display); glutIdleFunc(spinCube); glutMouseFunc(mouse); glutMainLoop(); （二）Bezier曲线绘制bezierCurve.cpp /Bezier曲线绘制程序#include / The number of control points for this curveGLint nNumPoints = 4; /control point group1GLfloat ctrlPoints43= -4.0f, 0.0f, 0.0f,/ End Point -6.0f, 4.0f, 0.0f,/ C

24、ontrol Point 6.0f, -4.0f, 0.0f,/ Control Point 4.0f, 0.0f, 0.0f ;/ End Pointvoid ChangeSize(int w, int h);void DrawPoints(void);void RenderScene(void);void SetupRC();int main(int argc, char *argv) glutInit(&argc, argv); /初始化GLUT库；glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB); /设置显示模式；（缓冲，颜色类型）glutInit

25、WindowSize(500, 500);glutInitWindowPosition(1024 / 2 - 250, 768 / 2 - 250);glutCreateWindow(Bezier Curve); /创建窗口，标题为“Rotating 3D World”；glutReshapeFunc(ChangeSize);SetupRC();glutDisplayFunc(RenderScene); /用于绘制当前窗口；glutMainLoop(); /表示开始运行程序，用于程序的结尾；return 0;void DrawPoints(void) int i;/ Counting vari

26、able / Set point size larger to make more visible glPointSize(5.0f); / Loop through all control points for this example glBegin(GL_POINTS); for(i = 0; i nNumPoints; i+) glVertex2fv(ctrlPointsi); glEnd(); / Called to draw scenevoid RenderScene(void) int i; / Clear the window with current clearing col

27、or glClear(GL_COLOR_BUFFER_BIT); / Sets up the bezier / This actually only needs to be called once and could go in / the setup function glMap1f(GL_MAP1_VERTEX_3,/ Type of data generated 0.0f,/ Lower u range 100.0f,/ Upper u range 3,/ Distance between points in the data nNumPoints,/ number of control

28、 points &ctrlPoints00);/ array of control points / Enable the evaluator glEnable(GL_MAP1_VERTEX_3);/ Use a line strip to connect-the-dotsglBegin(GL_LINE_STRIP);for(i = 0; i = 100; i+)/ Evaluate the curve at this pointglEvalCoord1f(GLfloat) i); glEnd(); / Use higher level functions to map to a grid,

29、then evaluate the / entire thing. / Put these two functions in to replace above loop / Map a grid of 100 points from 0 to 100 /glMapGrid1d(100,0.0,100.0); / Evaluate the grid, using lines /glEvalMesh1(GL_LINE,0,100); / Draw the Control Points DrawPoints(); / Flush drawing commands glutSwapBuffers();

30、 / This function does any needed initialization on the rendering/ context. void SetupRC() / Clear Window to white glClearColor(1.0f, 1.0f, 1.0f, 1.0f ); / Draw in Blue glColor3f(0.0f, 0.0f, 1.0f); / Set 2D Projectionvoid ChangeSize(int w, int h)/ Prevent a divide by zeroif(h = 0)h = 1;/ Set Viewport to window dimensions glViewport(0, 0, w, h);glMatrixMode(GL_PROJECTION);glLoadIdentity();gluOrtho2D(-10.0f, 10.0f, -10.0f, 10.0f);/ Modelview matrix resetglMatrixMode(GL_MODELVIEW);glLoadIdentity();11 / 11