OPENGLc++曲面构造的详细介绍
发信人: yxy (田丝丝#冬眠的小肥鹰), 信区: GAME_Designer标 题: OPENGL(14)
发信站: BBS 水木清华站 (Tue Feb 17 16:24:53 1998)
曲面的构造可以是网格线和填充曲面形式，其实与曲线很类似只是变为
二维而已。
1.曲面定义
void glMap2{fd}(GLenum target,TYPE u1,TYPE u2,GLint ustride,GLint uorder,
TYPE v1,TYPE v2,GLint vstride,GLint vorder,TYPE points);
target的定义同上次介绍的曲线中target的定义。
U V是二维曲面坐标
uorder,vorder;ustride,vstride的定义都类似曲线定义。
points是控制点坐标
2.曲面任意一点的计算
void glEvalCoord2{fd}[v](TYPE u,TYPE v);
以曲线坐标U V来计算曲面内任意一点的世界坐标的位置
3.曲面绘制的控制
void glMapGrid2{fd}(GLenum nu,TYPE u1,TYPE u2,GLenum nv,TYPE v1,TYPE v2);
定义曲面参数空间均匀网格，从u1到u2分为等间隔nu步，从v1到v2分为等间隔nv步。
下面给出一个以网格线描绘曲面的例子：
////////////////////////////////////////////////////////////
//sample.cpp
#include "glos.h"
#include
#include
#include "windows.h"
void myinit(void);
void CALLBACK display(void);
void CALLBACK reshape(GLsizei w,GLsizei h);
//控制点坐标
GLfloat points[4][4][3]={
{{-1.5,-1.5,2.0},{-0.5,-1.5,2.0},
{0.5,-1.5,-1.0},{1.5,-1.5,2.0}},
{{-1.5,-0.5,1.0},{-0.5,1.5,2.0},
{0.5,0.5,1.0},{1.5,-0.5,-1.0}},
{{-1.5,0.5,2.0},{-0.5,0.5,1.0},
{0.5,0.5,3.0},{1.5,-1.5,1.5}},
{{-1.5,1.5,-2.0},{-0.5,1.5,-2.0},
{0.5,0.5,1.0},{1.5,1.5,-1.0}}};
//为了清楚显示控制点而设置的一组颜色
GLfloat color[4][3]={
{1.0,0.0,0.0},{0.0,1.0,0.0},{0.0,0.0,1.0},{1.0,1.0,1.0}};
void myinit(void)
{
auxInitDisplayMode(AUX_SINGLE|AUX_RGBA);
auxInitPosition(0,0,500,500);
auxInitWindow("sample1");
glClearColor(0.0,0.0,0.0,0.0);
glClear(GL_COLOR_BUFFER_BIT);
//利用glEnable()来启用曲面模式
glMap2f(GL_MAP2_VERTEX_3,0,1,3,4,0,1,12,4,&points[0][0][0]);
glEnable(GL_MAP2_VERTEX_3);
glMapGrid2f(20,0.0,1.0,20,0.0,1.0);
glEnable(GL_DEPTH_TEST);
}
void CALLBACK reshape(GLsizei w,GLsizei h)
{
glViewport(0,0,w,h);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
if(w<=h)
glOrtho(-5.0,5.0,-5.0*(GLfloat)h/(GLfloat)w,
5.0*(GLfloat)h/(GLfloat)w,-5.0,5.0);
else
glOrtho(-5.0*(GLfloat)h/(GLfloat)w,
5.0*(GLfloat)h/(GLfloat)w,-5.0,5.0,-5.0,5.0);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
}
void CALLBACK display(void)
{
glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT);
glColor3f(0.0,0.0,1.0);
glPushMatrix();
glRotatef(35.0,1.0,1.0,1.0);
//用直线段的连接描绘曲面结构
glBegin(GL_LINE_STRIP);
int i,j;
//在U V方向各画出8条网格线，用以构造曲面结构
for(j=0;j<=8;j++)
{
//在U方向用30条直线段描绘一条曲线
glBegin(GL_LINE_STRIP);
for(i=0;i<=30;i++)
glEvalCoord2f((GLfloat)i/30.0,(GLfloat)j/8.0);
glEnd();
//在V方向用30条直线段描绘一条曲线
glBegin(GL_LINE_STRIP);
for(i=0;i<=30;i++)
glEvalCoord2f((GLfloat)j/8.0,(GLfloat)i/30.0);
glEnd();
}
//用不同的颜色把控制点显示出来
glPointSize(4.0);
glBegin(GL_POINTS);
for(i=0;i<4;i++)
for(j=0;j<4;j++)
{
glColor3fv(color[i]);
glVertex3fv(&points[i][j][0]);
}
glEnd();
glPopMatrix();
glFlush();
}
void main(void)
{
myinit();
auxReshapeFunc(reshape);
auxMainLoop(display);
}
//end of sample
///////////////////////////////////////////////////////
应用中常常不满足曲面的框架结构。下面就介绍填充曲面的绘制方法：
void glEvalMesh2(GLenum mode,GLint p1,GLint p2,GLint q1,GLint q2);
把用glMapGrid2{fd}()设置的网格应用到已经启用的曲面计算上。
mode可以是GL_POINT GL_LINE GL_FILL。顾名思义，GL_FILL就是生成填充曲面
这里给出一个有光照处理的BEZIER曲面的例子（这个曲面除了绘制方法不同，数学
形式和前面的是一样的）。
///////////////////////////////////////////////////////
//sample.cpp
#include "glos.h"
#include
#include
#include "windows.h"
void myinit(void);
void CALLBACK display(void);
void CALLBACK reshape(GLsizei w,GLsizei h);
GLfloat points[4][4][3]={
{{-1.5,-1.5,2.0},{-0.5,-1.5,2.0},
{0.5,-1.5,-1.0},{1.5,-1.5,2.0}},
{{-1.5,-0.5,1.0},{-0.5,1.5,2.0},
{0.5,0.5,1.0},{1.5,-0.5,-1.0}},
{{-1.5,0.5,2.0},{-0.5,0.5,1.0},
{0.5,0.5,3.0},{1.5,-1.5,1.5}},
{{-1.5,1.5,-2.0},{-0.5,1.5,-2.0},
{0.5,0.5,1.0},{1.5,1.5,-1.0}}};
GLfloat color[4][3]={
{1.0,0.0,0.0},{0.0,1.0,0.0},{0.0,0.0,1.0},{1.0,1.0,1.0}};
//初始化光照、材质的过程
void initlights(void)
{
GLfloat ambient[]={0.4,0.6,0.2,1.0};
GLfloat position[]={0.0,1.0,3.0,1.0};
GLfloat mat_diffuse[]={0.2,0.4,0.8,1.0};
GLfloat mat_specular[]={1.0,1.0,1.0,1.0};
GLfloat mat_shininess[]={80.0};
glEnable(GL_LIGHTING);
glEnable(GL_LIGHT0);
glLightfv(GL_LIGHT0,GL_AMBIENT,ambient);
glLightfv(GL_LIGHT0,GL_POSITION,position);
glMaterialfv(GL_FRONT,GL_DIFFUSE,mat_diffuse);
glMaterialfv(GL_FRONT,GL_SPECULAR,mat_specular);
glMaterialfv(GL_FRONT,GL_SHININESS,mat_shininess);
}
void myinit(void)
{
auxInitDisplayMode(AUX_SINGLE|AUX_RGBA);
auxInitPosition(0,0,500,500);
auxInitWindow("sample1");
glClearColor(0.0,0.0,0.0,0.0);
glClear(GL_COLOR_BUFFER_BIT);
glMap2f(GL_MAP2_VERTEX_3,0,1,3,4,0,1,12,4,&points[0][0][0]);
glEnable(GL_MAP2_VERTEX_3);
glEnable(GL_AUTO_NORMAL);
// glEnable(GL_NORMALIZE);
glMapGrid2f(20,0.0,1.0,20,0.0,1.0);
glEnable(GL_DEPTH_TEST);
//初始化光照、材质
initlights();
// glShadeModel(GL_FLAT);
}
void CALLBACK reshape(GLsizei w,GLsizei h)
{
glViewport(0,0,w,h);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
if(w<=h)
glOrtho(-5.0,5.0,-5.0*(GLfloat)h/(GLfloat)w,
5.0*(GLfloat)h/(GLfloat)w,-5.0,5.0);
else
glOrtho(-5.0*(GLfloat)h/(GLfloat)w,
5.0*(GLfloat)h/(GLfloat)w,-5.0,5.0,-5.0,5.0);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
}
void CALLBACK display(void)
{
{
glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT);
glColor3f(0.0,0.0,1.0);
glPushMatrix();
glRotatef(35.0,1.0,1.0,1.0);
//将原来网格的绘制部分注释掉，代替以填充曲面的绘制方法
glEvalMesh2(GL_FILL,0,20,0,20);
int i,j;
/* for(j=0;j<=8;j++)
{
glBegin(GL_LINE_STRIP);
for(i=0;i<=30;i++)
glEvalCoord2f((GLfloat)i/30.0,(GLfloat)j/8.0);
glEnd();
glBegin(GL_LINE_STRIP);
for(i=0;i<=30;i++)
glEvalCoord2f((GLfloat)j/8.0,(GLfloat)i/30.0);
glEnd();
}
*/
glPointSize(4.0);
glBegin(GL_POINTS);
for(i=0;i<4;i++)
for(j=0;j<4;j++)
{
glColor3fv(color[i]);
glVertex3fv(&points[i][j][0]);
}
glEnd();
glPopMatrix();
glFlush();
}
void main(void)
{
myinit();
auxReshapeFunc(reshape);
auxMainLoop(display);
}
//end of sample
////////////////////////////////////////////////////////////////
一个真正具有实体的曲面就展现出来乐。控制点的不同，可以控制曲面的形状
可以看出OPENGL的强大功能，只用很少的原代码就产生真实的3D效果。
在以此篇结束复杂建模前，给出一个绘制NURBS曲面（非均匀B样条曲面）的例子，
这里用到乐一些OPENGL实用库提供的专门函数。所有的新东东都在程序中做乐注
释，注释给出过程的含义，具体函数的操作可以详细查阅联机手册。
///////////////////////////////////////////////////////////////
//sample.cpp
#include "glos.h"
#include
#include
#include "windows.h"
void myinit(void);
void CALLBACK display(void);
void CALLBACK reshape(GLsizei w,GLsizei h);
//定义一组控制点的存储空间
GLfloat points[4][4][3];
//定义一个指向NURBS曲面对象的指针
GLUnurbsObj *theNurb;
//用来生成控制点的过程，取代被注释掉的原来直接赋值方式生成控制点
void init_surface(void)
{
int u,v;
for(u=0;u<4;u++)
{
for(v=0;v<4;v++)
{
points[u][v][0]=2.0*((GLfloat)u-1.5);
points[u][v][1]=2.0*((GLfloat)v-1.5);
if((u==1||u==2)&&(v==1||v==2))
points[u][v][2]=3.0;
else
points[u][v][2]=-3.0;
}
}
}
/*
GLfloat points[4][4][3]={
{{-1.5,-1.5,2.0},{-0.5,-1.5,4.0},
{0.5,-1.5,3.0},{1.5,-1.5,2.0}},
{{-1.5,-0.5,3.0},{-0.5,1.5,4.0},
{0.5,0.5,2.0},{1.5,-0.5,-1.0}},
{{-1.5,0.5,2.0},{-0.5,0.5,4.0},
{0.5,0.5,5.0},{1.5,-1.5,1.5}},
{{-1.5,1.5,-2.0},{-0.5,1.5,3.0},
{0.5,0.5,1.0},{1.5,1.5,-1.0}}};
*/
GLfloat color[4][3]={
{1.0,0.0,0.0},{0.0,1.0,0.0},{0.0,0.0,1.0},{1.0,1.0,1.0}};
void initlights(void)
{
GLfloat ambient[]={0.4,0.6,0.2,1.0};
GLfloat position[]={0.0,1.0,3.0,1.0};
GLfloat mat_diffuse[]={0.2,0.4,0.8,1.0};
GLfloat mat_specular[]={1.0,1.0,1.0,1.0};
GLfloat mat_shininess[]={80.0};
glEnable(GL_LIGHTING);
glEnable(GL_LIGHT0);
glLightfv(GL_LIGHT0,GL_AMBIENT,ambient);
glLightfv(GL_LIGHT0,GL_POSITION,position);
glMaterialfv(GL_FRONT,GL_DIFFUSE,mat_diffuse);
glMaterialfv(GL_FRONT,GL_SPECULAR,mat_specular);
glMaterialfv(GL_FRONT,GL_SHININESS,mat_shininess);
//首先初始化控制点
init_surface();
//创建一个NURBS曲面的对象
theNurb=gluNewNurbsRenderer();
//修改此曲面对象的属性
gluNurbsProperty(theNurb,GLU_SAMPLING_TOLERANCE,25.0);
gluNurbsProperty(theNurb,GLU_DISPLAY_MODE,GLU_FILL);
}
void myinit(void)
{
auxInitDisplayMode(AUX_SINGLE|AUX_RGBA);
auxInitPosition(0,0,500,500);
auxInitWindow("sample1");
glClearColor(0.0,0.0,0.0,0.0);
glClear(GL_COLOR_BUFFER_BIT);
glMap2f(GL_MAP2_VERTEX_3,0,1,3,4,0,1,12,4,&points[0][0][0]);
glEnable(GL_MAP2_VERTEX_3);
glEnable(GL_AUTO_NORMAL);
glEnable(GL_NORMALIZE);
glMapGrid2f(20,0.0,1.0,20,0.0,1.0);
glEnable(GL_DEPTH_TEST);
initlights();
// glShadeModel(GL_FLAT);
}
void CALLBACK reshape(GLsizei w,GLsizei h)
{
glViewport(0,0,w,h);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
if(w<=h)
glOrtho(-5.0,5.0,-5.0*(GLfloat)h/(GLfloat)w,
5.0*(GLfloat)h/(GLfloat)w,-5.0,5.0);
else
glOrtho(-5.0*(GLfloat)h/(GLfloat)w,
5.0*(GLfloat)h/(GLfloat)w,-5.0,5.0,-5.0,5.0);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
}
void CALLBACK display(void)
{
//B样条曲面（NURBS）的控制向量，可以参阅图形学的相关书籍
GLfloat knots[8]={0.0,0.0,0.0,0.0,1.0,1.0,1.0,1.0};
glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT);
glColor3f(0.0,0.0,1.0);
glPushMatrix();
glRotatef(35.0,1.0,1.0,1.0);
glRotatef(-60.0,1.0,0.0,0.0);
glScalef(0.5,0.5,0.5);
//注释掉原来的曲面绘制函数，代之以新的NURBS曲面绘制函数
// glEvalMesh2(GL_FILL,0,20,0,20);
//定义曲面的数学模型，确定其形状
gluNurbsSurface(theNurb,
8,knots,
8,knots,
4*3,
3,
&points[0][0][0],
4,4,
GL_MAP2_VERTEX_3);
//结束曲面的绘制，此结构很类似于标准的glBegin()...glEnd()
gluEndSurface(theNurb);
int i,j;
glPointSize(4.0);
glBegin(GL_POINTS);
for(i=0;i<4;i++)
for(j=0;j<4;j++)
{
glColor3fv(color[i]);
glVertex3fv(&points[i][j][0]);
}
glEnd();
glPopMatrix();
glFlush();
}
void main(void)
{
myinit();
auxReshapeFunc(reshape);
auxMainLoop(display);
}
//end of sample
//////////////////////////////////////////////////////////////////
至此，复杂建模告于段落。下次介绍特殊光照
--
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