opengl实现任意两点间画圆柱体

1，问题提出

两点间画线简单：

glBegin(GL_LINES);  //注意是LINES不是LINE，这个错误一定要注意。

glVertexf(x1, y1, z1);

glVertexf(x2, y2, z2);

glEnd();

画线函数不会影响opengl的矩阵堆栈。

但是很多时候线条效果会比较差，比如我要做一个骨骼动画，关节点间的骨头用线条太难看，即使使用glLineWidth设置线宽，视觉效果还是一塌糊涂。还有利用分形绘制3D树的时候，树干用线条（宽线条）绘制效果也不佳。所以此时需要实现一个函数，3D空间中任意两点间用几何体绘制，我下面介绍一种思路。

2，原理介绍

要在A(x1,y1,z1), B(x2,y2,z2)之间绘制圆柱体，首先在原点处，沿着Y轴方向完成几何体绘制，然后旋转到AB向量方向，最后平移到A点处。关键在旋转矩阵的计算，使用向量叉乘：AB向量和Y轴单位向量叉乘计算出右手side向量，然后side单位化，side和AB叉乘计算出最终的up方向。

代码如下：

void RenderBone(float x0, float y0, float z0, float x1, float y1, float z1 ){GLdouble dir_x = x1 - x0;GLdouble dir_y = y1 - y0;GLdouble dir_z = z1 - z0;GLdouble bone_length = sqrt( dir_x*dir_x + dir_y*dir_y + dir_z*dir_z );static GLUquadricObj * quad_obj = NULL;if ( quad_obj == NULL )quad_obj = gluNewQuadric();gluQuadricDrawStyle( quad_obj, GLU_FILL );gluQuadricNormals( quad_obj, GLU_SMOOTH );glPushMatrix();// 平移到起始点glTranslated( x0, y0, z0 );// 计算长度double length;length = sqrt( dir_x*dir_x + dir_y*dir_y + dir_z*dir_z );if ( length < 0.0001 ) { dir_x = 0.0; dir_y = 0.0; dir_z = 1.0; length = 1.0;}dir_x /= length; dir_y /= length; dir_z /= length;GLdouble up_x, up_y, up_z;up_x = 0.0;up_y = 1.0;up_z = 0.0;double side_x, side_y, side_z;side_x = up_y * dir_z - up_z * dir_y;side_y = up_z * dir_x - up_x * dir_z;side_z = up_x * dir_y - up_y * dir_x;length = sqrt( side_x*side_x + side_y*side_y + side_z*side_z );if ( length < 0.0001 ) {side_x = 1.0; side_y = 0.0; side_z = 0.0; length = 1.0;}side_x /= length; side_y /= length; side_z /= length;up_x = dir_y * side_z - dir_z * side_y;up_y = dir_z * side_x - dir_x * side_z;up_z = dir_x * side_y - dir_y * side_x;// 计算变换矩阵GLdouble m[16] = { side_x, side_y, side_z, 0.0,up_x, up_y, up_z, 0.0,dir_x, dir_y, dir_z, 0.0,0.0, 0.0, 0.0, 1.0 };glMultMatrixd( m );// 圆柱体参数GLdouble radius= 20;// 半径GLdouble slices = 8.0;//段数GLdouble stack = 3.0;// 递归次数gluCylinder( quad_obj, radius, radius, bone_length, slices, stack ); glPopMatrix();} 

上面的代码绘制圆柱体使用了glu几何库，如果绘制其他几何体：比如四棱锥，或其它几何体，只需要修改下面的框架：

void RenderBone(float x0, float y0, float z0, float x1, float y1, float z1 ){GLdouble dir_x = x1 - x0;GLdouble dir_y = y1 - y0;GLdouble dir_z = z1 - z0;GLdouble bone_length = sqrt( dir_x*dir_x + dir_y*dir_y + dir_z*dir_z );glPushMatrix();// 平移到起始点glTranslated( x0, y0, z0 );// 计算长度double length;length = sqrt( dir_x*dir_x + dir_y*dir_y + dir_z*dir_z );if ( length < 0.0001 ) { dir_x = 0.0; dir_y = 0.0; dir_z = 1.0; length = 1.0;}dir_x /= length; dir_y /= length; dir_z /= length;GLdouble up_x, up_y, up_z;up_x = 0.0;up_y = 1.0;up_z = 0.0;double side_x, side_y, side_z;side_x = up_y * dir_z - up_z * dir_y;side_y = up_z * dir_x - up_x * dir_z;side_z = up_x * dir_y - up_y * dir_x;length = sqrt( side_x*side_x + side_y*side_y + side_z*side_z );if ( length < 0.0001 ) {side_x = 1.0; side_y = 0.0; side_z = 0.0; length = 1.0;}side_x /= length; side_y /= length; side_z /= length;up_x = dir_y * side_z - dir_z * side_y;up_y = dir_z * side_x - dir_x * side_z;up_z = dir_x * side_y - dir_y * side_x;// 计算变换矩阵GLdouble m[16] = { side_x, side_y, side_z, 0.0,up_x, up_y, up_z, 0.0,dir_x, dir_y, dir_z, 0.0,0.0, 0.0, 0.0, 1.0 };glMultMatrixd( m );// 原点处向Y轴方向绘制几何体renderGeometryInYAxis();glPopMatrix();} 

注意上面的renderGeometryInYAxis();必须是在Y轴上绘制几何体。

3，测试代码：

#include <gl/glut.h>#include <cstdio>#include <cstdlib>#include <cmath>voidinit(void);voidreshape(int w,int h);voiddisplay(void);void RenderBone(float x0, float y0, float z0, float x1, float y1, float z1 );int main(int argc, char** argv){glutInit(&argc, argv);glutInitDisplayMode (GLUT_SINGLE | GLUT_RGB | GLUT_DEPTH); glutInitWindowSize (500, 500);glutInitWindowPosition (100, 100);glutCreateWindow("Sphere");init ();glutReshapeFunc(reshape);glutDisplayFunc(display);glutMainLoop();return 0;}void init (void){ glClearColor (0.0, 0.0, 0.0, 0.0);glClearDepth(1);glShadeModel(GL_SMOOTH);GLfloat _ambient[]={1.0,1.0,1.0,1.0};GLfloat _diffuse[]={1.0,1.0,0.0,1.0};GLfloat _specular[]={1.0,1.0,1.0,1.0};GLfloat _position[]={200,200,200,0};glLightfv(GL_LIGHT0,GL_AMBIENT,_ambient);glLightfv(GL_LIGHT0,GL_DIFFUSE,_diffuse);glLightfv(GL_LIGHT0,GL_SPECULAR,_specular);glLightfv(GL_LIGHT0,GL_POSITION,_position);glEnable(GL_TEXTURE_2D);glEnable(GL_LIGHTING);glEnable(GL_LIGHT0);glEnable(GL_DEPTH_TEST);glHint(GL_PERSPECTIVE_CORRECTION_HINT, GL_NICEST);}void reshape(int w, int h){glViewport (0, 0, (GLsizei) w, (GLsizei) h);glMatrixMode(GL_PROJECTION);glLoadIdentity();glOrtho(0.0, 500, 0.0, 500, -500, 500);glMatrixMode(GL_MODELVIEW);glLoadIdentity();}void display(void){glMatrixMode(GL_MODELVIEW);glLoadIdentity();glClear (GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT);glPushMatrix();{RenderBone(100, 100, 100, 200, 300, 500);} glPopMatrix();glFlush();glutPostRedisplay();}void RenderBone(float x0, float y0, float z0, float x1, float y1, float z1 ){GLdouble dir_x = x1 - x0;GLdouble dir_y = y1 - y0;GLdouble dir_z = z1 - z0;GLdouble bone_length = sqrt( dir_x*dir_x + dir_y*dir_y + dir_z*dir_z );static GLUquadricObj * quad_obj = NULL;if ( quad_obj == NULL )quad_obj = gluNewQuadric();gluQuadricDrawStyle( quad_obj, GLU_FILL );gluQuadricNormals( quad_obj, GLU_SMOOTH );glPushMatrix();// 平移到起始点glTranslated( x0, y0, z0 );// 计算长度double length;length = sqrt( dir_x*dir_x + dir_y*dir_y + dir_z*dir_z );if ( length < 0.0001 ) { dir_x = 0.0; dir_y = 0.0; dir_z = 1.0; length = 1.0;}dir_x /= length; dir_y /= length; dir_z /= length;GLdouble up_x, up_y, up_z;up_x = 0.0;up_y = 1.0;up_z = 0.0;double side_x, side_y, side_z;side_x = up_y * dir_z - up_z * dir_y;side_y = up_z * dir_x - up_x * dir_z;side_z = up_x * dir_y - up_y * dir_x;length = sqrt( side_x*side_x + side_y*side_y + side_z*side_z );if ( length < 0.0001 ) {side_x = 1.0; side_y = 0.0; side_z = 0.0; length = 1.0;}side_x /= length; side_y /= length; side_z /= length;up_x = dir_y * side_z - dir_z * side_y;up_y = dir_z * side_x - dir_x * side_z;up_z = dir_x * side_y - dir_y * side_x;// 计算变换矩阵GLdouble m[16] = { side_x, side_y, side_z, 0.0,up_x, up_y, up_z, 0.0,dir_x, dir_y, dir_z, 0.0,0.0, 0.0, 0.0, 1.0 };glMultMatrixd( m );// 圆柱体参数GLdouble radius= 20;// 半径GLdouble slices = 8.0;//段数GLdouble stack = 3.0;// 递归次数gluCylinder( quad_obj, radius, radius, bone_length, slices, stack ); glPopMatrix();} 

最终效果图：