OpenGL中的轨迹球问题

OpenGL鼠标轨迹球（Trackball）原理

什么是鼠标轨迹球

类似AutoCAD里的“动态观察”，三维模型都是要投影到二维的屏幕上才能显示给用户，而用户如果想观察一下三维模型的立体形状使用“动态观察”是再好不过了。我们一般的操作是这样的：鼠标（按中健或者其他健）在二维屏幕上拖动，之后三维模型就会以屏幕中心点为中心进行相应的旋转，鼠标拖动得越长，三维模型旋转的角度就越大。AutoCAD这种重量级的商业软件在这方面的用户体验自然是非常完美的了，可你知道它的原理么，如果自己用OpenGL如果实现呢？

OpenGL里的轨迹球

计算机的三维显示类似生活中的摄影，屏幕就是一个相机，三维模型就是被摄物体。我们可以调整相机与被摄物之间的距离来在屏幕显示不同大小影像。轨迹球就是在屏幕之外虚构一个球形曲面，使鼠标在二维屏幕上的移动投影到球形曲面上，这样就能得到更佳的用户体验（不使用轨迹球也能实现动态观察，只是效果很生硬）。

以屏幕为中心为球心，x轴向右，Y轴向上，z轴向屏幕之外，很容易建立一个球体的几何方程如下：

x2+y2+z2=r2x2+y2+z2=r2

这里,r代表球体的半径。

当鼠标在球面的范围内移动时，我们可以由鼠标在二维屏幕上的二维点坐标P（x,y）通过数学关系求得其在球面上的投影点P'，鼠标从P1点移动到P2点，对应的在球面上就是从P1'移动到P2'。P1'和P2'与球心之间可以形成两个向量，鼠标移动转化成了向量从V1（OP1'向量）转到V2（OP2'向量），V1和V2的向量叉乘得到向量N即是三维物体的旋转轴，V1到V2的转角量就是三维物体的旋转角度。

使轨迹球更连续

实际的屏幕是个矩形，而球体在平面的投影只会是个圆，因此只要轨迹球的半径不是无限大，就总会有一些区域的点投影后会落在球面之外。此时怎么办呢？

一个好的办法就是在球体投影不能覆盖的区域使用另外一个曲面与之拼接。一个现成的二次曲面能够胜任，它的表达式如下：

z(x,y)=r2/2x2+y2−−−−−−√

这个曲面与球面的交线正好一个圆（下图中所示红线），其半径为r/2–√r/2。

经过这样处理的轨迹球就比较平滑，于是整个坐标计算过程如下：

由于一般安装opengl时，并没有包含glew32.dll和头文件及.lib文件，所以要先将相关文件包含到相关目录中，这里给出glew的下载链接:点击打开链接点击打开链接

这里给出实现轨迹球的代码

ArcBall.h:

#include "StdAfx.h"#ifndef _ArcBall_h
#define _ArcBall_h#include <stdlib.h>// 仅在Debug模式下，启用断言
#ifdef _DEBUG
# include "assert.h"
#else
# define assert(x) { }
#endif//2维点
typedef union Tuple2f_t
{struct{GLfloat X, Y;} s;GLfloat T[2];
} Tuple2fT;     //3维点
typedef union Tuple3f_t
{struct{GLfloat X, Y, Z;} s;GLfloat T[3];
} Tuple3fT;      //4维点
typedef union Tuple4f_t
{struct{GLfloat X, Y, Z, W;} s;GLfloat T[4];
} Tuple4fT;      //3x3矩阵
typedef union Matrix3f_t
{struct{//column majorunion { GLfloat M00; GLfloat XX; GLfloat SX; };  union { GLfloat M10; GLfloat XY;             };  union { GLfloat M20; GLfloat XZ;             };  union { GLfloat M01; GLfloat YX;             };  union { GLfloat M11; GLfloat YY; GLfloat SY; };  union { GLfloat M21; GLfloat YZ;             };  union { GLfloat M02; GLfloat ZX;             };  union { GLfloat M12; GLfloat ZY;             };  union { GLfloat M22; GLfloat ZZ; GLfloat SZ; };  } s;GLfloat M[9];
} Matrix3fT;    //4x4矩阵
typedef union Matrix4f_t
{struct{//column majorunion { GLfloat M00; GLfloat XX; GLfloat SX; };  union { GLfloat M10; GLfloat XY;             };  union { GLfloat M20; GLfloat XZ;             };  union { GLfloat M30; GLfloat XW;             };  union { GLfloat M01; GLfloat YX;             };  union { GLfloat M11; GLfloat YY; GLfloat SY; };  union { GLfloat M21; GLfloat YZ;             };  union { GLfloat M31; GLfloat YW;             };  union { GLfloat M02; GLfloat ZX;             };  union { GLfloat M12; GLfloat ZY;             };  union { GLfloat M22; GLfloat ZZ; GLfloat SZ; };  union { GLfloat M32; GLfloat ZW;             };  union { GLfloat M03; GLfloat TX;             };  union { GLfloat M13; GLfloat TY;             };  union { GLfloat M23; GLfloat TZ;             };  union { GLfloat M33; GLfloat TW; GLfloat SW; };  } s;GLfloat M[16];
} Matrix4fT;    //定义类型的别名
#define Point2fT    Tuple2fT
#define Quat4fT     Tuple4fT
#define Vector2fT   Tuple2fT
#define Vector3fT   Tuple3fT
#define FuncSqrt    sqrtf
# define Epsilon 1.0e-5//2维点相加
inlinestatic void Point2fAdd(Point2fT* NewObj, const Tuple2fT* t1)
{assert(NewObj && t1);NewObj->s.X += t1->s.X;NewObj->s.Y += t1->s.Y;
}//2维点相减
inlinestatic void Point2fSub(Point2fT* NewObj, const Tuple2fT* t1)
{assert(NewObj && t1);NewObj->s.X -= t1->s.X;NewObj->s.Y -= t1->s.Y;
}//3维点矢积
inlinestatic void Vector3fCross(Vector3fT* NewObj, const Vector3fT* v1, const Vector3fT* v2)
{Vector3fT Result; assert(NewObj && v1 && v2);Result.s.X = (v1->s.Y * v2->s.Z) - (v1->s.Z * v2->s.Y);Result.s.Y = (v1->s.Z * v2->s.X) - (v1->s.X * v2->s.Z);Result.s.Z = (v1->s.X * v2->s.Y) - (v1->s.Y * v2->s.X);*NewObj = Result;
}//3维点点积
inlinestatic GLfloat Vector3fDot(const Vector3fT* NewObj, const Vector3fT* v1)
{assert(NewObj && v1);return  (NewObj->s.X * v1->s.X) +(NewObj->s.Y * v1->s.Y) +(NewObj->s.Z * v1->s.Z);
}//3维点的长度的平方
inlinestatic GLfloat Vector3fLengthSquared(const Vector3fT* NewObj)
{assert(NewObj);return  (NewObj->s.X * NewObj->s.X) +(NewObj->s.Y * NewObj->s.Y) +(NewObj->s.Z * NewObj->s.Z);
}//3维点的长度
inlinestatic GLfloat Vector3fLength(const Vector3fT* NewObj)
{assert(NewObj);return FuncSqrt(Vector3fLengthSquared(NewObj));
}//设置3x3矩阵为0矩阵
inlinestatic void Matrix3fSetZero(Matrix3fT* NewObj)
{NewObj->s.M00 = NewObj->s.M01 = NewObj->s.M02 = NewObj->s.M10 = NewObj->s.M11 = NewObj->s.M12 = NewObj->s.M20 = NewObj->s.M21 = NewObj->s.M22 = 0.0f;
}//设置4x4矩阵为0矩阵
inlinestatic void Matrix4fSetZero(Matrix4fT* NewObj)
{NewObj->s.M00 = NewObj->s.M01 = NewObj->s.M02 = NewObj->s.M10 = NewObj->s.M11 = NewObj->s.M12 = NewObj->s.M20 = NewObj->s.M21 = NewObj->s.M22 = NewObj->s.M30 = NewObj->s.M31 = NewObj->s.M32 = 0.0f;
}//设置3x3矩阵为单位矩阵
inlinestatic void Matrix3fSetIdentity(Matrix3fT* NewObj)
{Matrix3fSetZero(NewObj);NewObj->s.M00 = NewObj->s.M11 = NewObj->s.M22 = 1.0f;
}//设置4x4矩阵为单位矩阵
inlinestatic void Matrix4fSetIdentity(Matrix4fT* NewObj)
{Matrix4fSetZero(NewObj);NewObj->s.M00 = 1.0f;NewObj->s.M11 = 1.0f;NewObj->s.M22 = 1.0f;NewObj->s.M33=1.0f;
}//从四元数设置旋转矩阵
inlinestatic void Matrix3fSetRotationFromQuat4f(Matrix3fT* NewObj, const Quat4fT* q1)
{GLfloat n, s;GLfloat xs, ys, zs;GLfloat wx, wy, wz;GLfloat xx, xy, xz;GLfloat yy, yz, zz;assert(NewObj && q1);n = (q1->s.X * q1->s.X) + (q1->s.Y * q1->s.Y) + (q1->s.Z * q1->s.Z) + (q1->s.W * q1->s.W);s = (n > 0.0f) ? (2.0f / n) : 0.0f;xs = q1->s.X * s;  ys = q1->s.Y * s;  zs = q1->s.Z * s;wx = q1->s.W * xs; wy = q1->s.W * ys; wz = q1->s.W * zs;xx = q1->s.X * xs; xy = q1->s.X * ys; xz = q1->s.X * zs;yy = q1->s.Y * ys; yz = q1->s.Y * zs; zz = q1->s.Z * zs;NewObj->s.XX = 1.0f - (yy + zz); NewObj->s.YX =         xy - wz;  NewObj->s.ZX =         xz + wy;NewObj->s.XY =         xy + wz;  NewObj->s.YY = 1.0f - (xx + zz); NewObj->s.ZY =         yz - wx;NewObj->s.XZ =         xz - wy;  NewObj->s.YZ =         yz + wx;  NewObj->s.ZZ = 1.0f - (xx + yy);
}//3x3矩阵相乘
inlinestatic void Matrix3fMulMatrix3f(Matrix3fT* NewObj, const Matrix3fT* m1)
{Matrix3fT Result; assert(NewObj && m1);Result.s.M00 = (NewObj->s.M00 * m1->s.M00) + (NewObj->s.M01 * m1->s.M10) + (NewObj->s.M02 * m1->s.M20);Result.s.M01 = (NewObj->s.M00 * m1->s.M01) + (NewObj->s.M01 * m1->s.M11) + (NewObj->s.M02 * m1->s.M21);Result.s.M02 = (NewObj->s.M00 * m1->s.M02) + (NewObj->s.M01 * m1->s.M12) + (NewObj->s.M02 * m1->s.M22);Result.s.M10 = (NewObj->s.M10 * m1->s.M00) + (NewObj->s.M11 * m1->s.M10) + (NewObj->s.M12 * m1->s.M20);Result.s.M11 = (NewObj->s.M10 * m1->s.M01) + (NewObj->s.M11 * m1->s.M11) + (NewObj->s.M12 * m1->s.M21);Result.s.M12 = (NewObj->s.M10 * m1->s.M02) + (NewObj->s.M11 * m1->s.M12) + (NewObj->s.M12 * m1->s.M22);Result.s.M20 = (NewObj->s.M20 * m1->s.M00) + (NewObj->s.M21 * m1->s.M10) + (NewObj->s.M22 * m1->s.M20);Result.s.M21 = (NewObj->s.M20 * m1->s.M01) + (NewObj->s.M21 * m1->s.M11) + (NewObj->s.M22 * m1->s.M21);Result.s.M22 = (NewObj->s.M20 * m1->s.M02) + (NewObj->s.M21 * m1->s.M12) + (NewObj->s.M22 * m1->s.M22);*NewObj = Result;
}//4x4矩阵相乘
inlinestatic void Matrix4fSetRotationScaleFromMatrix4f(Matrix4fT* NewObj, const Matrix4fT* m1)
{assert(NewObj && m1);NewObj->s.XX = m1->s.XX; NewObj->s.YX = m1->s.YX; NewObj->s.ZX = m1->s.ZX;NewObj->s.XY = m1->s.XY; NewObj->s.YY = m1->s.YY; NewObj->s.ZY = m1->s.ZY;NewObj->s.XZ = m1->s.XZ; NewObj->s.YZ = m1->s.YZ; NewObj->s.ZZ = m1->s.ZZ;
}//进行矩阵的奇异值分解，旋转矩阵被保存到rot3和rot4中，返回矩阵的缩放因子
inlinestatic GLfloat Matrix4fSVD(const Matrix4fT* NewObj, Matrix3fT* rot3, Matrix4fT* rot4)
{GLfloat s, n;assert(NewObj);s = FuncSqrt(( (NewObj->s.XX * NewObj->s.XX) + (NewObj->s.XY * NewObj->s.XY) + (NewObj->s.XZ * NewObj->s.XZ) + (NewObj->s.YX * NewObj->s.YX) + (NewObj->s.YY * NewObj->s.YY) + (NewObj->s.YZ * NewObj->s.YZ) +(NewObj->s.ZX * NewObj->s.ZX) + (NewObj->s.ZY * NewObj->s.ZY) + (NewObj->s.ZZ * NewObj->s.ZZ) ) / 3.0f );if (rot3)   {rot3->s.XX = NewObj->s.XX; rot3->s.XY = NewObj->s.XY; rot3->s.XZ = NewObj->s.XZ;rot3->s.YX = NewObj->s.YX; rot3->s.YY = NewObj->s.YY; rot3->s.YZ = NewObj->s.YZ;rot3->s.ZX = NewObj->s.ZX; rot3->s.ZY = NewObj->s.ZY; rot3->s.ZZ = NewObj->s.ZZ;n = 1.0f / FuncSqrt( (NewObj->s.XX * NewObj->s.XX) +(NewObj->s.XY * NewObj->s.XY) +(NewObj->s.XZ * NewObj->s.XZ) );rot3->s.XX *= n;rot3->s.XY *= n;rot3->s.XZ *= n;n = 1.0f / FuncSqrt( (NewObj->s.YX * NewObj->s.YX) +(NewObj->s.YY * NewObj->s.YY) +(NewObj->s.YZ * NewObj->s.YZ) );rot3->s.YX *= n;rot3->s.YY *= n;rot3->s.YZ *= n;n = 1.0f / FuncSqrt( (NewObj->s.ZX * NewObj->s.ZX) +(NewObj->s.ZY * NewObj->s.ZY) +(NewObj->s.ZZ * NewObj->s.ZZ) );rot3->s.ZX *= n;rot3->s.ZY *= n;rot3->s.ZZ *= n;}if (rot4)  {if (rot4 != NewObj){Matrix4fSetRotationScaleFromMatrix4f(rot4, NewObj); }n = 1.0f / FuncSqrt( (NewObj->s.XX * NewObj->s.XX) +(NewObj->s.XY * NewObj->s.XY) +(NewObj->s.XZ * NewObj->s.XZ) );rot4->s.XX *= n;rot4->s.XY *= n;rot4->s.XZ *= n;n = 1.0f / FuncSqrt( (NewObj->s.YX * NewObj->s.YX) +(NewObj->s.YY * NewObj->s.YY) +(NewObj->s.YZ * NewObj->s.YZ) );rot4->s.YX *= n;rot4->s.YY *= n;rot4->s.YZ *= n;n = 1.0f / FuncSqrt( (NewObj->s.ZX * NewObj->s.ZX) +(NewObj->s.ZY * NewObj->s.ZY) +(NewObj->s.ZZ * NewObj->s.ZZ) );rot4->s.ZX *= n;rot4->s.ZY *= n;rot4->s.ZZ *= n;}return s;
}//从3x3矩阵变为4x4的旋转矩阵
inlinestatic void Matrix4fSetRotationScaleFromMatrix3f(Matrix4fT* NewObj, const Matrix3fT* m1)
{assert(NewObj && m1);NewObj->s.XX = m1->s.XX; NewObj->s.YX = m1->s.YX; NewObj->s.ZX = m1->s.ZX;NewObj->s.XY = m1->s.XY; NewObj->s.YY = m1->s.YY; NewObj->s.ZY = m1->s.ZY;NewObj->s.XZ = m1->s.XZ; NewObj->s.YZ = m1->s.YZ; NewObj->s.ZZ = m1->s.ZZ;
}//4x4矩阵的与标量的乘积
inlinestatic void Matrix4fMulRotationScale(Matrix4fT* NewObj, GLfloat scale)
{assert(NewObj);NewObj->s.XX *= scale; NewObj->s.YX *= scale; NewObj->s.ZX *= scale;NewObj->s.XY *= scale; NewObj->s.YY *= scale; NewObj->s.ZY *= scale;NewObj->s.XZ *= scale; NewObj->s.YZ *= scale; NewObj->s.ZZ *= scale;
}//设置旋转矩阵
inlinestatic void Matrix4fSetRotationFromMatrix3f(Matrix4fT* NewObj, const Matrix3fT* m1)
{GLfloat scale;assert(NewObj && m1);scale = Matrix4fSVD(NewObj, NULL, NULL);Matrix4fSetRotationScaleFromMatrix3f(NewObj, m1);Matrix4fMulRotationScale(NewObj, scale);
}typedef class ArcBall_t
{
protected://把二维点映射到三维点inlinevoid _mapToSphere(const Point2fT* NewPt, Vector3fT* NewVec) const;public://构造/析构函数ArcBall_t(GLfloat NewWidth, GLfloat NewHeight);~ArcBall_t() { };//设置边界inlinevoid    setBounds(GLfloat NewWidth, GLfloat NewHeight){assert((NewWidth > 1.0f) && (NewHeight > 1.0f));//设置长宽的调整因子this->AdjustWidth  = 1.0f / ((NewWidth  - 1.0f) * 0.5f);this->AdjustHeight = 1.0f / ((NewHeight - 1.0f) * 0.5f);}//鼠标点击void    click(const Point2fT* NewPt);//鼠标拖动计算旋转void    drag(const Point2fT* NewPt, Quat4fT* NewRot);//更新鼠标状态void    upstate();//void    mousemove(WPARAM wParam,LPARAM lParam);protected:Vector3fT   StVec;          //保存鼠标点击的坐标Vector3fT   EnVec;          //保存鼠标拖动的坐标GLfloat     AdjustWidth;    //宽度的调整因子GLfloat     AdjustHeight;   //长度的调整因子
public:Matrix4fT   Transform;      //计算变换            Matrix3fT   LastRot;        //上一次的旋转 Matrix3fT   ThisRot;        //这次的旋转float zoomRate;float lastZoomRate;bool        isDragging;     // 是否拖动bool        isRClicked;     // 是否右击鼠标bool        isClicked;      // 是否点击鼠标bool        isZooming;    //是否正在缩放Point2fT    LastPt;        Matrix4fT origTransform;Point2fT    MousePt;        // 当前的鼠标位置} ArcBallT;#endif

ArcBall.cpp:文件

/** KempoApi: The Turloc Toolkit *****************************/
/** *    *                                                  **/
/** **  **  Filename: ArcBall.cpp                           **/
/**   **    Version:  Common                                **/
/**   **                                                    **/
/**                                                         **/
/**  Arcball class for mouse manipulation.                  **/
/**                                                         **/
/**                                                         **/
/**                                                         **/
/**                                                         **/
/**                              (C) 1999-2003 Tatewake.com **/
/**   History:                                              **/
/**   08/17/2003 - (TJG) - Creation                         **/
/**   09/23/2003 - (TJG) - Bug fix and optimization         **/
/**   09/25/2003 - (TJG) - Version for NeHe Basecode users  **/
/**                                                         **/
/*************************************************************/
//
#include "StdAfx.h"
#include <windows.h>
#include <GL/glew.h>        #include <math.h>
#include "ArcBall.h"                                 //轨迹球参数:
//直径                    2.0f
//半径                    1.0f
//半径平方                1.0fvoid ArcBall_t::_mapToSphere(const Point2fT* NewPt, Vector3fT* NewVec) const
{Point2fT TempPt;GLfloat length;//复制到临时变量TempPt = *NewPt;//把长宽调整到[-1 ... 1]区间TempPt.s.X  =        (TempPt.s.X * this->AdjustWidth)  - 1.0f;TempPt.s.Y  = 1.0f - (TempPt.s.Y * this->AdjustHeight);//计算长度的平方length      = (TempPt.s.X * TempPt.s.X) + (TempPt.s.Y * TempPt.s.Y);//如果点映射到球的外面if (length > 1.0f){GLfloat norm;//缩放到球上norm    = 1.0f / FuncSqrt(length);//设置z坐标为0NewVec->s.X = TempPt.s.X * norm;NewVec->s.Y = TempPt.s.Y * norm;NewVec->s.Z = 0.0f;}//如果在球内else   {//利用半径的平方为1,求出z坐标NewVec->s.X = TempPt.s.X;NewVec->s.Y = TempPt.s.Y;NewVec->s.Z = FuncSqrt(1.0f - length);}
}ArcBall_t::ArcBall_t(GLfloat NewWidth, GLfloat NewHeight)
{this->StVec.s.X     = 0.0f;this->StVec.s.Y     = 0.0f;this->StVec.s.Z     = 0.0f;this->EnVec.s.X     = 0.0f;this->EnVec.s.Y     = 0.0f;this->EnVec.s.Z     = 0.0f;Matrix4fSetIdentity(&Transform);Matrix3fSetIdentity(&LastRot);Matrix3fSetIdentity(&ThisRot);this->isDragging=false;this->isClicked= false;this->isRClicked = false;this->isZooming = false;this->zoomRate = 1;this->setBounds(NewWidth, NewHeight);
}void ArcBall_t::upstate()
{if(!this->isZooming && this->isRClicked){                    // 开始拖动this->isZooming = true;                                        // 设置拖动为变量为true        this->LastPt = this->MousePt;this->lastZoomRate = this->zoomRate;}else if(this->isZooming){//正在拖动if(this->isRClicked){  //拖动        Point2fSub(&this->MousePt, &this->LastPt);this->zoomRate = this->lastZoomRate + this->MousePt.s.X * this->AdjustWidth * 2;}else{                                            //停止拖动this->isZooming = false;}}else if (!this->isDragging && this->isClicked){                                                // 如果没有拖动this->isDragging = true;                                        // 设置拖动为变量为truethis->LastRot = this->ThisRot;                                        this->click(&this->MousePt);                                }else if(this->isDragging){if (this->isClicked){                                            //如果按住拖动Quat4fT     ThisQuat;this->drag(&this->MousePt, &ThisQuat);                        // 更新轨迹球的变量Matrix3fSetRotationFromQuat4f(&this->ThisRot, &ThisQuat);        // 计算旋转量Matrix3fMulMatrix3f(&this->ThisRot, &this->LastRot);                Matrix4fSetRotationFromMatrix3f(&this->Transform, &this->ThisRot);    }else                                                        // 如果放开鼠标，设置拖动为falsethis->isDragging = false;}
}//按下鼠标,记录当前对应的轨迹球的位置
void    ArcBall_t::click(const Point2fT* NewPt)
{this->_mapToSphere(NewPt, &this->StVec);
}//鼠标拖动,计算旋转四元数
void    ArcBall_t::drag(const Point2fT* NewPt, Quat4fT* NewRot)
{//新的位置this->_mapToSphere(NewPt, &this->EnVec);//计算旋转if (NewRot){Vector3fT  Perp;//计算旋转轴Vector3fCross(&Perp, &this->StVec, &this->EnVec);//如果不为0if (Vector3fLength(&Perp) > Epsilon)    {//记录旋转轴NewRot->s.X = Perp.s.X;NewRot->s.Y = Perp.s.Y;NewRot->s.Z = Perp.s.Z;//在四元数中,w=cos(a/2)，a为旋转的角度NewRot->s.W= Vector3fDot(&this->StVec, &this->EnVec);}//是0，说明没有旋转else                                 {NewRot->s.X = NewRot->s.Y = NewRot->s.Z = NewRot->s.W = 0.0f;}}
}

sample.cpp:

#include "StdAfx.h"
#pragma comment( lib, "opengl32.lib" )
#pragma comment( lib, "glut32.lib")
#pragma comment( lib, "glew32.lib")
#include <GL/glew.h>
#include <GL/glut.h>
#include <GL/glu.h>
#include <math.h>
#include "ArcBall.h"                                                                                                                            //初始化，必须用全局变量的方式，不能用new
ArcBallT arcBall(600.0f,400.0f);
ArcBallT*    ArcBall =&arcBall;// new ArcBallT(600.0f,400.0f);//&arcBall;void reshape(int w, int h){glViewport(0,0, w, h);glMatrixMode(GL_PROJECTION);glLoadIdentity();glFrustum(-1, 1, -1, 1, 1.5, 20);glMatrixMode(GL_MODELVIEW);ballArcBall->setBounds((GLfloat)w, (GLfloat)h);//1. 设置窗口边界
}
void init(){glClearColor(0,0,0,0);glShadeModel(GL_FLAT);
}void display (void)
{glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);                glColor3f(1.0,1.0,1.0);glLoadIdentity();gluLookAt(0.0, 0.0, 5.0,0.0, 0.0, 0.0,0.0, 1.0, 0.0);glScalef(1.0, 2.0, 1.0);//glPushMatrix();                glTranslatef(0,0,-3);            glScalef(ArcBall->zoomRate, ArcBall->zoomRate, ArcBall->zoomRate);//2. 缩放glMultMatrixf(ArcBall->Transform.M);                        //3. 旋转glutWireCube(1.0);//glPopMatrix();                                                    glFlush ();
}
//移动
void move(int x, int y)
{ArcBall->MousePt.s.X = x;ArcBall->MousePt.s.Y = y;ArcBall->upstate();glutPostRedisplay();
}
//点击
void mouse(int button, int state, int x, int y)
{if(button == GLUT_LEFT_BUTTON && state==GLUT_DOWN){ArcBall->isClicked = true;move(x,y);}else if(button == GLUT_LEFT_BUTTON && state==GLUT_UP)ArcBall->isClicked = false;else if(button == GLUT_RIGHT_BUTTON && state==GLUT_DOWN){ArcBall->isRClicked = true;move(x,y);}else if(button == GLUT_RIGHT_BUTTON && state == GLUT_UP)ArcBall->isRClicked = false;ArcBall->upstate();glutPostRedisplay();
}
int main(int argc, char** argv)
{glutInit(&argc, argv);glutInitDisplayMode(GLUT_SINGLE|GLUT_RGB);glutInitWindowSize(640,480);glutCreateWindow("HI");init();glutDisplayFunc(display);glutReshapeFunc(reshape);glutMouseFunc(mouse);        //registered the mouse event.glutMotionFunc(move);        //registered the move eventglutMainLoop();return 0;
}

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