OpenGL 5.2.6 二维组合变换的实例

                                                                   OpenGL  5.2.6 二维组合变换的实例

 

 

 download here:

 

http://download.youkuaiyun.com/user/rorger

 

包括：

      1.绕任意一点旋转

      2. 关于任意一点的缩放和剪切

      3. 关于任意一点的剪切

 

我更新了nrblbase.h 和cpp文件

 

 //nrglbase.h //rorger, 2011 /* Any problem,contact me:rorger@hotmail.com last modified:5/30/2011*/ #ifndef NRGLBASE_H #define NRGLBASE_H #include "iostream" #include "vector" using namespace std ; /////////////////////////////////////////点和向量////////////////////////////////////////////////////// class NRVector2{ public: float x, y ; NRVector2(); NRVector2(float x, float y); void set(float x, float y); void set(NRVector2&p); friend NRVector2 operator +(NRVector2&lhs,NRVector2&rhs); friend NRVector2 operator - (NRVector2&lhs,NRVector2& rhs); friend NRVector2 operator - (NRVector2&lhs,NRVector2& rhs); friend float operator *(NRVector2&lhs,NRVector2& rhs); friend NRVector2 operator *(NRVector2&lhs,float rhs); friend NRVector2 operator *(float lhs,NRVector2& rhs); friend ostream& operator << (ostream& outputStream,NRVector2&rhs); friend bool operator == (NRVector2&lhs,NRVector2& rhs); NRVector2 operator /(float rhs); float GetLength(); void Normalized(); NRVector2 GetNormalVector(); }; class NRVector3{ public: float x, y, z; NRVector3(); void set(float x, float y,float z); void set(NRVector3&p); friend NRVector3 operator +(NRVector3&lhs,NRVector3&rhs); friend NRVector3 operator - (NRVector3&lhs,NRVector3& rhs); friend float operator *(NRVector3&lhs,NRVector3& rhs); friend NRVector3 operator *(NRVector3&lhs,float rhs); friend ostream& operator << (ostream& outputStream,NRVector3& rhs); friend bool operator == (NRVector3&lhs,NRVector3& rhs); NRVector3 operator /(float rhs); float GetLength(); void Normalized(); NRVector3 GetNormalVector(); }; class NRPoint2{ public: float x, y ; NRPoint2(); NRPoint2(float x, float y); void set(float x, float y); void set(NRPoint2& p); friend NRPoint2 operator +(NRPoint2& lhs,NRVector2& rhs); friend NRPoint2 operator +(NRPoint2& lhs,NRPoint2& rhs); friend NRPoint2 operator - (NRPoint2& lhs,NRVector2& rhs); friend NRVector2 operator - (NRPoint2& lhs,NRPoint2& rhs); friend NRPoint2 operator* (NRPoint2& lhs,float rhs); friend NRPoint2 operator* (float lhs,NRPoint2& rhs); friend ostream& operator << (ostream& outputStream,NRPoint2&rhs); friend bool operator == (NRPoint2& lhs,NRPoint2& rhs); NRPoint2 operator /(float rhs); }; class NRPoint3{ public: float x, y, z ; NRPoint3(); void set(float x, float y,float z); void set(NRPoint3& p); friend NRPoint3 operator +(NRPoint3& lhs,NRVector3& rhs); friend NRVector3 operator - (NRPoint3& lhs,NRPoint3& rhs); friend NRPoint3 operator* (NRPoint3& lhs,float rhs); friend ostream& operator << (ostream& outputStream,NRPoint3& rhs); friend bool operator == (NRPoint3&lhs,NRPoint3& rhs); NRPoint3 operator /(float rhs); }; /////////////////////////////////////线段/射线/直线/////////////////////////////////////// //线段类 class NRLine2Segment { public: NRPoint2 first ; NRPoint2 second ; NRVector2 norm(); NRLine2Segment(); NRLine2Segment(NRPoint2 first,NRPoint2 second); NRLine2Segment(NRLine2Segment& line2); }; //点法向量表示的直线类 class NRLine2 { public: NRPoint2 pt ; NRVector2 norm; NRLine2(); NRLine2(NRPoint2 pt,NRVector2 norm); NRLine2(const NRLine2& line2); }; //////////////////////////////////////////////多边形/////////////////////////////////////////// //点法向量表示的多边形 class NRLine2List { public: vector<NRLine2> line; int num(); void push_back(NRLine2 newLine); NRLine2& operator[](int index); }; //多边形向量数组 class NRPolygonList { public: vector<NRLine2List> polygons; int num(); void push_back(NRLine2List newPolygon); NRLine2List& operator[](int index); }; ////////////////////////////////齐次坐标////////////////////////////////////////// class NRHomogeneousPoint2D { public: float x, y, ho; NRHomogeneousPoint2D(); }; class NRHomogeneousPoint3D { public: float x, y, z, ho ; NRHomogeneousPoint3D(); }; class NRHomogeneousVector2D { public: float x, y, ho; NRHomogeneousVector2D(); }; class NRHomogeneousVector3D { public: float x, y, z, ho ; NRHomogeneousVector3D(); }; //////////////////////////////////仿射变换/////////////////////////////////////// class NRMatrix2D { public: float matrixArray[3][3]; NRMatrix2D(); void Identity(); float* operator [](int i); NRMatrix2D operator *(NRMatrix2D rhs); NRHomogeneousPoint2D operator*( NRHomogeneousPoint2D rhs); }; class NRTranslateTransform2D { public: NRMatrix2D translateMatrix; NRTranslateTransform2D(); void Translate(float x, float y); void Identity(); NRHomogeneousPoint2D operator*( NRHomogeneousPoint2D rhs); NRTranslateTransform2D GetInverseTransform2D(); }; class NRScaleTransform2D { public: NRMatrix2D scaleMatrix; NRHomogeneousPoint2D center ; NRScaleTransform2D(); void Scale(float x, float y); void Identity(); NRHomogeneousPoint2D operator*( NRHomogeneousPoint2D rhs); NRScaleTransform2D GetInverseTransform2D(); }; class NRRotateTransform2D { public: NRMatrix2D rotateMatrix ; NRHomogeneousPoint2D center ; NRRotateTransform2D(); void Rotate(float angle); void Identity(); NRHomogeneousPoint2D operator*( NRHomogeneousPoint2D rhs); NRRotateTransform2D GetInverseTransform2D(); }; class NRClipTransform2D { public: NRMatrix2D clipMatrix ; NRHomogeneousPoint2D center ; NRClipTransform2D() ; void Clip(float h, float g) ; void Identity() ; NRHomogeneousPoint2D operator*( NRHomogeneousPoint2D rhs) ; NRClipTransform2D GetInverseTransform2D(); }; class NRCompositeTransform2D { public: NRMatrix2D compositeMatrix ; NRHomogeneousPoint2D center ; NRCompositeTransform2D(); void AddTransform(NRTranslateTransform2D transLateTransform); void AddTransform(NRScaleTransform2D scaleTransform); void AddTransform(NRRotateTransform2D rotateTransform); void AddTransform(NRClipTransform2D clipTransform) ; void Translate(float x, float y) ; void Scale(float x, float y) ; void Rotate(float angle) ; void Clip(float h, float g) ; void Identity(); NRHomogeneousPoint2D operator*( NRHomogeneousPoint2D rhs); NRCompositeTransform2D GetInverseTransform2D(); }; #endif //NRGLBASE_H

 

 

//nrglbase.cpp //rorger, 2011 /* Any problem,contact me:rorger@hotmail.com last modified:5/30/2011*/ #include "nrglbase.h" #include "math.h" #include "nrmath.h" /////////////////////////////////////////点和向量////////////////////////////////////////////////////// NRPoint2::NRPoint2() { this->x=0; this->y=0; } NRPoint2::NRPoint2(float x, float y) { this->x=x; this->y=y; } void NRPoint2::set(NRPoint2& p) { this->x=p.x; this->y=p.y; } void NRPoint2::set(float x, float y) { this->x=x; this->y=y; } NRPoint2 NRPoint2::operator /(float rhs) { NRPoint2 result ; result.x=x/rhs; result.y=y/rhs; return result; } NRPoint2 operator +(NRPoint2& lhs,NRVector2& rhs) { NRPoint2 result ; result.x = lhs.x+rhs.x; result.y = lhs.y+rhs.y; return result; } NRPoint2 operator +(NRPoint2& lhs,NRPoint2& rhs) { NRPoint2 result ; result.x = lhs.x+rhs.x; result.y = lhs.y+rhs.y; return result; } NRPoint2 operator - (NRPoint2& lhs,NRVector2& rhs) { return lhs + ((-1)*rhs); } NRVector2 operator - (NRPoint2& lhs,NRPoint2& rhs) { NRVector2 result ; result.x = lhs.x-rhs.x; result.y = lhs.y-rhs.y; return result; } NRPoint2 operator* (NRPoint2& lhs,float rhs) { NRPoint2 result ; result.x=lhs.x * rhs ; result.y = lhs.y * rhs ; return result; } NRPoint2 operator* (float lhs,NRPoint2& rhs) { return rhs* lhs; } ostream& operator << (ostream& outputStream,NRPoint2&rhs) { outputStream<<"("<<rhs.x<<","<<rhs.y<<")"; return outputStream ; } bool operator == (NRPoint2& lhs,NRPoint2& rhs) { return IsEqual(lhs.x,rhs.x) && IsEqual(lhs.y,rhs.y); } //implementation for class NRVector2 NRVector2::NRVector2() { this->x=0; this->y=0; } NRVector2::NRVector2(float x, float y) { this->x=x; this->y=y; } void NRVector2::set(NRVector2&p) { this->x=p.x; this->y=p.y; } void NRVector2::set(float x, float y) { this->x= x ; this->y=y ; } NRVector2 NRVector2::operator /(float rhs) { NRVector2 result ; result.x = this->x / rhs ; result.y = this->y / rhs ; return result; } NRVector2 operator +(NRVector2&lhs,NRVector2&rhs) { NRVector2 result ; result.x = lhs.x + rhs.x ; result.y = lhs.y + rhs.y ; return result; } NRVector2 operator - (NRVector2&lhs,NRVector2& rhs) { NRVector2 result ; result.x = lhs.x - rhs.x ; result.y = lhs.y - rhs.y ; return result; } float operator *(NRVector2&lhs,NRVector2& rhs) { float result ; result = lhs.x * rhs.x + lhs.y * rhs.y ; return result; } NRVector2 operator *(NRVector2&lhs,float rhs) { NRVector2 result ; result.x = lhs.x*rhs ; result.y = lhs.y*rhs ; return result; } NRVector2 operator *(float lhs,NRVector2& rhs) { return rhs*lhs; } float NRVector2::GetLength() { return sqrt(this->x*this->x+this->y*this->y); } void NRVector2::Normalized() { float length = GetLength(); this->x = x / length ; this->y = y / length ; } NRVector2 NRVector2::GetNormalVector() { NRVector2 result ; result.x = -1*this->y; result.y = this->x ; return result ; } ostream& operator << (ostream& outputStream,NRVector2&rhs) { outputStream<<"("<<rhs.x<<","<<rhs.y<<")"; return outputStream ; } bool operator == (NRVector2& lhs,NRVector2& rhs) { return IsEqual(lhs.x,rhs.x) && IsEqual(lhs.y,rhs.y); } //implementation for NRVector3 NRVector3::NRVector3() { this->x= this->y=this->z=0; } void NRVector3::set(NRVector3&p) { this->x = p.x ; this->y =p.y ; this->z =p.z; } void NRVector3::set(float x, float y, float z) { this->x=x; this->y=y; this->z=z; } float NRVector3::GetLength() { return sqrt(this->x*this->x+this->y*this->y+this->z*this->z); } void NRVector3::Normalized() { float length=GetLength(); this->x=x/length; this->y=y/length; this->z=z/length; } NRVector3 NRVector3::GetNormalVector() { throw "NotImplemented Implementation."; } NRVector3 operator +(NRVector3&lhs,NRVector3&rhs) { NRVector3 result ; result.x = lhs.x + rhs.x ; result.y = lhs.y + rhs.y ; result.z = lhs.z + rhs.z ; return result; } NRVector3 operator - (NRVector3&lhs,NRVector3& rhs) { NRVector3 result ; result.x = lhs.x - rhs.x ; result.y = lhs.y - rhs.y ; result.z = lhs.z - rhs.z ; return result; } float operator *(NRVector3&lhs,NRVector3& rhs) { float result ; result = lhs.x * rhs.x +lhs.y * rhs.y + lhs.z * rhs.z ; return result; } NRVector3 operator *(NRVector3&lhs,float rhs) { NRVector3 result ; result.x = lhs.x * rhs ; result.y = lhs.y * rhs ; result.z = lhs.z * rhs ; return result; } NRVector3 NRVector3::operator /(float rhs) { NRVector3 result ; result.x = this->x / rhs ; result.y = this->y / rhs ; result.z = this->z / rhs ; return result ; } ostream& operator << (ostream& outputStream,NRVector3& rhs) { cout <<"("<< rhs.x<<","<<rhs.y<<","<<rhs.z<<")"; return outputStream; } bool operator == (NRVector3& lhs,NRVector3& rhs) { return IsEqual(lhs.x,rhs.x) && IsEqual(lhs.y,rhs.y) && IsEqual(lhs.z,rhs.z); } //implementation for NRPoint3 NRPoint3::NRPoint3() { this->x = this->y = this->z = 0 ; } void NRPoint3::set(NRPoint3& p) { this->x = p.x ; this->y = p.y ; this->z = p.z ; } void NRPoint3::set(float x, float y, float z) { this->x = x ; this->y = y ; this->z = z ; } NRPoint3 NRPoint3::operator /(float rhs) { NRPoint3 result ; result.x = this->x / rhs; result.y = this->y / rhs ; result.z = this->z / rhs ; return result ; } NRPoint3 operator +(NRPoint3& lhs,NRVector3& rhs) { NRPoint3 result ; result.x = lhs.x + rhs.x ; result.y = lhs.y + rhs.y ; result.z = lhs.z + rhs.z ; return result ; } NRVector3 operator - (NRPoint3& lhs,NRPoint3& rhs) { NRVector3 result ; result.x = lhs.x - rhs.x ; result.y = lhs.y - rhs.y ; result.z = lhs.z - rhs.z ; return result ; } NRPoint3 operator* (NRPoint3& lhs,float rhs) { NRPoint3 result ; result.x = lhs.x * rhs ; result.y = lhs.y * rhs; result.z = lhs.z * rhs ; return result ; } ostream& operator << (ostream& outputStream,NRPoint3& rhs) { cout <<"("<< rhs.x<<","<<rhs.y<<","<<rhs.z<<")"; return outputStream; } //友元等号操作符 bool operator == (NRPoint3& lhs,NRPoint3& rhs) { return IsEqual(lhs.x,rhs.x) && IsEqual(lhs.y,rhs.y) && IsEqual(lhs.z,rhs.z); } /////////////////////////////////////线段/射线/直线/////////////////////////////////////// //线段类 NRLine2Segment::NRLine2Segment() { first.x=first.y=0; second.x=second.y=0; } NRLine2Segment::NRLine2Segment(NRPoint2 first,NRPoint2 second) { this->first = first; this->second = second; } NRLine2Segment::NRLine2Segment(NRLine2Segment& line2) { first = line2.first; second = line2.second; } NRVector2 NRLine2Segment::norm() { NRVector2 c = second - first ; NRVector2 normalVector = c.GetNormalVector(); return normalVector; } //点法向量表示的直线类 NRLine2::NRLine2() { pt.x=pt.y=0; norm.x=0; norm.y=0; } NRLine2::NRLine2(NRPoint2 pt,NRVector2 norm) { this->pt=pt; this->norm=norm; } NRLine2::NRLine2(const NRLine2& line2) { pt=line2.pt; norm = line2.norm; } ///////////////////////////////////////////////凸多边形//////////////////////////////////////////////////// //点法向量表示的多边形 int NRLine2List::num() { return line.size(); } void NRLine2List::push_back(NRLine2 newLine) { line.push_back(newLine); } NRLine2& NRLine2List::operator[](int index) { if ((unsigned int)index >= line.size()) //注意size是unsigned int { throw "Out of range in NRLine2List"; } return line[index]; } //多边形向量数组 int NRPolygonList::num() { return polygons.size(); } void NRPolygonList::push_back(NRLine2List newPolygon) { polygons.push_back(newPolygon); } NRLine2List& NRPolygonList::operator[](int index) { if ((unsigned int)index >= polygons.size()) //注意size是unsigned int { throw "Out of range in NRLine2List"; } return polygons[index]; } ////////////////////////////////齐次坐标////////////////////////////////////////// NRHomogeneousPoint2D::NRHomogeneousPoint2D() { x=y=0; ho=1; // 表示一个点 }; NRHomogeneousPoint3D::NRHomogeneousPoint3D() { x=y=z=0; ho=1; //表示一个点 }; NRHomogeneousVector2D::NRHomogeneousVector2D() { x=y=0; ho=0; //表示一个向量 }; NRHomogeneousVector3D::NRHomogeneousVector3D() { x=y=z=0; ho=0;//表示一个向量 }; //////////////////////////////////仿射变换/////////////////////////////////////// NRMatrix2D::NRMatrix2D() { Identity(); } float* NRMatrix2D::operator [](int i) { return matrixArray[i]; } void NRMatrix2D::Identity() { for (int i=0;i<3;i++) { for (int j=0;j<3;j++) { this->matrixArray[i][j]=(i==j?(float)1.0:(float)0.0); } } } NRMatrix2D NRMatrix2D::operator *(NRMatrix2D rhs) { NRMatrix2D result ; for (int i=0;i<3;i++) { for (int j=0;j<3;j++) { result[i][j] = matrixArray[i][0]*rhs.matrixArray[0][j]+matrixArray[i][1]*rhs.matrixArray[1][j]+matrixArray[i][2]*rhs.matrixArray[2][j]; } } return result ; } NRHomogeneousPoint2D NRMatrix2D::operator*( NRHomogeneousPoint2D rhs) { NRHomogeneousPoint2D result ; result.x = matrixArray[0][0]*rhs.x + matrixArray[0][1]*rhs.y + matrixArray[0][2]*rhs.ho ; result.y = matrixArray[1][0]*rhs.x + matrixArray[1][1]*rhs.y + matrixArray[1][2]*rhs.ho ; result.ho = matrixArray[2][0]*rhs.x + matrixArray[2][1]*rhs.y + matrixArray[2][2]*rhs.ho ; return result ; } //NRTranslateTransform2D NRTranslateTransform2D::NRTranslateTransform2D() { } void NRTranslateTransform2D::Translate(float x, float y) { translateMatrix[0][2] += x; translateMatrix[1][2] += y; } void NRTranslateTransform2D::Identity() { translateMatrix.Identity(); } NRHomogeneousPoint2D NRTranslateTransform2D::operator*( NRHomogeneousPoint2D rhs) { return translateMatrix * rhs ; } NRTranslateTransform2D NRTranslateTransform2D::GetInverseTransform2D() { NRTranslateTransform2D result ; result.translateMatrix[0][2] = - translateMatrix[0][2] ; result.translateMatrix[1][2] = - translateMatrix[1][2] ; return result; } //NRScaleTransform2D NRScaleTransform2D::NRScaleTransform2D() { } void NRScaleTransform2D::Scale(float x, float y) { NRMatrix2D lhs ; lhs.matrixArray[0][0] = x ; lhs.matrixArray[0][2] = -x * center.x + center.x ; lhs.matrixArray[1][1] = y ; lhs.matrixArray[1][2] = -y*center.y + center.y ; scaleMatrix = lhs* scaleMatrix ; } void NRScaleTransform2D::Identity() { scaleMatrix.Identity(); } NRHomogeneousPoint2D NRScaleTransform2D::operator*( NRHomogeneousPoint2D rhs) { return scaleMatrix * rhs ; } NRScaleTransform2D NRScaleTransform2D::GetInverseTransform2D() { NRScaleTransform2D result ; if (scaleMatrix[0][0] != 0 && scaleMatrix[1][1] != 0) { result.scaleMatrix[0][0] =(float)1.0/scaleMatrix[0][0]; result.scaleMatrix[1][1] = (float) 1.0 / scaleMatrix[1][1] ; } return result; } //NRRotateTransform2d NRRotateTransform2D::NRRotateTransform2D() { } void NRRotateTransform2D::Identity() { rotateMatrix.Identity(); } void NRRotateTransform2D::Rotate(float angle) { // counterclockwise NRMatrix2D lhs ; lhs.Identity(); float costheta= cos(angle); float sintheta = sin(angle); float dx = -costheta*center.x + sintheta*center.y + center.x ; float dy = -sintheta * center.x - costheta * center.y + center.y ; lhs.matrixArray[0][0] = costheta ; lhs.matrixArray[0][1] = -sintheta ; lhs.matrixArray[1][0] = sintheta ; lhs.matrixArray[1][1] = costheta ; lhs.matrixArray[0][2] = dx ; lhs.matrixArray[1][2] = dy ; rotateMatrix = lhs * rotateMatrix ; } NRHomogeneousPoint2D NRRotateTransform2D::operator*( NRHomogeneousPoint2D rhs) { return rotateMatrix * rhs ; } NRRotateTransform2D NRRotateTransform2D::GetInverseTransform2D() { NRRotateTransform2D result ; result.rotateMatrix[0][0] = rotateMatrix[0][0]; result.rotateMatrix[0][1] = - rotateMatrix[0][1] ; result.rotateMatrix[1][0] = - rotateMatrix[1][0] ; result.rotateMatrix[1][1] = rotateMatrix[1][1] ; return result; } //class for NRClipTransform2D NRClipTransform2D::NRClipTransform2D() { } void NRClipTransform2D::Clip(float h, float g) { NRMatrix2D lhs ; lhs.matrixArray[0][1] = h ; lhs.matrixArray[0][2] = -h*center.y; lhs.matrixArray[1][0] = g; lhs.matrixArray[1][2] = -g * center.x; clipMatrix = lhs * clipMatrix ; } void NRClipTransform2D::Identity() { clipMatrix.Identity(); } NRHomogeneousPoint2D NRClipTransform2D::operator*( NRHomogeneousPoint2D rhs) { return clipMatrix* rhs ; } NRClipTransform2D NRClipTransform2D::GetInverseTransform2D() { NRClipTransform2D result ; result.clipMatrix[0][1] = -clipMatrix[0][1] ; result.clipMatrix[1][0] = -clipMatrix[1][0]; return result; } //class NRCompositeTransform NRCompositeTransform2D::NRCompositeTransform2D() { } void NRCompositeTransform2D::AddTransform(NRTranslateTransform2D transLateTransform) { compositeMatrix = transLateTransform.translateMatrix *compositeMatrix ; } void NRCompositeTransform2D::AddTransform(NRScaleTransform2D scaleTransform) { compositeMatrix = scaleTransform.scaleMatrix * compositeMatrix ; } void NRCompositeTransform2D::AddTransform(NRRotateTransform2D rotateTransform) { compositeMatrix = rotateTransform.rotateMatrix * compositeMatrix ; } void NRCompositeTransform2D::AddTransform(NRClipTransform2D clipTransform) { compositeMatrix = clipTransform.clipMatrix * compositeMatrix ; } void NRCompositeTransform2D::Translate(float x, float y) { NRMatrix2D lhs ; lhs.matrixArray[0][2] = x ; lhs.matrixArray[1][2] = y ; compositeMatrix = lhs * compositeMatrix ; } void NRCompositeTransform2D::Scale(float x, float y) { NRMatrix2D lhs ; lhs.matrixArray[0][0] = x ; lhs.matrixArray[0][2] = -x * center.x + center.x ; lhs.matrixArray[1][1] = y ; lhs.matrixArray[1][2] = -y*center.y + center.y ; compositeMatrix = lhs* compositeMatrix; } void NRCompositeTransform2D::Rotate(float angle) { // counterclockwise NRMatrix2D lhs ; lhs.Identity(); float costheta= cos(angle); float sintheta = sin(angle); float dx = -costheta*center.x + sintheta*center.y + center.x ; float dy = -sintheta * center.x - costheta * center.y + center.y ; lhs.matrixArray[0][0] = costheta ; lhs.matrixArray[0][1] = -sintheta ; lhs.matrixArray[1][0] = sintheta ; lhs.matrixArray[1][1] = costheta ; lhs.matrixArray[0][2] = dx ; lhs.matrixArray[1][2] = dy ; compositeMatrix = lhs * compositeMatrix ; } void NRCompositeTransform2D::Clip(float h, float g) { NRMatrix2D lhs ; lhs.matrixArray[0][1] = h ; lhs.matrixArray[0][2] = -h*center.y; lhs.matrixArray[1][0] = g; lhs.matrixArray[1][2] = -g * center.x; compositeMatrix = lhs * compositeMatrix ; } void NRCompositeTransform2D::Identity() { compositeMatrix.Identity(); } NRHomogeneousPoint2D NRCompositeTransform2D::operator*( NRHomogeneousPoint2D rhs) { return compositeMatrix * rhs ; } NRCompositeTransform2D NRCompositeTransform2D::GetInverseTransform2D() { throw "Not Implemented Method"; }

 

 

 

 

看看Demo吧：我在前一篇的基础上修改的；

主要增加了center的点：

 

//TransformOpenGL.cpp //rorger, 2011 #include "nrglbase.h" #include "nrdraw.h" #include "nrmath.h" #include "glut.h" #include "math.h" void drawRect(NRHomogeneousPoint2D rect[]) { glBegin(GL_LINE_LOOP); for (int i=0;i<4;i++) { glVertex2f(rect[i].x,rect[i].y); } glEnd(); } void doTransform2D(NRHomogeneousPoint2D rect[],NRTranslateTransform2D transform) { for (int i=0;i<4;i++) { rect[i]=transform*rect[i]; } } void doTransform2D(NRHomogeneousPoint2D rect[],NRScaleTransform2D transform) { for (int i=0;i<4;i++) { rect[i]=transform*rect[i]; } } void doTransform2D(NRHomogeneousPoint2D rect[],NRRotateTransform2D transform) { for (int i=0;i<4;i++) { rect[i]=transform*rect[i]; } } void doTransform2D(NRHomogeneousPoint2D rect[],NRClipTransform2D transform) { for (int i=0;i<4;i++) { rect[i]=transform*rect[i]; } } void doTransform2D(NRHomogeneousPoint2D rect[],NRCompositeTransform2D transform) { for (int i=0;i<4;i++) { rect[i]=transform*rect[i]; } } void initRect(NRHomogeneousPoint2D rect[]) { rect[0].x=0; rect[0].y=0; rect[1].x=4; rect[1].y=0; rect[2].x=4; rect[2].y=3; rect[3].x=0; rect[3].y=3; } void testTransform() { double pi = acos(-1.0); NRHomogeneousPoint2D rect[4] ; initRect(rect); drawRect(rect); //test translate NRTranslateTransform2D translateTransform; translateTransform.Translate(5,4); doTransform2D(rect,translateTransform); glColor3f(0.5,0.5,0.3); drawRect(rect); //testScale initRect(rect); NRScaleTransform2D scaleTransform ; scaleTransform.center.x = 2 ; scaleTransform.center.y = 1.5 ; scaleTransform.Scale(0.5,0.4); doTransform2D(rect,scaleTransform); glColor3f(1.0,0.5,0.5); drawRect(rect); //testRotate initRect(rect); NRRotateTransform2D rotateTransform ; rotateTransform.center.x = 2 ; rotateTransform.center.y = 1.5 ; rotateTransform.Rotate(pi/3); //为什么看起来是平行四边形? doTransform2D(rect,rotateTransform); glColor3f(0.5,0.2,0.7); drawRect(rect); //testClip initRect(rect); NRClipTransform2D clipTransform ; clipTransform.center.x = 2 ; clipTransform.center.y = 1.5 ; clipTransform.Clip(0.0,0.3); //在x方向上剪切 doTransform2D(rect,clipTransform); glColor3f(0.2,0.5,0.7); drawRect(rect); //testComposite NRCompositeTransform2D compositeTransform ; compositeTransform.center.x = 2 ; compositeTransform.center.y = 1.5 ; compositeTransform.AddTransform(rotateTransform); compositeTransform.AddTransform(scaleTransform); initRect(rect); doTransform2D(rect,compositeTransform); glColor3f(0.3,0.5,0.3); drawRect(rect); } void myDisplay(void) { glClear(GL_COLOR_BUFFER_BIT); NRDrawCoordinate(); glColor3f(0.0f, 1.0f, 0.0f); testTransform(); glFlush(); } void myInit(void) { glClearColor(0.0, 0.0, 0.0, 0.0); glColor3f(0.0f, 1.0f, 0.0f); glPointSize(4.0); glMatrixMode(GL_PROJECTION); glLoadIdentity(); gluOrtho2D(-5, 15, -5, 15); glLineWidth(2.0); } int main(int argc,char** argv) { glutInit(&argc, argv); glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB); glutInitWindowSize(640,480); glutInitWindowPosition(100,150); glutCreateWindow("LineInterSectoin"); glutDisplayFunc(myDisplay); myInit( ); glutMainLoop( ); }

 

 

 

看看效果吧：虽然有些乱，但是只要认真分析，总还是懂的：