说明：本实验代码在vs下可正常运行，本实验适配于计算机图形学新版（VC++ MFC ）第二版

1.实验目的

1）掌握3*3矩阵乘法运算的编程实现

2）掌握平移，比例，旋转三种基本二维几何变换矩阵生成

3）掌握相对于任意参考点的二维复合变换矩阵生成

2.实验要求

1)设计实现二维图形变换类，具有平移、比例、旋转二维几何变换功能，以及相对于任意参考点的二维复合变换功能；

2)将2.2节直线类所绘制的如图2-3所示的菱形线框，绕最上端A点匀速旋转，并要求相对于A点来回缩放。

3)使用双缓冲机制进行图形绘制，避免运动闪烁，所有图形先绘制到用户自定的DC，绘制完成后再统一拷贝到屏幕DC。

3.实验步骤

本次实是对上一次直线扫描转换的代码进行增改，无需新建工程。

代码实现：

1)Line.h

#pragma onceclass CP2{public:CP2();virtual~CP2();CP2(double, double);public:double x;double y;double w;};class CLine{public:CLine();virtual~CLine();void SetLineColor(COLORREF);void MoveTo(CP2);void MoveTo(double, double);void LineTo(CP2, CDC*);void LineTo(double, double, CDC*);public:CP2 P0;CP2 P1;COLORREF clr;};

2)Line.cpp

#include"pch.h"#include"Line.h"#include"math.h"#define Round(d) int(floor(d+0.5))CP2::CP2(){x = 0.0;y = 0.0;w = 1.0;};CP2::~CP2(){}CP2::CP2(double x, double y){this->x = x;this->y = y;this->w = 1;};CLine::CLine(){}CLine::~CLine(){}void CLine::SetLineColor(COLORREF color){clr = color;}void CLine::MoveTo(CP2 p0){P0 = p0;}void CLine::MoveTo(double x, double y){P0.x = x;P0.y = y;}void CLine::LineTo(double x, double y, CDC* pDC){CP2 p;p.x = x;p.y = y;LineTo(p, pDC);}void CLine::LineTo(CP2 p1, CDC* pDC){P1 = p1;CP2 p, t;if (fabs(P0.x - P1.x) < 1e-6){if (P0.y > P1.y){t = P0; P0 = P1; P1 = t;}for (p = P0; p.y < P1.y; p.y++){pDC->SetPixelV(Round(p.x), Round(p.y), clr);}}else{double k, d;k = (P1.y - P0.y) / (P1.x - P0.x);if (k > 1.0){if (P0.y > P1.y){t = P0; P0 = P1; P1 = t;}d = 1 - 0.5 * k;for (p = P0; p.y < P1.y; p.y++){pDC->SetPixelV(Round(p.x), Round(p.y), clr);if (d >= 0){p.x++;d += 1 - k;}elsed += 1;}}if (0.0 <= k && k <= 1.0){if (P0.x > P1.x){t = P0; P0 = P1; P1 = t;}d = 0.5 - k;for (p = P0; p.x < P1.x; p.x++){pDC->SetPixelV(Round(p.x), Round(p.y), clr);if (d < 0){p.y++;d += 1 - k;}elsed -= k;}}if (k >= -1.0 && k < 0.0){if (P0.x > P1.x){t = P0; P0 = P1; P1 = t;}d = -0.5 - k;for (p = P0; p.x < P1.x; p.x++){pDC->SetPixelV(Round(p.x), Round(p.y), clr);if (d > 0){p.y--;d -= 1 + k;}elsed -= k;}}if (k < -1.0){if (P0.y > P1.y){t = P0; P0 = P1; P1 = t;}d = -1 - 0.5 * k;for (p = P0; p.y > P1.y; p.y--){pDC->SetPixelV(Round(p.x), Round(p.y), clr);if (d < 0){p.x++;d -= 1 + k;}elsed -= 1;}}}P0 = p1;}

3)新建头文件CTrans2D.h

#pragma once#include "Line.h"class CTrans2D // 二维几何转换{public:CTrans2D();virtual~CTrans2D();void SetPoints(CP2*, int);void Identity();void Translate(double, double); // 平移变换矩阵void Rotate(double); // 旋转变换矩阵void Scale(double, double); // 比例变换矩阵void RotatePoint(double, CP2); // 相对于任意点的旋转变换矩阵void ScalePoint(double, double, CP2); // 相对于任意点的比例变换矩阵protected:void MultiMatrix(); // 矩阵相乘public:double m_aT[3][3];CP2* m_pPoints;int m_iNum;};

4)新建源文件CTrans2D.cpp

#include "pch.h"#include"CTrans2D.h"#include"math.h"#define PI 3.14159CTrans2D::CTrans2D(){}CTrans2D::~CTrans2D(){}void CTrans2D::SetPoints(CP2 *p, int n) {m_pPoints = p;m_iNum = n;}void CTrans2D::Identity()//单位矩阵{m_aT[0][0] = 1.0; m_aT[0][1] = 0.0; m_aT[0][2] = 0.0;m_aT[1][0] = 0.0; m_aT[1][1] = 1.0; m_aT[1][2] = 0.0;m_aT[2][0] = 0.0; m_aT[2][1] = 0.0; m_aT[2][2] = 1.0;}void CTrans2D::Translate(double tx, double ty)//平移变换矩阵{Identity();m_aT[2][0] = tx;m_aT[2][1] = ty;MultiMatrix();}void CTrans2D::Rotate(double beta)//旋转变换矩阵{Identity();double rad = beta*PI/180;m_aT[0][0] = cos(rad); m_aT[0][1] = sin(rad);m_aT[1][0] = -sin(rad); m_aT[1][1] = cos(rad);MultiMatrix();}void CTrans2D::Scale(double sx, double sy)//比例变换矩阵{Identity();m_aT[0][0] = sx;m_aT[1][1] = sy;MultiMatrix();}void CTrans2D::RotatePoint(double beta, CP2 p)//相对于任意点的旋转变换矩阵{Translate(-p.x, -p.y);Rotate(beta);Translate(p.x, p.y);}void CTrans2D::ScalePoint(double sx, double sy, CP2 p)//相对于任意点的整体比例变换矩阵{Translate(-p.x, -p.y);Scale(sx, sy);Translate(p.x, p.y);//baotu}void CTrans2D::MultiMatrix()//矩阵相乘{CP2 * PNew = new CP2[m_iNum];for (int i = 0; i < m_iNum; i++) {PNew[i] = m_pPoints[i];}for (int j = 0; j < m_iNum; j++){m_pPoints[j].x = PNew[j].x*m_aT[0][0] + PNew[j].y*m_aT[1][0] + PNew[j].w*m_aT[2][0];m_pPoints[j].y = PNew[j].x*m_aT[0][1] + PNew[j].y*m_aT[1][1] + PNew[j].w*m_aT[2][1];m_pPoints[j].w = PNew[j].x*m_aT[0][2] + PNew[j].y*m_aT[1][2] + PNew[j].w*m_aT[2][2];}delete []PNew;}

5）TestView.cpp

只对TestView.cpp中的绘制函数进行修改，其他代码不变

需要导入头文件

#include "CTrans2D.h"void CTestView::OnDraw(CDC* pDC){CTestDoc* pDoc = GetDocument();ASSERT_VALID(pDoc);if (!pDoc)return;CRect rect;GetClientRect(&rect);pDC->SetMapMode(MM_ANISOTROPIC);pDC->SetWindowExt(rect.Width(), rect.Height());pDC->SetViewportExt(rect.Width(), -rect.Height());pDC->SetViewportOrg(rect.Width() / 2, rect.Height() / 2);/*rect.OffsetRect(-rect.Width() / 2, -rect.Height() / 2);*/CDC MemDC; // 内存DCCBitmap NewBitmap, * pOldBitmap; // 内存中承载的临时位图MemDC.CreateCompatibleDC(pDC); // 建立与屏幕pDC兼容的MemDCNewBitmap.CreateCompatibleBitmap(pDC, rect.Width(), rect.Height()); // 创建兼容位图pOldBitmap = MemDC.SelectObject(&NewBitmap); // 将兼容位图选入MemDCMemDC.FillSolidRect(rect, pDC->GetBkColor()); // 按原来背景填充客户区，否则未黑色MemDC.SetMapMode(MM_ANISOTROPIC); // MemDC自定义坐标系与pDC相同MemDC.SetWindowExt(rect.Width(), rect.Height());MemDC.SetViewportExt(rect.Width(), -rect.Height());MemDC.SetViewportOrg(rect.Width() / 2, rect.Height() / 2);CLine* line = new CLine;line->SetLineColor(RGB(0, 0, 0));line->MoveTo(CP2(-rect.Width() / 2, 0));line->LineTo(CP2(rect.Width() / 2, 0), &MemDC);line->MoveTo(CP2(0, -rect.Height() / 2));line->LineTo(CP2(0, rect.Height() / 2), &MemDC);//绘制动态旋转int a = 200;CP2 points[4];points[0].x = 0, points[0].y = a;points[1].x = a, points[1].y = 0;points[2].x = 0, points[2].y = -a;points[3].x = -a, points[3].y = 0;//===================================================CP2 A(0, a);CTrans2D tans;tans.SetPoints(points, 4);static float s = 1.0;static float step = 0.01;if (s >= 2.0 || s <= 0.5)step = -step;s += step;tans.ScalePoint(s, s, A);//匀速逆时针旋转static float theta = 0.0;theta += 1.0;if (theta >= 360.0)theta = 0.0;tans.RotatePoint(theta, A);//====================================================//CP2 B(a, 0);//CP2 C(0, -a);//CP2 D(-a, 0);line->SetLineColor(RGB(255, 0, 0));//红色line->MoveTo(points[0]);line->LineTo(points[1], &MemDC);line->SetLineColor(RGB(0, 255, 0));//绿色line->LineTo(points[2], &MemDC);line->SetLineColor(RGB(0, 0, 255));//蓝色line->LineTo(points[3], &MemDC);line->SetLineColor(RGB(255, 255, 0));//黄色line->LineTo(points[0], &MemDC);delete line;//====================================================pDC->BitBlt(-rect.Width() / 2, -rect.Height() / 2, rect.Width(), rect.Height(), &MemDC, -rect.Width() / 2, -rect.Height() / 2, SRCCOPY);MemDC.SelectObject(pOldBitmap);NewBitmap.DeleteObject();Invalidate(FALSE);}

实验结果：