说明：本实验代码在vs2022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 once
class 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;
				}
				else
					d += 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;
				}
				else
					d -= 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;
				}
				else
					d -= 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;
				}
				else
					d -= 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 3.14159
CTrans2D::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DC
	CBitmap NewBitmap, * pOldBitmap; // 内存中承载的临时位图
	MemDC.CreateCompatibleDC(pDC); // 建立与屏幕pDC兼容的MemDC
	NewBitmap.CreateCompatibleBitmap(pDC, rect.Width(), rect.Height()); // 创建兼容位图
	pOldBitmap = MemDC.SelectObject(&NewBitmap); // 将兼容位图选入MemDC
	MemDC.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：