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
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。
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:
#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;
};
#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;
}
#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;
};
#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;
}
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: