使用MFC的CDC类绘制二维坐标系及正余弦函数 / 源码
使用MFC的CDC类绘制三维坐标系及球面函数 / 源码
概述本文使用MFC的CDC类绘制三维坐标系及球面函数。首先计算推导出三维坐标在二维平面显示的坐标变换方程（使用斜二测视图），使用球面的参数方程，然后定义图形缩放比例规模、坐标轴位移，变换坐标系和规模等，最后绘制坐标轴及球面函数。
如果对绘制二维坐标系还不太熟悉可以先看上面系列链接的：使用MFC的CDC类绘制二维坐标系及正余弦函数，本文对二维绘制及绘制函数部分不再赘述。因为二维坐标系的博文已经分模块讲解地比较清楚了，而与三维坐标系的基本思路相同，所以本文大部分直接使用注释讲解。
三维转二维的推导上图可知，只要使用Transform3Dto2D()函数，即可方便的把三维坐标转化为二维坐标（斜二测视图）。
球面参数方程在三维空间直角坐标系中，以原点为球心、半径为 r 的球面的方程为 x^2 + y^2 + z^2 = r^2，其参数方程为
新建项目Visual Studio- 新建项目 - MFC应用程序 - 命名为GraphicsExercise3D - 确定 - 下一步 - 应用程序类型选择单个文档 - 完成
GraphicsExercise3DView.h在GraphicsExercise3DView.h添加以下内容
// 操作public:void SetScale(int scale);void SetTransformOrigin(float transformOriginX, float transformOriginY);void SetPlotSphere(float radius, float stepPhi, float stepTheta); void SetSlantRadian(float slant);float TransformScale(float num);float TransformOriginX(float x);float TransformOriginY(float y);float TransformOriginScaleX(float x);float TransformOriginScaleY(float y);void Transform3Dto2D(float &x, float &y, float z);private: int scale; float radius, stepPhi, stepTheta, slant, transformOriginX, transformOriginY; GraphicsExercise3DView.cpp引入数学函数库
#include <math.h>定义π
#ifndef PI#define PI 3.14159#endif // !PI在构造函数初始化
CGraphicsExercise3DView::CGraphicsExercise3DView(){// TODO: 在此处添加构造代码// 设置斜二测视图倾斜角度（弧度制）SetSlantRadian(PI / 4);// 设置规模比例SetScale(70);// 设置坐标系在x、y方向的位移（不改变规模情况下，即移动像素）SetTransformOrigin(300, 350);// 设置球面半径radius、取样步长stepPhi、stepThetaSetPlotSphere(2.0, 0.01, 0.1);}设置初始化参数的Set函数
// 设置规模void CGraphicsExercise3DView::SetScale(int scale){this->scale = scale;}// 设置坐标系原点在x、y方向的位移（不改变规模情况下，即移动像素）void CGraphicsExercise3DView::SetTransformOrigin(float transformOriginX, float transformOriginY){this->transformOriginX = transformOriginX;this->transformOriginY = transformOriginY;}// 设置球面半径radius、取样步长stepPhi、stepThetavoid CGraphicsExercise3DView::SetPlotSphere(float radius, float stepPhi, float stepTheta){this->radius = radius;this->stepPhi = stepPhi;this->stepTheta = stepTheta;}// 设置斜二测视图的倾斜角（单位弧度）void CGraphicsExercise3DView::SetSlantRadian(float slant){this->slant = slant;}坐标及规模变换
// 变换规模float CGraphicsExercise3DView::TransformScale(float num){return num * scale;}// 坐标系X轴方向位移float CGraphicsExercise3DView::TransformOriginX(float x){return x + transformOriginX / scale;}// 坐标系y轴方向位移float CGraphicsExercise3DView::TransformOriginY(float y){return y - transformOriginY / scale;}// 变换坐标系X和规模float CGraphicsExercise3DView::TransformOriginScaleX(float x){return TransformScale(TransformOriginX(x));}// 变换坐标系Y和规模float CGraphicsExercise3DView::TransformOriginScaleY(float y){return -TransformScale(TransformOriginY(y));}三维坐标转化为二维坐标
// 使用斜二测视图，把三维坐标点转化为二维平面上的点void CGraphicsExercise3DView::Transform3Dto2D(float &x, float &y, float z){x = x - (z * cos(slant)) / 2;y = y - (z * sin(slant)) / 2;}绘制坐标轴及函数图形
// CGraphicsExercise2View 绘制void CGraphicsExercise3DView::OnDraw(CDC* pDC){CGraphicsExercise3DDoc* pDoc = GetDocument();ASSERT_VALID(pDoc);if (!pDoc)return;// TODO: 在此处为本机数据添加绘制代码float x, y, z;// -------------------- 绘制坐标系 -------------------------// 坐标x轴pDC->MoveTo(TransformOriginScaleX(0), TransformOriginScaleY(0));pDC->LineTo(TransformOriginScaleX(radius + 2), TransformOriginScaleY(0));// 坐标y轴pDC->MoveTo(TransformOriginScaleX(0), TransformOriginScaleY(0));pDC->LineTo(TransformOriginScaleX(0), TransformOriginScaleY(radius + 2));// 坐标z轴x = 0, y = 0;Transform3Dto2D(x, y, radius + 5);pDC->MoveTo(TransformOriginScaleX(0), TransformOriginScaleY(0));pDC->LineTo(TransformOriginScaleX(x), TransformOriginScaleY(y));// 坐标x轴的箭头pDC->MoveTo(TransformOriginScaleX(radius + 1.8), TransformOriginScaleY(0.2));pDC->LineTo(TransformOriginScaleX(radius + 2), TransformOriginScaleY(0));pDC->LineTo(TransformOriginScaleX(radius + 1.8), TransformOriginScaleY(-0.2));// 坐标y轴的箭头pDC->MoveTo(TransformOriginScaleX(-0.2), TransformOriginScaleY(radius + 1.8));pDC->LineTo(TransformOriginScaleX(0), TransformOriginScaleY(radius + 2));pDC->LineTo(TransformOriginScaleX(0.2), TransformOriginScaleY(radius + 1.8));// 坐标z轴的箭头x = 0, y = 0.2;Transform3Dto2D(x, y, radius + 5 - 0.2);pDC->MoveTo(TransformOriginScaleX(x), TransformOriginScaleY(y));x = 0, y = 0;Transform3Dto2D(x, y, radius + 5);pDC->LineTo(TransformOriginScaleX(x), TransformOriginScaleY(y));x = 0.2, y = 0;Transform3Dto2D(x, y, radius + 5 - 0.2);pDC->LineTo(TransformOriginScaleX(x), TransformOriginScaleY(y));// -------------------- 绘制刻度线 -------------------------// 绘制x轴刻度线for (float scaleX = 0.2; scaleX < radius + 1; scaleX += 0.2){pDC->MoveTo((int)TransformOriginScaleX(scaleX), (int)TransformOriginScaleY(0));pDC->LineTo((int)TransformOriginScaleX(scaleX), (int)TransformOriginScaleY(0.1));}// 绘制y轴刻度线for (float scaleY = 0.2; scaleY <= radius + 1; scaleY += 0.2){pDC->MoveTo((int)TransformOriginScaleX(0), (int)TransformOriginScaleY(scaleY));pDC->LineTo((int)TransformOriginScaleX(0.1), (int)TransformOriginScaleY(scaleY));}// 绘制z轴刻度线for (float x = 0, y = 0, scaleZ = 0.2; scaleZ <= radius + 4; scaleZ += 0.2, x = 0, y = 0){Transform3Dto2D(x, y, scaleZ);pDC->MoveTo((int)TransformOriginScaleX(x), (int)TransformOriginScaleY(y));pDC->LineTo((int)TransformOriginScaleX(x + 0.1), (int)TransformOriginScaleY(y));}// -------------------- 绘制文字 -------------------------// 绘制x轴的xpDC->TextOutW(TransformOriginScaleX(radius + 1.6), TransformOriginScaleY(-0.2), CString("x"));// 绘制y轴的ypDC->TextOutW(TransformOriginScaleX(-0.2), TransformOriginScaleY(radius + 1.6), CString("y"));// 绘制z轴的zx = 0.2, y = 0;Transform3Dto2D(x, y, radius + 5 - 0.4);pDC->TextOutW(TransformOriginScaleX(x), TransformOriginScaleY(y), CString("z"));CString s;// 绘制x轴刻度文字for (float ScaleTextX = 0.4; ScaleTextX < radius + 1; ScaleTextX += 0.4){s.Format(_T("%.1f"), ScaleTextX);pDC->TextOutW(TransformOriginScaleX(ScaleTextX - 0.1), TransformOriginScaleY(-0.1), s);}// 绘制y轴刻度文字for (float ScaleTextY = 0.4; ScaleTextY <= radius + 1; ScaleTextY += 0.4){s.Format(_T("%.1f"), ScaleTextY);pDC->TextOutW(TransformOriginScaleX(-0.4), TransformOriginScaleY(ScaleTextY + 0.1), s);}// 绘制z轴刻度文字for (float ScaleTextZ = 0.6; ScaleTextZ <= radius + 4; ScaleTextZ += 0.6){s.Format(_T("%.1f"), ScaleTextZ);x = 0, y = 0;Transform3Dto2D(x, y, ScaleTextZ);pDC->TextOutW(TransformOriginScaleX(x + 0.15), TransformOriginScaleY(y + 0.12), s);}// 绘制函数图的Titlex = 0, y = 0;Transform3Dto2D(x, y, radius + 5);pDC->TextOutW(TransformOriginScaleX(x + 3), TransformOriginScaleY(y), CString("x^2 + y^2 + z^2 = r^2"));// -------------------- 绘制函数 -------------------------// 球面float phi, theta;for (phi = 0; phi < 2 * PI; phi += stepPhi){for (theta = 0; theta < PI; theta += stepTheta){x = radius * sin(phi) * cos(theta);y = radius * sin(phi) * sin(theta);z = radius * cos(phi);Transform3Dto2D(x, y, z);srand(z);pDC->SetPixel(TransformOriginScaleX(x), TransformOriginScaleY(y), RGB(rand() % 255, rand() % 255, rand() % 255));}} 三棱锥（测试用）//x = 1, y = 0, z = 0;//Transform3Dto2D(x, y, z);//pDC->MoveTo((int)TransformOriginScaleX(x), (int)TransformOriginScaleY(y));//x = 0, y = 1, z = 0;//Transform3Dto2D(x, y, z);//pDC->LineTo((int)TransformOriginScaleX(x), (int)TransformOriginScaleY(y));//x = 0, y = 0, z = 1;//Transform3Dto2D(x, y, z);//pDC->LineTo((int)TransformOriginScaleX(x), (int)TransformOriginScaleY(y));//x = 1, y = 0, z = 0;//Transform3Dto2D(x, y, z);//pDC->LineTo((int)TransformOriginScaleX(x), (int)TransformOriginScaleY(y));} 效果图