/// <summary>  /// Refer to : http://www.codeproject.com/KB/graphics/BezierSpline.aspx  /// Solves a tridiagonal system for one of coordinates (x or y) of first Bezier control points.  /// </summary>  /// <param name="rhs">Right hand side vector.</param>  /// <param name="x">Solution vector.</param>  void GetFirstControlPoints(      __in const std::vector<FLOAT>& rhs,      __out std::vector<FLOAT>& x )  {      ATLASSERT(rhs.size()==x.size());      int n = rhs.size();      std::vector<FLOAT> tmp(n);    // Temp workspace.      FLOAT b = 2.0f;      x[0] = rhs[0] / b;      for (int i = 1; i < n; i++) // Decomposition and forward substitution.      {          tmp[i] = 1 / b;          b = (i < n-1 ? 4.0f : 3.5f) - tmp[i];          x[i] = (rhs[i] - x[i-1]) / b;      }      for (int i = 1; i < n; i++)      {          x[n-i-1] -= tmp[n-i] * x[n-i]; // Back substitution.      }  }  /// <summary>  /// Refer to : http://www.codeproject.com/KB/graphics/BezierSpline.aspx  /// Get open-ended Bezier Spline Control Points.  /// </summary>  /// <param name="knots">Input Knot Bezier spline points.</param>  /// <param name="firstCtrlPt">Output First Control points array of knots.size()-1 length.</param>  /// <param name="secondCtrlPt">Output Second Control points array of knots.size()-1 length.</param>  void GetCurveControlPoints(      __in const std::vector<D2D1_POINT_2F>& knots,      __out std::vector<D2D1_POINT_2F>& firstCtrlPt,      __out std::vector<D2D1_POINT_2F>& secondCtrlPt )  {      ATLASSERT( (firstCtrlPt.size()==secondCtrlPt.size())          && (knots.size()==firstCtrlPt.size()+1) );      int n = knots.size()-1;      ATLASSERT(n>=1);      if (n == 1)      {          // Special case: Bezier curve should be a straight line.          // 3P1 = 2P0 + P3          firstCtrlPt[0].x = (2 * knots[0].x + knots[1].x) / 3.0f;          firstCtrlPt[0].y = (2 * knots[0].y + knots[1].y) / 3.0f;          // P2 = 2P1 – P0          secondCtrlPt[0].x = 2 * firstCtrlPt[0].x - knots[0].x;          secondCtrlPt[0].y = 2 * firstCtrlPt[0].y - knots[0].y;          return;      }      // Calculate first Bezier control points      // Right hand side vector      std::vector<FLOAT> rhs(n);      // Set right hand side X values      for (int i = 1; i < (n-1); ++i)      {          rhs[i] = 4 * knots[i].x + 2 * knots[i+1].x;      }      rhs[0] = knots[0].x + 2 * knots[1].x;      rhs[n-1] = (8 * knots[n-1].x + knots[n].x) / 2.0f;      // Get first control points X-values      std::vector<FLOAT> x(n);      GetFirstControlPoints(rhs,x);      // Set right hand side Y values      for (int i = 1; i < (n-1); ++i)      {          rhs[i] = 4 * knots[i].y + 2 * knots[i+1].y;      }      rhs[0] = knots[0].y + 2 * knots[1].y;      rhs[n-1] = (8 * knots[n-1].y + knots[n].y) / 2.0f;      // Get first control points Y-values      std::vector<FLOAT> y(n);      GetFirstControlPoints(rhs,y);      // Fill output arrays.      for (int i = 0; i < n; ++i)      {          // First control point          firstCtrlPt[i] = D2D1::Point2F(x[i],y[i]);          // Second control point          if (i < (n-1))          {              secondCtrlPt[i] = D2D1::Point2F(2 * knots[i+1].x - x[i+1], 2*knots[i+1].y-y[i+1]);          }          else          {              secondCtrlPt[i] = D2D1::Point2F((knots[n].x + x[n-1])/2, (knots[n].y+y[n-1])/2);          }      }  }  HRESULT CreateBezierSpline(      __in ID2D1Factory* pD2dFactory,      __in const std::vector<D2D1_POINT_2F>& points,      __out ID2D1PathGeometry** ppPathGeometry )  {      CHECK_PTR(pD2dFactory);      CHECK_OUTPUT_PTR(ppPathGeometry);      ATLASSERT(points.size()>1);      int n = points.size();      std::vector<D2D1_POINT_2F> firstCtrlPt(n-1);      std::vector<D2D1_POINT_2F> secondCtrlPt(n-1);      GetCurveControlPoints(points,firstCtrlPt,secondCtrlPt);      HRESULT hr = pD2dFactory->CreatePathGeometry(ppPathGeometry);      CHECKHR(hr);      if (FAILED(hr))          return hr;      CComPtr<ID2D1GeometrySink> spSink;      hr = (*ppPathGeometry)->Open(&spSink);      CHECKHR(hr);      if (SUCCEEDED(hr))      {          spSink->SetFillMode(D2D1_FILL_MODE_WINDING);          spSink->BeginFigure(points[0],D2D1_FIGURE_BEGIN_FILLED);          for (int i=1;i<n;i++)              spSink->AddBezier(D2D1::BezierSegment(firstCtrlPt[i-1],secondCtrlPt[i-1],points[i]));          spSink->EndFigure(D2D1_FIGURE_END_OPEN);          spSink->Close();      }      return hr;  }

 #pragma once  #include "stdafx.h"  #include <Direct2DHelper.h>  using D2D1::Point2F;  using D2D1::SizeU;  using D2D1::ColorF;  using D2D1::Matrix3x2F;  using D2D1::BezierSegment;  using D2D1::RectF;  #include <vector>  using std::vector;  #include <algorithm>  #include <boost/math/distributions/normal.hpp>  class CMainWindow :      public CWindowImpl<CMainWindow,CWindow,CSimpleWinTraits>  {  public:      BEGIN_MSG_MAP(CMainWindow)          MSG_WM_PAINT(OnPaint)          MSG_WM_ERASEBKGND(OnEraseBkgnd)          MSG_WM_SIZE(OnSize)          MSG_WM_CREATE(OnCreate)          MSG_WM_DESTROY(OnDestroy)      END_MSG_MAP()      int OnCreate(LPCREATESTRUCT /*lpCreateStruct*/)      {          CreateDeviceIndependentResource();          CreateDeviceResource();          CreateCurve();          return 0;      }      void OnDestroy()      {          PostQuitMessage(0);      }      void OnPaint(CDCHandle)      {          CPaintDC dc(m_hWnd);          Render();      }      BOOL OnEraseBkgnd(CDCHandle dc)      {          return TRUE;    // we have erased the background      }      void OnSize(UINT /*nType*/, CSize size)      {          if (m_spHwndRT)          {              m_spHwndRT->Resize(SizeU(size.cx,size.cy));              CreateCurve();          }      }  private:      void Render()      {          if (!m_spHwndRT)              CreateDeviceResource();          m_spHwndRT->BeginDraw();          m_spHwndRT->Clear(ColorF(ColorF::CornflowerBlue));          m_spHwndRT->SetTransform(Matrix3x2F::Identity());          D2D1_SIZE_F size = m_spHwndRT->GetSize();          FLOAT width = size.width-50, height = size.height-50;          D2D1_MATRIX_3X2_F reflectY = Direct2DHelper::ReflectYMatrix();          D2D1_MATRIX_3X2_F translate = Matrix3x2F::Translation(size.width/2.0f,size.height/2.0f);          m_spHwndRT->SetTransform(reflectY*translate);          // draw coordinate axis          m_spSolidBrush->SetColor(ColorF(ColorF::Red));          m_spHwndRT->DrawLine(Point2F(-width*0.5f,0),Point2F(width*0.5f,0),m_spSolidBrush,2.0f);          m_spSolidBrush->SetColor(ColorF(ColorF::DarkGreen));          m_spHwndRT->DrawLine(Point2F(0,-height*0.5f),Point2F(0,height*0.5f),m_spSolidBrush,2.0f);          // draw curve          m_spSolidBrush->SetColor(ColorF(ColorF::Blue));          m_spHwndRT->DrawGeometry(m_spPathGeometry,m_spSolidBrush,1.0f);          // draw point marks          m_spSolidBrush->SetColor(ColorF(ColorF::Red));          for (auto p=m_Points.cbegin();p!=m_Points.cend();p++)          {              Direct2DHelper::DrawRectPoint(m_spHwndRT,m_spSolidBrush,(*p),5.0f);          }          HRESULT hr = m_spHwndRT->EndDraw();          if (hr == D2DERR_RECREATE_TARGET)              DiscardDeviceResource();      }      void CreateDeviceIndependentResource()      {          Direct2DHelper::CreateD2D1Factory(&m_spD2dFactory);      }      void CreateDeviceResource()      {          CRect rc;          GetClientRect(&rc);          CHECK_PTR(m_spD2dFactory);          IFR(m_spD2dFactory->CreateHwndRenderTarget(              D2D1::RenderTargetProperties(),              D2D1::HwndRenderTargetProperties(m_hWnd,SizeU(rc.Width(),rc.Height())),              &m_spHwndRT));          IFR(m_spHwndRT->CreateSolidColorBrush(ColorF(ColorF::Red),&m_spSolidBrush));      }      void DiscardDeviceResource()      {          m_spSolidBrush.Release();          m_spHwndRT.Release();      }      void CreateCurve()      {          if (!m_spHwndRT)              return;          if (m_spPathGeometry)          {              m_spPathGeometry.Release();              m_Points.clear();          }          const int ptCount = 100;          D2D1_SIZE_F size = m_spHwndRT->GetSize();          FLOAT width = size.width-50.0f, height = size.height*0.4f;  #define SIN_CURVE     #ifdef SIN_CURVE    // create sin curve          FLOAT factor = static_cast<FLOAT>(4.0f*M_PI/width);          FLOAT x = -width*0.5f, y = 0, dx = width/ptCount;          for (int i=0;i<ptCount+1;i++)          {              y = height*sin(factor*x);              m_Points.push_back(Point2F(x,y));              x += dx;          }  #else                // create normal distribute curve          FLOAT factor = 10.0f/width;          FLOAT x = -width*0.5f, y = 0, dx = width/ptCount;          boost::math::normal nd;          for (int i=0;i<ptCount+1;i++)          {              y = height*static_cast<FLOAT>(boost::math::pdf(nd,factor*x));              m_Points.push_back(Point2F(x,y));              x += dx;          }  #endif // SIN_CURVE          // create Bezier spline          Direct2DHelper::CreateBezierSpline(m_spD2dFactory,m_Points,&m_spPathGeometry);          CHECK_PTR(m_spPathGeometry);      }  private:      CComPtr<ID2D1Factory> m_spD2dFactory;      CComPtr<ID2D1HwndRenderTarget> m_spHwndRT;      CComPtr<ID2D1SolidColorBrush> m_spSolidBrush;      CComPtr<ID2D1PathGeometry> m_spPathGeometry;      vector<D2D1_POINT_2F> m_Points;  };