样条之贝塞尔(Bezier)

我曾经发过两篇关于贝塞尔的文章：数学图形(1.47)贝塞尔(Bézier)曲线，数学图形之贝塞尔(Bézier)曲面。那是使用我自己定义的脚本语言生成贝塞尔图形。由于我自己定义的脚本语法功能有限，所以最多只能支持5次贝塞尔函数，而这里将实现N次。

N阶贝塞尔曲线可如下推断:

给定点P₀、P₁、…、P_n，其贝塞尔曲线即

看其公式需要先为之生成一套杨辉三角形数组。

关于插值与样条的介绍请看：http://www.cnblogs.com/WhyEngine/p/4020294.html

.h文件

 /****************************************************************

   File name   :  YcBezierSpline.h
   Author      :  叶峰
   Version     :  2.0
   Create Date :  2014/08/18
   Description :  Bezier样条

 *****************************************************************/

 #ifndef __YcBezierSpline_H__
 #define __YcBezierSpline_H__

 // INCLUDES -----------------------------------------------------------------------------

 #include "YicSpline.h"

 // --------------------------------------------------------------------------------------

 #define YD_MAX_BEZIER_CONTROL_VALUE 33

 // --------------------------------------------------------------------------------------

 class YcBezierSpline : public YicSpline
 {
 public:
     YcBezierSpline();

     ~YcBezierSpline();

     // 设置输出样条值的数目
     void    SetSplineValuesCount(Yuint count);

     // 获得输出样条值的数目
     Yuint   GetSplineValuesCount() const;

     // 计算样条数值
     bool    BuildSpline(const void* ctrlValuesPtr, Yuint ctrlStride, Yuint ctrlCount,
         void* splineValuesPtr, Yuint splineStride) const;

 protected:
     void    ClearPowT();

     void    BuildPowT();

     Yreal    GetValueT(Yint t, Yint p) const
     {
         return m_pow_t[YD_MAX_BEZIER_CONTROL_VALUE*t + p];
     }

 protected:
     Yuint   m_valuesCount;
     Yreal*  m_pow_t;

 protected:
     static void    BuildYanghuiTriangle();
     static Yint m_yanghuiRowIndex[YD_MAX_BEZIER_CONTROL_VALUE];
     static Yint m_yanghuiTriangle[(YD_MAX_BEZIER_CONTROL_VALUE+)*YD_MAX_BEZIER_CONTROL_VALUE/];
 };

 // --------------------------------------------------------------------------------------

 #endif

CPP文件

 /****************************************************************

   File name   :  YcBezierSpline.cpp
   Author      :  叶峰
   Version     :  2.0
   Create Date :  2014/08/18
   Description :  

 *****************************************************************/

 // INCLUDES -----------------------------------------------------------------------------

 #include "..\..\YCommon_h\YSpline\YcBezierSpline.h"
 #include <assert.h>

 // --------------------------------------------------------------------------------------

 Yint    YcBezierSpline::m_yanghuiRowIndex[YD_MAX_BEZIER_CONTROL_VALUE] = {};
 Yint    YcBezierSpline::m_yanghuiTriangle[(YD_MAX_BEZIER_CONTROL_VALUE+)*YD_MAX_BEZIER_CONTROL_VALUE/] = {};

 void    YcBezierSpline::BuildYanghuiTriangle()
 {
     // 第0行
     m_yanghuiRowIndex[] = ;
     m_yanghuiTriangle[] = ;

     Yint index = ;
     Yint t0,t1;
     Yint* lastRow;
     for (Yint i = ; i < YD_MAX_BEZIER_CONTROL_VALUE; i++)
     {
         m_yanghuiRowIndex[i] = index;
         m_yanghuiTriangle[index] = ;
         index++;

         for (Yint j = ; j <= i; j++)
         {
             lastRow = m_yanghuiTriangle + m_yanghuiRowIndex[i-];
             t0 = lastRow[j - ];
             t1 = (j < i) ? lastRow[j] : ;

             m_yanghuiTriangle[index] = t0 + t1;
             index++;
         }
     }

     assert(index == (YD_MAX_BEZIER_CONTROL_VALUE+)*YD_MAX_BEZIER_CONTROL_VALUE/);
 }

 // --------------------------------------------------------------------------------------

 YcBezierSpline::YcBezierSpline()
 {
     if (m_yanghuiTriangle[] == )
     {
         BuildYanghuiTriangle();
     }

     m_valuesCount = ;
     m_pow_t = NULL;

     SetSplineValuesCount();
 }

 YcBezierSpline::~YcBezierSpline()
 {
     ClearPowT();
 }

 // 设置输出样条值的数目
 void   YcBezierSpline::SetSplineValuesCount(Yuint count)
 {
     if (count < )
     {
         count = ;
     }

     if (count == m_valuesCount)
     {
         return;
     }
     m_valuesCount = count;
     BuildPowT();
 }

 // 获得输出样条值的数目
 Yuint   YcBezierSpline::GetSplineValuesCount() const
 {
     return m_valuesCount;
 }

 void    YcBezierSpline::ClearPowT()
 {
     if (m_pow_t)
     {
         free(m_pow_t);
         m_pow_t = NULL;
     }
 }

 void    YcBezierSpline::BuildPowT()
 {
     ClearPowT();

     m_pow_t = (Yreal*)malloc(m_valuesCount*YD_MAX_BEZIER_CONTROL_VALUE*sizeof(Yreal));
     Yreal t;
     for (Yuint i = ; i < m_valuesCount; i++)
     {
         t = i/(m_valuesCount - 1.0f);

         m_pow_t[i*YD_MAX_BEZIER_CONTROL_VALUE] = 1.0f;
         for (Yint j = ; j < YD_MAX_BEZIER_CONTROL_VALUE; j++)
         {
             m_pow_t[i*YD_MAX_BEZIER_CONTROL_VALUE + j] = m_pow_t[i*YD_MAX_BEZIER_CONTROL_VALUE + j - ]*t;
         }
     }
 }

 // 计算样条数值
 bool    YcBezierSpline::BuildSpline(const void* ctrlValuesPtr, Yuint ctrlStride, Yuint ctrlCount,
     void* splineValuesPtr, Yuint splineStride) const
 {
     if (ctrlCount <  || ctrlCount > YD_MAX_BEZIER_CONTROL_VALUE)
     {
         return false;
     }

     Yreal* destValue;
     Yreal* srcValue;
     Yreal v;
     const Yint* yanghuiRow = m_yanghuiTriangle + m_yanghuiRowIndex[ctrlCount - ];

     for (Yuint i = ; i < m_valuesCount; i++)
     {
         v = 0.0f;
         for (Yuint j = ; j < ctrlCount; j++)
         {
             srcValue = (Yreal*)((char*)ctrlValuesPtr + ctrlStride*j);
             v += yanghuiRow[j] * (*srcValue) * GetValueT(i, j) * GetValueT(m_valuesCount -  - i, ctrlCount -  - j);
         }

         destValue = (Yreal*)((char*)splineValuesPtr + splineStride*i);
         *destValue = v;
     }

     return true;
 }

 // --------------------------------------------------------------------------------------

图像：

相关软件的下载地址为：http://files.cnblogs.com/WhyEngine/TestSpline.zip