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P、P、…、P，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