mathglpp::GLBernsteinPolynomial Class Reference

#include <BernsteinPolynomial.h>

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[legend]List of all members.

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Detailed Description

Bernstein Polynomials are the basis for Bezier curves.

They are called evaluators in the OpenGL API.

Author:

Jacques Gasselin

Definition at line 35 of file BernsteinPolynomial.h.

Public Member Functions
	GLBernsteinPolynomial (GLuint n)
	Create a bernstein polynomial of order at least n.
	~GLBernsteinPolynomial ()
	Default destructor.
void	setOrder (GLuint)
	Use to ensure that the polynomial is capable of using the desired order.
const GLfloat	get (const GLuint order, const GLuint c, const GLfloat u)
	Get interpolation product for control point c, where c = [0,.
const void	getVector (const GLuint order, const GLfloat u, GLfloat *vec)
	Get interpolation product vector for all control points c, where u = [0,1] This is normally used for post multiplying with a control point matrix.
	GLBernsteinPolynomial (GLuint n)
	Create a bernstein polynomial of order at least n.
	~GLBernsteinPolynomial ()
	Default destructor.
void	setOrder (GLuint)
	Use to ensure that the polynomial is capable of using the desired order.
const GLfloat	get (const GLuint order, const GLuint c, const GLfloat u)
	Get interpolation product for control point c, where c = [0,.
const void	getVector (const GLuint order, const GLfloat u, GLfloat *vec)
	Get interpolation product vector for all control points c, where u = [0,1] This is normally used for post multiplying with a control point matrix.
Protected Member Functions
void	extendPascal (GLuint)
	Extends Pascal's triangle as needed.
const GLuint	getCoeff (const GLuint order, const GLuint choice)
	This is exactly the same as "c choose n" in statistics.
void	extendPascal (GLuint)
	Extends Pascal's triangle as needed.
const GLuint	getCoeff (const GLuint order, const GLuint choice)
	This is exactly the same as "c choose n" in statistics.

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Constructor & Destructor Documentation

mathglpp::GLBernsteinPolynomial::GLBernsteinPolynomial

(

GLuint

n

)

Create a bernstein polynomial of order at least n.

Definition at line 27 of file GLBernsteinPolynomial.cpp.

References extendPascal().

{
   if(ord >= pascalsTriangle.size() )
      extendPascal(ord);
}

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mathglpp::GLBernsteinPolynomial::~GLBernsteinPolynomial

(

)

Default destructor.

Definition at line 33 of file GLBernsteinPolynomial.cpp.

{
}

mathglpp::GLBernsteinPolynomial::GLBernsteinPolynomial

(

GLuint

n

)

Create a bernstein polynomial of order at least n.

mathglpp::GLBernsteinPolynomial::~GLBernsteinPolynomial

(

)

Default destructor.

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Member Function Documentation

void mathglpp::GLBernsteinPolynomial::setOrder

(

GLuint

)

Use to ensure that the polynomial is capable of using the desired order.

Definition at line 37 of file GLBernsteinPolynomial.cpp.

References extendPascal().

{
   if(ord >= pascalsTriangle.size())
       extendPascal(ord);
}

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const GLfloat mathglpp::GLBernsteinPolynomial::get	(	const GLuint	order,
		const GLuint	c,
		const GLfloat	u
	)

Get interpolation product for control point c, where c = [0,.

..,order] & u = [0,1]

Definition at line 71 of file GLBernsteinPolynomial.cpp.

{
   assert(choice <= order);

   if(choice == 0)
   {
      if( u <= 0.0000001 )
         return 1;
      else
      if( u >= 0.9999999 )
         return 0;
      else
                  return pow(GLfloat(1-u), GLint(order));
   }
   else
   if(choice == order)
   {
      if( u <= 0.0000001 )
         return 0;
      else
      if( u >= 0.9999999 )
         return 1;
      else
         return pow((GLfloat)u, (GLint)choice);
   }
   else
   if( u <= 0.0000001 )
      return 0;
   else
   if( u >= 0.9999999 )
      return 0;
   else
      return pascalsTriangle[order][choice]
           * pow((GLfloat)u, (GLint)choice)
       * pow((GLfloat)(1-u), (GLint)(order - choice));
}

const void mathglpp::GLBernsteinPolynomial::getVector	(	const GLuint	order,
		const GLfloat	u,
		GLfloat *	vec
	)

Get interpolation product vector for all control points c, where u = [0,1] This is normally used for post multiplying with a control point matrix.

Definition at line 108 of file GLBernsteinPolynomial.cpp.

{
   assert(vec);
   for(register GLuint i = 0; i < order; ++i)
       vec[i] = get(order,i,u);
}

void mathglpp::GLBernsteinPolynomial::extendPascal

(

GLuint

)

[protected]

Extends Pascal's triangle as needed.

Definition at line 43 of file GLBernsteinPolynomial.cpp.

Referenced by GLBernsteinPolynomial(), and setOrder().

{
   if(pascalsTriangle.size() < 2)
   {
      std::vector<GLuint> row;
      row.push_back(1);

      pascalsTriangle.push_back(row);
      row.push_back(1);
      pascalsTriangle.push_back(row);
   }

   if(level >= pascalsTriangle.size() )
   {
      std::vector<GLuint> row;
      row.push_back(1);

      for(register GLuint i = 1; i < pascalsTriangle.size(); ++i)
         row.push_back( pascalsTriangle[pascalsTriangle.size()-1][i-1] +
                        pascalsTriangle[pascalsTriangle.size()-1][i] );

      row.push_back(1);
      pascalsTriangle.push_back(row);

      extendPascal(level);
   }
}

const GLuint mathglpp::GLBernsteinPolynomial::getCoeff	(	const GLuint	order,
		const GLuint	choice
	)			[inline, protected]

This is exactly the same as "c choose n" in statistics.

Definition at line 61 of file BernsteinPolynomial.h.

   {  return pascalsTriangle[order][choice]; }

void mathglpp::GLBernsteinPolynomial::setOrder

(

GLuint

)

Use to ensure that the polynomial is capable of using the desired order.

const GLfloat mathglpp::GLBernsteinPolynomial::get	(	const GLuint	order,
		const GLuint	c,
		const GLfloat	u
	)

Get interpolation product for control point c, where c = [0,.

..,order] & u = [0,1]

const void mathglpp::GLBernsteinPolynomial::getVector	(	const GLuint	order,
		const GLfloat	u,
		GLfloat *	vec
	)

Get interpolation product vector for all control points c, where u = [0,1] This is normally used for post multiplying with a control point matrix.

void mathglpp::GLBernsteinPolynomial::extendPascal

(

GLuint

)

[protected]

Extends Pascal's triangle as needed.

const GLuint mathglpp::GLBernsteinPolynomial::getCoeff	(	const GLuint	order,
		const GLuint	choice
	)			[inline, protected]

This is exactly the same as "c choose n" in statistics.

Definition at line 62 of file GLBernsteinPolynomial.h.

   {  return pascalsTriangle[order][choice]; }

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The documentation for this class was generated from the following files:

• BernsteinPolynomial.h
• GLBernsteinPolynomial.h
• GLBernsteinPolynomial.cpp

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