Linear Class Reference

Linear polynomials. More...

#include <linear.h>

Public Member Functions
	Linear ()
	Empty.
	Linear (const double &, const double &)
	Creates a linear function.
	Linear (const double &)
	Creates a constant function.
	~Linear ()
	Empty.
constexpr double &	operator[] (int)
	Access class components.
constexpr double	operator[] (int) const
	Overloaded.
Linear	operator- () const
	Unary.
Linear &	operator+= (const Linear &)
	Destructive sum of two linear polynomials.
Linear &	operator-= (const Linear &)
	Destructive difference of two linear polynomials.
Linear &	operator*= (const double &)
	Scale a linear polynomial by a double value.
Linear &	operator/= (const double &)
	Scales a linear polynomial by a double value.
constexpr double	operator() (const double &) const
	Evaluates the linear function.
int	Solve (double &) const
	Solve linear equations.
int	Solve (double &, const double &, const double &) const
	Search the roots of a linear equation over a given interval.
void	Range (double &, double &, const double &=0.0, const double &=1.0) const
	This function computes the range of values taken by a Linear over a given interval.

Static Public Member Functions
static double	Step (const double &, const double &, const double &)
	Create a linear step.
static double	Step (const double &, const double &, const double &, const double &, const double &)
	Create a linear step.
static double	Affine (const double &, const double &, const double &)
	Create the linear part of a linear step.
static double	Solve (const double &, const double &, const double &, const double &)
	Compute the root of a linear function such that f(a)=va and f(b)=vb.
static double	SolveAlpha (const double &, const double &, const double &, const double &)
	Compute the root of a linear function.

Protected Attributes
double	c [2] = { 0.0 }
	Array of coefficients.

Friends
Linear	operator+ (const Linear &u, const Linear &v)
	Overloaded.
Linear	operator- (const Linear &v, const Linear &u)
	Overloaded.
Linear	operator* (const Linear &u, const double &e)
	Multiply a polynomial by a scalar value.
Linear	operator* (const double &a, const Linear &p)
	Overloaded.
Linear	operator/ (const Linear &p, const double &a)
	Overloaded.
std::ostream &	operator<< (std::ostream &s, const Linear &p)
	Overloaded output-stream operator.

Detailed Description

Linear polynomials.

When using constructors, the coefficients are given in descending order:

Linear p(-1.0,1.0); // Linear polynomial -x + 1

Constructor & Destructor Documentation

Linear() [1/2]

Linear::Linear ( const double & a, const double & b )

inlineexplicit

Creates a linear function.

The function is defined as f(x) = a x + b.

Parameters

a,b	Coefficients.

Linear() [2/2]

Linear::Linear ( const double & a )

inlineexplicit

Creates a constant function.

Parameters

a

Constant.

Member Function Documentation

Affine()

double Linear::Affine ( const double & x, const double & a, const double & b )

inlinestatic

Create the linear part of a linear step.

This function does not test limits.

Parameters

x	Value
a,b	Interval values.

Returns

Real in unit inverval.

See also

Linear::Step

operator()()

double Linear::operator() ( const double & x ) const

inlineconstexpr

Evaluates the linear function.

Parameters

x

Argument.

Range()

void Linear::Range	(	double &	x,
		double &	y,
		const double &	a = 0.0,
		const double &	b = 1.0 ) const

This function computes the range of values taken by a Linear over a given interval.

Parameters

a,b	Interval.
x,y	Returned range.

Solve() [1/3]

double Linear::Solve ( const double & a, const double & b, const double & va, const double & vb )

inlinestatic

Compute the root of a linear function such that f(a)=va and f(b)=vb.

Assuming that the root exists, this function reads easier than the following code, and avoids constructor and parameter computation.

double t;
int n=Linear((vb-va)/(b-a),b*va+a*vb).Solve(t);

See also

Vector::Solve(const Vector& a, const Vector& b, const double&, const double&);

Solve() [2/3]

int Linear::Solve

(

double &

x

)

const

Solve linear equations.

This function store the root (ifit exists) in a double and returns the number of roots.

Parameters

x

Solution.

Solve() [3/3]

int Linear::Solve	(	double &	x,
		const double &	a,
		const double &	b ) const

Search the roots of a linear equation over a given interval.

Parameters

x	Solution.
a,b	Interval.

SolveAlpha()

double Linear::SolveAlpha ( const double & a, const double & b, const double & va, const double & vb )

static

Compute the root of a linear function.

The linear function satisfies the constraints: f(a)=va and f(b)=vb; the function returns an interpolant t such that the root satisties r=(1-t) a+t b.

See also

Linear::Solve(const Vector& a, const Vector& b, const double&, const double&);

Step() [1/2]

double Linear::Step ( const double & x, const double & a, const double & b )

inlinestatic

Create a linear step.

Parameters

x	Value
a,b	Interval values.

Returns

Real in unit inverval.

See also

Cubic::SmoothStep, Quintic::SmoothStep

Step() [2/2]

double Linear::Step ( const double & x, const double & a, const double & b, const double & ya, const double & yb )

inlinestatic

Create a linear step.

This function is the same as coding:

double y=Math::Lerp(ya,yb,Linear::Step(x,a,b));

Parameters

x	Value
a,b	Interval values.
ya,yb	Output interval values.

See also

Cubic::SmoothStep, Quintic::SmoothStep

Friends And Related Symbol Documentation

operator<<

std::ostream & operator<< ( std::ostream & s, const Linear & p )

friend

Overloaded output-stream operator.

Parameters

s	Stream.
p	Linear polynomial.