Defines the Klein's bottle (a parametric surface), a closed surface with no interior and exterior. More...

Inheritance diagram for IG.Num.Func3d2dExamples.KleinBottle1:

Collaboration diagram for IG.Num.Func3d2dExamples.KleinBottle1:

Public Member Functions
	KleinBottle1 ()

Public Member Functions inherited from IG.Num.Func3d2dExamples.ParametricSurface
void	SetBounds (double minX, double maxX, double minY, double maxY)
	Sets the bounds. More...

void	SetNumPoints (int numX, int numY)
	Sets recommended number of plot points along parameter curves. More...

override double	Value1 (double x, double y)
	Calculates and returns value of the first component of the current function. More...

override double	Value2 (double x, double y)
	Calculates and returns value of the second component of the current function. More...

override double	Value3 (double x, double y)
	Calculates and returns value of the third component of the current function. More...

Public Member Functions inherited from IG.Num.Func3d2dBaseNoGradient
override void	Gradient1 (double x, double y, out double gradx, out double grady)
	Function for calculating gradient of the first component of vector function, just throws the NotImplementedException exception. More...

override void	Gradient2 (double x, double y, out double gradx, out double grady)
	Function for calculating gradient of the second component of vector function, just throws the NotImplementedException exception. More...

override void	Gradient3 (double x, double y, out double gradx, out double grady)
	Function for calculating gradient of the third component of vector function, just throws the NotImplementedException exception. More...

override void	Hessian1 (double x, double y, out double dxx, out double dyy, out double dxy)
	Function for calculating Hessian of the first component, just throws the NotImplementedException exception. More...

override void	Hessian2 (double x, double y, out double dxx, out double dyy, out double dxy)
	Function for calculating Hessian of the second component, just throws the NotImplementedException exception. More...

override void	Hessian3 (double x, double y, out double dxx, out double dyy, out double dxy)
	Function for calculating Hessian of the third component, just throws the NotImplementedException exception. More...

Public Member Functions inherited from IG.Num.Func3d2dBase
virtual double	Value1 (vec2 parameters)
	Calculates and returns value of the first component of the current function. More...

virtual double	Value2 (vec2 parameters)
	Calculates and returns value of the second component of the current function. More...

virtual double	Value3 (vec2 parameters)
	Calculates and returns value of the third component of the current function. More...

virtual vec2	Gradient1 (vec2 parameters)
	Calculates and returns gradient of the first component of the current function. More...

virtual vec2	Gradient2 (vec2 parameters)
	Calculates and returns gradient of the second component of the current function. More...

virtual vec2	Gradient3 (vec2 parameters)
	Calculates and returns gradient of the third component of the current function. More...

virtual mat2	Hessian1 (vec2 parameters)
	Calculates and returns Hessian of the first component of the current function and returns it (in the form of a mat2 struct). More...

virtual mat2	Hessian2 (vec2 parameters)
	Calculates and returns Hessian of the second component of the current function and returns it (in the form of a mat2 struct). More...

virtual mat2	Hessian3 (vec2 parameters)
	Calculates and returns Hessian of the third component of the current function and returns it (in the form of a mat2 struct). More...

Public Attributes
const double	Defaulta = 0.5

double	a = Defaulta

Protected Member Functions
override double	f1 (double u, double v)

override double	f2 (double u, double v)

override double	f3 (double u, double v)

Protected Member Functions inherited from IG.Num.Func3d2dExamples.ParametricSurface
	ParametricSurface ()
	Base class for classes that define various parametric surfaces. More...

	ParametricSurface (double minX, double maxX, double minY, double maxY)
	Base class for classes that define various parametric surfaces. More...

Protected Member Functions inherited from IG.Num.Func3d2dBaseNoGradient
	Func3d2dBaseNoGradient ()

Protected Member Functions inherited from IG.Num.Func3d2dBase
	Func3d2dBase ()

Additional Inherited Members
Static Public Member Functions inherited from IG.Num.Func3d2dBase
static void	Example ()
	Example of use of a 2D function. More...

Static Protected Member Functions inherited from IG.Num.Func3d2dBase
static void	TestFunction (IFunc2d f)
	Demonstrates use of a 2D function by printing to the console 5 values and gradients of the function on the line connecting the two points (0, 0, 0) and (1, 1, 1). More...

static void	TestFunction (IFunc2d f, double xmin, double xmax, double ymin, double ymax, int numPoints)
	Demonstrates use of a 2D function by printing to the console some values and gradients of the function on the line connecting the two specified points. More...

Properties inherited from IG.Num.Func3d2dExamples.ParametricSurface
double	MinX `[get, set]`
	Minimal value of the first parameter. More...

double	MaxX `[get, set]`
	Maximal value of the first parameter. More...

double	MinY `[get, set]`
	Minimal value of the second parameter. More...

double	MaxY `[get, set]`
	Maximal value of the second parameter. More...

int	NumX `[get, set]`
	Recommended number of points along the first parameter used to plot the surface. More...

int	NumY `[get, set]`
	Recommended number of points along the second parameter used to plot the surface. More...

Properties inherited from IG.Num.Func3d2dBase
virtual bool	ValueDefined `[get, protected set]`
	Whether calculation of function value is defined. Defaulet is true. More...

virtual bool	GradientDefined `[get, protected set]`
	Whether calculation of functio ngradient is defined. Default is false. More...

virtual bool	HessianDefined `[get, protected set]`
	Whether calculation of function Hessian is defined. Default is false. More...

int	NumParam `[get]`
	Gets number of parameters. More...

int	NumValues `[get]`
	Gets number of components of the current vector function. More...

virtual Func2dBase	Component1 `[get]`
	Returns the scalar function that represents the first component of the current 3D vector function of 2 variables. More...

virtual Func2dBase	Component2 `[get]`
	Returns the scalar function that represents the second component of the current 3D vector function of 2 variables. More...

virtual Func2dBase	Component3 `[get]`
	Returns the scalar function that represents the third component of the current 3D vector function of 2 variables. More...

Properties inherited from IG.Num.IFunc3d2d
bool	ValueDefined `[get]`
	Whether calculation of function value is defined. More...

bool	GradientDefined `[get]`
	Whether calculation of function ngradient is defined. More...

bool	HessianDefined `[get]`
	Whether calculation of function Hessian is defined. More...

Func2dBase	Component1 `[get]`
	Returns the scalar function that represents the first component of the current 3D vector function of 2 variables. More...

Func2dBase	Component2 `[get]`
	Returns the scalar function that represents the second component of the current 3D vector function of 2 variables. More...

Func2dBase	Component3 `[get]`
	Returns the scalar function that represents the third component of the current 3D vector function of 2 variables. More...

Detailed Description

Defines the Klein's bottle (a parametric surface), a closed surface with no interior and exterior.

See also: http://www.vtk.org/VTK/img/ParametricSurfaces.pdf . Precise parameterization is taken from the Mathematica notebook ParametricSurfaces.nb.

$A Igor Oct11;

Constructor & Destructor Documentation

IG.Num.Func3d2dExamples.KleinBottle1.KleinBottle1 ( )

inline

Member Function Documentation

override double IG.Num.Func3d2dExamples.KleinBottle1.f1	(	double	u,
		double	v
	)

inlineprotectedvirtual

Implements IG.Num.Func3d2dExamples.ParametricSurface.

override double IG.Num.Func3d2dExamples.KleinBottle1.f2	(	double	u,
		double	v
	)

inlineprotectedvirtual

Implements IG.Num.Func3d2dExamples.ParametricSurface.

override double IG.Num.Func3d2dExamples.KleinBottle1.f3	(	double	u,
		double	v
	)

inlineprotectedvirtual

Implements IG.Num.Func3d2dExamples.ParametricSurface.

Member Data Documentation

const double IG.Num.Func3d2dExamples.KleinBottle1.Defaulta = 0.5

double IG.Num.Func3d2dExamples.KleinBottle1.a = Defaulta

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

igbase/numeric/geometry/Function3d2d.cs

Public Member Functions

Public Attributes

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation