scse

Introduction

The Spatial Constraint System with Extrusion class.

Discussion

Derived constraint systems inherit the functionality of this class. It implements extrusion functions with property-checking on them.

Member Functions

e

Gets the image of element c in the extrusion function i.

e_inv

Gets the inverse image of element c in the extrusion function i.

e_map

eᵢ(elems) = image

e_properties

Checks whether the extrusion function i satisfies certain property.

print_efunc

Prints (on std::cout) the extrusion function i using elements' ID's.

scse(const scs &, E_CHOICE_FUNCTION)

Constructor.

scse(const scse &)

Copy Constructor.

~scse

Destructor.

e

Gets the image of element c in the extrusion function i.

protected

ELEM_TYPE e(
    unsigned int i,
    ELEM_TYPE c ); 

Parameters

Return Value

eᵢ(c)

Complexity

Constant.

e_inv

Gets the inverse image of element c in the extrusion function i.

protected

std::vector<ELEM_TYPE> e_inv(
    unsigned int i,
    ELEM_TYPE c ); 

Parameters

Return Value

eᵢ^-1(c)

Complexity

O(n) where n is the number of elements of the SCS.

e_map

eᵢ(elems) = image

protected

void e_map(
    unsigned int i,
    std::vector<ELEM_TYPE> elems,
    ELEM_TYPE image ); 

Parameters

Discussion

The function will do nothing if the elements or the image are not in the elements of the SCS.

Complexity

O(n) where n is the number of elements to map.

e_properties

Checks whether the extrusion function i satisfies certain property.

protected

bool e_properties(
    unsigned int i,
    E_FUNCTION_PROPERTY property ); 

Parameters

Return Value

true if the extrusion function satisfies the property, false otherwise. Prints to std::cerr the troublesome elements' ID's.

Complexity

O(n) if property = EP_TOTAL or property = EP_RIGHT_INVERSE_S and O(n²) otherwise.

print_efunc

Prints (on std::cout) the extrusion function i using elements' ID's.

protected

void print_efunc(
    unsigned int i ); 

Parameters

Complexity

O(n) where n is the number of elements of the SCS.

scse(const scs &, E_CHOICE_FUNCTION)

Constructor.

protected

scse (
    const scs<ELEM_TYPE>& SCS,
    E_CHOICE_FUNCTION e_choice ); 

Parameters

Discussion

This constructor will create n extrusion functions and map them according to e_choice

Complexity

O(n) where n is the number of elements in the SCS.

scse(const scse &)

Copy Constructor.

protected

scse (
    const scse<ELEM_TYPE>& SCSE ); 

Parameters

Complexity

Constant.

~scse

Destructor.

protected

~scse(
    void ); 

Complexity

Constant.

Typedefs

E_CHOICE_FUNCTION

Enumeration of possible canonical ways of constructing the extrusion functions.

E_FUNCTION_PROPERTY

Enumeration of possible properties of a space function.

E_CHOICE_FUNCTION

Enumeration of possible canonical ways of constructing the extrusion functions.

public

enum class E_CHOICE_FUNCTION {
    EC_SUPREMA,
    EC_INFIMA,
    EC_MANUAL,
    EC_RANDOM 
}; 

Discussion

can be

- EC_SUPREMA: eᵢ(c) = ⨆(sᵢ^-1(c)) (i.e. each element is mapped to the LUB of its fiber in the corresponding space function).

- EC_INFIMA: eᵢ(c) = ⨅(sᵢ^-1(c)) (i.e. each element is mapped to the GLB of its fiber in the corresponding space function).

- EC_MANUAL: elements are mapped manually using e_map.

- EC_RANDOM: elements are mapped to a random element of their respective fibers in the corresponding space function.

E_FUNCTION_PROPERTY

Enumeration of possible properties of a space function.

protected

enum class E_FUNCTION_PROPERTY {
    EP_TOTAL,
    EP_SURJECTIVE,
    EP_INJECTIVE,
    EP_BIJECTIVE,
    EP_JOIN_DISTRIBUTIVE,
    EP_MEET_DISTRIBUTIVE,
    EP_RIGHT_INVERSE_S 
}; 

Discussion

each property has a one-on-one correspondance with the properties of FUNCTION_PROPERTY(specified in SCS) with one adition

-EP_RIGHT_INVERSE_S: function is the right inverse of its corresponding space function (i.e. it satisfies E.1).

Member Data

e_func

e_func

protected

std::vector< std::map<ELEM_TYPE, ELEM_TYPE> > e_func; 

Discussion

Vector containing the extrusion functions of the CS.