Pattern Former Concept

A Pattern Former has the job of constructing the cells in a Pattern and of determining their connectivity.

Notation

PF is a type that models the Pattern Former concept.

Associated Types

Name Expression Description

Pattern type PF::Pattern The type of the pattern to be formed. This type must model the Pattern concept.

Name	Expression	Description
Pattern type	`PF::Pattern`	The type of the pattern to be formed. This type must model the Pattern concept.

Valid Expressions

The following expressions must be valid.

Name Expression Type Requirements Return Type

Pattern cell count PF::countCells(p) p must be an Argument Pack object. PF::Pattern::CellIndex

Pattern cell creation PF::makeCells(cell_iter, p)

cell_iter must be an Output Iterator with a value type that is the same as PF::Pattern::Cell.

p must be an Argument Pack object.

void

Pattern edge legality PF::isLegalEdge(src_cell, tgt_cell, p)

src_cell and tgt_cell must be of type const PF::Pattern::Cell&.

p must be an Argument Pack object.

bool

Name	Expression	Type Requirements	Return Type
Pattern cell count	`PF::countCells(p)`	`p` must be an Argument Pack object.	`PF::Pattern::CellIndex`
Pattern cell creation	`PF::makeCells(cell_iter, p)`	`cell_iter` must be an Output Iterator with a value type that is the same as `PF::Pattern::Cell`. `p` must be an Argument Pack object.	`void`
Pattern edge legality	`PF::isLegalEdge(src_cell, tgt_cell, p)`	`src_cell` and `tgt_cell` must be of type `const PF::Pattern::Cell&`. `p` must be an Argument Pack object.	`bool`

Expression Semantics

Name Expression Precondition Semantics Postcondition

Pattern cell count PF::countCells(p) p was used to initialize the pattern for which the number of cells to be created will be counted. Counts the number of cells to be created according to the specified named arguments. Used for memory allocation of the cell container. PF::countCells(p) >= 0

Pattern cell creation PF::makeCells(cell_iter, p)

cell_iter can be dereferenced, then incremented, as many as PF::countCells(p) times.

p was used to initialize the pattern for which the cells will be created.

Creates the cells according to the specified named arguments and inserts them in the pattern using the specified iterator.

Pattern edge legality PF::isLegalEdge(src_cell, tgt_cell, p)

src_cell and tgt_cell are contained in the same pattern.

p was used to initialize this pattern.

Returns true if this Pattern Former allows the two cells to be connected together according to the specified named arguments, false otherwise. Depending on this result, the underlying graph will or will not contain the corresponding edge.

Name	Expression	Precondition	Semantics	Postcondition
Pattern cell count	`PF::countCells(p)`	`p` was used to initialize the pattern for which the number of cells to be created will be counted.	Counts the number of cells to be created according to the specified named arguments. Used for memory allocation of the cell container.	`PF::countCells(p) >= 0`
Pattern cell creation	`PF::makeCells(cell_iter, p)`	`cell_iter` can be dereferenced, then incremented, as many as `PF::countCells(p)` times. `p` was used to initialize the pattern for which the cells will be created.	Creates the cells according to the specified named arguments and inserts them in the pattern using the specified iterator.
Pattern edge legality	`PF::isLegalEdge(src_cell, tgt_cell, p)`	`src_cell` and `tgt_cell` are contained in the same pattern. `p` was used to initialize this pattern.	Returns `true` if this Pattern Former allows the two cells to be connected together according to the specified named arguments, `false` otherwise. Depending on this result, the underlying graph will or will not contain the corresponding edge.

Invariants and Runtime Complexity Guarantees

Runtime complexity is measured in turms of cell count. The following invariants must hold.

Name Invariants Runtime complexity

Pattern cell count Linear time

Pattern cell creation Linear time

Pattern edge legality Amortized constant time

Name	Invariants	Runtime complexity
Pattern cell count		Linear time
Pattern cell creation		Linear time
Pattern edge legality		Amortized constant time

Models

All models of the Tesselation Former concept.

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