Physical Pattern Concept

Notation

• P is a type that models the Physical Pattern concept.
• pattern is an object of type P.

Refinement of

Pattern

Associated Types

In addition to the types defined in the Pattern concept, the following types are introduced.

Name	Expression	Description
Coordinate type	P::Coordinate	A type for representing the coordinates of each cell.
Direction change type	P::DirectionChange	A type for representing the change in course or bearing that occurs when traversing two consecutive edges in the underlying graph.

In addition, the requirements for the cell and indexability types are strengthened: the cell type must model the Physical Cell concept, and the indexability type must be equivalent to boost::mpl::false_.

Valid Expressions

In addition to the expressions defined in the Pattern concept, the following expressions must be valid.

Name	Expression	Type Requirements	Return Type
Yaw turn	p.getYawTurn(source_index, parent_index, target_index)	All three arguments must be convertible to P::CellIndex.	P::DirectionChange

Expression Semantics

After initialization, the following semantics must apply.

Name	Expression	Precondition	Semantics	Postcondition
Yaw turn	pattern.getYawTurn(source_index, parent_index, target_index)	0 < parent_index && parent_index <= pattern.getCellCount() If source_index == parent_index, then the underlying graph must contain an edge between the vertices that correspond to pattern.getEntranceCell() and pattern.getCell(parent_index). Otherwise, 0 < source_index && source_index <= pattern.getCellCount(), and the underlying graph must contain an edge between the vertices that correspond to pattern.getCell(source_index) and pattern.getCell(parent_index). If target_index == pattern.getCellCount(), then the underlying graph must contain an edge between the vertices that correspond to pattern.getCell(parent_index) and pattern.getExitCell(). Otherwise, 0 < target_index && target_index <= pattern.getCellCount(), and the underlying graph must contain an edge between the vertices that correspond to pattern.getCell(parent_index) and pattern.getCell(target_index).	Returns the change in course or bearing that occurs when traversing the corresponding edges in the underlying graph.

Invariants and Runtime Complexity Guarantees

In addition to the invariants and guarantees defined in the Pattern concept, the following invariants must hold.

Name	Invariants	Runtime complexity
Entrance and source cell connection	The entrance cell will be connected to the closest indexable cell in the tesselation; this cell will be the source cell.
Exit and target cell connection	The exit cell will be connected to the closest indexable cell in the tesselation; this cell will be the target cell.
Yaw turn	Valid after initialization.	Amortized constant time

Models

• Concrete classes deriving from PhysicalPattern:

  • Parallelepiped
  • SpherePattern