pymead.core.gcs.GCS

class GCS

Bases: DiGraph

A Geometric Constraint Solver (GCS) used to maintain constraints between points in pymead, implemented using the directed graph class in networkx. Instances of this class should not normally be created directly; the geometry collection creates objects of this class when GeometryCollection.add_constraint is called.

This constraint solver, while not powerful enough to handle arbitrary systems of equations, is nevertheless sufficient for handling many common types of constraints needed for airfoil systems. The constraints are solved using a graph-constructive approach and maintained using simple rigid body transformations. These transformations occur for a given set of points when the parameter value of a constraint “upstream” of this set of points is modified. All the points downstream of this constraint are handled as a rigid body (even if they are not fully constrained as such) to preserve each of the relative constraints.

The primary constraints in pymead are distance constraints and relative angle constraints (with specialized options for perpendicular and antiparallel constraints). The angle constraints are formed between three points (start, vertex, and end). Two other special kinds of constraints, symmetry constraints and radius of curvature constraints, are solved following the rigid body transformation.

__init__()

Constructor for the geometric constraint solver.

Methods

add_constraint(constraint)	Adds a geometric constraint to the graph.
add_point(point)	Adds a point (node) to the graph (and to the "points" attribute).
check_constraint_for_duplicates(geo_con)	Wrapper function for _check_distance_constraint_for_duplicates and _check_angle_constraint_for_duplicates that applies the duplicate check depending on the constraint type.
move_root(new_root)	Moves the root status of a constraint cluster from one point to a new point
remove_constraint(constraint)	Removes a geometric constraint from the graph.
remove_point(point)	Removes a point (node) from the graph (and from the "points" attribute).
rotate_cluster(rotation_handle[, ...])	Rotates the constraint cluster defined by the input rotation handle by either the angle specified by new_rotation_angle or by the angle difference specified by the angle between the cluster root and (new_rotation_handle_x, new_rotation_handle_y) and the initial angle between the root and rotation handle.
solve(source)	Wrapper around the difference constraint solution methods that applies a solution based on the input constraint type.
solve_other_constraints(points)	Solves all radius of curvature and symmetry constraints associated with a list of points that was modified in some way, either by direct user input or indirectly via constraint solving.
solve_roc_constraint(constraint)	Solves a radius of curvature constraint by translating the \(G^2\) points along a fixed angle.
solve_roc_constraints(points)	Solves all radius of curvature constraints associated with a list of points that was modified in some way, either by direct user input or indirectly via constraint solving.
solve_symmetry_constraint(constraint)	Solves a symmetry constraint by modifying the position of the target point to be the mirror of the tool point about the line defined by the first two points in the constraint.
solve_symmetry_constraints(points)	Solves all symmetry constraints associated with a list of points that was modified in some way, either by direct user input or indirectly via constraint solving.
translate_cluster(root, dx, dy)	Translate the constraint cluster (defined by the root point) by a given \(\Delta x\) and \(\Delta y\).
update_canvas_items(points_solved)	Updates the visual representation in the airfoil canvas of all geometric objects modified by the process of solving the constraint system.

Attributes

add_constraint(constraint: GeoCon)

Adds a geometric constraint to the graph.

Warning

This method should generally not be called directly. Instead, the GeometryCollection.add_constraint method that calls this method should be used.

Parameters:

constraint (GeoCon) – Geometric constraint to add

add_point(point: Point)

Adds a point (node) to the graph (and to the "points" attribute). Also assigns this graph to the point.

Parameters:

point (Point) – Point to add

check_constraint_for_duplicates(geo_con: GeoCon)

Wrapper function for _check_distance_constraint_for_duplicates and _check_angle_constraint_for_duplicates that applies the duplicate check depending on the constraint type.

Parameters:

geo_con (GeoCon) – Geometric constraint being added to the graph

move_root(new_root: Point)

Moves the root status of a constraint cluster from one point to a new point

Parameters:

new_root (Point) – Node that will be elevated to root status. The old root is discovered from this new root and the root status of the old root is removed.

remove_constraint(constraint: GeoCon)

Removes a geometric constraint from the graph.

Warning

This method should generally not be called directly. Instead, the GeometryCollection.remove_pymead_obj method that calls this method should be used.

Parameters:

constraint (GeoCon) – Geometric constraint to remove

remove_point(point: Point)

Removes a point (node) from the graph (and from the "points" attribute).

Parameters:

point (Point) – Point to remove

rotate_cluster(rotation_handle: ~pymead.core.point.Point, new_rotation_handle_x: float | None = None, new_rotation_handle_y: float | None = None, new_rotation_angle: float | None = None) -> (typing.List[pymead.core.point.Point], <class 'pymead.core.point.Point'>)

Rotates the constraint cluster defined by the input rotation handle by either the angle specified by new_rotation_angle or by the angle difference specified by the angle between the cluster root and (new_rotation_handle_x, new_rotation_handle_y) and the initial angle between the root and rotation handle.

Parameters:

• rotation_handle (Point) – Rotation handle of the constraint cluster

• new_rotation_handle_x (float or None) – \(x\)-location of the new rotation handle point position. Default: None

• new_rotation_handle_y (float or None) – \(y\)-location of the new rotation handle point position. Default: None

• new_rotation_angle (float or None) – New rotation angle for the cluster. Can only be specified if new_rotation_handle_x and new_rotation_handle_y are not specified.

Returns:

List of points solved after rotating the constraint cluster and the root point of the constraint cluster

Return type:

List[Point], Point

solve(source: GeoCon) → List[Point]

Wrapper around the difference constraint solution methods that applies a solution based on the input constraint type.

Parameters:

source (GeoCon) – The constraint to solve

Returns:

List of points solved during the solution process

Return type:

List[Point]

solve_other_constraints(points: List[Point]) → List[Point]

Solves all radius of curvature and symmetry constraints associated with a list of points that was modified in some way, either by direct user input or indirectly via constraint solving.

Parameters:

points (List[Point]) – Points for which to solve radius of curvature or symmetry constraints if needed

Returns:

Points solved during the solution process

Return type:

List[Point]

static solve_roc_constraint(constraint: ROCurvatureConstraint) → List[Point]

Solves a radius of curvature constraint by translating the \(G^2\) points along a fixed angle.

Parameters:

constraint (ROCurvatureConstraint) – Radius of curvature constraint to solve

Returns:

The child nodes of the radius of curvature constraint (the \(G^1\) and \(G^2\) points)

Return type:

List[Point]

solve_roc_constraints(points: List[Point]) → List[Point]

Solves all radius of curvature constraints associated with a list of points that was modified in some way, either by direct user input or indirectly via constraint solving.

Parameters:

points (List[Point]) – Points for which to solve radius of curvature constraints if needed

Returns:

Points solved during the solution process

Return type:

List[Point]

solve_symmetry_constraint(constraint: SymmetryConstraint) → List[Point]

Solves a symmetry constraint by modifying the position of the target point to be the mirror of the tool point about the line defined by the first two points in the constraint.

Parameters:

constraint (SymmetryConstraint) – The symmetry constraint to solve

Returns:

The child nodes of the symmetry constraint (the line-defining points, the tool point, and the target point)

Return type:

List[Point]

solve_symmetry_constraints(points: List[Point]) → List[Point]

Solves all symmetry constraints associated with a list of points that was modified in some way, either by direct user input or indirectly via constraint solving.

Parameters:

points (List[Point]) – Points for which to solve symmetry constraints if needed

Returns:

Points solved during the solution process

Return type:

List[Point]

translate_cluster(root: Point, dx: float, dy: float) → List[Point]

Translate the constraint cluster (defined by the root point) by a given \(\Delta x\) and \(\Delta y\).

Parameters:

• root (Point) – Root of the constraint cluster

• dx (float) – Amount to translate in the \(x\)-direction

• dy (float) – Amount to translate in the \(y\)-direction

Returns:

List of points solved during the solution process of constraints attached to the points that were translated

Return type:

List[Point]

static update_canvas_items(points_solved: List[Point])

Updates the visual representation in the airfoil canvas of all geometric objects modified by the process of solving the constraint system.

Parameters:

points_solved (List[Point]) – A list of all the points solved in the constraint system