Polygon Sponsor

Polygon Set Concept
The polygon_set concept tag is
polygon_set_concept
The semantic of a polygon_set
is zero or more geometry regions. A Polygon Set Concept may be
defined with floating point coordinates, but a snap rounding distance
of one integer unit will still be applied, furthermore, geometry
outside the domain where one integer unit is sufficient to provide
robustness may lead to undefined behavior in algorithms. It is
recommended to use integer coordinates for robust operations. In
the case that data represented contains only Manhattan geometry a
runtime check will default to the Manhattan algorithm. The
results of which are identical to what the general algorithm would do,
but obtained more efficiently. In the case that the data
represented contains only Manhattan and 45degree geometry a runtime
check will default to the faster 45degree algorithm. The results
of which may differ slight from what the general algorithm would do
because noninteger intersections will be handled differently.
Users are recommended to use std::vector and std::list of user
defined polygons or library provided
polygon_set_data<coordinate_type> objects. Lists and
vectors of models of polygon_concept or polygon_with_holes_concept are
automatically models of polygon_set_concept.
Example code custom_polygon_set.cpp
demonstrates mapping a user defined class to the library
polygon_set_concept
An object that is a model of
polygon_set_concept can be viewed as a model of
polygon_90_set_concept or
polygon_45_set_concept if it is determined at runtime to conform
to the restrictions of those concepts. This concept casting is
accomplished through the view_as<>()
function.
view_as<polygon_90_set_concept>(polygon_set_object)
view_as<polygon_45_set_concept>(polygon_set_object)
The return value of view_as<>()
can be passed into any interface that expects an object of the
conceptual type specified in its template parameter. Polygon sets
cannot be viewed as single polygons or rectangles since it generally
cannot be known whether a polygon set contains only a single polygon
without converting to polygons.
Operators
The return type of some operators is the polygon_set_view operator template
type. This type is itself a model of the polygon 90 set concept,
but furthermore can be used as an argument to the polygon_set_data constructor and assignment
operator. The operator template exists to eliminate temp copies
of intermediate results when Boolean operators are chained together.
Operators are declared inside the namespace boost::polygon::operators.
template
<typename T1, typename T2>
polygon_set_view operator(const T1& l, const T2& r) 
Boolean OR operation (polygon set union). Accepts
two objects that model polygon_set or one of its refinements.
Returns an operator template that performs the operation on demand when
chained or or nested in a library function call such as assign().
Expected n log n runtime, worst case quadratic runtime wrt. vertices +
intersections. 
template
<typename T1, typename T2>
polygon_set_view operator+(const T1& l, const T2& r) 
Same as operator. The plus sign is also used for
OR operations in Boolean logic expressions. Expected n log n
runtime, worst case quadratic runtime wrt. vertices + intersections. 
template
<typename T1, typename T2>
polygon_set_view operator&(const T1& l, const T2& r) 
Boolean AND operation (polygon set intersection).
Accepts two objects that model polygon_set or one of its
refinements. Expected n log n runtime, worst case quadratic
runtime wrt. vertices + intersections. 
template
<typename T1, typename T2>
polygon_set_view operator*(const T1& l, const T2& r) 
Same as operator&. The multiplication symbol
is also used for AND operations in Boolean logic expressions.
Expected n log n runtime, worst case quadratic runtime wrt. vertices +
intersections. 
template
<typename T1, typename T2>
polygon_set_view operator^(const T1& l, const T2& r) 
Boolean XOR operation (polygon set
disjointunion). Accepts two objects that model polygon_set or
one of its refinements. Expected n log n runtime, worst case
quadratic runtime wrt. vertices + intersections. 
template
<typename T1, typename T2>
polygon_set_view operator(const T1& l, const T2& r) 
Boolean SUBTRACT operation (polygon set
difference). Accepts two objects that model polygon_set or one of
its refinements. Expected n log n runtime, worst case quadratic
runtime wrt. vertices + intersections. 
template
<typename T1, typename T2>
T1& operator=(const T1& l, const T2& r) 
Same as operator, but with self assignment, left
operand must model polygon_set and not one of it's refinements.
Expected n log n runtime, worst case quadratic runtime wrt. vertices +
intersections. 
template
<typename T1, typename T2>
T1& operator+=(T1& l, const T2& r) 
Same as operator+, but with self assignment, left
operand must model polygon_set and not one of it's refinements.
Expected n log n runtime, worst case quadratic runtime wrt. vertices +
intersections. 
template
<typename T1, typename T2>
T1& operator&=(const T1& l, const T2& r) 
Same as operator&, but with self assignment, left
operand must model polygon_set and not one of it's refinements.
Expected n log n runtime, worst case quadratic runtime wrt. vertices +
intersections. 
template
<typename T1, typename T2>
T1& operator*=(T1& l, const T2& r) 
Same as operator*, but with self assignment, left
operand must model polygon_set and not one of it's refinements.
Expected n log n runtime, worst case quadratic runtime wrt. vertices +
intersections. 
template
<typename T1, typename T2>
T1& operator^=(const T1& l, const T2& r) 
Same as operator^, but with self assignment, left
operand must model polygon_set and not one of it's refinements.
Expected n log n runtime, worst case quadratic runtime wrt. vertices +
intersections. 
template
<typename T1, typename T2>
T1& operator=(T1& l, const T2& r) 
Same as operator, but with self assignment, left
operand must model polygon_set and not one of it's refinements.
Expected n log n runtime, worst case quadratic runtime wrt. vertices +
intersections. 
template
<typename T1>
T1 operator+(const T1&, coordinate_type bloating) 
Performs resize operation, inflating by bloating
ammount. If negative the result is a shrink instead of
bloat. Note: returns result by value. Expected n log n
runtime, worst case quadratic runtime wrt. vertices + intersections. 
template
<typename T1, typename T2>
T1 operator(const T1&, coordinate_type shrinking) 
Performs resize operation, deflating by bloating
ammount. If negative the result is a bloat instead of
shrink. Note: returns result by value. Expected n log n
runtime, worst case quadratic runtime wrt. vertices + intersections. 
template
<typename T1, typename T2>
T1& operator+=(const T1&, coordinate_type bloating) 
Performs resize operation, inflating by bloating
ammount. If negative the result is a shrink instead of
bloat. Returns reference to modified argument. Expected n
log n runtime, worst case quadratic runtime wrt. vertices +
intersections. 
template
<typename T1, typename T2>
T1& operator=(const T1&, coordinate_type shrinking) 
Performs resize operation, deflating by bloating
ammount. If negative the result is a bloat instead of
shrink. Returns reference to modified argument. Expected n
log n runtime, worst case quadratic runtime wrt. vertices +
intersections. 
Functions
template
<typename T1, typename T2>
T1& assign(T1& lvalue, const T2& rvalue) 
Eliminates overlaps in geometry and copies from an
object that models polygon_set or any of its refinements into an object
that models polygon_set. Expected n log n runtime, worst case
quadratic runtime wrt. vertices + intersections. 
template
<typename T1, typename T2>
bool equivalence(const T1& lvalue, const T2& rvalue) 
Returns true if an object that models polygon_set or
one of its refinements covers the exact same geometric regions as
another object that models polygon_set or one of its refinements.
For example: two of polygon objects. Expected n log n runtime,
worst case quadratic runtime wrt. vertices + intersections. 
template
<typename output_container_type, typename T>
void get_trapezoids(output_container_type& output,
const T& polygon_set) 
Output container is expected to be a standard
container. Slices geometry of an object that models polygon_set
or one of its refinements into non overlapping trapezoids along a
vertical slicing orientation and appends them to the output, which must
have a value type that models polygon or polygon_with_holes.
Expected n log n runtime, worst case quadratic runtime wrt. vertices +
intersections. 
template
<typename output_container_type, typename T>
void get_trapezoids(output_container_type& output,
const T& polygon_set,
orientation_2d orient) 
Output container is expected to be a standard
container. Slices geometry of an object that models polygon_set
or one of its refinements into non overlapping trapezoids along a the
specified slicing orientation and appends them to the output, which
must have a value type that models polygon or polygon_with_holes.
Expected n log n runtime, worst case quadratic runtime wrt. vertices +
intersections. 
template
<typename polygon_set_type>
void clear(polygon_set_type& polygon_set) 
Makes the object empty of geometry. 
template
<typename polygon_set_type>
bool empty(const polygon_set_type& polygon_set) 
Checks whether the object is empty of geometry.
Polygons that are completely covered by holes will result in empty
returning true. Expected n log n runtime, worst case quadratic
runtime wrt. vertices + intersections. 
template
<typename T, typename rectangle_type>
bool extents(rectangle_type& extents_rectangle,
const T& polygon_set) 
Computes bounding box of an object that models
polygon_set and stores it in an object that models rectangle. If
the polygon set is empty returns false. If there are holes
outside of shells they do not contribute to the extents of the polygon
set. Expected n log n runtime, worst case quadratic runtime wrt.
vertices + intersections. 
template
<typename T>
area_type area(const T& polygon_set) 
Computes the area covered by geometry in an object that
models polygon_set. Expected n log n runtime, worst case
quadratic runtime wrt. vertices + intersections. 
template
<typename T>
T& bloat(T& polygon_set, unsigned_area_type bloating) 
Same as getting all the polygons, bloating them and
putting them back. Expected n log n runtime, worst case quadratic
runtime wrt. vertices + intersections. 
template
<typename T>
T& shrink(T& polygon_set, unsigned_area_type shrinking) 
Same as getting all the polygons, shrinking them and
overwriting the polygon set with the resulting regions. Expected
n log n runtime, worst case quadratic runtime wrt. vertices +
intersections. 
template
<typename T, typename coord_type>
T& resize(T& polygon_set, coord_type resizing,
bool
corner_fill_arc = false,
unsigned int
num_circle_segments = 0) 
Same as bloat if resizing is positive, same as shrink
if resizing is negative. Original topology at acute angle
vertices is preserved by default, segmented circular arcs are inserted
if corner_fill_arc is true. num_circle_segments specifies number
of segments to introduce on a full circle when filling acute angle
corners with circular arcs. Expected n log n runtime, worst case
quadratic runtime wrt. vertices + intersections. 
template
<typename T>
T& scale_up(T& polygon_set, unsigned_area_type factor) 
Scales geometry up by unsigned factor. Expected n
log n runtime, worst case quadratic runtime wrt. vertices +
intersections. 
template
<typename T>
T& scale_down(T& polygon_set, unsigned_area_type factor) 
Scales geometry down by unsigned factor. Expected
n log n runtime, worst case quadratic runtime wrt. vertices +
intersections. 
template
<typename T, typename transformation_type>
T& transform(T& polygon_set,
const transformation_type& transformation) 
Applies transformation.transform() on all
vertices. Expected n log n runtime, worst case quadratic runtime
wrt. vertices + intersections. 
template
<typename T>
T& keep(T& polygon_set,
unsigned_area_type min_area,
unsigned_area_type max_area,
unsigned_area_type min_width,
unsigned_area_type max_width,
unsigned_area_type
min_height,
unsigned_area_type
max_height) 
Retains only regions that satisfy the min/max criteria
in the argument list. Note: useful for visualization to cull too
small polygons. Expected n log n runtime, worst case quadratic
runtime wrt. vertices + intersections. 
Polygon Set Data Object
The polygon set data type encapsulates the internal data
format that serves as the input to the sweepline algorithm that
implements polygonclipping Boolean operations. It also
internally keeps track of whether that data has been sorted or scanned
and maintains the invariant that when its flags indicate that the data
is sorted or scanned the data has not been changed to violate that
assumption. Using the Polygon Set Data type directly can be more
efficient than using lists and vectors of polygons in the functions
above because of the invariants it can enforce which provide the
opportunity to maintain the data is sorted form rather than going all
the way out to polygons then resorting those vertices for a subsequent
operation.
The declaration of Polygon Set Data is the following:
template <typename T>
class polygon_set_data;
The class is parameterized on the coordinate data type.
Algorithms that benefit from knowledge of the invariants enforced by
the class are implemented as member functions to provide them access to
information about those invariants.
Example code polygon_set_usage.cpp
demonstrates using the library provided polygon set data types and
functions
Member Functions
polygon_set_data() 
Default constructor. 
template
<typename iT>
polygon_set_data(iT input_begin, iT input_end) 
Construct with scanning orientation from an iterator
range of insertable objects. 
polygon_set_data(const
polygon_set_data& that) 
Copy construct. 
template
<typename l, typename r, typename op>
polygon_set_data(const
polygon_set_view<l,r,op>& t) 
Copy construct from a Boolean operator template. 
polygon_set_data&
operator=(const polygon_set_data& that) 
Assignment from another polygon set, may change
scanning orientation. 
template
<typename l, typename r, typename op>
polygon_set_data&
operator=(const polygon_set_view<l, r,
op>& that) 
Assignment from a Boolean operator template. 
template
<typename geometry_object>
polygon_set_data& operator=(const geometry_object& geo) 
Assignment from an insertable object. 
template <typename iT>
void insert(iT input_begin, iT input_end) 
Insert objects of an iterator range. Linear wrt
vertices inserted. 
void insert(const polygon_set_data& polygon_set) 
Insert a polygon set. Linear wrt vertices
inserted. 
template <typename geometry_type>
void insert(const geometry_type& geometry_object,
bool
is_hole = false) 
Insert a geometry object, if is_hole is true then the
inserted region is subtractive rather than additive. Linear wrt
vertices inserted. 
template
<typename output_container>
void get(output_container& output) const 
Expects a standard container of polygons objects.
Will scan and eliminate overlaps. Converts polygon set geometry
to objects of the polygon type and appends them to the container.
Polygons will be output with counterclockwise winding, hole polygons
will be output with clockwise winding. The last vertex of an
output polygon is the duplicate of the first, and the number of points
is equal to the number of edges plus 1. If required by the output
data type, polygons will have holes fractured out to the outer boundary
along the positive y direction and off grid intersections on the outer
boundary introduced by this fracture will be truncated downward.
Expected n log n runtime, worst case quadratic runtime wrt. vertices +
intersections. 
template
<typename output_container>
void get_trapezoids(output_container& output) const 
Expects a standard container of polygon objects.
Will scan and eliminate overlaps. Slices polygon set geometry to
trapezoids vertically and appends them to the container. Expected
n log n runtime, worst case quadratic runtime wrt. vertices +
intersections. 
template <typename output_container>
void get_trapezoids(output_container& output,
orientation_2d slicing_orientation) const 
Expects a standard container of polygon objects.
Will scan and eliminate overlaps. Slices polygon set geometry to
trapezoids along the given orientation and appends them to the
container. Expected n log n runtime, worst case quadratic runtime
wrt. vertices + intersections. 
bool operator==(const polygon_set_data& p) const 
Once scanned the data representation of geometry within
a polygon set is in a mathematically canonical form. Comparison
between two sets is therefore a linear time operation once they are in
the scanned state. Will scan and eliminate overlaps in both polygon
sets. Expected n log n runtime, worst case quadratic runtime wrt.
vertices + intersections. 
bool operator!=(const
polygon_set_data& p) const 
Inverse logic of equivalence operator. 
void clear() 
Make the polygon set empty. Note: does not
deallocate memory. Use shrink to fit idiom and assign default
constructed polygon set to deallocate. 
bool empty()
const 
Check whether the polygon set contains no
geometry. Will scan and eliminate overlaps because subtractive
regions might make the polygon set empty. Expected n log n
runtime, worst case quadratic runtime wrt. vertices + intersections. 
void clean()
const 
Scan and eliminate overlaps. Expected n log n
runtime, worst case quadratic runtime wrt. vertices + intersections the
first time, constant time subsequently. 
template
<typename input_iterator_type>
void set(input_iterator_type input_begin,
input_iterator_type
input_end) 
Overwrite geometry in polygon set with insertable
objects in the iterator range. 
template
<typename rectangle_type>
bool extents(rectangle_type& extents_rectangle) const 
Given an object that models rectangle, scans and
eliminates overlaps in the polygon set because subtractive regions may
alter its extents then computes the bounding box and assigns it to
extents_rectangle. Expected n log n runtime, worst case quadratic
runtime wrt. vertices + intersections the first time, linear
subsequently. 
polygon_set_data&
resize(coord_type resizing,
bool corner_fill_arc = false,
unsigned int num_circle_segments =
0) 
Inflates if resizing is positive, deflates if resizing
is negative. Original topology at acute angle vertices is
preserved by default, segmented circular arcs are inserted if
corner_fill_arc is true. num_circle_segments specifies number of
segments to introduce on a full circle when filling acute angle corners
with circular arcs. Specifying zero for num_circle_segments
results in only a single segment being inserted at acute corners.
Expected n log n runtime, worst case quadratic runtime wrt. vertices +
intersections. 
template
<typename transformation_type>
polygon_set_data&
transform(const transformation_type&
transformation) 
Applies transformation.transform() on vertices stored
within the polygon set. Expected n log n runtime, worst case
quadratic runtime wrt. vertices + intersections. 
polygon_set_data&
scale_up(unsigned_area_type factor) 
Scales vertices stored within the polygon set up by
factor. Expected n log n runtime, worst case quadratic runtime
wrt. vertices + intersections. 
polygon_set_data&
scale_down(unsigned_area_type factor) 
Scales vertices stored within the polygon set down by
factor. Expected n log n runtime, worst case quadratic runtime
wrt. vertices + intersections. 
template
<typename scaling_type>
polygon_set_data&
scale(const scaling_type& f) 
Scales vertices stored within the polygon set by
applying f.scale(). Expected n log n runtime, worst case
quadratic runtime wrt. vertices + intersections. 
