diff --git a/doc/src/sgml/func.sgml b/doc/src/sgml/func.sgml
index 6cb2467dca..90a2582dfd 100644
--- a/doc/src/sgml/func.sgml
+++ b/doc/src/sgml/func.sgml
@@ -9446,188 +9446,576 @@ CREATE TYPE rainbow AS ENUM ('red', 'orange', 'yellow', 'green', 'blue', 'purple
linkend="functions-geometry-conv-table"/>.
+
+ Geometric Operators
+
+
+
+
+ OperatorDescriptionExample(s)
+
+
+
+
+
+
+
+ geometric_type + point
+ geometric_type
+
+ Adds the coordinates of the second point to those of each
+ point of the first argument, thus performing translation.
+ Available for point, box, path,
+ circle.
+
+ box '(1,1),(0,0)' + point '(2,0)'
+ (3,1),(2,0)
+
+
+
+
+
+ path + path
+ path
+
+ Concatenates two open paths (returns NULL if either path is closed).
+
+ path '[(0,0),(1,1)]' + path '[(2,2),(3,3),(4,4)]'
+ [(0,0),(1,1),(2,2),(3,3),(4,4)]
+
+
+
+
+
+ geometric_type - point
+ geometric_type
+
+ Subtracts the coordinates of the second point from those
+ of each point of the first argument, thus performing translation.
+ Available for point, box, path,
+ circle.
+
+ box '(1,1),(0,0)' - point '(2,0)'
+ (-1,1),(-2,0)
+
+
+
+
+
+ geometric_type * point
+ geometric_type
+
+ Multiplies each point of the first argument by the second
+ pointFor this purpose, the
+ product of two points
+ (x1,y1) and
+ (x2,y2) is
+ defined as
+ (x1*x2 -
+ y1*y2,
+ x1*y2 +
+ y1*x2)..
+ Interpreting the point as a vector, this is equivalent to
+ scaling the object's size and distance from the origin by the length
+ of the vector, and rotating it counterclockwise around the origin by
+ the vector's angle from the x axis.
+ Available for point, box, path,
+ circle.
+
+ path '((0,0),(1,0),(1,1))' * point '(3.0,0)'
+ ((0,0),(3,0),(3,3))
+
+ path '((0,0),(1,0),(1,1))' * point(cosd(45), sind(45))
+ ((0,0),&zwsp;(0.7071067811865475,0.7071067811865475),&zwsp;(0,1.414213562373095))
+
+
+
+
+
+ geometric_type / point
+ geometric_type
+
+ Divides each point of the first argument by the
+ second pointFor this purpose, the
+ quotient of two points
+ (x1,y1) and
+ (x2,y2) is
+ defined as
+ ((x1*x2 +
+ y1*y2) /
+ L,
+ (y1*x2 -
+ x1*y2) /
+ L),
+ where L =
+ x2*x2 +
+ y2*y2..
+ Interpreting the point as a vector, this is equivalent to
+ scaling the object's size and distance from the origin down by the
+ length of the vector, and rotating it clockwise around the origin by
+ the vector's angle from the x axis.
+ Available for point, box, path,
+ circle.
+
+ path '((0,0),(1,0),(1,1))' / point '(2.0,0)'
+ ((0,0),(0.5,0),(0.5,0.5))
+
+ path '((0,0),(1,0),(1,1))' / point(cosd(45), sind(45))
+ ((0,0),&zwsp;(0.7071067811865476,-0.7071067811865476),&zwsp;(1.4142135623730951,0))
+
+
+
+
+
+ @-@ geometric_type
+ double precision
+
+ Computes the total length.
+ Available for lseg, path.
+
+ @-@ path '[(0,0),(1,0),(1,1)]'
+ 2
+
+
+
+
+
+ @@ geometric_type
+ point
+
+ Computes the center point.
+ Available for box, lseg, path,
+ polygon, circle.
+
+ @@ box '(2,2),(0,0)'
+ (1,1)
+
+
+
+
+
+ # geometric_type
+ integer
+
+ Returns the number of points.
+ Available for path, polygon.
+
+ # path '((1,0),(0,1),(-1,0))'
+ 3
+
+
+
+
+
+ geometric_type # geometric_type
+ point
+
+ Computes the point of intersection, or NULL if there is none.
+ Available for lseg, line.
+
+ lseg '[(0,0),(1,1)]' # lseg '[(1,0),(0,1)]'
+ (0.5,0.5)
+
+
+
+
+
+ box # box
+ box
+
+ Computes the intersection of two boxes, or NULL if there is none.
+
+ box '(2,2),(-1,-1)' # box '(1,1),(-2,-2)'
+ (1,1),(-1,-1)
+
+
+
+
+
+ geometric_type ## geometric_type
+ point
+
+ Computes the closest point to the first object on the second object.
+ Available for these pairs of types:
+ (point, box),
+ (point, lseg),
+ (point, line),
+ (lseg, box),
+ (lseg, lseg),
+ (lseg, line),
+ (line, box),
+ (line, lseg).
+
+ point '(0,0)' ## lseg '[(2,0),(0,2)]'
+ (1,1)
+
+
+
+
+
+ geometric_type <-> geometric_type
+ double precision
+
+ Computes the distance between the objects.
+ Available for all seven geometric types, for all combinations
+ of point with another geometric type, and for
+ these additional pairs of types:
+ (box, lseg),
+ (box, line),
+ (lseg, line),
+ (polygon, circle)
+ (and the commutator cases).
+
+ circle '<(0,0),1>' <-> circle '<(5,0),1>'
+ 3
+
+
+
+
+
+ geometric_type @> geometric_type
+ boolean
+
+ Does first object contain second?
+ Available for these pairs of types:
+ (box, point),
+ (box, box),
+ (path, point),
+ (polygon, point),
+ (polygon, polygon),
+ (circle, point),
+ (circle, circle).
+
+ circle '<(0,0),2>' @> point '(1,1)'
+ t
+
+
+
+
+
+ geometric_type <@ geometric_type
+ boolean
+
+ Is first object contained in or on second?
+ Available for these pairs of types:
+ (point, box),
+ (point, lseg),
+ (point, line),
+ (point, path),
+ (point, polygon),
+ (point, circle),
+ (box, box),
+ (lseg, box),
+ (lseg, line),
+ (polygon, polygon),
+ (circle, circle).
+
+ point '(1,1)' <@ circle '<(0,0),2>'
+ t
+
+
+
+
+
+ geometric_type && geometric_type
+ boolean
+
+ Do these objects overlap? (One point in common makes this true.)
+ Available for box, polygon,
+ circle.
+
+ box '(1,1),(0,0)' && box '(2,2),(0,0)'
+ t
+
+
+
+
+
+ geometric_type << geometric_type
+ boolean
+
+ Is first object strictly left of second?
+ Available for point, box,
+ polygon, circle.
+
+ circle '<(0,0),1>' << circle '<(5,0),1>'
+ t
+
+
+
+
+
+ geometric_type >> geometric_type
+ boolean
+
+ Is first object strictly right of second?
+ Available for point, box,
+ polygon, circle.
+
+ circle '<(5,0),1>' >> circle '<(0,0),1>'
+ t
+
+
+
+
+
+ geometric_type &< geometric_type
+ boolean
+
+ Does first object not extend to the right of second?
+ Available for box, polygon,
+ circle.
+
+ box '(1,1),(0,0)' &< box '(2,2),(0,0)'
+ t
+
+
+
+
+
+ geometric_type &> geometric_type
+ boolean
+
+ Does first object not extend to the left of second?
+ Available for box, polygon,
+ circle.
+
+ box '(3,3),(0,0)' &> box '(2,2),(0,0)'
+ t
+
+
+
+
+
+ geometric_type <<| geometric_type
+ boolean
+
+ Is first object strictly below second?
+ Available for box, polygon,
+ circle.
+
+ box '(3,3),(0,0)' <<| box '(5,5),(3,4)'
+ t
+
+
+
+
+
+ geometric_type |>> geometric_type
+ boolean
+
+ Is first object strictly above second?
+ Available for box, polygon,
+ circle.
+
+ box '(5,5),(3,4)' |>> box '(3,3),(0,0)'
+ t
+
+
+
+
+
+ geometric_type &<| geometric_type
+ boolean
+
+ Does first object not extend above second?
+ Available for box, polygon,
+ circle.
+
+ box '(1,1),(0,0)' &<| box '(2,2),(0,0)'
+ t
+
+
+
+
+
+ geometric_type |&> geometric_type
+ boolean
+
+ Does first object not extend below second?
+ Available for box, polygon,
+ circle.
+
+ box '(3,3),(0,0)' |&> box '(2,2),(0,0)'
+ t
+
+
+
+
+
+ box <^ box
+ boolean
+
+ Is first object below second (allows edges to touch)?
+
+ box '((1,1),(0,0))' <^ box '((2,2),(1,1))'
+ t
+
+
+
+
+
+ point <^ point
+ boolean
+
+ Is first object strictly below second?
+ (This operator is misnamed; it should be <<|.)
+
+ point '(1,0)' <^ point '(1,1)'
+ t
+
+
+
+
+
+ box >^ box
+ boolean
+
+ Is first object above second (allows edges to touch)?
+
+ box '((2,2),(1,1))' >^ box '((1,1),(0,0))'
+ t
+
+
+
+
+
+ point >^ point
+ boolean
+
+ Is first object strictly above second?
+ (This operator is misnamed; it should be |>>.)
+
+ point '(1,1)' >^ point '(1,0)'
+ t
+
+
+
+
+
+ geometric_type ?# geometric_type
+ boolean
+
+ Do these objects intersect?
+ Available for these pairs of types:
+ (box, box),
+ (lseg, box),
+ (lseg, lseg),
+ (lseg, line),
+ (line, box),
+ (line, line),
+ (path, path).
+
+ lseg '[(-1,0),(1,0)]' ?# box '(2,2),(-2,-2)'
+ t
+
+
+
+
+
+ ?- geometric_type
+ boolean
+
+ Is line horizontal?
+ Available for lseg, line.
+
+ ?- lseg '[(-1,0),(1,0)]'
+ t
+
+
+
+
+
+ point ?- point
+ boolean
+
+ Are points horizontally aligned (that is, have same y coordinate)?
+
+ point '(1,0)' ?- point '(0,0)'
+ t
+
+
+
+
+
+ ?| geometric_type
+ boolean
+
+ Is line vertical?
+ Available for lseg, line.
+
+ ?| lseg '[(-1,0),(1,0)]'
+ f
+
+
+
+
+
+ point ?| point
+ boolean
+
+ Are points vertically aligned (that is, have same x coordinate)?
+
+ point '(0,1)' ?| point '(0,0)'
+ t
+
+
+
+
+
+ geometric_type ?-| geometric_type
+ boolean
+
+ Are lines perpendicular?
+ Available for lseg, line.
+
+ lseg '[(0,0),(0,1)]' ?-| lseg '[(0,0),(1,0)]'
+ t
+
+
+
+
+
+ geometric_type ?|| geometric_type
+ boolean
+
+ Are lines parallel?
+ Available for lseg, line.
+
+ lseg '[(-1,0),(1,0)]' ?|| lseg '[(-1,2),(1,2)]'
+ t
+
+
+
+
+
+ geometric_type ~= geometric_type
+ boolean
+
+ Are these objects the same?
+ Available for point, box,
+ polygon, circle.
+
+ polygon '((0,0),(1,1))' ~= polygon '((1,1),(0,0))'
+ t
+
+
+
+
+
+
- Note that the same as
operator, ~=, represents
- the usual notion of equality for the point,
+ Note that the same as
operator, ~=,
+ represents the usual notion of equality for the point,
box, polygon, and circle types.
- Some of these types also have an = operator, but
- = compares
- for equal areas only. The other scalar comparison operators
- (<= and so on) likewise compare areas for these types.
+ Some of the geometric types also have an = operator, but
+ = compares for equal areas only.
+ The other scalar comparison operators (<= and so
+ on), where available for these types, likewise compare areas.
-
- Geometric Operators
-
-
-
- Operator
- Description
- Example
-
-
-
-
- +
- Translation
- box '((0,0),(1,1))' + point '(2.0,0)'
-
-
- -
- Translation
- box '((0,0),(1,1))' - point '(2.0,0)'
-
-
- *
- Scaling/rotation
- box '((0,0),(1,1))' * point '(2.0,0)'
-
-
- /
- Scaling/rotation
- box '((0,0),(2,2))' / point '(2.0,0)'
-
-
- #
- Point or box of intersection
- box '((1,-1),(-1,1))' # box '((1,1),(-2,-2))'
-
-
- #
- Number of points in path or polygon
- # path '((1,0),(0,1),(-1,0))'
-
-
- @-@
- Length or circumference
- @-@ path '((0,0),(1,0))'
-
-
- @@
- Center
- @@ circle '((0,0),10)'
-
-
- ##
- Closest point to first operand on second operand
- point '(0,0)' ## lseg '((2,0),(0,2))'
-
-
- <->
- Distance between
- circle '((0,0),1)' <-> circle '((5,0),1)'
-
-
- &&
- Overlaps? (One point in common makes this true.)
- box '((0,0),(1,1))' && box '((0,0),(2,2))'
-
-
- <<
- Is strictly left of?
- circle '((0,0),1)' << circle '((5,0),1)'
-
-
- >>
- Is strictly right of?
- circle '((5,0),1)' >> circle '((0,0),1)'
-
-
- &<
- Does not extend to the right of?
- box '((0,0),(1,1))' &< box '((0,0),(2,2))'
-
-
- &>
- Does not extend to the left of?
- box '((0,0),(3,3))' &> box '((0,0),(2,2))'
-
-
- <<|
- Is strictly below?
- box '((0,0),(3,3))' <<| box '((3,4),(5,5))'
-
-
- |>>
- Is strictly above?
- box '((3,4),(5,5))' |>> box '((0,0),(3,3))'
-
-
- &<|
- Does not extend above?
- box '((0,0),(1,1))' &<| box '((0,0),(2,2))'
-
-
- |&>
- Does not extend below?
- box '((0,0),(3,3))' |&> box '((0,0),(2,2))'
-
-
- <^
- Is below (allows touching)?
- circle '((0,0),1)' <^ circle '((0,5),1)'
-
-
- >^
- Is above (allows touching)?
- circle '((0,5),1)' >^ circle '((0,0),1)'
-
-
- ?#
- Intersects?
- lseg '((-1,0),(1,0))' ?# box '((-2,-2),(2,2))'
-
-
- ?-
- Is horizontal?
- ?- lseg '((-1,0),(1,0))'
-
-
- ?-
- Are horizontally aligned?
- point '(1,0)' ?- point '(0,0)'
-
-
- ?|
- Is vertical?
- ?| lseg '((-1,0),(1,0))'
-
-
- ?|
- Are vertically aligned?
- point '(0,1)' ?| point '(0,0)'
-
-
- ?-|
- Is perpendicular?
- lseg '((0,0),(0,1))' ?-| lseg '((0,0),(1,0))'
-
-
- ?||
- Are parallel?
- lseg '((-1,0),(1,0))' ?|| lseg '((-1,2),(1,2))'
-
-
- @>
- Contains?
- circle '((0,0),2)' @> point '(1,1)'
-
-
- <@
- Contained in or on?
- point '(1,1)' <@ circle '((0,0),2)'
-
-
- ~=
- Same as?
- polygon '((0,0),(1,1))' ~= polygon '((1,1),(0,0))'
-
-
-
-
-
Before PostgreSQL 8.2, the containment
@@ -9637,308 +10025,532 @@ CREATE TYPE rainbow AS ENUM ('red', 'orange', 'yellow', 'green', 'blue', 'purple
-
- area
-
-
- center
-
-
- diameter
-
-
- height
-
-
- isclosed
-
-
- isopen
-
-
- length
-
-
- npoints
-
-
- pclose
-
-
- popen
-
-
- radius
-
-
- width
-
-
- Geometric Functions
-
-
-
- Function
- Return Type
- Description
- Example
-
-
-
-
- area(object)
- double precision
- area
- area(box '((0,0),(1,1))')
-
-
- center(object)
- point
- center
- center(box '((0,0),(1,2))')
-
-
- diameter(circle)
- double precision
- diameter of circle
- diameter(circle '((0,0),2.0)')
-
-
- height(box)
- double precision
- vertical size of box
- height(box '((0,0),(1,1))')
-
-
- isclosed(path)
- boolean
- a closed path?
- isclosed(path '((0,0),(1,1),(2,0))')
-
-
- isopen(path)
- boolean
- an open path?
- isopen(path '[(0,0),(1,1),(2,0)]')
-
-
- length(object)
- double precision
- length
- length(path '((-1,0),(1,0))')
-
-
- npoints(path)
- int
- number of points
- npoints(path '[(0,0),(1,1),(2,0)]')
-
-
- npoints(polygon)
- int
- number of points
- npoints(polygon '((1,1),(0,0))')
-
-
- pclose(path)
- path
- convert path to closed
- pclose(path '[(0,0),(1,1),(2,0)]')
-
-
- popen(path)
- path
- convert path to open
- popen(path '((0,0),(1,1),(2,0))')
-
-
- radius(circle)
- double precision
- radius of circle
- radius(circle '((0,0),2.0)')
-
-
- width(box)
- double precision
- horizontal size of box
- width(box '((0,0),(1,1))')
-
-
-
+ Geometric Functions
+
+
+
+
+ FunctionDescriptionExample(s)
+
+
+
+
+
+
+
+
+ area
+
+ area ( geometric_type )
+ double precision
+
+ Computes area.
+ Available for box, path, circle.
+ A path input must be closed, else NULL is returned.
+ Also, if the path is self-intersecting, the result may be
+ meaningless.
+
+ area(box '(2,2),(0,0)')
+ 4
+
+
+
+
+
+
+ center
+
+ center ( geometric_type )
+ point
+
+ Computes center point.
+ Available for box, circle.
+
+ center(box '(1,2),(0,0)')
+ (0.5,1)
+
+
+
+
+
+
+ diagonal
+
+ diagonal ( box )
+ lseg
+
+ Extracts box's diagonal as a line segment
+ (same as lseg(box)).
+
+ diagonal(box '(1,2),(0,0)')
+ [(1,2),(0,0)]
+
+
+
+
+
+
+ diameter
+
+ diameter ( circle )
+ double precision
+
+ Computes diameter of circle.
+
+ diameter(circle '<(0,0),2>')
+ 4
+
+
+
+
+
+
+ height
+
+ height ( box )
+ double precision
+
+ Computes vertical size of box.
+
+ height(box '(1,2),(0,0)')
+ 2
+
+
+
+
+
+
+ isclosed
+
+ isclosed ( path )
+ boolean
+
+ Is path closed?
+
+ isclosed(path '((0,0),(1,1),(2,0))')
+ t
+
+
+
+
+
+
+ isopen
+
+ isopen ( path )
+ boolean
+
+ Is path open?
+
+ isopen(path '[(0,0),(1,1),(2,0)]')
+ t
+
+
+
+
+
+
+ length
+
+ length ( geometric_type )
+ double precision
+
+ Computes the total length.
+ Available for lseg, path.
+
+ length(path '((-1,0),(1,0))')
+ 4
+
+
+
+
+
+
+ npoints
+
+ npoints ( geometric_type )
+ integer
+
+ Returns the number of points.
+ Available for path, polygon.
+
+ npoints(path '[(0,0),(1,1),(2,0)]')
+ 3
+
+
+
+
+
+
+ pclose
+
+ pclose ( path )
+ path
+
+ Converts path to closed form.
+
+ pclose(path '[(0,0),(1,1),(2,0)]')
+ ((0,0),(1,1),(2,0))
+
+
+
+
+
+
+ popen
+
+ popen ( path )
+ path
+
+ Converts path to open form.
+
+ popen(path '((0,0),(1,1),(2,0))')
+ [(0,0),(1,1),(2,0)]
+
+
+
+
+
+
+ radius
+
+ radius ( circle )
+ double precision
+
+ Computes radius of circle.
+
+ radius(circle '<(0,0),2>')
+ 2
+
+
+
+
+
+
+ slope
+
+ slope ( point, point )
+ double precision
+
+ Computes slope of a line drawn through the two points.
+
+ slope(point '(0,0)', point '(2,1)')
+ 0.5
+
+
+
+
+
+
+ width
+
+ width ( box )
+ double precision
+
+ Computes horizontal size of box.
+
+ width(box '(1,2),(0,0)')
+ 1
+
+
+
+
- Geometric Type Conversion Functions
-
-
-
- Function
- Return Type
- Description
- Example
-
-
-
-
-
-
- box
-
- box(circle)
-
- box
- circle to box
- box(circle '((0,0),2.0)')
-
-
- box(point)
- box
- point to empty box
- box(point '(0,0)')
-
-
- box(point, point)
- box
- points to box
- box(point '(0,0)', point '(1,1)')
-
-
- box(polygon)
- box
- polygon to box
- box(polygon '((0,0),(1,1),(2,0))')
-
-
- bound_box(box, box)
- box
- boxes to bounding box
- bound_box(box '((0,0),(1,1))', box '((3,3),(4,4))')
-
-
-
-
- circle
-
- circle(box)
-
- circle
- box to circle
- circle(box '((0,0),(1,1))')
-
-
- circle(point, double precision)
- circle
- center and radius to circle
- circle(point '(0,0)', 2.0)
-
-
- circle(polygon)
- circle
- polygon to circle
- circle(polygon '((0,0),(1,1),(2,0))')
-
-
- line(point, point)
- line
- points to line
- line(point '(-1,0)', point '(1,0)')
-
-
-
-
- lseg
-
- lseg(box)
-
- lseg
- box diagonal to line segment
- lseg(box '((-1,0),(1,0))')
-
-
- lseg(point, point)
- lseg
- points to line segment
- lseg(point '(-1,0)', point '(1,0)')
-
-
-
-
- path
-
- path(polygon)
-
- path
- polygon to path
- path(polygon '((0,0),(1,1),(2,0))')
-
-
-
-
- point
-
- point(double
- precision, double precision)
-
- point
- construct point
- point(23.4, -44.5)
-
-
- point(box)
- point
- center of box
- point(box '((-1,0),(1,0))')
-
-
- point(circle)
- point
- center of circle
- point(circle '((0,0),2.0)')
-
-
- point(lseg)
- point
- center of line segment
- point(lseg '((-1,0),(1,0))')
-
-
- point(polygon)
- point
- center of polygon
- point(polygon '((0,0),(1,1),(2,0))')
-
-
-
-
- polygon
-
- polygon(box)
-
- polygon
- box to 4-point polygon
- polygon(box '((0,0),(1,1))')
-
-
- polygon(circle)
- polygon
- circle to 12-point polygon
- polygon(circle '((0,0),2.0)')
-
-
- polygon(npts, circle)
- polygon
- circle to npts-point polygon
- polygon(12, circle '((0,0),2.0)')
-
-
- polygon(path)
- polygon
- path to polygon
- polygon(path '((0,0),(1,1),(2,0))')
-
-
-
+ Geometric Type Conversion Functions
+
+
+
+
+ FunctionDescriptionExample(s)
+
+
+
+
+
+
+
+
+ box
+
+ box ( circle )
+ box
+
+ Computes box inscribed within the circle.
+
+ box(circle '<(0,0),2>')
+ (1.414213562373095,1.414213562373095),&zwsp;(-1.414213562373095,-1.414213562373095)
+
+
+
+
+
+ box ( point )
+ box
+
+ Converts point to empty box.
+
+ box(point '(1,0)')
+ (1,0),(1,0)
+
+
+
+
+
+ box ( point, point )
+ box
+
+ Converts any two corner points to box.
+
+ box(point '(0,1)', point '(1,0)')
+ (1,1),(0,0)
+
+
+
+
+
+ box ( polygon )
+ box
+
+ Computes bounding box of polygon.
+
+ box(polygon '((0,0),(1,1),(2,0))')
+ (2,1),(0,0)
+
+
+
+
+
+
+ bound_box
+
+ bound_box ( box, box )
+ box
+
+ Computes bounding box of two boxes.
+
+ bound_box(box '(1,1),(0,0)', box '(4,4),(3,3)')
+ (4,4),(0,0)
+
+
+
+
+
+
+ circle
+
+ circle ( box )
+ circle
+
+ Computes smallest circle enclosing box.
+
+ circle(box '(1,1),(0,0)')
+ <(0.5,0.5),0.7071067811865476>
+
+
+
+
+
+ circle ( point, double precision )
+ circle
+
+ Constructs circle from center and radius.
+
+ circle(point '(0,0)', 2.0)
+ <(0,0),2>
+
+
+
+
+
+ circle ( polygon )
+ circle
+
+ Converts polygon to circle. The circle's center is the mean of the
+ positions of the polygon's points, and the radius is the average
+ distance of the polygon's points from that center.
+
+ circle(polygon '((0,0),(1,3),(2,0))')
+ <(1,1),1.6094757082487299>
+
+
+
+
+
+
+ line
+
+ line ( point, point )
+ line
+
+ Converts two points to the line through them.
+
+ line(point '(-1,0)', point '(1,0)')
+ {0,-1,0}
+
+
+
+
+
+
+ lseg
+
+ lseg ( box )
+ lseg
+
+ Extracts box's diagonal as a line segment.
+
+ lseg(box '(1,0),(-1,0)')
+ [(1,0),(-1,0)]
+
+
+
+
+
+ lseg ( point, point )
+ lseg
+
+ Constructs line segment from two endpoints.
+
+ lseg(point '(-1,0)', point '(1,0)')
+ [(-1,0),(1,0)]
+
+
+
+
+
+
+ path
+
+ path ( polygon )
+ path
+
+ Converts polygon to a closed path with the same list of points.
+
+ path(polygon '((0,0),(1,1),(2,0))')
+ ((0,0),(1,1),(2,0))
+
+
+
+
+
+
+ point
+
+ point ( double precision, double precision )
+ point
+
+ Constructs point from its coordinates.
+
+ point(23.4, -44.5)
+ (23.4,-44.5)
+
+
+
+
+
+ point ( box )
+ point
+
+ Computes center of box.
+
+ point(box '(1,0),(-1,0)')
+ (0,0)
+
+
+
+
+
+ point ( circle )
+ point
+
+ Computes center of circle.
+
+ point(circle '<(0,0),2>')
+ (0,0)
+
+
+
+
+
+ point ( lseg )
+ point
+
+ Computes center of line segment.
+
+ point(lseg '[(-1,0),(1,0)]')
+ (0,0)
+
+
+
+
+
+ point ( polygon )
+ point
+
+ Computes center of polygon (the mean of the
+ positions of the polygon's points).
+
+ point(polygon '((0,0),(1,1),(2,0))')
+ (1,0.3333333333333333)
+
+
+
+
+
+
+ polygon
+
+ polygon ( box )
+ polygon
+
+ Converts box to a 4-point polygon.
+
+ polygon(box '(1,1),(0,0)')
+ ((0,0),(0,1),(1,1),(1,0))
+
+
+
+
+
+ polygon ( circle )
+ polygon
+
+ Converts circle to a 12-point polygon.
+
+ polygon(circle '<(0,0),2>')
+ ((-2,0),&zwsp;(-1.7320508075688774,0.9999999999999999),&zwsp;(-1.0000000000000002,1.7320508075688772),&zwsp;(-1.2246063538223773e-16,2),&zwsp;(0.9999999999999996,1.7320508075688774),&zwsp;(1.732050807568877,1.0000000000000007),&zwsp;(2,2.4492127076447545e-16),&zwsp;(1.7320508075688776,-0.9999999999999994),&zwsp;(1.0000000000000009,-1.7320508075688767),&zwsp;(3.673819061467132e-16,-2),&zwsp;(-0.9999999999999987,-1.732050807568878),&zwsp;(-1.7320508075688767,-1.0000000000000009))
+
+
+
+
+
+ polygon ( integer, circle )
+ polygon
+
+ Converts circle to an n-point polygon.
+
+ polygon(4, circle '<(3,0),1>')
+ ((2,0),&zwsp;(3,1),&zwsp;(4,1.2246063538223773e-16),&zwsp;(3,-1))
+
+
+
+
+
+ polygon ( path )
+ polygon
+
+ Converts closed path to a polygon with the same list of points.
+
+ polygon(path '((0,0),(1,1),(2,0))')
+ ((0,0),(1,1),(2,0))
+
+
+
+
+
@@ -9951,22 +10563,6 @@ CREATE TYPE rainbow AS ENUM ('red', 'orange', 'yellow', 'green', 'blue', 'purple
as an array of two point values.
-
- The area function works for the types
- box, circle, and path.
- The area function only works on the
- path data type if the points in the
- path are non-intersecting. For example, the
- path
- '((0,0),(0,1),(2,1),(2,2),(1,2),(1,0),(0,0))'::PATH
- will not work; however, the following visually identical
- path
- '((0,0),(0,1),(1,1),(1,2),(2,2),(2,1),(1,1),(1,0),(0,0))'::PATH
- will work. If the concept of an intersecting versus
- non-intersecting path is confusing, draw both of the
- above paths side by side on a piece of graph paper.
-
-