Shape comparison language

形状比较语言, 九交模型

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About shape comparison language

In the interest of supporting the Open Geodata Interoperability Specification (OGIS) and SQL3/MM initiatives, ESRI is implementing in SDE a language syntax for the evaluation of relationships between shapes, which will eventually replace the use of SDE search methods and search masks for defining search criteria, and for expressing relationships between shapes. The syntax of the shape comparison language (SCL) is based on the Calculus-Based Method (CBM) as described and defined by Clementini and Felice, with extensions.

The CBM defines shape relationships by the intersection of their boundary, interior, and exterior, taking the dimensionality of the intersection into account. The following are the five basic relationships: Touch, Overlap, In, Cross, and Disjoint. These relationships are defined such that for any two given shapes, only one of these five relationships is true. In addition, SCL supports the additional relationship of IDENTICAL, which is true only when two shapes are geometrically identical and share correct topological integrity.

The CBM and SCL perform relationship comparison to a maximum of two dimensions, thus SCL can only be used to describe zero, one, and two dimensional relationships. This is consistent with previous versions of SDE wherein the SDE search methods only described two dimensional relationships.

Dimensionality

To use SCL you must understand the following concepts of shape boundary and interior, as well as dimensionality:

All point shapes are zero dimensional
All linear shapes are one dimensional
All area shapes are two dimensional

The previous is true for SCL regardless that the shape may or may not have z-coordinates or that it may have measures.

Interior—The dimension of the interior of a shape is always that of the shape. Thus, the dimension of the interior of a linear shape is one. All shapes have interior. The interior of a shape is defined as the entire shape minus its boundary.
Boundary—The dimension of the boundary of a shape is always that of the shape minus one. Thus, the dimension of the boundary of a linear shape is zero and the dimension of the boundary of any point shape is –1 or NIL. Linear and area shapes have boundary, but point shapes do not. The boundary of linear shapes consists of the end points of all linear parts. The boundary of area shapes consists of the linear boundary of the polygon shell or shells.
Exterior—The dimension of the exterior of any shape is always two. All shapes have an exterior.

Extensions to the CBM

The CBM does not differentiate between an intersection that occurs at a shape vertice and an intersection that occurs between shape vertices. Because it is often crucial to maintain topological integrity between shapes, and to know when there is a lack of topological integrity between shapes, SCL has been extended as follows:

TOPOFORM—A unary function that evaluates to true if topological integrity exists between two shapes, and false if there is a lack of topological integrity. A lack of topological integrity is defined as intersection that is other than topological adjacency.

SCL syntactical

SCL is used to describe the relationship between two specific or in the case of spatial searches, hypothetical shapes. SCL expressions evaluate to true or false, except in the case of the DIM functions, which evaluate to a dimension value.

The general form of an SCL statement consists of one or more spatial assertions. Multiple assertions may be connected into a single assertion using the logical connecting operators AND, OR, and XOR. Parenthetical expression hierarchy is supported. SCL expressions are not case dependent.

Example 1: G1 NOT DISJOINT G2—The previous case evaluates true if the shapes g1 and g2 touch or overlap. Both G1 and G2 are reserved words that refer, respectively, to shape #1 and shape #2.
Example 2: (g1 overlap g2 and dim (g2) = area) or (g2 cross g1 and dim (g2) = linear)—The previous case evaluates true if the g2 shape is an area and meets the intersection criteria defined by the overlap keyword or if the g2 shape is linear and meets the intersection criteria defined by the cross keyword.

SCL uses the numeric constants TRUE, FALSE, POINT, LINEAR, AREA, NIL, and NULL, rather than numeric literals. SCL does not support user variables or numeric literals. The terms NIL and NULL can be used interchangeably and are used to refer to a lack of a specific type of intersection.

SCL allows binary spatial relationships to be expressed as a function or as an operation between the two shape constants G1 and G2. For example, the expression G1 cross G2 is equivalent to the expression cross (g1, g2) = true. The expression G1 not cross G2 is equivalent to the expression cross (g1, g2) = false or cross (g1, g2) != true.

In SCL, the DIM function is two different functions, depending upon the number of arguments. If there is only one argument, it returns the dimensionality of a shape or shape component, such as dim (g1) or dim (g1.boundary). If there are two arguments, the dim function returns the dimension of intersection between the two expressed shapes or shape components, such as dim (g1, g2) or dim (g1.interior, g2.boundary).

Dimension functions

The dimension functions are the most powerful functions in SCL for the assertion of spatial relationships. The dimension function DIM takes one or two spatial object arguments and performs a different function depending on the number of arguments used. All of the Clementini relationship operators can be defined using these two DIM functions.

The spatial object modifiers boundary, interior, and exterior can only be used as modifiers for the spatial entity arguments to the DIM function. The modifier use form is: <spatial entity reference><period><spatial-modifier> in the form g1.boundary.

DIM function form 1

Returns the spatial dimension of a spatial entity or a component (boundary, interior, or exterior) of a spatial entity.

Syntax: DIM (spatial-object)—Where spatial-object is one of the following:
G1
G1.BOUNDARY
G1.INTERIOR
G1.EXTERIOR
G2
G1.BOUNDARY
G1.INTERIOR
G1.EXTERIOR

Returns the spatial dimension of the referenced spatial object, which evaluates to one of the following supported dimension constants:

NIL, NULL (-1)
POINT 0
LINEAR 1
AREA 2
Usage examples:
"dim (g1.interior) >= linear"
"dim (g1) = dim(g2)"
"dim (g1) >= dim(g2.interior)"

DIM function form 2

Returns the spatial dimension of intersection between two spatial entities or components (boundary, interior, or exterior) of the entities.

Syntax: DIM (spatial-object1, spatial-object2)—Where spatial-object1 and spatial-object2 are one of the following and both spatial objects may not refer to the same shape (G1 or G2):
G1
G1.BOUNDARY
G1.INTERIOR
G1.EXTERIOR
G2
G1.BOUNDARY
G1.INTERIOR
G1.EXTERIOR

Returns the spatial dimension of intersection between the referenced spatial objects, which evaluates to one of the following supported dimension constants:

NULL (-1)
POINT 0
LINEAR 1
AREA 2
Usage examples:
"dim(g1.interior,g2) >= linear"
"dim(g1,g2) = dim(g2)"
"dim(g1.boundary,g2.boundary) > point"

Spatial relationship functions and expressions

The CBM and SCL are not intuitive. It is essential to commit the following definitions to memory before using SCL. The following are the criteria for relationship evaluation:

The seven spatial relationships can be expressed as functions or relations. For example, the following TOUCH relationship can be expressed as: A relation, "G1 TOUCH G2" or as a function, "touch (g1,g2) = true."
The function form is "<function (spatial entity, spatial entity)> <equality operator> <truth constant>." The relation form is "<spatial entity> <relation name> <spatial entity>."
The logic requirements of the relations TOUCH, CROSS, IN, CONTAIN, OVERLAP, and DISJOINT preclude the use of modifiers to spatial entity specifications; use G1 or G2 as spatial arguments and the use of modifiers, such as "G1.BOUNDARY" are not allowed.
The INTERSECT relation does allow the use of the modifiers BOUNDARY, INTERIOR, and EXTERIOR to the spatial arguments G1 and G2. Examples of appropriate usage form are "g1.interior intersects g2.exterior" and "g1.boundary intersect g2."
If the relationship is expressed as a function, you must compare the result of the function to the constants TRUE or FALSE, e.g., "intersect (g1,g2) = true."

TOUCH spatial relation
Applies to area/area, line/line, line/area, point/area, and point/line groups with the following criteria:

The dimension of intersection between G1 and G2 is not null.
The dimension of intersection between the interior of G1 and the interior of G2 is null.

"G1 TOUCH G2" is equivalent to the following statement: "dim(g1.interior, g2.interior) = null and dim(g1,g2) != null."