The Management of Spatial and Temporal Constraints in GIS using Pictorial Interaction on the Web Fernando Ferri IRPPS-CNR-Italy Patrizia Grifoni IRPPS-CNR-Italy Maurizio Rafanelli IASI-CNR-Italy

The problem To make available geographical databases by Web

The aim of the paper XPQL (eXtended Pictorial Query Language) mapped in Geographic Markup Language (GML 3.0).

The eXtended Pictorial Query Language The XPQL query language has: a set of spatial operators – G-union, G-difference, G-disjunction, G-touching, G- inclusion, G-crossing, G-pass-through, G-overlapping, G- equality, G-distance, G-any and G-alias a set of temporal operators: – T-before, T-meets, T-overlaps, T-starts, T-during, T-finishes and T-equals symbolic geographical objects (sgo).

Symbolic geographical objects sgo definition: where: id is the sgo identifier; objclass is the set (possibly empty) of classes iconized by ψ ; Σ represents the attributes to which the user can assign a set of values. Some attributes can be referred to a temporal dimension; Λ is the ordered set of pairs (h, v), which defines the spatial characteristics and position of the sgo with respect to a reference point in the working area.

Geometric characteristics of an sgo  Let  be an sgo, we have: ∂  = geometric border of  it is defined as: a) if  is a polygon, ∂  is the set of its accumulation points (as defined in the set theory);  if  is an open polyline, ∂  is formed by its extreme points;  if  is a point ∂  is the empty set.   °=  - ∂  geometrical interior of 

Geometric characteristics of an sgo Dim(  ) 0 if  contains at least one point but no polylines or polygons 1 if  contains at least one polyline but no polygons 2 if  contains at least one polygon.

The spatial operators of XPQL G-union definition (Uni): The G-union of two sgo  i and  j is a new sgo defined as the set of all points belonging to  i e and/or  j. G-touching definition (Tch): G-touching between two sgo  i and  j exists iff the points common to the two  are all contained in the union of their boundaries. If this condition is satisfied, the result of this operation between  i and  j is a new ψ called ψh and defined by the set of points common to  i and  j.

The spatial operators of XPQL G-inclusion definition (Inc): An sgo  i G- includes another sgo  j (and we write ψ i Inc ψ j) iff all the points of  j are also points of  i. The result is an sgo  h which coincides with the second operand  j. G-disjunction definition (Dsj): Two sgo  i and  j are G-disjoined between them (formally ψ i Dsj ψ j) if the intersection of their borders AND the intersection of their internal points is null.

The spatial operators of XPQL G-pass-through definition (Pth): Let  i be a polyline and let  j be a polygon. Then, the operator G-pass-through is applicable iff the polyline is partially inside the polygon (formally ψ i Pth ψ j).

The spatial operators of XPQL G-distance definition (Dst): Let  i,  j  A be two sgo of any type. Their distance is valuable and and  iff their intersection is null. The (minimum) distance Dst (  = min) between them is a numeric value that represents this distance. This operator can be used to find all sgo having distance θ (θ being one of the following symbols: >, <, =,,, ≠) from the reference sgo. The distance (  ) value is given by:  (  i,  j)   =  h where –  h indicates a bi-oriented segment representing the distance operator between  i,  j –  is the qualifier which solves this ambiguity –  is a selection expression that includes conventional operators (>, <, =, ≠, etc.) or methods that behave like operators.

The spatial operators of XPQL G-difference definition (Dif): Let  i,  j  A be two sgo. The difference between two symbolic objects  i and  j is defined as a new sgo (  h) which contains all the points which belong to  i but not to  j. G-crossing definition (Crs): Let,  i  A be two polylines, and let  °i   °j ≠ . Then, Cross:  i Crs  j :=  h={x: x  °i   °j } and  h  A. G-overlapping Definition (Ovl): Let  i,  j  A be two sgo of the same type. A non-null overlap exists between them iff their intersection is also non-null and has the same dimension as the sgo.

The spatial operators of XPQL G-equality definition (Eql): Two symbolic geographical objects  i and  j are topologically equal if they are of the same type and have the same shape. G-any Definition (Any): Let ψi, ψj ∈ A be two sgo. Between them any admissible relationship is valid if the G-any operator is applied between them. G-alias Definition (Als): Let  i be a sgo.  j is an alias of  i if the only difference between them is their shape.

The temporal operators of XPQL T-before (Bef) Definition : An attribute   i h of the sgo  i is T-before another attribute   j k of the sgo  j if   i h takes values (of the interval or instant) temporally “before”   j k (of the interval or instant). The attributes can take both intervals and instants as values. T-meets (Mts) Definition : An attribute   i h of the sgo  i T-meets another attribute   j k of the sgo  j if   i h takes the maximum value (of the interval or instant) temporally “coincident” with the minimum value of   j k (of the interval or instant). The attributes can take both intervals and instants as values.

The temporal operators of XPQL T-overlap (TOv) Definition : An attribute   i h of the sgo  i T-overlaps another attribute   j k of the sgo  j if   i h takes the minimum value temporally “before” the minimum value of σψ jk and the maximum value temporally “after” the minimum value of   j k. Both attributes can take intervals as values. T-starts (Sts) Definition : An attribute   i h of the sgo  i T- starts another attribute   j k of the sgo  j if   i h takes the minimum value (of the interval or instant) temporally “coincident” with the minimum value of   j k (of the interval or instant). The attributes can take both intervals and instant as values.

The temporal operators of XPQL T-during (Drg) Definition : An attribute   i h of the sgo  i is defined as T-during another attribute   j k of the sgo  j if   i h takes the minimum value temporally “after” the minimum value of σψ jk and the maximum value temporally “before” the maximum value of   j k. Both attributes can take intervals as values. T-finishes (Fns) Definition : An attribute σψ i of the sgo T- finishes another attribute   j k of the sgo  j if   i h takes the maximum value (of the attribute or instant) temporally “coincident” with the maximum value of   j k (of the interval or instant). The attributes can take both intervals and instants as values.

The temporal operators of XPQL T-equals (Tes) Definition : An attribute σψ i h of the sgo ψ i T-equals another attribute   j k of the sgo  j if   i h takes the minimum and maximum values (of the interval or instant) temporally “coincident” with the minimum and maximum values of   j k (of the interval or instant). The attributes can take both intervals and instants as values.

Translating from XPQL to GML GML is used for coding the XPQL operands, operators. There are spatial and temporal operands

Spatial feature XPQL features are: Point, Polyline, Polygon. Their GML representation: geometric classes PointType, LineStringType and PolygonType

PointType Complex Type PointType <element ref="gml:coordinates" <element ref="gml:coord"

LineStringType Complex Type LineStringType

PolygonType Complex Type PolygonType

Temporal features XPQL features are: Instant and interval. Their GML representation: TimeInstant and TimePeriod

TimeInstant <element name="TimeInstant" type="gml:TimeInstantType" substitutionGroup= "gml:_TimePrimitive"/>

TimePeriod

Coding spatial and temporal operators The XPQL temporal operators are derived from GML: AssociationType For the XPQL spatial operators, FeaturePropertyType is a particular class of properties (using the gml:AssociationType pattern) which defines associations between features.

AssociationType <element name="_association" type="gml:AssociationType" abstract="true"/>

FeaturePropertyType

Query expressed by GML “Find all roads built between the years 1980 and 1990 that pass through provinces created after 1975”

Query expressed by GML type definitions for operators =========================== --> ………… …………………….. ………… ……………………..

Query expressed by GML Query expressed by GML <!-- ============================= type definitions for different geographical layers ================================--> ………… ………………….. ………… ………………………… …………

Query expressed by GML <!-- ============================ the query example ============================= --> Example ………………….. ……………….. ……………….. ……………….. ………………..

Conclusion We are now focusing our activities on designing and implementing a new pictorial language in areas different from the geographical one. Our hope is to be able to specify relational queries in this way, without the end user needing to understand the intricacies of boolean logic or set theory.