Spatial data types inSQL Server 2008: computation and

visualizationMarko TintorDanica PorobićMicrosoft Development Center Serbia

Agenda

Spatial in SQL Server 2008

• What is spatial about?• Applications• Types, operations and indexing

Computation on Earth surface

• Numerical operations• Set operations

Projections and visualization

• 3D visualization tool• Extensible projection framework

Q/A

Virtual Earth with SQL Server

What is Spatial about?

TraditionalGIS

NowConsumer

DevelopingLOBUbiquity

Spatial Data ScenariosCustomer-base

management and development

Environmental-related data

impact, analysis, and planning

Financial and economic analysis in

communities

Government-based planning

and development analysis

Market segmentation and analysis

Scientific research study

design and analysis

Real-estate development and analysis

Spatial in SQL 2008

We’re providing vector supportWe’re targeting geospatial...

Spatial data which is referenced to a location on the EarthTypically uses spherical coordinates or projected planar coordinates I’ll come back to this distinction in a moment

...but, there is no restriction that the data is actually geospatialOnly 2D for now (Geodetic is 2D)

What is Spatial Data?Vector

PointsLineStringsPolygons (Areas, Regions)

RasterSatellite ImageryDigitized Aerial Photos

Sample QueryWhich roads intersect Microsoft’s main campus?

SELECT * FROM roads WHERE roads.geom.Intersects(@ms)=1

It’s a big problem…

It can be complex, too...

All Flat Maps Are Wrong

Flat maps are projections from the spheroid

Small areas don’t distort too muchLarge areas do, so no good global projectionStill very important for legislative and historical reasons

conic secant projection

Comprehensive Spatial SupportSpatial Data Types

geography data type• Geodetic (“Round Earth”)

geospatial model• Define points, lines, and areas

with longitude and latitude• Account for planetary

curvature and obtain accurate “great circle” distances

geometry data type• Planar (“Flat Earth”)

geospatial model• Define points, lines, and

areas with coordinates• Use for localized areas or

non-projected surfaces such as interior spaces

Planar and Geodetic Cover Different Scenarios

Planar (flat-earth)Supports legacy and legal mapping requirements: surveyors and the specialist GIS crowdComputationally simplerConceptually more difficult for geospatial

Geodetic (round-earth)

Supports existing long-range mapping requirements: military, shipping, etc.Computationally more complexConceptually simpler for geospatial

Spatial Operators World Class

Relationships

• Intersects• Touches• Disjoint

Constructions

• Intersection, Union, Difference

Numeric Computations

• Distance, Length• Area

Special Operations

• Point in polygon• Buffer• Reduce

Planar TypeNew type: geometryBuilt on the same infrastructure Geometry can store instances of various types

PointsLine stringsPolygonsCollections of the above

Methods for computingSpatial relationships: intersects, disjoint, etc.Spatial constructions: intersection, union, etc.Metric functions: distance, area

Geodetic Type

Second type: geographyVery similar interface to geometry

Some methods have different semanticsMost data commonly available user data is geodetic

Anything expressed as latitude/longitudeThis is the type we expect most people to be interested in

Demo Architecture

Web Server

Client

VirtualEarth

Service

SQL Server

Demo Data

E75 and Counties

Flood Analysis

Economic Development Analysis

High Performance Spatial CapabilitiesSpatial Indexing

Spatial indexing is built into the query engineGrid-based quad-tree index structure

Multi-Level Grid

42.3

Spatial Index Performance

Indexed Operations

• g1.STIntersects(geometry2) = 1• g1.STTouches(geometry2) = 1• g1.STEquals(geometry2) = 1• g1.STWithin(geometry2) = 1• g1.STContains(geometry2) = 1• g1.STDistance(geometry2) < number• No native support for nearest neighbor

Defining edges on round Earth

Requirements:Locally: edge should appear straightPair of points should define unique edgeEdge should have differentiable parameterization

Possible solution: Geodesic curves (shortest path between points)

Not suitable for points that are not on surfaceTwo points define more than one edgeComputations are extremely difficult

Definition in SQL Server Spatial

Space of directions:Geographic coordinates of a point on the globe are defined by the direction of a vector that is normal to the surface of the globe at that pointSpace of directions – nonzero normal vectors

Definition:An edge is the image under the Inverse Gaussian Mapping (IGM) of the short great circle arc on the sphere of directions between the unit normal vectors at its endpointsAn edge is the image under the IGM of a line segment in the space of directions

Mapping from normal vectors to points on ellipsoid

Surface of rotational ellipsoid:

Let (u,v,w) be normal at the surface of (x,y,z), so under IGM:

Mapping is:

12

2

2

2

2

2

b

z

a

y

a

x

222

2,

2,

2),,(

b

z

a

y

a

xrwvu

222222

222 ),,(),,(

wbvaua

wbvauawvuE

Parameterization of an edge

Great-circle arc on the sphere of unit normal vectors

Edge on ellipsoid

Linear parameterization of great circle arc’s chord

Parameterization

}10:))(),(),({( ttwtvtu

}10:))(),(),(({ ttwtvtuE

}10:)1()({ ttBAttL

}10:)({)( ttLEtX

Numeric computations

Velocity vector:

Length of an edge:

Area: sum of integrals over edges

Computation using Gauss Legendre quadratureLong edges broken into pieces

))('),('),('()(' tztytxtX

1

)(')('o

tXtX

Boolean operations

Spherical arcs projected to lines using gnomonic projectionsBoolean operations on sphere transform to their planar counterparts after projectionPlanar operations rely on geometric library from Windows VistaGnomonic projection works for smaller objectsLarger objects handled by tiled projection

Simple gnomonic projection

Central projection from the origin to a plane that is tangent to the unit sphereThe image of a polygon on sphere is a polygon in the planeLet C be the point of tangencyBasis vectors: two mutually orthogonal unit vectors A and B, orthogonal to CProjection of vector U:

V = U/U∙CPlanar coordinates: (V-C)∙A and (V-C)∙B

Tiled projection

Map the scene with simple projections onto four facets of the tetrahedronAffine projection along the axis into the plane

Crease

Tile

Visualization of geography

Building blocksPointsLineStringsPolygons

Points and LineStrings are easy to displayBut, how to display the polygons?

Rendering polygons on Earth

Even polygons with small number of vertices can have unintuitive shape

Polygon rendering issues

curved (spherical) surfacepolygons can have holespolygons can be non-convexpolygons can be near / span over polespolygons can cross ±180 degrees meridian

Possible solutions

VectorSubdivide the polygon untilall parts are simple enough

RasterRender the polygon to the textureand wrap that texture around sphere

Our idea

Subdivide entire Earth into patchesRender only the patches that are on the inside of the polygonUse smaller patches near the border of polygon

Possible relations ofpatch and the polygon

Completely insideOn the borderCompletely outside

Core algorithm

FUNC RenderPatch(patch, polygon)IF patch is INSIDE the polygon

Render(patch)IF patch is ON BORDER of the polygon

AND patch is not too smallFOREACH piece IN

Subdivide(patch) RenderPatch(piece, polygon)

IF patch is OUTSIDE polygonignore it

Best choice for patch shape

TriangleEasy to renderEasy to subdivideEasy to tile

How to subdivide the Earth?

Start from octahedronSubdivide each triangle recursively

End result in wireframe

Questions?

Thank you!

Resources

Sql Server Spatialhttp://

www.microsoft.com/sqlserver/2008/en/us/spatial-data.aspx

Microsoft Development Center Serbiahttp://www.microsoft.com/scg/mdcs/default.mspx

Defining Edges on a Round EarthMichael Kallay, Microsoft CorporationACM GIS ’07, Seattle, November 2007