LandXML Encoding of Mixed 2D and 3D Survey Plans with Multi-Level Topology †
Abstract
:1. Introduction
Methodology
2. Background
2.1. Survey Plans
2.2. Topology in Cadastral Data
3. Topological Representation of 2D and 3D Spatial Units
- The 2D Land Parcel;
- The Building Format Unit (where the definition of the parcel is the actual building walls);
- The Polygonal Slice (where the units are described by vertical planes, with height limits);
- The Single-Valued Stepped Slice (where all surfaces are vertical or horizontal, and the unit does not have parts overlying other parts);
- The Multi-Valued Stepped Slice (where all surfaces are vertical or horizontal, but parts may overlie others); and
- General 3D Parcels (with few restrictions beyond validity).
3.1. 2D Cadastral Spatial Unit
- (1)
- Line segment a has Lot 25 and Easement C on left; Lot 26 on right;
- (2)
- Line segment b has Lot 25, Easement A and C on left; Lot 26 and Easement A on right;
- (3)
- Line segment c has Lot 25 and Easement A on left; Lot 26 and Easement A on right;
- (4)
- Line segment d has Lot 25 on left, Lot 26 on right;
- (5)
- Line segment e has Lot 25 on left;
- Therefore, Lot 25 is defined as being on the left of line segments a,b,c,d,e,f,g,h,i,j and both sides of t,s,r,v,u;
- Lot 26 is left of k,l,m,n, right of a,b,c,d and both sides of q,p;
- Easement A is left i and m, right of t,p,q,r,s and both sides of b,c,v.
3.2. Extension to 3D
3.3. Simple 3D Spatial Unit
3.4. Complex 3D Spatial Units
3.5. Multi-Level Case of a Tunnel Below a Building
3.6. Multi-Level Hierarchical Case—A High-Rise Building
Lot 3 Part K
4. Representation in LandXML
- Parcel: in LandXML, the term “parcel” is overloaded to include volumes, faces, and face strings. The class attribute of the parcel element makes this explicit (Face, Lot, FaceString, etc.)
- Parcels: Parcels are a collections of parcels that are used to define a higher-level parcel. For example, a set of Faces and FaceStrings that define a volume.
- CoordGeom: Strictly speaking, this defines a chain of straight line segments, but traditionally in LandXML encoding, a closed CoordGeom is assumed to be a planar surface (polygon).
4.1. 2D Cadastral Spatial Units
<Parcel class=“FaceString” name=“a”> <CoordGeom><Line><Start pntRef=“1”/><End pntRef=“2”/></Line> </CoordGeom></Parcel> <Parcel class=“FaceString” name=“b”> <CoordGeom><Line><Start pntRef=“2”/><End pntRef=“3”/></Line> </CoordGeom></Parcel> (etc.) <Parcel class=“Lot” name=“25” parcelFormat=“Standard”> <Parcels> <Parcel pclRef=“a” /> <Parcel pclRef=“b”/> (etc.) <Parcel pclRef=“i”/> (etc.) </Parcels> </Parcel> <Parcel class=“Lot” name=“26” parcelFormat=“Standard”> <Parcels> <Parcel pclRef=“a” /> <Parcel pclRef=“b”/> (etc.) <Parcel pclRef=“k”/> (etc.) </Parcels> </Parcel> <Parcel class=“Easement” name=“A” parcelFormat=“Standard”> <Parcels> <Parcel pclRef=“i” /> <Parcel pclRef=“r”/> (etc.) </Parcels> </Parcel> … etc. |
4.2. Simple 3D Spatial Unit
<Parcel class=“FaceString” name=“U1”> <CoordGeom><Line><Start pntRef=“2”/><End pntRef=“21”/></Line> <Line><Start pntRef=“21”/><End pntRef=“22”/></Line> <Line><Start pntRef=“22”/><End pntRef=“9”/></Line> </CoordGeom></Parcel> <Parcel class=“FaceString” name=“K1”> <CoordGeom><Line><Start pntRef=“9”/><End pntRef=“8”/></Line> </CoordGeom></Parcel> <Parcel class=“FaceString” name=“K2”> <CoordGeom><Line><Start pntRef=“8”/><End pntRef=“7”/></Line> </CoordGeom></Parcel> <Parcel class=“Face” name=“t1”> <CoordGeom><Line><Start pntRef=“2b”/><End pntRef=“74b”/></Line> <Line><Start pntRef=“74b”/><End pntRef=“3b”/></Line> <Line><Start pntRef=“3b”/><End pntRef=“2b”/></Line> </CoordGeom></Parcel> (etc.) <Parcel class=“Lot” name=“904” parcelFormat=“Volumetric”> <Parcels> <Parcel pclRef=“U1”/> <Parcel pclRef=“K1”/> <Parcel pclRef=“K2”/> (etc.) <Parcel pclRef=“t1”/> <Parcel pclRef=“t2”/> (etc.) </Parcels> </Parcel> <Parcel class=“Road” parcelFormat=“Standard”> <Parcels> <Parcel pclRef=“K1” /> <Parcel pclRef=“K2”/> (etc.) <Parcel pclRef=“¬t1”/> <Parcel pclRef=“¬t2”/> <Parcel pclRef=“u1”/> (etc.) </Parcels> </Parcel> etc. |
4.3. Complex 3D Spatial Units
<Parcel class=“FaceString” name=“a”> <CoordGeom> detail </CoordGeom></Parcel> <Parcel class=“FaceString” name=“b”> <CoordGeom> detail </CoordGeom></Parcel> <Parcel class=“FaceString” name=“c”> <CoordGeom> detail </CoordGeom></Parcel> <Parcel class=“FaceString” name=“d”> <CoordGeom> detail </CoordGeom></Parcel> <Parcel class=“Face” name=“e”> <CoordGeom> detail </CoordGeom></Parcel> <Parcel class=“Face” name=“f”> <CoordGeom> detail </CoordGeom></Parcel> <Parcel class=“Face” name=“g”> <CoordGeom> detail </CoordGeom></Parcel> <Parcel class=“Face” name=“h”> <CoordGeom> detail </CoordGeom></Parcel> <Parcel class=“Face” name=“i”> <CoordGeom> detail </CoordGeom></Parcel> <Parcel class=“Lot” name=“L1” parcelFormat=“Volumetric”> <Parcels> <Parcel pclRef=“a”/> <Parcel pclRef=“b”/> <Parcel pclRef=“c”/> <Parcel pclRef=“d”/> <Parcel pclRef=“e”/> <Parcel pclRef=“f”/> <Parcel pclRef=“g”/> <Parcel pclRef=“h”/> <Parcel pclRef=“i”/> </Parcels> </Parcel> <Parcel class=“Lot” name=“Common Property” parcelFormat=“Standard”> <Parcels> <Parcel pclRef=“a”/> <Parcel pclRef=“b”/> <Parcel pclRef=“c”/> <Parcel pclRef=“d”/> <Parcel pclRef=“e”/> < Parcel pclRef=“f”/> <Parcel pclRef=“g”/> <Parcel pclRef=“h”/> <Parcel pclRef=“i”/> </Parcels> </Parcel> etc. |
4.4. Case of a Tunnel Below a Building (from Section 3.5)
4.5. Multi-Level Hierarchical Case—High-Rise Building from Section 3.6
4.5.1. Encoding of Lot 3 Part K
<Parcel class=“FaceString” name=“TowerOuter”> <CoordGeom><Line><Start pntRef=“271”/><End pntRef=“276”/></Line> <Line><Start pntRef=“276”/><End pntRef=“275”/></Line> <Line><Start pntRef=“275”/><End pntRef=“274”/></Line> <Line><Start pntRef=“274”/><End pntRef=“273”/></Line> <Line><Start pntRef=“273”/><End pntRef=“272”/></Line> <Line><Start pntRef=“272”/><End pntRef=“271”/></Line> </CoordGeom></Parcel> <Parcel class=“FaceString” name=“LiftWell5Inner”> <CoordGeom><Line><Start pntRef=“23”/><End pntRef=“20”/></Line> <Line><Start pntRef=“20”/><End pntRef=“21”/></Line> <Line><Start pntRef=“21”/><End pntRef=“22”/></Line> <Line><Start pntRef=“22”/><End pntRef=“23”/></Line> </CoordGeom></Parcel> |
<Parcel class=“Face” name=“KTop”> <CoordGeom><Line><Start pntRef=“271b”/><End pntRef=“276b”/></Line> <Line><Start pntRef=“276b”/><End pntRef=“275b”/></Line> <Line><Start pntRef=“275b”/><End pntRef=“274b”/></Line> <Line><Start pntRef=“274b”/><End pntRef=“273b”/></Line> <Line><Start pntRef=“273b”/><End pntRef=“272b”/></Line> <Line><Start pntRef=“272b”/><End pntRef=“271b”/></Line> </CoordGeom></Parcel> |
<Parcel class=“Face” name=“KTop” a=“0” b=“0” c=“-1” d=“137.625”/> |
<Parcel class=“FaceString” name=“LiftWell2Outer”> <CoordGeom><Line><Start pntRef=“25”/><End pntRef=“24”/></Line> <Line><Start pntRef=“24”/><End pntRef=“28”/></Line> <Line><Start pntRef=“28”/><End pntRef=“29”/></Line> <Line><Start pntRef=“29”/><End pntRef=“25”/></Line> </CoordGeom></Parcel> <Parcel class=“FaceString” name=“LiftWell4Outer”> <CoordGeom><Line><Start pntRef=“23”/><End pntRef=“132”/></Line> <Line><Start pntRef=“132”/><End pntRef=“131”/></Line> <Line><Start pntRef=“131”/><End pntRef=“22”/></Line> <Line><Start pntRef=“22”/><End pntRef=“23”/></Line> </CoordGeom></Parcel> |
<Parcel class=“LOT” name=“3K” parcelFormat=“Volumetric”> <Parcels> <Parcel pclRef=“TowerOuter”/> <Parcel pclRef=“LiftWell5Inner”/> <Parcel pclRef=“KTop”/> <Parcel pclRef=“JTop” /> <Parcel pclRef=“¬LiftWell2Outer”/> <Parcel pclRef=“¬LiftWell4Outer”/> </Parcels> |
<Parcel class=“FaceString” name=“Lot5Outer”> <CoordGeom> (the definition of the original 2D lot as a footprint face string) </CoordGeom></Parcel> <Parcel class=“LOT” name=“5” parcelFormat=“Volumetric”> <Parcels> <Parcel pclRef=“Lot5Outer” /> <Parcel pclRef=“-4” /> <Parcel pclRef=“-3”/> <Parcel pclRef=“-2” /> <Parcel pclRef=“-Road” /> ... </Parcels> </Parcel> |
4.5.2. Encoding the Units within Lot 3
<Parcel class=“LOT” name=“3701U” parcelFormat=“Building”> <Parcels> <Parcel pclRef=“Unit3101-3102” /> <Parcel pclRef=“Unit3101Outer”/> etc. <Parcel pclRef=“36Top”/> <Parcel pclRef=“37Top”/> </Parcels> </Parcel> <Parcel class=“LOT” name=“3801U” parcelFormat=“Building”> <Parcels> <Parcel pclRef=“Unit3101-3102” /> <Parcel pclRef=“Unit3101Outer”/> etc. <Parcel pclRef=“¬37Top”/> <Parcel pclRef=“38Top”/> </Parcels> </Parcel> |
<Parcel class=“LOT” name=“3201” parcelFormat=“Building”> <Parcels> <Parcel pclRef=“+3201U” /> <Parcel pclRef=“+3201P”/> </Parcels> </Parcel> |
4.6. Spatial Logic Issues
<Parcel class=“LOT” name=“L” parcelFormat=“Volumetric”> <Parcels> <Parcel pclRef=“OuterFootprint”/> <Parcel pclRef=“CourtyardFootprint”/> <Parcel pclRef=“Top1”/> <Parcel pclRef=“¬Top2” /> <Parcel pclRef=“-LiftWell”/> <Parcel pclRef=“+RoofShed”/> </Parcels> </Parcel> |
4.7. Curved Surfaces
<Parcel class=“FaceString” name=“Outer”> <CoordGeom><Curve radius=“25” rot=“acw”> <Start pntRef=“1”/><End pntRef=“1”/></Curve> </CoordGeom></Parcel> <Parcel class=“Face” name=“Top” a=“0” b=“0” c=“-1” d=“130”/> <Parcel class=“Face” name=“Bottom” a=“0” b=“0” c=“1” d=“-120”/> |
4.8. Alternate Encodings
5. Implementation Issues
5.1. Completeness of Implementation
5.2. Conversion to Polyhedron Form
5.3. Conversion from Polyhedra Form
- (1)
- The parameters (a,b,c,d) of each face are calculated. This is not trivial, involving a least-squares fitting of the function aX + bY + cZ + d to the set of vertices of the face, but this is a necessary action in any case to validate the face. Where c < 0, this is a top face, and it is replaced by a 2D polygon, with Z = 0 for each vertex. Where c ≥ 0, the face is discarded.
- (2)
- These polygons are then dissolved to produce a (multi) polygon (with possible holes). This becomes the footprint boundary face string.
- (3)
- The faces are then re-scanned, and any with c = 0 are tested against the boundary face string. If they fall within it, they are discarded. Otherwise, they are retained, along with all faces with c ≠ 0, as boundary faces.
- (4)
- This produces a non-topological encoding of the spatial units of the plan. Normal 2D algorithms can be used to convert the face strings to a topological network that encodes the individual spatial units in 2D. In a similar way, shared faces can be detected and encoded.
5.4. Viewing and Manipulating Data Using 2D Software
5.5. Calculations and Rounding Errors
6. Analysis of Results
6.1. Sharing of Data
- Some definitions are not shared: Face strings at the edge of the plan, and faces that surround a secondary interest (not excised from the enclosing spatial unit) are examples.
- Many definitions are shared by exactly two spatial units—where they form the boundary between them.
- A significant number of face strings are shared a large number of times: For example, the face string “Unit3101–3102” defined in Section 4.5.2 would be used in the units 3101 to 3910 (9 units), and reversed in 3102 to 3902. A total of 18 usages.
7. Conclusions and Future Research
7.1. Major Results
- It is a close fit to current cadastral survey practice (Section 3.2).
- It permits efficient encoding, explicit semantics on neighbors, reduction of redundancy, and avoids inconsistencies. (Section 6.1)
- It is capable of being viewed and even manipulated by software that is strictly 2D (not 3D-aware) (see Section 5.4).
7.2. Future Work
Author Contributions
Conflicts of Interest
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Face String | + Spatial Unit(s) | − Spatial Unit(s) |
---|---|---|
a | Lot 25 | Lot 26 |
b | Lot 25 | Lot 26 |
d | Lot 25 | Lot 26 |
i | Easement A, Lot 25 | |
p | Easement A | |
q | Easement A |
Line | + Spatial Unit(s) | − Spatial Unit(s) |
---|---|---|
A1 | Lot CP | Mark Lane (road) |
A2 | Lot CP, Easement A | Mark Lane (road) |
B | Lot CP, Easement A | Lot 1/RP11181 |
B1 | Easement A | |
C2 | Lot CP, Easement A | Lot 9/SP184393 |
C1 | Lot CP | Lot 9/SP184393 |
D | Lot CP, Lot 210 | Lot 9 and Lot 209/SP184393 |
E1 | Lot CP, Lot 210 | Main Street (road) |
E2 | Lot 210, New Road | Main Street (road) |
F2 | Lot 210, New Road | Mark Lane (road) |
F1 | Lot CP, Lot 210 | Mark Lane (road) |
G | Lot 210 | |
K | Lot CP | New Road |
L | Unit 10 part 1, Unit 4 | |
M | Unit 10 part 1, Unit 4 | |
N | Unit 10 part 1, Unit 4 | Unit 10 part 2, Unit 10 part 4 |
P | Unit 10 part 1, Unit 4 | |
Q | Unit 10 part 1, Unit 4 |
Face | + Spatial Unit(s) | − Spatial Unit(s) |
---|---|---|
t1 | Lot 210 | Lot CP |
t2 | Lot 210 | Lot CP |
t3 | Lot 210 | New Road |
b1 | Lot CP | Lot 210 |
b2 | Lot CP | Lot 210 |
b3 | New Road | Lot 210 |
g | Lot 210 | Lot CP |
ab10 | Unit 10 part 1 | Common Property |
bc4 | Unit 4 | Unit 10 part 1 |
cd7 | Unit 7 (not in diagram) | Unit 4 |
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Thompson, R.J.; Van Oosterom, P.; Soon, K.H. LandXML Encoding of Mixed 2D and 3D Survey Plans with Multi-Level Topology. ISPRS Int. J. Geo-Inf. 2017, 6, 171. https://doi.org/10.3390/ijgi6060171
Thompson RJ, Van Oosterom P, Soon KH. LandXML Encoding of Mixed 2D and 3D Survey Plans with Multi-Level Topology. ISPRS International Journal of Geo-Information. 2017; 6(6):171. https://doi.org/10.3390/ijgi6060171
Chicago/Turabian StyleThompson, Rodney James, Peter Van Oosterom, and Kean Huat Soon. 2017. "LandXML Encoding of Mixed 2D and 3D Survey Plans with Multi-Level Topology" ISPRS International Journal of Geo-Information 6, no. 6: 171. https://doi.org/10.3390/ijgi6060171