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Title
Abstract
Figures
Introduction
Previous Work
System Overview
Data Structure
Algorithm Overview
Results
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Computer Science

Procedural Generation of Parcels in Urban Modeling

Profile image of Carlos Alberto González VanegasCarlos Alberto González Vanegas

2012, Computer Graphics Forum

https://doi.org/10.1111/J.1467-8659.2012.03047.X
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10 pages

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Abstract

Procedural Parcel Generation. Our method creates parcels inside city blocks (f,i) using two different subdivision techniques-skeleton (g, shaded part of f) or OBB (h, unshaded part of f). The subdivision attributes are automatically extracted from observed real-world cities (a,b,c) or determined by the user. The resulting parcel configurations closely resemble real-world subdivisions, as shown by our statistical and visual comparison of procedural and observed parcel datasets (d,e).

Figures (10)
Figure 1: Procedural Parcel Generation. Our method creates parcels inside city blocks (f,i) using two different subdivision techniques — skeleton (g, shaded part of f) or OBB (h, unshaded part of f). The subdivision attributes are automatically extracted from observed real-world cities (a,b,c) or determined by the user. The resulting parcel configurations closely resemble real-world subdivisions, as shown by our statistical and visual comparison of procedural and observed parcel datasets (d,e). Carlos A. Vanegas”! Tom Kelly* 31 Basil Weber!, Jan Halatsch*, Daniel G. Aliaga2*, and Pascal Miiller!
Figure 1: Procedural Parcel Generation. Our method creates parcels inside city blocks (f,i) using two different subdivision techniques — skeleton (g, shaded part of f) or OBB (h, unshaded part of f). The subdivision attributes are automatically extracted from observed real-world cities (a,b,c) or determined by the user. The resulting parcel configurations closely resemble real-world subdivisions, as shown by our statistical and visual comparison of procedural and observed parcel datasets (d,e). Carlos A. Vanegas”! Tom Kelly* 31 Basil Weber!, Jan Halatsch*, Daniel G. Aliaga2*, and Pascal Miiller!
Figure 2: Comparison to existing approaches. Given a street network (a), several systems have been proposed to create parcels. The Voronoi tessellation of points near the bor- der of the street is one geometrical approach (b), while a minimum area bounding box approach has also been sug- gested [WCP* 11] (c). Cube packing is another approach that leads to badly formed parcels in concave areas (d). We show our result (e) which gives a statistically realistic result. A comparison to [WMWG09] is presented in Appendix C.
Figure 2: Comparison to existing approaches. Given a street network (a), several systems have been proposed to create parcels. The Voronoi tessellation of points near the bor- der of the street is one geometrical approach (b), while a minimum area bounding box approach has also been sug- gested [WCP* 11] (c). Cube packing is another approach that leads to badly formed parcels in concave areas (d). We show our result (e) which gives a statistically realistic result. A comparison to [WMWG09] is presented in Appendix C.
Figure 3: Left: The straight skeleton of a polygon (black) consists of arcs (dark blue) which define faces adjacent to each polygon edge. Right: A partial application of the straight skeleton computes the offset contour C’(B) (dashed lines). Note that the contour may split the innermost, or pa- tio, region into several portions (a,b). The individual faces of the straight skeleton conform to our definition of a strip, and we may take the supporting edges to be portions of the boundary of input polygon. We take these faces to be the ini- tial set of a-strips.
Figure 3: Left: The straight skeleton of a polygon (black) consists of arcs (dark blue) which define faces adjacent to each polygon edge. Right: A partial application of the straight skeleton computes the offset contour C’(B) (dashed lines). Note that the contour may split the innermost, or pa- tio, region into several portions (a,b). The individual faces of the straight skeleton conform to our definition of a strip, and we may take the supporting edges to be portions of the boundary of input polygon. We take these faces to be the ini- tial set of a-strips.
Figure 4: The a-strips (solid colors, a) are recovered from the skeleton and logical streets (bold lines, a). This leaves undesirable diagonal edges (red dashed lines, a). Given the classification T(vj) € None, Previous (P) or Next (N), we reassign regions (shaded, b), to create the set of B- strips. In the example (c-e) we use the classification scheme StreetLength, specifying the direction Previous. The subse- quent splits are computed over these $-strips (f).
Figure 4: The a-strips (solid colors, a) are recovered from the skeleton and logical streets (bold lines, a). This leaves undesirable diagonal edges (red dashed lines, a). Given the classification T(vj) € None, Previous (P) or Next (N), we reassign regions (shaded, b), to create the set of B- strips. In the example (c-e) we use the classification scheme StreetLength, specifying the direction Previous. The subse- quent splits are computed over these $-strips (f).
Figure 5: The slice operation divides a B-strip’s area (solid color) into parcels using the supporting edges (bold lines) to position rays (dashed lines) (a). An example showing the skeleton arcs guiding the rays (b). C. Vanegas, T. Kelly, B. Weber, J. Halatsch, D. Aliaga and P. Miiller / Procedural Generation of Parcels in Urban Modeling
Figure 5: The slice operation divides a B-strip’s area (solid color) into parcels using the supporting edges (bold lines) to position rays (dashed lines) (a). An example showing the skeleton arcs guiding the rays (b). C. Vanegas, T. Kelly, B. Weber, J. Halatsch, D. Aliaga and P. Miiller / Procedural Generation of Parcels in Urban Modeling
Figure 6: Oriented bounding box subdivision. This adap- tive algorithm recursively splits a parcel into two smaller parcels along the minor axis of the oriented bounding box of the original parcel. The subdivision continues until user- specified shape attributes are satisfied.
Figure 6: Oriented bounding box subdivision. This adap- tive algorithm recursively splits a parcel into two smaller parcels along the minor axis of the oriented bounding box of the original parcel. The subdivision continues until user- specified shape attributes are satisfied.
Figure 7: A street network (bottom left) may be interactively modified in several ways (a-f). We use our matching func- tion to compute the location of each parcel, and show the location of a given parcel (blue house) after each editing operation; moving a street graph vertex to enclose a block (a); moving an edge (b); editing the curve of two edges(c); changing the width of a street (d); changing the subdivision style (e) or scaling the street network (f).
Figure 7: A street network (bottom left) may be interactively modified in several ways (a-f). We use our matching func- tion to compute the location of each parcel, and show the location of a given parcel (blue house) after each editing operation; moving a street graph vertex to enclose a block (a); moving an edge (b); editing the curve of two edges(c); changing the width of a street (d); changing the subdivision style (e) or scaling the street network (f).
Figure 8: Relative Parcel Position Consistency. Live urban layout editing requires computing a correspondence relation between the parcels in a block before and after an editing op- eration. Our approach uses a generalization of barycentric coordinates and a distance function to estimate the relative location of a parcel inside a block and a matching parcel.
Figure 8: Relative Parcel Position Consistency. Live urban layout editing requires computing a correspondence relation between the parcels in a block before and after an editing op- eration. Our approach uses a generalization of barycentric coordinates and a distance function to estimate the relative location of a parcel inside a block and a matching parcel.
Figure 10: Skeleton Subdivision with Offsets. Residential blocks are subdivided in offset style. The similarity between the observed parcels (a,b,c) and the procedural parcels is demonstrated in the color-coded maps showing the number of neighbors of each parcel (f), and in the histograms of other geometric attributes (d,e).
Figure 10: Skeleton Subdivision with Offsets. Residential blocks are subdivided in offset style. The similarity between the observed parcels (a,b,c) and the procedural parcels is demonstrated in the color-coded maps showing the number of neighbors of each parcel (f), and in the histograms of other geometric attributes (d,e).

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