Roofs

Styles

• There are styles of roof which have well-known meanings in architecture, although terminology does vary somewhat
• A guide (no longer offline) showed 14 different styles
  • flat, salt box, hip, gable, kicked eaves (bonnet), gambrel, mansard, pyramid, cross gable, conical, hip and gable, shed, hip with cross gables
  • a page on roofhelper has illustrations of many of these
• Unfortunately many buildings (especially modern buildings) don't use a single roof style, but combine many of them, in complex ways
• Roof Plan Components (no longer online) has great explanations and examples
  • (part of the book Architectural Drafting & Design, Alan Jefferis, Chapter 20)
  • lists 8 styles : flat, shed, gable, A-frame (half-story gable), gambrel, hip, Dutch hip (hip and gable), mansard

Terminology

• mechanicals are the things (like vents and air conditioners) placed on top of roofs
• a parapet is when a section of roof extends upward above the height of the building, useful for hiding the mechanicals - sometimes the highest part of the building's facade
• roof angle (pitch) is conventionally expressed as a rise/run fraction over 12, e.g. 3/12
• a dormer is a extension of part of the roof to allow a vertical window to be added (picture on right)
• a cornice is the overhanging part of the roof (the part that sticks out past the walls), although generally the term is used more often for horizontal cornice features in classical architecture - not be confused with a stripe of internal moulding, generally at the ceiling, also called a cornice
• an eave is the beam ends of the roof that extend over the walls to allow water to drip off away from the building's walls - it can be thought of as the structure elements which supports the cornice
• a fascia is the outward-facing edge of the cornice

Roof Materials

• 4 general types: rolled roofing, shingles, tiles, panels

Constructing roof geometry for complex polygons : Straight Skeletons

• with a given roof outline, how do you construct a roof in a particular style (hip, gable, etc.)
• this is relatively easy for rectangular outlines, but very difficult for more complex polygons
• the solution is in the domain of computation geometry, academically known as the problem of finding the straight skeleton, which in this case is the set of roof lines: "the straight skeleton provides a canonical way of constructing a polygonal roof above a general layout of ground walls"
• the straight skeleton can be considered as a "linearization" of a more general process, finding the medial axis
  • the medial axis of a polygon P is the set of all interior points whose closest point on P's boundary is not unique
  • is P is convex then the straight skeleton and the medial axis are identical
  • finding the medial axis is related to finding the Voronoi diagram, but a straight skeleton is defined not by a distance function but by a shrinking process
• Designing Roofs of Buildings by David Bélanger
  • great site with overview of all the academic papers and even a live Java applet which demonstrates finding the straight skeleton, which leverages some routines from the book Computational Geometry in C, Second Edition, Joseph O'Rourke
  • the applet is fairly robust, but i was able to consistently create simple polygons for which it failed to terminate

Academic Papers for Roofs

• Towards fully automatic generation of city models (pdf), C. Brenner, July 2000
  • main focus is constructing roofs from ground plans, given knowledge from a hi-resolution DSM (elevation points)
  • the do a lot of sophisticated extensions of the straight skeleton algorithm
• A Novel Type of Skeleton for Polygons (Gzipped PostScript, pdf)
  • O. Aichholzer, D. Alberts, F. Aurenhammer, B. Gärtner, 1995
  • describes the straight skeleton and its application to roofs
  • states that fast Voronoi-style solutions will fail, so a procedural process is required to determine it, but does not describe that process
• Straight skeletons for general polygonal figures in the plane (O. Aichholzer and F. Aurenhammer) 1998 (Gzipped PostScript)
  • great quote: "Even when the slopes of the roof faces are prescribed, a roof is a highly ambiguous object."
  • proposes an algorithm which is "conceptually simple and easy to implement", with O(n log n) behavior in the typical case
  • interestingly, this approach also has an application for constructing terrain elevation, when your only input is vector data for a coastline and river map, by making assumptions about the slope at each vector
• Raising roofs, crashing cycles, and playing pool (David Eppstein, Jeff Erickson) 1999
• Straight Skeleton Implementation (P. Felkel, Š. Obdržálek) 1998
  • has actual pseudocode
  • handles convex, non-convex, even polygons with holes in them
  • states that C++ code is available upon request, so 02.08.05 sent in a request
• Automatically Generating Roof Models from Building Footprints (pdf)
  • R. G. Laycock, A. M. Day, University of East Anglia, UK, 2003
  • They describe using the Felkel algorithm for generation of roofs, and observe that it produces poor results for "many vernacular buildings start their life as simple footprints with few vertices and become more complicated through the addition of extensions."
  • For these buildings, an extended algorithm is described starting with the straight skeleton, then using rectilinear analysis to guess original structure and intersect the resulting roofs.

Commercial Software for Roofs

• Etercalc is a Java application that builds roofs from perimeter
  • by a Brazilian roofing company (Eternit) so the site is in Portuguese
  • you do have to register at Eternit site to try it
• There was once a package called Roofer, a "a library of routines for generating the roof geometry of a house given the ground plan and wall parameters".  It was Copyright © 1996 Geometric Software Services Co. Ltd., India.  Sadly it seems to be no longer in existence, nor was it bought or continued by any other company (?)  An old archived copy of their web page is here.
• ArCon (€230) is architectural design software which includes a roof editor
• most high-end CAD packages (e.g. Nemetschek Allplan FT and ArchiCAD) have significant functionality for roof design
• reportedly, BuildersCAD ($1000) has a very capable Roof Generator and is much less expensive than ArchiCAD or Allplan