Building topology

extensions/topology/ builds a cell complex from storey plans. Each room is a cell. Two rooms that share a wall share one face, and a floor is one face with a room above and a room below. The building model, the structural view and the thermal view read adjacency from this complex.

Modules

Module	What it gives
ids	VertexId, EdgeId, FaceId, CellId and RegionId
weld	Welder, which merges points within a tolerance
arrangement	Point2, Region, arrange and the polygon helpers polygon_area and contains
complex	CellComplex, Face, Edge and FaceKind
storeys	build_storeys and StoreyComplex

Coordinates are in meters, z up. A plan point (x, y) lies at height z.

Build a complex from plans

Give one plan per storey and one more level than storeys. A plan is a list of Region values on layer zero. Each region has an id that is unique on its storey.

var ground = List[Region]()
ground.append(Region(0, RegionId(0), [Point2(0, 0), Point2(4, 0), Point2(4, 4), Point2(0, 4)]))
ground.append(Region(0, RegionId(1), [Point2(4, 0), Point2(8, 0), Point2(8, 4), Point2(4, 4)]))
var plans = List[List[Region]]()
plans.append(ground^)
var levels = [Length64(0, METER), Length64(3, METER)]
var built = build_storeys(levels, plans, Length64(1e-6, METER))
built.complex.validate()
var room = built.cell_of(0, RegionId(0)).value()

build_storeys makes these faces:

Face	Source	Sides
Wall	Each plan edge with different regions on its two sides	The two rooms, or a room and the outside
Floor	Each face of the overlay of a plan on the plan below	The room below and the room above
Ground	Each face of the first plan	The outside below, the room above
Roof	Each face of the last plan, and each part of a lower plan with nothing above	The room below, the outside above

A plan can differ from the plan below it. The overlay splits each floor where the two plans cross. A vertex of one plan that lies on an edge of the other splits the wall along that edge too, so every cell is closed.

Query the complex

Method	Returns
faces_of(cell)	The faces that bound a cell
other_side(face, cell)	The cell across a face, or None for the outside
neighbors(cell)	The cells that share a face with a cell, once each
shared_faces(a, b)	The faces between two cells
exterior_faces(cell)	The faces of a cell with the outside across them
face_area(face), face_normal(face), face_centroid(face)	The area, the unit normal toward the positive side, and the mean corner
outward_normal(face, cell)	The unit normal that points out of a cell
cell_volume(cell)	The volume, by the divergence theorem
validate()	Nothing. It raises if a cell is not closed.

Each face has a kind: VERTICAL for a wall or HORIZONTAL for a floor, a ground or a roof. StoreyComplex.face_level gives each wall's storey and each horizontal face's level. Level i is the bottom of storey i.

A face's loop winds counterclockwise seen from its positive side. The positive cell is on the side the normal points to. The negative cell is behind the face.

Arrange polygons in a plane

arrange(regions, layers, tolerance) cuts the plane by the edges of every region. It splits edges where they cross, where an end touches another edge, and where two edges overlap. It returns the vertices, the edges with the face on each side, and the bounded faces.

Each bounded face has one label per layer: the region that covers it, or NO_REGION. Regions of one layer must not overlap. Regions of different layers can overlap. build_storeys uses two layers for each floor: the plan below and the plan above.

A component inside a face of another component gets a bridge edge. The bridge joins the inner component's leftmost corner to the nearest corner it can see. The face then has one loop that runs along the bridge in both directions. A smaller crown above a shaft makes such a face.

Errors

Case	Function
A region has fewer than three corners, a short edge, no area, or crosses or touches itself	arrange, build_storeys
Two regions of one layer overlap	arrange, build_storeys
A region id repeats on a storey	build_storeys
The levels do not increase, or their count is not one more than the storeys	build_storeys
A face has fewer than three corners, repeats a corner, or has one cell on both sides	CellComplex.add_face
An id is out of range	Every CellComplex query

Limits

• Cells are prisms between two levels. A sloped roof or a double-height room that spans storeys is not a cell of this complex.
• A plan region is a simple polygon. A room with a hole in it is not supported. A region can stand inside an uncovered court.
• The arrangement compares every pair of edges. A plan with thousands of edges is slow.
• Points closer than the tolerance are one point. Keep features of a plan larger than the tolerance.

References

• de Berg, Cheong, van Kreveld and Overmars, "Computational Geometry: Algorithms and Applications", 3rd edition, 2008, chapter 2.
• O'Rourke, "Computational Geometry in C", 2nd edition, 1998, section 1.6.
• Aish and Pratap, "Spatial information modeling of buildings using non-manifold topology with ASM and DesignScript", 2013.