Foundations of 3d Graphics II

3d Architectural Data Structures

Kyle Steinfeld

A technical overview of the most common 3d data structures in architectural design, from the various surface representations to logical models of geometric relationships.

Continuous Surfaces

Any boundary defined by a mathematical function results in a smooth and continuous surface.

Rational Surfaces

from Autodesk

Many surfaces may be described by well-known equations, and are often controlled by the relevant geometric properties. Planes, cylinders, cones, spheres are often defined in this way in CAD packages, which express them as unique objects rather than general surfaces, and offer direct control over properties such as their radius, axis, or dimensions.

Classical Surfaces

Four types of classical surface
Regular (or classical) surfaces include those that may be described through some sort of procedure, such as surfaces of revolution (such as tori) or ruled surfaces (linear in one direction, such as surfaces of extrusion). These are less likely to be described as unique objects in CAD, but sometimes to retain properties that led to their generation (such as sweep angle).

Free-Form Surfaces

A fifth-order Bezier Curve

So-called free-form surfaces are generally described by some sort of interpolation function through a set of control points. There are many such functions, but the most prevalent by far in architectural applications are NURBS, which are discussed in detail below.

Discrete Surfaces

Increasingly detailed mesh models of a horse
Not all surfaces described in CAD software are smooth, and we can group together any surface boundary description that is defined by discrete faces, typically triangles or quads.

Polygon Mesh

A polygon mesh is a collection of vertices, edges and faces that defines the shape of an object, and may be used in both solid and surface modeling. The faces usually consist of triangles (triangle mesh), quadrilaterals, or a combination of both. In contrast with other forms of surface representation, meshes are discrete.

Subdivsion Surfaces

A special case of mesh modeling, a subdivision surface is a method of representing a smooth surface via the specification of a coarser polygon mesh. Given this coarse 'control' mesh, a smooth surface can be calculated through a recursive process of subdividing each polygonal face into smaller faces.

Solid-Based Modeling

Solid modeling may be seen as an extension of one of the above surface definition schemas, but is distinguished from surface modeling by its emphasis on the maintenance of physical fidelity, including the property of water-tightness. Solid modeling is often used in engineering, manufacturing and fabrication applications, as it is appropriate for the creation, exchange, visualization, animation, interrogation, and annotation of digital models of physical objects.

Boundary Surfaces

Nested solids
A combination of rational and free-form surface models above, boundary solids may maintain closed forms while applying a modified subset of surface creation and manipulation operations.


A voxel model
A voxel, a portmentau of "volume" and "pixel", represents a value on a regular grid in three-dimensional space. As with pixels, voxels do not typically have their spatial position explicitly encoded along with their values, instead, this information is inferred based upon its position relative to other voxels (i.e., its position in the data structure that makes up a single volumetric image). In contrast, other forms of solid and surface representation operate much like 2d vector graphics, wherein positions are explicitly represented by the coordinates of their vertices. A consequence of this difference is other forms of solid and surface geometry efficiently represent simple 3D structures with lots of empty space, while voxels are good at representing regularly sampled spaces that are non-homogeneously filled.

Voxels are not often employed in architectural design, and are more often used in medical imaging, the simulation of volumetric dynamics (such as wind or water movements), structural analysis and the representation of terrain in games and simulations.

Logical Modeling

Given their increasing prominence in architectural design, the "logical" model for defining form is worth a mention here. Although these are more rightly defined as a variety of approaches to the interface and data-structure of CAD (rather than as descriptions of form) we should be familiar with the following models of CAD software.

Parametric Models

Parametric modeling is an activity focused on the relationships between geometries rather than their description. Grasshopper is a popular plugin for Rhino that facilitates parametric modeling.

BIM Models

Building Information Modeling applies the techniques and structures of a database to the design of a building. Autodesk's Revit software is quickly becoming the industry standard for "product delivery" in the AEC industries.