## The AIM@SHAPE Glossary

### Alphabetical list of terms

- range image
- A grid of distances (range points) that describe a surface in Cartesian (height field) or cylindrical coordinates. A range scanner senses 3D positions on an objects surface and returns an array of distance values.
- range scan
- See Range image.
- rapid prototyping
- The speedy fabrication of sample parts of a product for demonstration, evaluation, or testing. It typically utilizes advanced layer manufacturing technologies that can quickly generate complex 3D objects directly from digital models. This computer representation is sliced into two-dimensional layers, whose descriptions are sent to the fabrication equipment to build the part layer by layer. Rapid prototyping includes many different fabrication technologies: stereolithography (STL), selective laser sintering (SLS), laminated object manufacturing (LOM), and fused deposition modelling (FDM) are a few examples.
- raster data
- One method of storing, representing or displaying spatial data in digital form. It consists of using cell data arranged in a regular grid pattern in which each unit (pixel or cell) within the grid is assigned an identifying value based on its characteristics.
- ray casting
- A central method for making photorealistic rendering.
- ray-surface intersection
- A specialization of Curve-surface intersection, where the space curve is an infinite straight line.
- reconstruction
- The process of making a surface geometry or volume type description of a 3D object based on measured points coordinates on the outer and inner surfaces of the 3D object. Automatic reconstruction is a very challenging process, as the point sets can have wrong points, can miss points or do not contain a sufficient amount of point to describe critical surface regions accurately. If a point set is produced by combining measurement from different camera positions, there is often drifting of the data between the measurements, Such drifting will often result in false surface features.
- recovery
- The process of rebuilding a valid 3D model that existed at an earlier stage in the design process after a crash of the modelling system, erroneous use of modelling functionality, rejection of the used design approach, or other mishaps.
- reeb graph
- A topological structure encoding the evolution and the arrangement of the level sets. It is defined as the quotient space of a compact manifold M with respect to a real valued, continuous map f defined on it defined by the equivalence relation that collapses two point on M if and only if they have same image of f and belong to the same connected component of f-1(f()).
- refinement operator
- Operator to add primitives to a surface description. This typically increases the geometric fidelity of the representation.
- reflectance
- The proportion of light aimed at an object that is reflected by it. An object’s reflectance determines whether the object is perceived as light or dark.
- reflection line
- A line consisting of all points p whose connection with some fixed point e, the eye, is reflected into a ray that meets a given fixed line L. Reflection lines, such as contour lines and isophotes, are very helpful to detect surface imperfections visually. They are very commonly in the automotive industry.
- registration
- A rigid transformation that brings points of one range image into alignment with portions of a surface it shares with another range image.
- regular mesh
- It is composed of simplices that are all similar (or belong to just few classes of congruent simplices) and have all vertices of the same degree (i.e. with the same number of incident simplices).
- regular square grid
- regular vertex
- A vertex of valence six for triangle meshes, valence four for quad meshes and valence three for hexagonal meshes. These valences correspond to the regular tessellations of the Euclidean plane. All major subdivision schemes refine the control mesh by inserting regular vertices, thus isolated the vertices with other valences.
- remeshing
- There is no precise definition, since it often varies according to the targeted goal or application. Nonetheless, it is possible to say that, given a 3D mesh, remeshing consists in computing another mesh, whose elements satisfy some quality requirements, while approximating well the input. Quality has several meanings. It can be related to the sampling, grading, regularity, size and shape of elements. Often a combination of these criteria is desired in real applications. Some remeshing techniques proceed by altering the input, and some generate a new mesh from scratch.
- rendering
- The process of creating an image on the screen from a mathematical model of a three-dimensional object or scene, including texture, lights and other graphical information.
- reparing
- The process of removing (if possible) or reducing the gaps the between the delimiting curves of different surface elements. When repairing the surfaces to ensure that the bounding curves fit better, the interior of the surfaces also have to be modified. Such modification can, if care is not taken, easily destroy important properties imposed on the interior of the surface. Automatic repair of CAD-models is thus an extremely challenging task.
- resultant
- A projection operator which is used to eliminate a set of variables in an over-constraint polynomial system.
- reverse engineering
- The process of recreating a design by analysing a final product, speeding up the design and the evaluation process. A point cloud typically acquired using scanning techniques is used as a basis for constructing 3D CAD surface data from a physical model.
- rgb
- An additive encoding of colors using the three primaries, red, green and blue. RGB is the common color model used in computer monitors and color images.
- ridge
- A ridge consists of the surface points where one of the principal curvatures attains an extremal value along its corresponding line of curvature.

### R