## The AIM@SHAPE Glossary

### Alphabetical list of terms

- sampling
- The process of obtaining a sequence of point coordinates from a 3D model.
- scanning
- The use of one or more Acquisition Devices in order to digitalize the shape of a real object.
- scattered data
- Point data not lying in a regular grid structure. Scattered data can have line structures, be clustered, be fairly evenly dispersed or have many other structures.
- segment
- (1) Portion of an H-Anim figure (Virtual Human) or Smart Object that represents its geometry and appearance.

(2) A collection of pixels that have similar properties (e.g., similar intensity values or texture) which differ from their surrounding pixels. (3) A subset of a data set classified according to similar characteristics of the basic entities or to given criteria. - segmentation
- To split a data set into smaller subsets based on given classifications or criteria. Frequently used in image processing to analyse pictures and for detection. When reconstructing geometry objects from sampled points, segmentation techniques can be used to detect subsets of points belonging to the same mathematical surface.
- selective refinement
- The extraction of shape representations from a LOD model in which the resolution varies continuously in different parts of the shape.
- self-intersection
- It occurs when a curve, surface or higher dimensional manifold intersects itself. For surfaces used in CAD self-intersections represents a situation that cannot be reproduced physically in production, and thus should be avoided.
- self-occlusion
- A surface is self-occluding when:
- Light cast from behind the surface does not illuminate it;
- The light source is in front of the surface but some closer portion of the surface blocks the incoming light;
- The light source is in front of the surface and the surface is illuminated, but some closer portion of the surface blocks the light coming from the surface.
- semantic
- Pertaining to meaning (from the Greek “semainein” = to signify/mean). Recently there has been much talk about the emergence of the "Semantic Web".
- semantic web
- Framework in which applications and information are organized in such a way that applications are intelligent systems where computers can effectively “understand” the meaning of the information, unlike HTML-based systems that are mostly concerned with how information is displayed.
- semi-algebraic curve/surface
- A curve or surface which can, in addition, be described as the solution set of polynomial equalities and inequalities (e.g. B-Spline curves and surfaces).
- sensor
- (1) An electronic device used to measure a physical quantity such as temperature, pressure or loudness and convert it into an electronic signal of some kind (e. g. a voltage).
Sensors can be classified in passive (not interacting with the scene) and active (interacting with the scene). Sensors are normally components of some larger electronic system such as a computer control and/or measurement system.

(2) Virtual entities that give to Virtual Humans the possibility to acquire information (stimuli) coming from their surrounding virtual environment. Virtual sensors let a VH see, hear and touch its virtual environment and react in consequence. The information acquired is then analyzed with different algorithms and/or Behavior Controllers that produce animation as output (the VH reacts to stimuli). - separatrix line
- An integral line which connects a minimum to a saddle, or a saddle to a maximum.
- shape classification
- Given a database D containing n shapes, which are grouped into m classes, classification aims at determining the class a query shape, not necessarily belonging to D, most reasonably belongs to.
- shape deformation
- Each operation or technique aiming at modifying a shape.
- shape descriptor
- shape from shading
- A method for determining the shape of a surface from the pattern of lights and shades in an image.
- shape grammar
- A shape grammar defines a language of design, i.e. it is a set of precise generating rules, which in turn, can be used to produce a language of shapes, to generate infinitely many instances of shape arrangements starting from an initial basic set of shapes. For example, shape grammars are widely used in architecture to model houses starting from pre-defined primitives (e.g. walls, windows, doors) and rules (e.g. each room must have at least one door).
- shape indexing
- Methodology relying on a lookup table approach for fast object labelling.
- shape interrogation
- The process of extraction of information from a geometric model. Shape interrogation methods are used to analyse shapes with respect to different aspects like visual pleasantness, technical smoothness, geometric constraints, intrinsic surface properties or to highlight shape imperfections.
- shape signature
- Compact representation of the essence of the shape commonly used as a fast indexing and matching mechanism for shape retrieval. Effective shape signatures capture some global (e.g. scale, translation and rotation invariant) and partial geometric properties.
- shock graph
- A directed, planar graph in which the shock sets are grouped and classified according to the number of contact points and the flow direction.
- shock set
- Dynamic view of the medial axis, which associates a direction and a speed of flow to the fire front propagation.
- silhouette
- The outline of an object when seen from a given position. Silhouette curves are frequently used to enhance the 3D display of a CAD-model and when making 2D drawings from 3D objects.
- simplex (k-dimensional)
- A k-dimensional simplex, or k-simplex, in the Euclidean space Rn is the locus of the points in Rn that can be expressed as the convex combination of k+1 affinely independent points.
- simplicial complex
- A d-dimensional simplicial complex is a collection of simplices of dimension at most d in Rn such that all simplices spanned by vertices of the complex belong to the complex and the intersection of any two simplices is either empty or is a simplex belonging to both simplices.
- simplicial mesh
- A simplicial mesh is a mesh in which all cells are simplices. A d-dimensional simplicial mesh is a simplicial mesh which contains simplices of dimension d or lower.
- simplification
- Simplification can relate to a number of shape processing operations in CAD:
- Replace a boundary structure CAD model consisting of many surface elements by a CAD-model with significantly fewer surface elements, without changing the shape or design intent behind the model. Such simplification can be important to ensure simple meshing and remeshing of CAD-models when preparing for simulation of the CAD-model, or just to clean up the CAD-model.
- Remove unnecessary details before a CAD-model is meshed. Details not important for the simulation are removed, and regions where the actual geometry does not play any role for the outcome the simulation are given a simpler description.
- simplified incidence graph
- For a tetrahedral mesh, it encodes the following information: for each vertex v, a pointer to one edge incident at t v; for each edge e, the indices of the two extreme vertices of e and of one of the triangles sharing e; for each triangle t, the indices of the three edges bounding t, and the indices of the two tetrahedra sharing it; for each tetrahedron s the indices of the four triangles bounding s.

For a triangle mesh, it encodes the following information: for each vertex v, a pointer to one edge incident at v; for each edge e, the indices of the two extreme vertices of e, and of the two triangles sharing e; for each triangle t, the indices of the three edges bounding t. - simulation post-processing
- Interpretation of the simulation results, which are typically scalar or vector values on finite element nodes applied on the input shape.
- simulation process
- Stage of the product development process which evaluates the physical behavior of any engineering component constituting the whole product subject to various kinds of loads and conditions. Finite Element (FE) approaches are techniques widespread in industry to analyze the mechanical behavior of a component. FE packages are able to solve sophisticated problems, ranging from structural analysis evaluating the performance of the product structure to thermal and electrical analysis, crash simulation, fluid flow and manufacturing processes, such as injection molding and metal forming.
- site
- A place holder to store information associated to a particular location on a 3D geometry. Landmarks can be anatomical structures used as a point of origin to locating other anatomical structures, or points from which measurements can be taken.
- skeletal linear structure
- One-dimensional representation which encodes the decomposition of a shape into its relevant parts, or features, which may have either a geometric or an application dependent meaning.
- skeleton
- (1) In algebraic topology, a p-skeleton is a simplicial sub-complex of a simplicial complex K that is the collection of all simplices of K of dimension at most p.

(2) Related with the notion of medial axis, the skeleton of a bounded open subset X is the set of centres of maximal balls, where an open ball B is maximal if every ball that contains B and is contained in X equals B.

(3) The skeleton of a shape is the reduced object representation that conforms to human visual perception and preserve the salient shape features.

(4) Implicit skeleton: in the field of implicit modelling, it is used for a set of geometric primitives to which a distance can be computed. These primitives are used for generating the field function that defines the surface. Skeleton-based implicit modelling can also be referred to as "Structural Implicit Modelling", since the skeleton defines an internal structure for the model. - skeleton animation
- Methods to animate an articulated skeleton by changing the values of the skeleton joints angles over time. The main methods are inverse and forward kinematics and Motion Capture. The result of a skeleton animation is stored as an animation sequence.
- skeleton articulation
- An articulation is the intersection of two limbs, which means it is a skeleton point where the limb which is linked to the point may move.
- skeleton-based implicit surface
- An implicit surface whose field function is generated by a set of geometric primitives called skeleton.
- skeleton-driven deformation
- It consists of deforming the skin to match the current posture of the control skeleton for articulated object animation or deformation. The basic approach consists in assigning a set of joints with weights to each vertex in the skin. The location of a vertex is then calculated by a weighted combination of the transformation of the influencing joints. Various extensions and enhanced complex methods have been proposed.
- skeletonisation
- The operation of extracting a skeleton.
- skeleton joint
- A joint is the intersection of two segments, which means it is a skeleton point where the limb which is linked to the point may move. Skeleton joints are usually 3D Degrees of Freedom (DoF) rotational joints: flexion, pivot and twist.
- skeleton joint angle
- The angle between two segments (limbs) connected by a joint is called the joint angle.
- skeleton pose
- Specification of joint values describing a posture for an articulated character. A skeleton posture can be defined using forward/inverse kinematics, forward/inverse dynamics or even motion capture.
- skeleton posing
- It consists in specifying all joints angles values to define a skeleton pose or posture.
- skeleton posture
- Specification of joint values describing a posture for an articulated character. A skeleton posture can be defined using forward/inverse kinematics, forward/inverse dynamics or even motion capture.
- skeleton skin
- A geometric shape that represents the outer shape of an articulated object. This shape is attached to the articulated skeleton and animated with skeleton driven deformations according to the skeleton animation.
- skeleton skinning
- (1) Applying skeleton driven deformation to the skeleton skin of an articulated character in order to adjust it to the current skeleton pose.

(2) Attaching geometric primitives or volumes to the joints and limbs of a control skeleton in order to define and control the shape of the skin. This information is further used in animation to control the skin deformation with respect to the control skeleton motion. - sketch
- Drawing or other composition that is not intended as a finished work, but captures the basic elements and structure.
- skin interpolation
- It consists in deforming a geometric surface (the skin) according to the animation of an underlying associated animation structure (skeleton, muscles) or to morph targets.
- skin mapping
- It consists of mapping a geometric surface called skin to a control skeleton in order to establish a direct correspondence between the control skeleton and the skin. This information is further used in animation to control the skin deformation with respect to the control skeleton motion.
- skinning
- Refer to the surface representation used to draw a character in skeletal animation.
- skinning file
- It describes a particular type of data used for animating deformable VH. A skinning file contains weights assigned to each vertex of the VH geometry. Such weights indicate the amount of deformation to apply when changing the posture. Deformations can be considered as vertex displacements driven by a function of rotation angles belonging to one or more joints. This allows for more aesthetical visual results when animating VH. Skinning algorithms can be used to obtain anatomically correct skin deformation by simulating the interaction between bones, muscles and skin.
- skin rigging
- See Skin mapping.
- smart object
- Virtual object with which virtual humans are capable of manipulations. To implement this, the environment should be extended with some form of knowledge on how interactions between virtual humans and objects are to be carried out. Typical interactions are grasping and manipulation operations. A Smart Object is constituted by a hierarchical collection of nodes. The hierarchical organization specifies the relations between different Geometry and Attribute Sets composing an object.
- smart object skeleton
- Hierarchical structure of object joints and/or object segments used to describe a smart object which usually including mobile parts.
- solid mechanics
- Area of application of the continuum mechanics. It includes structures which are fabricated with solids. The computational structural mechanics emphasises technological applications to the analysis and design of structures.
- solution
- In a FE context, phase of the finite element analysis in which the program derives the governing matrix equations from the model and solves for the primary quantities.
- space-time constraints dynamics
- It consists in attempting to meet specified constraints while minimising energy functions in order to add more control over the motion produced by dynamics.
- spline space
- A Spline space is solely defined by the knot sequences describing the continuity between polynomial segments and and the polynomial degrees. Both uniform and non-uniform knot sequences are considered. The use of uniform knot sequences allows the removal of every second knot, preserving the uniformity of the knot sequences and hence the pre-computation of the wavelet analysis.
- stable/unstable manifold of a critical point
- Integral lines that converge to (originate from) a critical point of index i form an i-dimensional cell ((2-i)-dimensional cell).
- static problem
- Continuum mechanics problem where the time dependence is not considered.
- stereo vision
- Vision is the act of perceiving and interpreting visual information. The word "stereo" comes from the Greek word "stereos" which means firm or solid. With stereo vision the objects are perceived as solid in 3D. In human beings the stereo vision is achieved by the presence of two eyes and the elaboration of the brain; in the digital world it is achieved by the presence of two sensors and the techniques to combine the measurements coming from them.
- straight-line skeleton
- It is a type of skeleton for polygons which is defined as the union of pieces of angular bisectors traced out by the wave-front vertices during the propagation process from the polygon boundary.
- strain
- Change per unit of length in a linear dimension of a part or specimen, usually expressed in %. Strain, as used with most mechanical tests, is based on original length of the specimen. True or natural strain is based on instantaneous length.
- strain energy
- Measure of energy absorption characteristics of a material under load up to fracture. It is equal to the area under the stress-strain curve, and is a measure of the toughness of a material.
- stress
- Load on a specimen divided by the area through which it acts. As used with most mechanical tests, stress is based on original cross-sectional area without taking into account changes in area due to applied load. This is sometimes called conventional or engineering stress. True stress is equal to the load divided by the instantaneous cross-sectional area through which it acts.
- structural descriptor
- Decomposition of a shape into their relevant sub-parts, together with the adjacency relationships among the parts.
- structural feature
- Aesthetic features of the shape. In accordance with the stylists? activity, they represent the basic entities created in the preliminary phase of design, which are used for defining the surfaces constituting the product, thus having an important aesthetic impact. Structural features consist of the so called contours and character lines.
- structured light
- Structured light is the projection of a light pattern (plane, grid, or more complex shape) at a known angle onto an object. This technique can be very useful for imaging and acquiring dimensional information. The most often used light pattern is generated by fanning out a light beam into a sheet-of-light. When a sheet-of-light intersects with an object, a bright line of light can be seen on the surface of the object. By viewing this line of light from an angle, the observed distortions in the line can be translated into height variations.
- styling process
- Process of specifying the shape of a product in consideration of aesthetical and visual aspects.
- subdivision
- The strategy often used in CAGD is to divide the geometric elements describing the problem into pieces. The idea behind subdivision is that the problem gets simpler when addressing sub pieces of the original geometry. In many cases this is true. However, if care is not taken and the subdivision is not performed in the proper location, the sub-problems can get more complicated than the original problem.
Subdivision algorithms play a central role in a number of algorithms in CAD:
- Visualization algorithms to produce an accurate triangulation of surfaces for display;
- Intersection algorithms for potentially simplifying the intersection problem.
- subdivision curve
- A curve described by an initial control polygon and a refinement rule. The subdivision curve is the limit of the progressively refined control polygon.
- subdivision matrix
- A matrix describing the transformation of a part of the control mesh under one subdivision step. The spectral analysis of subdivision matrices is the main tool for studying a subdivision scheme.
- subdivision surface
- A surface described by an initial control mesh and a mesh refinement rule. The subdivision surface is the limit of the progressively refined control mesh.
- sub-parabolic line
- It is formed by the surface points where one of the principal curvatures takes an extremal value along the opposite line of curvature.
- support
- The part of the subdivision surface affected by the change in position of a single point of the initial control mesh.
- support plane
- Frame used to compute surface properties in a parametric setting. The support plane is used as the parameter domain for a piece of surface, where the mapping between surface and support plane is established by orthogonal projection.
- support vector machines (svms)
- A family of algorithms that seek to divide a dataset using hyperplanes by margin maximisation. SVMs are often used as a supervised learning methods, applicable to both classification and regression.
- surface network
- Being f a Morse function defined over a domain D in R2, it is a graph in which the nodes represent the critical points of f and the arcs the integral lines connecting the critical points.
- surface patch
- A selected part of a larger surface. In B-Spline modelling, any of the sub-surfaces which the global shape is decomposed in.
- surface-surface intersection
- Points and curves of coincidence of two surfaces. The points and curves lie in both surfaces, and thus, it is a way to compute curves points on a surface.

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