Solid modeling: Wikis


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The geometry in solid modeling is fully described in 3‑D space; objects can be viewed from any angle. Modeled and ray traced in Cobalt

Solid modeling (or modelling) is a technique for representing solid objects suitable for computer processing. Other modeling methods include surface models (used extensively in automotive and consumer product design as well as entertainment animation)[citation needed] and wire frame models (which can be ambiguous about solid volume).[1]

Primary uses of solid modeling are for CAD, engineering analysis,[2] computer graphics and animation, rapid prototyping, medical testing, product visualization and scientific visualization.[citation needed]


Basic theoretical concepts

Solid modeling software originally used either constructive solid geometry (CSG) or Boundary representation (B-REP) techniques to define solid shapes.[3] Beginning in the late 1980s, software developers began applying higher-levels of abstraction to solid modeling construction techniques. The first of these techniques, called parametric feature-based solid-modelling, was introduced in commercial software by Parametric Technology Corporation in September 1987.[4] These approaches made solid-modeling software easier to use and increased its acceptance among mechanical engineers.[5]

A parametric feature-based modeler is a Computer-aided design (CAD) software package that allows designers to define shapes using geometric features instead of the CSG or b-rep techniques. Features are higher-order CAD entities. For example, if an engineer designs a 3D brick with a hole in it, the hole is considered a feature in the brick. Parametric feature-based modelers use change states to maintain information about building the model and use expressions to constrain associations among the geometric entities.[citation needed] This ability allows a user to make a modification at any state and to regenerate the model's boundary representation based on those changes. This ability is called a transmigration operation.

A transmigration operation refers to the changes in a part that must be propagated to changes in other parts which have a dependence on the first. Put simply it means that if something is moved, other things will be affected and must also be adjusted to preserve other established relationships. This expression came into existence when parametric modelers like SolidEdge gained acceptance.[citation needed] Parametric modelers generate the BREP from the CSG representation and its associations, usually in the form of LISP expressions.

A Euler Boolean operation is a series of modifications to solid modeling which preserves the Euler characteristic in the boundary representation at every stage. One or more of these Euler Boolean operations is stored in a change state, so as to only represent models which are physically realizable. Failing to maintain the Euler characteristic would result in geometric and topological entities often depicted by M. C. Escher. Escher's geometry artwork comes close to preserving the Euler characteristic (usually a problem with just the hole count).

List of techniques used to create or represent solid models. Modern modeling software may use a combination of concepts shown below.

  • Parameterized primitive instancing.
    • An object is specified by reference to a library of parameterized primitives.
    • For example, a bolt is modeled for a library, this model is used for all bolt sizes by modifying a set of its parameters.
  • Spatial occupancy enumeration (voxels)
    • The whole space is subdivided into regular cells, and the object is specified by the set of cells it occupies.
    • Models described this way lend themselves to Finite difference analysis.
    • This is usually done after a model is made, as part of automated preprocessing for analysis software.
  • Cellular decomposition
    • Similar to "spatial occupancy", but the cells are neither regular, nor "prefabricated".
    • Models described this way lend themselves to FEA.
    • This is usually done after a model is made, as part of automated preprocessing for analysis software.
  • Sweeping
    • An area feature is "swept out" by moving a primitive along a path to form a solid feature. These volumes either add to the object ("extrusion") or remove material ("cutter path").
    • Also known as 'sketch based modeling'.
    • Analogous to various manufacturing techniques such as extrusion, milling, lathe and others.
  • Constructive Solid Geometry (CSG)
    • Simple objects (primitives) are combined using Boolean operations (union, difference, intersection) and linear transformations.
    • A special data structure is called a CSG-tree, where primitives are leaves and operations are nodes.
  • Function representation (FRep)
    • Any object is represented by a single real function of point coordinates. A point is outside the object if the function is negative, inside the object if the function is positive, and on the boundary if the function is zero (isosurface).
    • The function is evaluated at a point by traversing a tree structure similar to the CSG-tree.
    • Such a representation can be converted to BRep using polygonization algorithms, for example, the marching cubes algorithm.
  • Feature based modeling
    • Complex combinations of objects and operators are considered together as a unit which can be modified or duplicated.
    • Order of operations is kept in a history tree, and parametric changes can propagate through the tree.
  • Parametric modeling
    • Attributes of features are parameterized, giving them labels rather than only giving them fixed numeric dimensions, and relationships between parameters in the entire model are tracked, to make changing numeric values of parameters easier.
    • Almost always combined with features, giving rise to parametric feature based modeling or parameterized primitive instancing, as described above.


Solid modeling has to be seen in context of the whole history of CAD, the key milestones being the development of the research system BUILD followed by its commercial spin-off Romulus which went on to influence the development of Parasolid and ACIS and thus the mid-range Windows based feature modelers such as IronCAD, Alibre Design, SolidWorks, Solid Edge and form•Z (Mac also) and the arrival of parametric solid models system like T-FLEX CAD and Pro/ENGINEER.

Practical applications


Parametric Solid modeling CAD

Solid modelers have become commonplace in engineering departments in the last ten years due to faster PCs and competitive software pricing. Solid modeling software creates a virtual 3D representation of components for machine design and analysis.[2] Interface with the human operator includes programmable macros, keyboard shortcuts and dynamic model manipulation. The ability to dynamically re-orient the model, in real-time shaded 3-D, is emphasized and helps the designer maintain a mental 3-D image.


A solid part model generally consists of a group of features, added one at a time, until the model is complete. Engineering solid models are built mostly with sketcher-based features; 2-D sketches that are swept along a path to become 3-D. These may be cuts, or extrusions for example.

Design work on components is usually done within context of the whole product using assembly modeling methods. An assembly model incorporates references to individual part models that comprise the product.[6]

Another type of modeling technique is 'surfacing' (Freeform surface modeling). Here, surfaces are defined, trimmed and merged, and filled to make solid. The surfaces are usually defined with datum curves in space and a variety of complex commands. Surfacing is more difficult, but better applicable to some manufacturing techniques, like injection molding. Solid models for injection molded parts usually have both surfacing and sketcher based features.

Engineering drawings are created semi-automatically and reference the solid models.

The learning curve for these software packages is steep, but a fluent machine designer who can master these software packages is highly productive.

The modeling of solids is only the minimum requirement of a CAD system’s capabilities.

Parametric modeling uses parameters to define a model (dimensions, for example). The parameter may be modified later, and the model will update to reflect the modification. Typically, there is a relationship between parts, assemblies, and drawings. A part consists of multiple features, and an assembly consists of multiple parts. Drawings can be made from either parts or assemblies.

Example: A shaft is created by extruding a circle 100 mm. A hub is assembled to the end of the shaft. Later, the shaft is modified to be 200 mm long (click on the shaft, select the length dimension, modify to 200). When the model is updated the shaft will be 200 mm long, the hub will relocate to the end of the shaft to which it was assembled, and the engineering drawings and mass properties will reflect all changes automatically.

Examples of parameters are: dimensions used to create model features, material density, formulas to describe swept features, imported data (that describe a reference surface, for example).

Related to parameters, but slightly different are Constraints. Constraints are relationships between entities that make up a particular shape. For a window, the sides might be defined as being parallel, and of the same length.

Parametric modeling is obvious and intuitive. But for the first three decades of CAD this was not the case. Modification meant re-draw, or add a new cut or protrusion on top of old ones. Dimensions on engineering drawings were created, instead of shown.

Parametric modeling is very powerful, but requires more skill in model creation. A complicated model for an injection molded part may have a thousand features, and modifying an early feature may cause later features to fail. Skillfully created parametric models are easier to maintain and modify.

Parametric modeling also lends itself to data re-use. A whole family of capscrews can be contained in one model, for example.


Animation of computer generated characters is, technically, an example of parametric modeling, though few in the industry would consider it to be. Characters' skin is modeled with NURBS patches and stitched together or polygon modeled. The skin of characters is then parametrically associated to a skeleton within characters (with many characters' skins now being driven by muscle simulation systems). The skeleton of a character is rotated into poses, which parametrically drives the shape of the characters' skin for each frame to create animation.

Medical solid modeling

Modern computed axial tomography and magnetic resonance imaging scanners can be used to create solid models of internal body features, so-called volume rendering. Optical 3D scanners can be used to create point clouds or polygon mesh models of external body features.

Uses of medical solid modeling;

  • Visualization
  • Visualization of specific body tissues (just blood vessels and tumor, for example)
  • Designing prosthetics, orthotics, and other medical and dental devices (this is sometimes called mass customization)
  • Creating polygon mesh models for rapid prototyping (to aid surgeons preparing for difficult surgeries, for example)
  • Combining polygon mesh models with CAD solid modeling (design of hip replacement parts, for example)
  • Computational analysis of complex biological processes, e.g. air flow, blood flow
  • Computational simulation of new medical devices and implants in vivo

If the use goes beyond visualisation of the scan data, processes like image segmentation and image-based meshing will be necessary to generate an accurate and realistic geometrical description of the scan data.

See also


  1. ^ Machover, Carl (1996). "8". in Joanne Slike. The CAD/CAM Handbook (1st ed.). McGraw-Hill. pp. 69. ISBN 0-07-039375-3. 
  2. ^ a b LaCourse, Donald (1995). "2". Handbook of Solid Modeling. McGraw Hill. pp. 2.5. ISBN 0-07-035788-9. 
  3. ^ LaCourse, Donald (1995). "2". Handbook of Solid Modeling. McGraw Hill. pp. 2.3. ISBN 0-07-035788-9. 
  4. ^ Weisberg, David (2008-09). "The Engineering Design Revolution". David E. Weisberg. pp. 16–5. Retrieved 2009-06-26. 
  5. ^ LaCourse, Donald (1995). "8". Handbook of Solid Modeling. McGraw Hill. pp. 8.2. ISBN 0-07-035788-9. 
  6. ^ LaCourse, Donald (1995). "11". Handbook of Solid Modeling. McGraw Hill. pp. 111.2. ISBN 0-07-035788-9. 

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