Стереометриско моделирање

**Цврсто моделирање** (или **моделирање**) е прецизна претстава на цврсти делови на објект, односно модели на цврсти објекти соодветни за компјутерска обработка. Исто така е познато како **просторно моделирање**.  Други методи на моделирање вклучуваат  површински модели  (користени интензивно во автомобилството и дизајн на потрожувачки производи, како и анимации во филската индустрија) и wire frame модели (кои можат да бидат повеќезначни за цврсти зафатнини).

Примарни употреби на цврсто моделирање се CAD, engineering анализи, комјутерска графика и анимација, рапидно прототипирање, медицинско тестирање, визуелизација на продукти и визуелизација на научни истражувања.

## Основни теоретски концепти
Постојат неколку начини на кои тврст модел може да се конструира, обично од едноставни објекти (како што се површина, линии, и/или точки). 
* **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.
* **[[Гранична претстава]]** (BRep)
** A solid object is represented by boundary surfaces and then filled to make solid.
** Also knowing as 'surfacing'.
** Analogous to various manufacturing techniques; Injection moulding, casting, forging, thermoforming, etc.
* **[[Инстанцирање на параметизирани примитиви]].**
** 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** (voxel)
** 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 not done after a model is made, as part of automated pre-processing for analysis software.
* **Клеточна декомпозиција**
** 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 pre-processing for analysis software.
* **[[Констуирачка цврста геометрија]]** (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.
* **[[Функциска претстава]]** (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.
* **[[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.
* **[[Параметарско моделирање]]**
** 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 parametric feature based modeling.
* Facet modeling
** Forming the outside surface form of the volume from any triangular planes
** Often used in reverse engineering of physical models.

## Историја
Solid modeling has to be seen in context of the whole history of CAD, the key milestones being the development of 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, and Solid Edge and the arrival of parametric solid models system like T-Flex and Pro/ENGINEER.

## Практични апликации
### Параметарско тврсто моделирање КАД
Solid modelers have become commonplace in engineering departments in the last ten years due to faster PCs and competitive software pricing. They are the workhorse of machine designers.

Solid modeling software creates a virtual 3D representation of components for machine design and analysis. Interface with the human operator is highly optimized and 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.

Design work on components is usually done within context of the whole product using assembly modeling methods.

A solid 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.

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&nbsp;mm. A hub is assembled to the end of the shaft. Later, the shaft is modified to be 200&nbsp;mm long (click on the shaft, select the length dimension, modify to 200). When the model is updated the shaft will be 200&nbsp;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.

### Забава
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 modelled with NURBS patches and stitched together or polygon modelled. 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.

### Мидицинско цврсто моделирање
Modern computed axial tomography and magnetic resonance imaging scanners can be used to create solid models of internal body features. 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)

## Поврзанотака
Сметачка графика
* Сметачка геометрија
* Euler Гранична претстава
* Инженерско цртање
* Техничко цртање
* Список на CAD-фирми

## Надворешни врски
* Example of relational solid modeling  
* Medical Solid Models - Heart and Skeleton  
* The Solid Modeling Association

Категорија:Сметачка графика
Категорија:3D сметачка графика
Моделирање