Structures and hierarchical modeling in computer graphics

In computer graphics, structures and hierarchical modeling play significant roles in creating and organizing complex virtual scenes and objects. Let’s delve into these concepts further:

  1. Structures:
    In computer graphics, structures refer to the arrangement and organization of various elements within a scene or object. These elements can include vertices, edges, faces, textures, and other relevant components. Structures help define the overall shape and form of the objects being modeled. They provide a framework for storing and representing data in a meaningful way, allowing efficient manipulation and rendering of the graphics.

For example, in 3D modeling, structures might involve the arrangement of vertices to form polygons, which, in turn, create the surface of an object. These polygons can be organized into meshes or other higher-level structures, such as patches or NURBS (Non-Uniform Rational B-Splines), to represent more complex surfaces.

  1. Hierarchical Modeling:
    Hierarchical modeling is a technique used to represent complex objects or scenes by organizing them into a hierarchical structure. This structure resembles a tree-like hierarchy, with a parent-child relationship between different components. Each component, or node, in the hierarchy, represents a part of the object or scene and can have its own properties, transformations, and sub-components.

The hierarchical structure allows for easy manipulation, transformation, and animation of objects. By applying transformations at different levels of the hierarchy, changes can be propagated down to the child nodes, enabling efficient updates to the entire structure.

For example, in a 3D scene, a car model can be represented hierarchically, with a root node representing the entire car and child nodes representing individual components like wheels, doors, and the chassis. Transformations applied to the root node would affect the entire car, while transformations applied to specific child nodes would affect only those components.

Hierarchical modeling is widely used in computer graphics to manage complexity, facilitate object composition, and enable efficient rendering and animation.

Overall, structures and hierarchical modeling are essential concepts in computer graphics that provide the foundation for representing, organizing, and manipulating complex objects and scenes. They play a crucial role in achieving realistic and visually appealing computer-generated imagery.

STRUCTURE CONCEPTS

In computer graphics, structures play a vital role in managing and organizing collections of output primitives and their associated attributes. A structure, also known as a segment (in GKS) or an object (on Silicon Graphics systems), is a labeled set of output primitives. These structures allow for efficient manipulation and management of complex graphics scenes. Similar functionality is available in other packages that handle labeled groups of primitives in pictures.

Basic Structure Functions

When creating a structure, the specified coordinate positions and attribute values are stored as a labeled group in a system structure list known as the central structure store. The function used to create a structure is:

openStructure(id)

Here, the label for the structure is a positive integer assigned to the parameter id. In some systems like PHIGS+, character strings can be used as structure labels instead of integer names, providing easier identification and remembrance of structure identifiers. The end of a structure is indicated with the closeStructure statement.

For example, consider the following program statements defining structure 6 as a line sequence specified in polyline with the designated line type and color:

openStructure(6);
setLineType(lt);
setPolylineColorIndex(lc);
polyline(pts);
closeStructure;

Multiple structures can be created for a picture, but only one structure can be open (in the creation process) at a time. An open structure must be closed before a new structure can be created. This eliminates the need for a structure identification number in the closeStructure statement.

Displaying and Removing Structures

To display a structure on a selected output device, the function postStructure(ws, id, priority) is used. The ws parameter represents the workstation identifier, id is the structure name, and priority is assigned a real value between 0 and 1. The priority determines the display priority of the structure relative to other structures. When overlapping structures are displayed, the one with the higher priority will be visible. Structures can be posted to multiple workstations.

To remove the display of a structure from a specific output device, the function unpostStructure(ws, id) is invoked. This removes the structure from the active list of structures for the designated output device without affecting the system structure list. On raster systems, removing a structure from the display involves redrawing the primitives in the background color, which may affect the display of other overlapping structures.

Deleting and Modifying Structures

To remove a particular structure from the system structure list, the function deleteStructure(id) is used. This function also removes the display of the structure from all posted output devices. Once a structure is deleted, its name can be reused for a different set of primitives.

The entire system structure list can be cleared using the function clearStructureStore(). This operation removes all structures from memory.

Relabeling a structure can be done with the function setLabel(id, newLabel). This allows for changing the label of a structure for various purposes, such as consolidating structure numbering or cycling through structure labels during testing.

Setting Structure Attributes

Workstation filters can be used to set display characteristics for structures. The three properties that can be set with filters are visibility, highlighting, and pickability.

Visibility settings for structures on a particular workstation and device are specified using the function setInvisibilityFilter(invisset, visset). The invisset parameter contains the names of structures that should be invisible, while the visset parameter contains the names of structures that should be visible. This filter allows structures to be selectively displayed or hidden on workstations without deleting them from the workstation lists.

Highlighting structures is achieved using the function `setHighlightingFilter(ws, devcode, highlightset, no

highlightset). Thehighlightsetparameter contains the names of structures to be highlighted, while thenohighlightset` parameter contains the names of structures that should not be highlighted. The type of highlighting used depends on the graphics system’s capabilities, such as displaying highlighted structures with brighter intensity or a reserved color.

Pickability refers to the ability of a structure to be selected with an interactive input device. The function setPickabilityFilter(ws, devcode, pickableset, nopickableset) allows structures to be declared as pickable or nonpickable. This feature is useful when certain structures should never be selectable in a display.

Editing structures

Editing structures is a common requirement when working with design applications or making changes based on new data in graphical arrangements. Modifying a structure involves adding or removing primitives and altering attribute settings. To add additional primitives to a structure, it can be reopened using the openstructure function and appending the desired statements. For example, you can create a structure with a single fill area and then add a second fill area by reopening the structure and appending the necessary statements. Deleting specific items, changing primitives or attribute settings, or inserting items at selected positions within the structure are general editing operations accomplished by accessing the sequence numbers of the structure’s components and setting the edit mode.

Each element within a structure, such as output primitives and attribute values, is assigned a position number as it is entered into the structure. The element pointer represents the current position in the structure and can be set or moved using functions like setElementPointer. Editing a structure involves setting the edit mode, which can be either “insert” or “replace.” In “insert” mode, new items are placed after the element pointer, automatically renumbering subsequent elements. In “replace” mode, the next item replaces the element at the position of the element pointer without changing the pointer’s position. Elements can be deleted using the deleteElement function, which also updates the element pointer.

To facilitate editing without relying on position numbers, elements within a structure can be labeled using the label function. Labels serve as identifiers for elements and allow for easy referencing during editing operations. The setElementPointerAtLabel function can be used to set the element pointer to the position of a labeled element. Labels provide a convenient way to locate structure elements without constantly referring to position numbers. Additionally, elements can be copied from one structure to another using the copyAllElementsFromStructure function, which inserts the elements into the open structure after the element pointer, updating the element pointer accordingly.

By utilizing these editing capabilities, designers and developers can effectively modify structures to experiment with different graphical arrangements, adjust designs based on new data, or manipulate complex graphics scenes in design applications.

#include <stdio.h>

// Function to open a structure
void openStructure(const char* name) {
    printf("Opening structure: %s\n", name);
    // Add code to open the structure
}

// Function to close a structure
void closeStructure() {
    printf("Closing structure\n");
    // Add code to close the structure
}

// Function to set interior style
void setInteriorStyle(const char* style) {
    printf("Setting interior style: %s\n", style);
    // Add code to set interior style
}

// Function to set interior color index
void setInteriorColorIndex(int index) {
    printf("Setting interior color index: %d\n", index);
    // Add code to set interior color index
}

// Function to fill an area
void fillArea(int n, const char* vertices) {
    printf("Filling area with %d vertices: %s\n", n, vertices);
    // Add code to fill the area
}

// Main function
int main() {
    // Creating a structure with a single fill area
    openStructure("shape");
    setInteriorStyle("solid");
    setInteriorColorIndex(141);
    fillArea(1, "vertsl");
    closeStructure();

    // Appending a second fill area to the structure
    openStructure("shape");
    setInteriorStyle("hollow");
    fillArea(2, "verts2");
    closeStructure();

    // Modifying the structure by replacing color attribute
    openStructure("gizmo");
    setElementPointer(5);
    setPolylineColorIndex("lc2New");
    closeStructure();

    // Deleting the second color attribute from the structure
    openStructure("gizmo");
    setElementPointer(5);
    deleteElement();
    closeStructure();

    // Copying elements from one structure to another
    openStructure("destination");
    copyAllElementsFromStructure("source");
    closeStructure();

    return 0;
}

BASIC MODELING CONCEPTS

Here are some basic modeling concepts commonly used in computer graphics:

  1. Vertices: Vertices are the fundamental building blocks of models. They represent the points or coordinates in 3D space where the edges of a model intersect. Vertices are often defined by their X, Y, and Z coordinates.
  2. Edges: Edges connect two vertices and form straight lines. They define the shape and structure of the model. Edges can be visible or hidden, depending on the rendering technique used.
  3. Faces: Faces are flat surfaces bounded by edges. They enclose a region in the model and give it a visual appearance. Faces are typically represented by a collection of vertices in a specific order.
  4. Polygons: Polygons are faces with three or more sides. Triangles and quadrilaterals are the most common types of polygons used in computer graphics. Polygons are widely used because they can efficiently represent complex surfaces.
  5. Mesh: A mesh is a collection of vertices, edges, and faces that form a complete 3D object. Meshes can be composed of various types of polygons and are used to represent solid objects.
  6. Normals: Normals are vectors perpendicular to the faces of a mesh. They define the orientation and shading of the surface. Normals are essential for smooth shading and determining how light interacts with the model.
  7. Texture Mapping: Texture mapping is a technique used to apply images or patterns onto the surfaces of a 3D model. It provides the appearance of surface details, such as color, texture, and patterns, by mapping the image onto the model’s polygons.
  8. Wireframe: A wireframe representation of a model shows only the edges and vertices, without any filled polygons or surface details. It provides a simplified view of the model’s structure.
  9. Rendering: Rendering is the process of generating a 2D image or animation from a 3D model. It involves applying lighting, shading, and other visual effects to create a realistic or stylized representation of the model.
  10. Transformation: Transformations involve manipulating the position, size, and orientation of a model in 3D space. Common transformations include translation (moving), rotation (turning), and scaling (resizing) of the model.

These concepts provide a foundation for creating and manipulating 3D models in computer graphics. They are used in various applications such as video games, virtual reality, animation, and architectural design.

Model Representations

In the field of computer science and engineering, modeling plays a crucial role in representing various systems and their behaviors. Model representations enable us to understand and analyze complex systems, such as logic circuits, by breaking them down into manageable components. This article explores the fundamental concepts and features commonly found in model representations, with a specific focus on a logic circuit example depicted in Figure 1

Model of a logic circuit
Fig 1: Model of a logic circuit

Basic Modeling Concepts:
Modeling involves several key concepts that serve as the foundation for representing systems effectively. Let’s explore these concepts in the context of logic circuit modeling:

  1. Vertices, Edges, and Faces:
    In logic circuit modeling, vertices represent points or coordinates where the edges of the circuit intersect. Edges, on the other hand, connect the vertices, forming the structure of the circuit. Faces, which are flat surfaces, are bounded by edges and enclose regions within the circuit.
  2. Symbols and Relationships:
    Logic circuit models utilize geometric structures known as symbols to represent component parts of the system. In Figure 1, standard symbols are used to represent logic gates, such as AND, OR, and NOT gates. These symbols are connected by lines that define the relationships between them, representing the flow of input and output through the system.
  3. Instances:
    Instances refer to the repeated positioning of basic symbols within a model. In the logic circuit depicted in Figure 7-6, we observe two instances of the AND gate symbol and one instance each of the OR and NOT gate symbols.
  4. Symbol Selection:
    The choice of graphical symbols to represent system components is often dictated by the system’s description. In circuit models, standard electrical or logic symbols are commonly used. However, models representing abstract concepts, such as political, financial, or economic systems, may employ any convenient geometric pattern as symbols.

Geometric and Nongeometric Information:
Model descriptions typically combine geometric and nongeometric data. Geometric information includes the coordinates of component parts, output primitives, attribute functions defining their structure, and data for constructing connections between the parts. Nongeometric information encompasses text labels, algorithms describing operational characteristics, and rules for determining relationships between components.

Methods for Specifying Model Information:
Two methods exist for specifying the information needed to construct and manipulate a model. The first method involves storing the information in data structures such as tables or linked lists. The second method entails specifying the information using procedures. Typically, a model specification includes a combination of both data structures and procedures, depending on the complexity of the model.

Symbol Hierarchies:
Many models can be organized hierarchically using symbols. The basic symbols, represented by simple geometric shapes, can be combined to form composite objects called modules. These modules can further be grouped to create higher-level modules, enabling the representation of complex systems.

Modeling Packages

A one-level hierarchical description of a circuit formed with logic gates
A one-level hierarchical description of a circuit formed with logic gates

Modeling packages are powerful software tools that are widely used in various industries and disciplines for system representation and analysis. These packages provide a range of features and functionalities to assist users in creating detailed models, simulating system behaviors, and conducting analyses. They offer intuitive interfaces, simulation engines, data analysis tools, and visualization capabilities, making them essential tools for engineers, designers, researchers, and analysts.

The benefits of using modeling packages are numerous. Firstly, these packages allow for visual representation of systems, enabling users to create models using graphical interfaces. This visual approach simplifies the understanding of complex systems and facilitates effective communication among team members. Additionally, modeling packages enhance efficiency and accuracy by providing libraries of prebuilt components and templates. This eliminates the need for starting from scratch and ensures consistency in the modeling process.

Simulation and analysis are key features of modeling packages. These tools enable users to simulate system behaviors under different conditions, helping them identify potential issues, analyze performance, and make informed decisions. By iteratively simulating and refining models, users can optimize system performance and validate design choices. Moreover, modeling packages often include data visualization and analysis capabilities, allowing users to generate graphs, plots, and reports to interpret and communicate model outputs effectively.

Modeling packages find applications across a wide range of domains. In engineering and manufacturing, these tools are used for designing and analyzing complex systems, such as structures, machinery, and electrical circuits. They help engineers optimize performance, evaluate safety, and minimize costs. In systems analysis, modeling packages assist in understanding the behavior of complex systems, identifying bottlenecks, and optimizing processes. They are also valuable in scientific research, aiding researchers in simulating and studying complex phenomena in fields such as physics, biology, chemistry, and environmental science.

Furthermore, modeling packages are utilized in business and economics for decision-making, forecasting, and risk analysis. They enable modeling of financial systems, market dynamics, and economic models, providing valuable insights to analysts and decision-makers.

HIERARCHICAL MODELING WITH STRUCTURES

Hierarchical modeling with structures is a powerful approach that allows for the organization and representation of complex systems in a systematic and efficient manner. This modeling technique involves breaking down a system into hierarchical levels or layers, where each level represents a different level of abstraction or detail. By structuring the model in this way, it becomes easier to understand, analyze, and modify the system.

The hierarchical modeling approach offers several advantages. Firstly, it provides a clear and organized representation of the system’s components and their relationships. The system is divided into subsystems, modules, or components, with each level encapsulating a specific set of functionalities or behaviors. This modular structure promotes modularity, reusability, and maintainability, as each component can be developed and tested independently.

Hierarchical modeling also enables the separation of concerns. Different aspects of the system can be represented at different levels of the hierarchy, allowing for focused analysis and design. This separation of concerns improves the overall clarity and comprehensibility of the model, making it easier to identify and address specific issues or requirements.

Another benefit of hierarchical modeling is scalability. Large and complex systems can be represented more effectively by breaking them down into smaller, manageable modules. Each module can be further divided into submodules, creating a hierarchical structure that can accommodate systems of any size. This scalability facilitates collaboration among multiple stakeholders, as different teams or individuals can work on specific modules without interfering with others.

Furthermore, hierarchical modeling promotes abstraction and encapsulation. Higher-level modules provide an abstract view of the system, focusing on its overall functionality and behavior. Lower-level modules, on the other hand, provide detailed implementations of specific functionalities. This abstraction allows users to focus on the relevant aspects of the system at each level, without getting overwhelmed by unnecessary details. Encapsulation ensures that the internal workings of a module are hidden from other modules, promoting information hiding and reducing system complexity.

Hierarchical modeling can be applied in various domains and disciplines. In software engineering, it is commonly used in object-oriented programming and software architecture design. Systems engineering utilizes hierarchical modeling to represent complex physical systems, such as aerospace or automotive systems, where each level represents different subsystems or components. Additionally, hierarchical modeling is prevalent in business process modeling, where it helps in organizing and representing complex business workflows and processes.

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