Virtual Reality and CAD Concepts Quiz

Designing and Building Virtual Environments - Chapter 4: Object and Scene Modeling

• Virtual objects are mapped into object-oriented system development

Understanding Virtual Objects in Virtual Reality Systems

• Object-Oriented System Development:
  • Virtual objects are modeled in a way that organizes both form and behavior.
  • Virtual objects are treated as individual "objects" within the VR system.
  • Complex VR environments become easier to manage.
  • Various computational services integrate and manage modeled objects.
  • These services include essential functions for device management, rendering control, object importing, and event processing, ensuring smooth VR operation.

Understanding Virtual Objects in Virtual Reality Systems (continued)

• Object Modeling:

  • Creating 3D representations of objects within a virtual environment.
  • Designed to represent objects' shape, structure, and behavior, simulating real-world items.

• Sequence in VR Development:

  • Form Modeling: Creating the geometry (shape and structure) of objects.
  • Function/Behavior Programming: Adding interactions and behaviors to objects within the VR environment.
  • Function and behavior modeling involves creating representations of how objects, environments, and user interactions behave within the virtual space.

VR Execution Environment

• VR Execution Environment: Software layer for displaying and interacting with 3D models

  • Import and conversion of CAD (computer-aided design) models are required for inclusion in VR environments.
    • Common CAD software includes AutoCAD and 3DS Max.
    • CAD files often require conversion to a compatible format (like .obj, .fbx, .glb) for smooth operation within VR engines.

• Components:

  • User Program interacts with the VR engine through graphics, operating system, and other resources, devices, etc.
  • Internal data structure that stores vertices, faces, colors, materials, polygons, etc.
    • A CAD program produces the data for a CAD file.
  • Operating system supports resources and devices.

• User Program and VR Execution:

  • VR execution environment is the platform for running VR applications.
  • Enables rendering, user interaction, and device integration.
  • Components within the execution environment include Graphics Rendering, Device Support, and Programming Libraries.
    • Example environments: Unity, Unreal Engine

From Modeling to VR Experience

• Step 1: Create models in software like Blender, AutoCAD, or 3DS Max.
• Step 2: Convert files to VR compatible formats such as .fbx or .obj.
• Step 3: Import and program interactions in engines like Unity or Unreal Engine.
• Important Considerations: Compatibility, optimization for real-time performance, interactivity
• Example: Creating a chair using basic geometric shapes (cubes for legs, a seat, and a backrest).

Introduction to Geometry Representations

• In object and scene modeling, geometry can be represented in various ways to define shape and structure.
• Example of representations includes:
  • Lines, curves, and surfaces can be mathematically represented.
  • Geometric entities such as spheres, planar surfaces, ellipsoids, and tori can be algebraically represented.

Different Types of Geometry Representations

• Mathematical Modeling:
  • Parametric: Geometry defined using control points or parameters.
  • Explicit: Object described directly through equations, e.g., coefficients for lines.
  • Implicit: Geometry represented indirectly, useful for calculations like collision detection, etc..

Various Representations

• Provide numeric representations examples for each described geometry.

Advantages of Different Representations

• Parametric: Useful for tasks such as locating points on curves or surfaces.
• Explicit: Straightforward equations used for basic shapes.
• Implicit: Ideal for operations requiring analysis such as collision detection.

Introduction to Primitives and Object Modelling

• Complex objects are difficult to represent but simpler basic shapes called primitives, used to represent complex shapes and are used in constructing more complex models.
• Example primitive shapes: Cubes, spheres, cones, tubes, tori.

Modeling with Primitives

• Primitives combined to make complex objects like chairs.
• Creating complex objects by placing together multiple primitives is a means to build more intricate objects.

Constructive Solid Geometry (CSG)

• CSG combines primitives using operations such as union, intersection, and difference.
• Union: Combines two objects into a single object.
• Intersection: Determines the overlapping parts of two objects.
• Difference: Subtracts one object from another.

Using Constraints in Object Placement

• Constraints assist in precisely positioning one object relative to another.
• Placement constraints align, for example, face X with edge Y and edge Z.

Using Constraints in Object Placement (continued)

• A complex object can be represented as a hierarchy of primitives.
• Sub-objects (children) are defined in relation to a parent object.
• Transformations like motion or scaling on a parent node will impact all its sub-objects (children).

Polygonal Modeling Using Vertices and Edges

• Objects are constructed using vertices, edges, and polygons in terms of their shape, boundary, and structure.
• Shapes are decomposed into polygons for rendering purposes using graphics hardware.
• Example: A cube modeled using polygons, with vertices connected by edges to form faces.

Boundary Representation (B-Rep) and Triangulation

• Boundary Representation (B-Rep) defines the exact surface of an object, but does not mathematically define interior characteristics.
• Triangulating polygons into triangles improves rendering and computations.

Limitations of Automatic Polygonalization

• Automatic processes, like polygonalization, may not always give complete polygon control.
• This can lead to performance issues.
• Advanced CAD systems allow users to specify more polygons for better performance in different parts of a model.

Procedural Modeling with Primitives

• Developers use programming code to generate objects, shapes, and attributes of the objects using primitives.
• Geometric shapes and properties can be adjusted and set programmatically.
• Procedural modeling facilitates efficient creation of geometry and attributes through predetermined actions.

Form Information in Object Modeling (NOTES)

• Object models incorporate non-geometric information, like color, material properties, mass, and hierarchy, beyond just shape.
• Issues can arise during VR import procedures when information like the hierarchy may be lost when importing models from other systems such as 3DS Max.

Performance-Conscious Form Modeling in VR

• Techniques for optimizing VR system performance include reducing polygons via image-based rendering, selectively rendering only visible parts of scenes using levels of detail (LOD), polygon budgeting, and mesh simplification.

EXAMPLE - Geometry modeling in Blender

• Blender modeling methods include Mesh Modeling (using vertices, edges, and faces), Sculpting (refining primitive-based meshes), Procedural Modeling (using node-based or algorithmic approaches), and NURBS modeling (Non-Uniform Rational B- Splines).

Introduction to Scene Construction

• Scene construction involves placing objects with defined forms and behaviors into a 3D virtual space.
• VR scenes can dynamically change as objects are introduced, moved, or removed.
• A world coordinate system is the main reference for positioning objects.

Introduction to Local Coordinate Systems

• Each object has a unique local coordinate system.
• Objects can be positioned relative to each other, with their own orientations and positions defined within their respective local coordinate systems.
• An example would be a virtual desk, where the X-axis runs along the length of the desk, Y along the depth, and Z is perpendicular to them all from the top corner of the desk.

Object Placement by Series of Action

• Fixed-Angle rotation involves rotating an object around a specified axis by an angle.

• Axes of rotation can be global coordinate axes (X, Y, Z) or arbitrary axes from local coordinate systems.

• Rotation angles are usually defined in degrees or radians.

• Euler rotations describe rotations through three sequential rotations (roll, pitch, yaw) about coordinate axes in a specific order.

Dealing with Multiple Frames of Reference

• Objects are often described within their own local coordinate, rather than within a unified global system.
• This creates a hierarchical structure to represent relationships among objects and their respective coordinate systems.
• A scene graph is used to organize the scene as a tree-like structure where each object has a parent node.
  • All children objects are affected by modifications made to their parent node.

Why Use a 4x4 Matrix for Transformations?

• A 4x4 matrix combines several transformation types (translation, rotation, and scaling).
• Homogeneous coordinates in a 3D space allow for a single matrix to represent multiple transformations.
• Coordinate system transformations allow accurate representations of position and orientation within a wider unified coordinate system.

A 4x4 Matrix for Transformations (Continued)

• The 4x4 matrix structure captures both rotation and translation between coordinate systems.
• The entire scene can be described as a series of transformations represented by 4x4 matrices.
• Changes in a VR scene can be achieved by altering the values in these 4x4 matrices.

Function Behavioral

• Defining object behavior is done through low-level programming or specialized libraries within a virtual environment.
• The addition of scripting languages allow specifying object behavior, through for example APIs and low-level libraries for greater control within a virtual space.
• Various approaches to specifying object behavior are common practice, including scripts, constraints, and state representations in virtual environments.

Notes (transformation): Changing Position and Orientation

• Modeling is defined by meshes of triangles.
• Transformations involve translation and/or rotation.

Notes (transformation): Translation

• 3D triangles consist of ((x1, y1, z1), (x2, y2, z2), (x3, y3, z3)) coordinates.
• Translation moves the original position in the respective coordinate axis (X, Y, Z) by the given values. This is represented mathematically by adding the amount of translation along each axis to the given coordinates.

Notes (transformation): Relativity

• Every transformation can be viewed as either (a) moving the object, or (b) moving the origin.
  • Example: A point (x1,y1,z1), can be considered moving the point from its original place, or it can be interpreted as moving the origin to the new location.

Notes (transformation): Rotation

• The number of independent motions of an object, or degree of freedom, is calculated.
• The number of degrees of freedom in 3D motion for a solid rigid object is six. These transformations are represented in the axes, and include Yaw, Pitch, and Roll.

Notes (transformation): Rotation (Continued)

• Rotating an object involves changing its orientation.
• Rotations in a 3D space are more complicated than translations.

Rotation (Continued)

• Combining rotations involves sequential applications of different rotation matrices, to attain any possible 3D rotation. Rotation Matrices, in particular; R(a,b,g) = Ry(a)Rx(b)Rz(g), combine to yield a single transformation capable of producing any possible 3D rotation through successive applications.