Three Dimensional (3D) Viewing in Computer Graphics

What is Three-Dimensional Viewing?

• Three-dimensional (3D) viewing in computer graphics involves the representation and visualization of three-dimensional objects on a two-dimensional display.
• The process of 3D viewing encompasses various techniques such as projections to accurately portray the spatial relationships of objects in a virtual environment.

Representation of Three-Dimensional Objects

• In computer graphics, three-dimensional objects are typically represented using mathematical models.
• These models define the geometry, topology, and other properties of objects in a digital space.
• Common representations include wireframes, surface models, and solid models.

what is Projections?

• Projections are a crucial aspect of 3D viewing as they transform three-dimensional points onto a two-dimensional plane.
• Different projection methods are used to simulate how objects appear when viewed from a particular perspective or angle.
• The two main types of projections are parallel projections and perspective projections.

Parallel Projections

• Parallel projections maintain parallel lines in the scene, resulting in a realistic representation of object shapes.
• There are two primary types of parallel projections: orthographic projections and oblique projections.

Orthographic Projections

• Orthographic projections involve projecting 3D objects onto a 2D plane along parallel lines.
• This type of projection preserves the relative sizes of objects but eliminates depth cues.
• An example is the top, front, and side views often used in engineering and architectural drawings.

What is Foreshortening?

• No Foreshortening: Orthographic projections do not introduce any foreshortening.
• The lengths of objects along each axis remain unchanged in the projection.
• Lacks Realistic Depth Cues: While orthographic projections provide accurate dimensions, they lack realistic depth cues.
• Simplicity and Clarity: Orthographic projections are known for their simplicity and clarity.

Axonometric Orthographic Projection

• In axonometric Orthographic projection, the object is projected onto the plane without any foreshortening along any axis.
• This means that all three axes of the object are equally foreshortened, resulting in a realistic and proportional representation.
• There are two primary subtypes:
• Isometric Projection: In isometric projection, the angles between the three axes are equal, resulting in a visually balanced representation.
• This projection is often used in technical and engineering drawings.
• Dimetric and Trimetric Projections: These are variations of axonometric projection where the angles between the three axes are not equal.
• Dimetric has two unequal angles, and trimetric has all three angles unequal, allowing for a more customizable representation of objects.

Oblique Projections

• Oblique projections introduce a level of skewness to the projection, providing a more natural representation of depth.
• These projections are often used when a more visually appealing representation is desired.
• One common example is the cavalier projection, which maintains one axis as true scale while skewing the other two.

Characteristics of Oblique Projections

• Foreshortening Along One Axis: Oblique projections involve foreshortening along one of the coordinate axes while maintaining the true scale along the other two axes.
• Unlike orthographic projections, oblique projections use projection lines that are not parallel to the coordinate axes.
• Types of Oblique Projections: There are different types of oblique projections, including cavalier and cabinet projections.
• Realism: Oblique projections offer an intermediate level of realism compared to orthographic and perspective projections

Cavalier Oblique Projection

• Cavalier projection is a type of oblique projection where the object is projected onto the 2D plane without any foreshortening along any axis.
• In other words, the length along each axis remains the same in the projection, providing a simple and direct representation.

• No Foreshortening: In Cavalier Oblique Projection, there is no reduction in the length of objects along any axis.
• Equal Scaling: Each axis is equally scaled in the projection, preserving the proportions of the original object.
• Simplicity: Cavalier projection is characterized by its simplicity, making it easy to visualize and understand.
• Limited Realism: While Cavalier Oblique Projection provides a sense of depth, it lacks the degree of realism as compared to perspective projection.
  

Cabinet Oblique Projection

• Cabinet projection combines the simplicity of orthographic projection with a slight degree of foreshortening along one axis.
• In cabinet projection, one axis is foreshortened by half its actual length, while the other two axes remain at their true scale.
• This creates a visually appealing representation that strikes a balance between realism and simplicity.

Key Characteristics of Cabinet Projection

• Partial Foreshortening: Unlike cavalier projection, cabinet projection introduces a degree of foreshortening along one axis, typically reduced to half its actual length.
• Equal Scaling on Two Axes: The other two axes maintain their true scale without foreshortening, preserving the proportions of the object.

Perspective Projection

• Unlike parallel projections, perspective projections simulate how objects appear in the real world by converging lines toward a vanishing point.
• This creates the illusion of depth and is crucial for creating realistic scenes.

Characteristics of Perspective Projection

• Size Diminution: Objects that are farther away from the viewer in perspective projection appear smaller in size.
• Application in Art and Design: Perspective projection is widely used in art, architecture, and design to create realistic and visually compelling representations.
• Three-Dimensional Illusion: Perspective projection is effective in creating a convincing illusion of three-dimensional space on a flat surface.

What is the Vanishing point?

• In perspective projection, the vanishing point refers to a point on the horizon line where parallel lines appear to converge or meet in the distance.
• A vanishing point occurs due to the way our eyes perceive objects in the three-dimensional space.
• In a perspective view, parallel lines that extend away from the viewer converge towards one or more vanishing points.

Classes of Perspective Projection

• one-point Perspective
• Two-point Perspective
• Three-point Perspective
• Multi-point Perspective

One-Point Perspective:

• In the one-point perspective, also known as the frontal or parallel perspective, there is a single vanishing point on the horizon line.
• This occurs when the object is positioned such that one set of parallel lines is directly facing the viewer.
• One-point perspective is commonly used when a road stretches into the distance.

Two-Point Perspective

• Two-point perspective involves two vanishing points on the horizon line.
• This occurs when the object or scene is oriented in such a way that two sets of parallel lines are not directly facing the viewer.
• Two-point perspective is frequently used when drawing objects like buildings or interiors where two sides are visible and have distinct sets of parallel lines.

Three-Point Perspective

• Three-point perspective introduces a third vanishing point, typically above or below the horizon line.
• This occurs when the object is tilted or when the viewer is looking up or down at the scene.
• Three-point perspective is often used in drawings of tall buildings.

Multi-Point or Panoramic Perspective

• Multi-point perspective involves more than three vanishing points, accommodating complex scenes or objects with various orientations.
• This type of perspective may be used in panoramic drawings or illustrations where multiple vanishing points are required.
  

Perspective vs. Parallel Projection

Perspective Projection

• Convergence of Lines: As objects move farther from the viewer, they appear smaller, creating a sense of depth.
• Depth Perception: Provides a realistic representation of depth, making objects appear more natural and lifelike.
• More complex, involves vanishing points.
• This is crucial for applications where visual realism is essential, such as 3D rendering for movies or video games.
• Classes of perspective projections are one-point,two-point and three point.
• Application in Art and Design: Widely used in artistic and architectural contexts where a realistic portrayal of space is crucial.
• Example: Imagine standing on a road and looking into the distance.

Parallel Projection

• Maintains Parallel Lines: In parallel projection, lines remain parallel in the projection, preserving the relative sizes of objects without converging toward a common point.
• This results in a more schematic and simplified representation.
• Lack of Depth Cues: Parallel projection does not provide inherent depth cues.
• Objects maintain the same size regardless of their distance from the viewer.
• Orthographic and Oblique Projections: Orthographic and oblique projections are common types of parallel projections.
• Frequently used in technical drawings and engineering designs where an accurate representation of object dimensions is crucial.
• Example: Consider an architectural floor plan where walls, doors, and windows are represented with parallel lines.
  

Conclusion

• 3D viewing involves the representation of objects in three-dimensional space and their projection onto a two-dimensional plane.
• Two types of projections parallel and perspective: parallel includes orthographic and oblique. while perspective includes classes such as one-point, two-point, and three-point.