# 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?

**Foreshortening**is a visual phenomenon in which objects or parts of objects appear shortened when viewed from a certain angle.

**Characteristics of Orthographic Projections:**

**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 a
**ll 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 us
**e 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.

**Characteristics of Cavalier Oblique Projection:**

**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.