Parallel projection is a fundamental method used in engineering drawing to represent three-dimensional objects on a two-dimensional surface, such as paper or a computer screen. It is characterized by projecting all points of the object onto a projection plane along parallel lines of sight.
In three-dimensional geometry, a parallel projection (or axonometric projection) is a projection of an object in three-dimensional space onto a fixed plane, known as the projection plane or image plane, where the rays, known as lines of sight or projection lines, are parallel to each other.
How Parallel Projection Works
Unlike perspective projection where lines converge at a vanishing point (mimicking human vision), parallel projection maintains the parallelism of lines. This means that lines that are parallel in 3D space remain parallel in the 2D projection. This characteristic is crucial in engineering because it preserves the relative proportions of the object, allowing for accurate measurement and representation.
- Lines of Sight: These are imaginary parallel lines extending from each point on the object to the projection plane.
- Projection Plane: The 2D surface onto which the object is projected.
- Projected Image: The resulting 2D representation of the 3D object.
Why is Parallel Projection Used in Engineering Drawing?
Parallel projection is widely used in engineering and technical drawing for several key reasons:
- Preservation of Proportions: Since projection lines are parallel, the relative sizes and shapes of features on the object are maintained. This allows engineers to take measurements directly from the drawing, which is essential for design, manufacturing, and analysis.
- Clarity: Different types of parallel projection can provide clear, unambiguous views of complex objects.
- Standardization: Specific types of parallel projection, like orthogonal projection, are standardized methods used universally in technical communication.
Types of Parallel Projection
Parallel projection is broadly classified into two main categories based on the relationship between the lines of sight and the projection plane:
1. Orthogonal Projection
In orthogonal projection, the lines of sight are perpendicular (orthogonal) to the projection plane. This is the most common type used in engineering.
- Multiview Projection: Projects the object onto six principal planes, typically showing front, top, and side views. This method provides true shapes and sizes of features parallel to the projection planes.
- Axonometric Projection: Projects the object so that multiple faces are visible in a single view. Lines of sight are still perpendicular to the projection plane, but the plane is tilted relative to the object's axes.
- Isometric Projection: All three axes are equally foreshortened, and the angles between them are 120 degrees. This is a popular method for creating illustrative technical drawings.
- Dimetric Projection: Two of the three axes are equally foreshortened.
- Trimetric Projection: All three axes are foreshortened differently.
2. Oblique Projection
In oblique projection, the lines of sight are parallel to each other but not perpendicular to the projection plane.
- Cavalier Projection: Lines projecting features parallel to the view plane are shown at their true length. The receding axis is often drawn at 45 degrees, with no foreshortening.
- Cabinet Projection: Similar to cavalier, but lines projecting features parallel to the view plane are foreshortened by half their length along the receding axis. This provides a more realistic appearance than cavalier projection.
Here's a brief comparison:
| Feature | Orthogonal Projection | Oblique Projection |
|---|---|---|
| Lines of Sight | Perpendicular to the projection plane | Not perpendicular to the projection plane |
| Preservation of Angle | Preserves right angles on projection plane | Generally distorts angles |
| Use Case | Detailed dimensioning, standard views | Pictorial views, showing one face true size |
By utilizing parallel projection methods, engineers can create accurate, scaled representations of three-dimensional objects, facilitating design, communication, and manufacturing processes.
