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What is projection in terms of 3D objects?
What is projection in terms of 3D objects?
The transformation of a three-dimensional (3D) object into a two-dimensional (2D) plane.
In orthographic projection, the projection is always perpendicular to the view plane.
In orthographic projection, the projection is always perpendicular to the view plane.
True
Which types of parallel projection are mentioned?
Which types of parallel projection are mentioned?
The angle of projection lines in cavalier projection is ___ degrees.
The angle of projection lines in cavalier projection is ___ degrees.
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The top orthographic projection is called ___ view.
The top orthographic projection is called ___ view.
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What is the center of projection in parallel projections?
What is the center of projection in parallel projections?
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Which of the following views are commonly used in orthographic projections?
Which of the following views are commonly used in orthographic projections?
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What does a multi-view orthographic projection represent?
What does a multi-view orthographic projection represent?
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Study Notes
Projection
- Projection is the mapping of a three-dimensional point (x, y, z) into its image (x', y', z') on a projection plane, which is the display surface.
- It transforms a 3D object into a 2D representation.
Classification of Projections
- Perspective Projection: Uses a single vanishing point and creates the illusion of depth.
- Parallel Projection: Uses parallel projection lines to represent the object.
Parallel Projection
- Projection lines are parallel to each other.
- Projection lines extend from the object and intersect the view plane, forming a 2D representation.
- Two types:
- Orthographic Projection: The projection lines are perpendicular to the view plane.
- Oblique Projection: The projection lines are not perpendicular to the view plane.
Orthographic Projection
- Depicts the object as it appears when viewed directly from the front, top, or side.
- Preserves relative sizes and shapes, making it suitable for technical drawings.
- Produces front, side, and rear views (elevations) and a top view (plan view).
- Engineering and architectural drawings utilize orthographic projection.
- Shows only one face of an object, which can make it challenging to visualize the object's full form.
Oblique Projection
- Presents a more pictorial representation of the object.
- Distorts the object's dimensions to provide a more three-dimensional perspective.
- Typically shows one face of the object in full view, while the other faces are depicted at an angle.
- Two main types:
- Cavalier Projection: Projection lines make a 30-degree angle with the view plane.
- Cabinet Projection: Projection lines make a 45-degree angle with the view plane, and depths are typically shortened by half for a more realistic representation.
Multi-View Orthographic Projections
- A collection of 2D drawings that together create a comprehensive representation of a 3D object.
- Each view shows a specific side of the object.
- Common combinations include front, top, and side views.
Orthographic Projection (DOP)
- DOP (Direction of Projection) is perpendicular to the projection plane to ensure correct geometric representation in the 2D drawing.
Standard Orthographic Projection
- A mathematical transformation that maps a 3D point to a 2D point.
- The formula uses a matrix operation.
- The formula transforms the (x, y, z) coordinates to (xp, yp, zp).
Parallel Projections Summary
- The center of projection is at infinity.
- Projectors are parallel.
- Parallel lines remain parallel in the projection.
- There is no foreshortening.
- Distances and angles are transformed consistently.
- Often used in engineering design and CAD systems.
Multi-View Orthographic Projections
- Show a single side of the object at a time.
- Produce front, top, and side views of an object.
- The direction of projection is parallel to a principal axis.
General Guidelines for Choosing Views
- Select a front view that is the most descriptive of the object.
- The longest dimension is typically chosen as the width (or depth) of the object.
- The most common combination of views is front, top, and side.
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Description
Explore the different methods of projecting three-dimensional points onto a two-dimensional display. This quiz covers perspective and parallel projections, including orthographic and oblique projections. Test your understanding of how these techniques transform 3D objects into 2D representations.
