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Understanding Parallel Projection: Methods and Applications in 3D Representation

This presentation delves into parallel projection, a crucial technique for rendering three-dimensional (3D) objects on two-dimensional (2D) surfaces. It addresses the historical challenges faced by artists, architects, and engineers in depicting 3D models accurately. The concept of projection is defined through the mapping of points onto a projection plane, utilizing projectors to maintain scale and shape consistency across different views. Furthermore, it explores the taxonomy of projection methods, highlighting the significance of parallel projection in creating precise working drawings, essential in various design and engineering fields.

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Understanding Parallel Projection: Methods and Applications in 3D Representation

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Presentation Transcript

  1. Presentation topic PARALLEL PROJECTION

  2. PARALLEL PROJECTION • PROJECTION • MAPPING • METHODS OF PROJECTION • PARALLEL PROJECTION

  3. PROJECTION • For centuries, artists, engineers, designers, drafters, and architects have been facing difficulties and constraints imposed by the problem of representing a three-dimensional object or scene in a two-dimensional medium. • The implementers of a computer graphics system face the same challenge.  

  4. PROJECTION • The subject of projection will help you to display three dimensional model on two dimensional medium (screen)…

  5. MAPPING • Projection can be defined as a mapping of point P(x,y,z) onto its image P`(x`,y`,z`) in the projection plane or view plane, which constitutes the display surface. • The mapping is determined by a projection line called the projector that passes through P and intersects the view plane.

  6. EXAMPLE

  7. MAPPING • We can mapping a point in three dimensional on a view plane Where viewer can view from their point of view..

  8. METHODS OF PROJECTION • PARALLEL PROJECTION • PERSPECTIVE PROJECTION

  9. TAXANOMY OF PROJECTION • We can construct different projections according to the view that is desired. • These methods are used to solve the basic problem of pictorial re presentation. • (how to display 3D model in 2D screen)

  10. TAXANOMY

  11. TAXANOMY OF PROJECTION

  12. PARALLEL PROJECTION • In parallel projection, image points are found as the intersection of the view plane with a projector drawn from the object point and having a fixed direction. • The direction of projection is the prescribed direction for all projections.

  13. USE OF PARALEL PROJECTION • Parallel projection methods are used by drafters and engineers to create working drawings of an object which preserves its scale and shape. • The complete representation of these details often requires two or more views (projections) of the object onto different view plan.

  14. Mathematical Description of a Parallel Projection • Projection rays (projectors) emanate from a Center of Projection (COP) and intersect Projection Plane (PP). • The COP for parallel projectors is at infinity. • The length of a line on the projection plane is the same as the "true Length".

  15. FIGURE:

  16. figure Center of projection at infinity Direction of projection(DOP) Same for all points.

  17. PURPOSE OF PARALLEL PROJECTION • To design model of exact measure of original model • So scale and shape will not change by changing of point of views.

  18. ~~~THE END~~~

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