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- 1. 3-D Transformations
- 2. 3-D ProjectionsWe can project the 3-D objects onto the 2-D plane. So Projection can be defined as a mapping of point P onto its image P’ in the projection plane or view plane.There are two basic projection methods: Parallel projection Perspective projection
- 3. Parallel Projection Coordinate positions are transformed to the view plane along parallel lines. The image points are found as the intersection of the view plane with the projector. View Plane P2 P2’ P1 P1’
- 4. Parallel Projection preserves relative proportions of objects. Accurate views of the various sides of an object are obtained with a parallel projection, but this does not give us a realistic representation of the appearance of a 3-D object. We can specify a parallel projection with a projection vector that defines the direction for the projection lines.
- 5. Types of Parallel Projections: (i) Orthographic Projection (ii) Oblique projection y P2 P1 Oblique ProjectionOrthographicProjection x P2’ P2’ z P1’ P1’
- 6. Orthographic parallel projection: When the projection is perpendicular to the view plane. And parallel to any of the principal axis this produces the front, top and side views. See next slide….
- 7. Types of Orthographic projections:(i) Axonometric projection: that display more than one face of an object. Most common axonometric is Isometric projection.Isometric projection is generated by aligning the projection plane so that it intersects each coordinate axis in which the object is defined at the same distance from the origin.The direction of projection makes equal angles with all the principal axis.
- 8. Oblique projection: If the direction of projection is not perpendicular to the projection plane. Types of Oblique Projection are:(i) Cavalier- the direction of projection is chosen so that there is no foreshortening of lines perpendicular to the xy plane.(ii) Cabinet- the direction of projection is chosen so that lines perpendicular to the xy planes are foreshortened by half their lengths.
- 9. Perspective ProjectionPoints on the body of an object is 3-D are transformed to the viewing plane along lines that converge to a point called vanishing point(center of projection). C Center Of projection (Vanishing Point
- 10. So the distance of a line from the projectionplane determines its size on the projectionplane, i.e. the farther the line is from theprojection plane, the smaller its image on theprojection plane.Characteristics:(i) Vanishing Point: The lines that are parallel to the viewing plane appear to converge at a point called Vanishing point.
- 11. (ii) Perspective Foreshortening : Objects that are farther from the viewing plane are projected smaller in size than the objects that are nearer to viewing plane.(iii) View confusion : When we project objects which are behind the center of projection appears to be projected upside down & backward onto the viewing plane.

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