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# Parallel projection

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This presentation was prepared during my MCA with Computer Graphics as a subject.

Veröffentlicht in: Ingenieurwesen
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### Parallel projection

1. 1. Presentation on Parallel Projection By- Prince Shahu MCA 4th Semester Assam Engineering College
2. 2. Types of Projections Perspective Projection Parallel Projection One principal vanishing point Two principal vanishing point Three principal vanishing point Oblique Orthographic Projectors not perpendicular to the projection plane. Projectors perpendicular to the projection plane. General Cavalier Cabinet Multiview Axonometric Projection plane parallel to principal planes. Projection plane not parallel to principal planes. 1. Three view 2. Auxiliary view 3. Sectional view 1. Isometric 2. Diametric 3. Trimetric
3. 3. PARALLAL PROJECTION • In parallel projection direction of Projection is same for all points • All projectors are parallel to each others Object View plane
4. 4. When the Direction of Projection is perpendicular ( at 90◦) to the view plane, then the projection is Orthographic Projection. Orthographic Projection
5. 5. Deriving equations of 𝑿 𝒑 and 𝒀 𝒑 for Orthographic Projection The view plane is placed at position 𝑍 𝑣𝑝 𝑎𝑙𝑜𝑛𝑔 𝑡ℎ𝑒 𝑍 𝑣 axis, then any point(x,y,z) in viewing coordinates is transformed to projection coordinate as 𝑥 𝑝=x, and 𝑦𝑝=y where the original z-coordinate value is preserved for the depth information needed in depth cuing and visible-surface determination procedures.
6. 6. Types of Orthographic Projections Multi-View Orthographic Projection 1. Orthographic projections that show only one side of an object are called multiview orthographic projections. 2. When direction of projection is parallel to any principal axis, this produces front, top and side view of an object
7. 7. Axonometric Projection 1. Orthographic projections that show more than 1 side of an object are called axonometric orthographic projections. 2. In axonometric orthographic projections, the direction of projection is not parallel to any of the principal axis.
8. 8. Sub categories of Axonometric orthographic Projections are: 1. Isometric : The direction of projection makes equal angles with all of the principal axis.
9. 9. 2. Di-metric : The direction of projection makes equal angles with exactly two of the principal axis. 3. Trimetric Projection: The direction of Projection makes unequal angles with the principal axis.
10. 10. Oblique Projection 1. Parallel projections that does not intersect the view plane perpendicularly. 2. Direction of Projection is perpendicular to view plane. Type of Oblique Projection. 1. Cavalier: the direction of projection is chosen so that there is no fore-shortening of lines perpendicular to the xy-lane. It is achived by projecting the projectors at an angle of 30 and 45 degree. 2. Cabinet: the direction of projection is chosen so that the line perpendicular to the xy-plane are fore-shortening by half of their length. For cabinet projection the angle is kept 63.40 degree.
11. 11. Deriving equations of 𝑿 𝒑 and 𝒀 𝒑 for Oblique Projection • It specifies two angles α and φ . • The line from (x,y,z) to (𝑥 𝑝, 𝑦𝑝)makes an angle α with the line on the projection plane that joins(𝑥 𝑝, 𝑦𝑝) and (x,y). • The line of length L, is at an angle φ with the horizontal direction in the projection plane. • So, we can write co-ordinates in terms of x,y,L and φ as 𝑥 𝑝 = x + L cos φ 𝑦𝑝 = y + L sin φ • Length L depends on the angle α and the z coordinate of the point to be projected is: tan α = 𝒛 𝑳 or L= 𝒛 𝒕𝒂𝒏α =z 𝑳 𝟏 Where 𝑳 𝟏 is the inverse of tanα, which is also L when z = 1. We can then write the equation as 𝑥 𝑝 = x + z(𝑳 𝟏cos φ) and 𝑦𝑝 = y + z(𝑳 𝟏sinφ). The transformation matrix for any parallel projection on the 𝑥 𝑣 𝑦𝑣 plane can be written as −−− −
12. 12. Parallel projection Difference between Parallel and Perspective projections. Perspective projection 1. Projection lines are always parallel to each other. 2. PRP(Projection Reference Point) are at infinite distance. 3. Size and Shape of the Object are preserved. 4. There is no foreshortening. 5. Doesn’t gives realistic view. 6. View Confusion never arises. 1. Projection lines are not parallel to each other, they appears to converse towards a fixed point(PRP). 2. PRP(Projection Reference Point) are at finite distance. 3. Size and Shape of the Object are not preserved. 4. There is perspective foreshortening, object close to view plane will look larger. 5. Gives realistic view. 6. View Confusion arises, objects formed behind PRP are projected in an inverted manner.
13. 13. BIBLIOGRAPHY • Computer Graphics version C by Donald D. Hearn and M. Pauline Baker. • Youtube.com • Slideshare.com