Projections What is Projection Representing a threedimensional object

Projections

What is Projection Representing a three-dimensional object or scene in a 2 D space is called projection. Two basic projections are: 1. Parallel projections 2. Perspective projections

Planar Projections Projection Taxonomy Parallel Oblique Perspective Orthographic Cavalier Cabinet Multiview 1 point Axonometric Isometric Dimetric Trimetric 2 point 3 point

Parallel Projections • Useful for engineers, and draftsmen to create working drawings • Preserve shape and scale of the drawing.

Multiview parallel projections • Represent the top, front and side views of an object. • These views play a very important role in engineering drawings, and architectural plans.

Axonometric projections • The view plane normal is not parallel to any principal axis and the projectors are orthogonal to view plane. • This ensures that the adjacent faces of an object are clearly visible. • Parallel lines remain parallel and foreshortening of receding lines take place by some factor. • Depending upon the foreshortening of the principal axis the three axonometric projections. 1. Isometric projections 2. Dimetric projections 3. Trimetric projections

Isometric projections The projection plane normal makes equal angles with each(x, y, z) principal axis. The three axes are equally foreshortened.

Dimetric projections The projection plane normal (projector) makes equal angles with two of three principal axes (two of three axes are equally foreshortened). Three different dimetric projections are shown below.

Trimetric projections The projection plane normal (projector) makes unequal angles with each principal axis (all three axes are unequally foreshortened)

Oblique parallel projections • Oblique projections have their projectors that are NOT perpendicular to the projection plane

Cavalier parallel projections The lines perpendicular to projection plane are preserved in length, that is, L=1

Cabinet parallel projections • Lines perpendicular to projection plane are 1/2 their true length, that is,

Perspective projections • Perspective projection used for drawing 3 D objects and scenes. • The plane containing the canvas is the view plane, with view plane normal. • Points on an object are projected to the view plane along lines that converge to a center of projection.

1 point perspective 2 point perspective 3 point perspective

Problems with perspective projections • Perspective foreshortening • vanishing point • Perspective projection of objects behind the center of projection makes image appear upside down and backward onto the viewplane • Relative dimensions of the objects not preserved