Transform 3-D objects on to a 2-D plane using projections  2 types of projections Perspective Parallel 6 PROJECTIONS PARALLEL (parallel projectors) PERSPECTIVE (converging projectors) One point (one principal vanishing point) Two point (Two principal vanishing point) Three point (Three principal vanishing point) Orthographic (projectors perpendicular to view plane) Oblique (projectors not perpendicular to view plane) General Cavalier Cabinet Multiview (view plane parallel to principal planes) Axonometric (view plane not parallel to principal planes) Isometric Dimetric Trimetric 7 Parallel Projection  Discards z-coordinate and parallel lines from each vertex  Specify a direction of projection instead of center of projection Project points on the object surface along parallel lines onto the display plane. Parallel lines are still parallel after projection 8 1. Orthographic projection : If the direction of projection is perpendicular to the projection plane then it is an orthographic projection. Parallel Projection: Types 9 2. Oblique projection : If the direction of projection is not perpendicular to the projection plane then it is an oblique projection. Parallel Projection: Types 10 Cavalier  The Cavalier projection makes 45° angle with the projection plane.  The projection of a line perpendicular to the view plane has the same length as the line itself in Cavalier projection. Oblique Projection: Types 11 Cabinet The Cabinet projection makes 63.4° angle with the projection plane. In Cabinet projection, lines perpendicular to the viewing surface are projected at ½ their actual length. Oblique Projection: Types 12 Perspective Projection Project points to the display plane along converging paths. This is the way that our eyes and a camera lens form images and so the displays are more realistic. Parallel lines appear to converge to a distant point in the background. Distant objects appear smaller than objects closer to the viewing position. 13 14 Types of Perspective Projection  One point perspective projection is simple to draw.  Two point perspective projection gives better impression of depth.  Three point perspective projection is most difficult to draw. 15 16 Types of Perspective Projection Perspective Projection When we do 3-D graphics, we think of the screen as a 2-D window onto the 3-D world: How tall should this bunny be? 17 Perspective Projection  The geometry of the situation is that of similar triangles. View from above: d X P (x, y, z) Z View plane (0,0,0) x’ = ? 18 Perspective vs. Parallel Projection Perspective projection Size varies inversely with distance - looks realistic Distance and angles are not (in general) preserved Parallel lines do not (in general) remain parallel Parallel projection Good for exact measurements Parallel lines remain parallel Angles are not (in general) preserved Less realistic looking 19 Depth Cueing