3D viewing and projection2.. Trang 4 3D viewing■ Part of the difficulty lies in trying to display three dimensional objects on a 2D display■ Different views on the same object eventually
Lesson Projection Transformation Trinh Thanh Trung School of ICT, HUST Content 3D viewing and projection Parallel projection Perspective projection 3D viewing and projection 3D viewing ■ Part of the difficulty lies in trying to display three dimensional objects on a 2D display ■ Different views on the same object eventually lead to different 2D representations at the projection stage □ The projected 2D image of a 3D object is viewer dependent ■ Different views can be specified based on several parameters e.g position, orientation, field of view 3D viewing methods ■ On 2D displays: □ perspective and depth of field □ depth cueing □ visible line/surface identification □ surface rendering □ exploded/cutaway scenes, cross-sections 3D viewing 3D viewing can be faked? 3D viewing methods (cont.) ■ On 3D display □ Hologram display Stereoscopic display ■ Faking depth in a 2D image ■ Based on natural stereoscopic eye-brain system ■ Objects are not viewed with just one eye, but two eyes ■ Each eye looks at the object from a slightly different location Stereoscopic display Axonometric projection ■ Axonometric projection is a type of orthographic projection, where the lines of sight are perpendicular to the plane of projection, and the object is rotated around one or more of its axes to reveal multiple sides Axonometric projection Isometric ■ Three axes of space appear equally foreshortened (~120°) ■ Corresponding rotating angles are 35.26° and 45° − sin2 sin = − sin f = cos2 = / = 0.8165 sin2 sin = − sin 2 2sin = sin2 1/3 2= =1/2 − sin −1 /3 sin =