Report

Projections Since our viewing surface is 2D, we must have some way of projecting 3D object onto 2D screen. Conceptual Model of the 3D viewing process 3D PROJECTIONS (Rays converge on eye position) Perspective (Rays parallel to view plane) Parallel Orthographic Elevations Axonometric Isometric Oblique Cavalier Cabinet PARALLEL PROJECTION All projection lines are parallel to each other and intersects view plane z- coordinate is discarded. Point of intersection is projection of vertex. preserve relative proportions Does not produce realistic views. Connect projected vertices which correspond to connections on the original object. PARALLEL PROJECTION(EG) View Plane DOP PARALLEL PROJECTIONS 2 principle types: orthographic and oblique. Orthographic : direction of projection = normal (means perpendicular) to the projection plane or view plane. Oblique : direction of projection != normal to the projection plane or view plane. (means not perpendicular) PARALLEL PROJECTIONS: ORTHOGRAPHIC AND OBLIQUE View plane Orthographic Oblique PARALLEL PROJECTIONS Orthographic (or orthogonal) projections: front elevation, top-elevation and side-elevation. In all these projection plane or view plane is normal to principal axes. Useful because angle and distance measurements can be made... However, As only one face of an object is shown, it can be hard to create a mental image of the object, even when several view are available. Parallel Projections Orthogonal projections: AXONOMETRIC PROJECTION The front , side and top view of an object resting in its simple position gives an incomplete idea of the shape of the object. In Axonometric projections, view planes are not parallel to principal axis. Parallelism of lines is preserved but angles are not. Isometric Projection “ Iso” means “equal” and “metric projection ” means “a projection to reduced measure”. An isometric projection is one type of pictorial projection in which the dimensions of a solid are not only shown in one view but also their dimensions can be scaled from this drawing. OBLIQUE PROJECTIONS It is parallel projection. Projection lines are parallel but not normal to the projection plane. Oblique means slanting. Projection lines are at an angle to the view plane. Let the angle be an angle the projection line makes with the view plane Notice that the view plane normal and direction of projection are not same. Cavalier projections The direction of projection makes 45° angle with view plane. The projection of a line perpendicular to the view plane has the same length as the line itself. 1 a 1 1 1 Cabinet projections The direction of projection makes angle of arc tan 63.4° angle with view plane. For this angle, line perpendicular to the viewing surface are projected at one – half their actual length. Cabinet projections appears more realistic than cavalier projection bcoz of this reduction in the length of perpendiculars 2 a 1 1/2 PERSPECTIVE PROJECTION Projection lines are intersecting the view plane and converge at a single point called centre of projection or projection reference point. Projection lines are not parallel Perspective projection produces realistic views Does not preserves relative proportions. The object positions are transformed to the view plane along these converged projection lines and projected view of an object is determined by calculating the intersection of converged projection lines with view plane. PERSPECTIVE PROJECTION Vanishing Point : the perspective projection of any set of parallel lines that are not parallel to the projection plane converge to a vanishing point. The vanishing point for any set of lines that are parallel to one of three principal axes of an object is referred to as a principal vanishing point or axis vanishing point Category of perspective projection 1 point perspective projection 2 point perspective projection 3 point perspective projection 1. 2. 3. ONE POINT PERSPECTIVE PROJECTION Based on single vanishing point. Object is placed so that one of surfaces is parallel to the plane of projection. TWO POINT PERSPECTIVE PROJECTION Based on two vanishing points. This is achieved by rotating object along y-axis so that lines along that axis remain parallel to viewing plane, but those along the two other axes have vanishing points THREE POINT PERSPECTIVE PROJECTION Based on three vanishing points. This achieved by positioning abject so that none of its axes are parallel to plane of projection PERSPECTIVE VS. PARALLEL 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 VIEWING PARAMETERS VIEWING PARAMETERS We can view the object from the top, or the side or from the behind. Therefore , it is necessary to choose a particular view for a picture by defining view plane. View plane : it is film in the camera ..on which we want to take photograph. View reference point: this point is the center of our viewing coordinate system. View plane normal vector: this normal vector is the direction perpendicular to the view plane. View distance: distance between the view plane and the view reference point. It is possible to obtain the different views by rotating the camera about the view plane normal vector and keeping view reference point and direction of N vector fixed. view-up vector V :Rotation of camera or view plane is specified by view-up vector V 3D Clipping ( clipping against volume) Cube Cohen – Sutherland clipping algo readily extend to 3D. Cohen- Sutherland algo uses two extra bit in out code for incorporating z<zmin and z > zmax regions. We to use outcode of 6 –bit instead of 4 – bit Bit 1 = if end point is to the left of the volume. Bit 2 = if end point is to the right of the volume. Bit 3 = if end point is to the bellow of the volume. Bit 4 = if end point is to the above of the volume. Bit 5 = if end point is to the front of the volume. Bit 6 = if end point is to the back of the volume. Otherwise bit is set to zero