University of Palestine Computer Graphics ITGD3107 Prepare: Mohammed J. el-masre Nidal M. El-Borbar Supervision: Dr. Sana'a Presentation name : Three Dimensional Viewing

Contents 3D Viewing Camera Analogy Viewing Pipeline Camera Modeling w/ OpenGL Projections Types of Projections Perspective Projection Parallel Projection Projection Matrix Projection of Lines 3D Viewing with OpenGL Matrix Modes Three Dimensional Viewing

3D Viewing The steps for computer generation of a view of a three dimensional scene are somewhat analogous to the processes involved in taking a photograph.

Camera Analogy Position Orientation Window (aperture) of the camera 1. Viewing position 2. Camera orientation 3. Size of clipping window

Viewing Pipeline The general processing steps for modeling and converting a world coordinate description of a scene to device coordinates:

Viewing Pipeline 1. Construct the shape of individual objects in a scene within modeling coordinate, and place the objects into appropriate positions within the scene (world coordinate).

Viewing Pipeline World coordinate positions are converted to viewing coordinates.

Viewing Pipeline Convert the viewing coordinate description of the scene to coordinate positions on the projection plane.

Viewing Pipeline Positions on the projection plane, will then mapped to the Normalized coordinate and output device.

Camera Modeling w/ OpenGL glMatrixMode(GL_MODELVIEW)... glMatrixMode(GL_PROJECTION)... glViewport(0,0,xres,yres) camera coordinate system viewport coordinate system device/screen coordinate system

Projections Once the view volume is determined, a projection transformation will convert the object in the 3D view volume to a 2D image on the projection plane.

Types of Projections Perspective Projection Parallel Projection

Perspective Projection (1/2) Give a realistic view of 3D objects, but does not preserve shape of object or scale Perspective images of parallel lines not parallel with projection plane converge to a point called vanishing point Size of object is diminished with distance Used in architectural, engineering, industrial design, and advertising drawings

Perspective Projection (2/2) 3-point perspective 1-point perspective 2-point perspective Most popular

Parallel Projection Accurate and same-scale measurements Not realistic, and may require multiple projections to get a complete feeling of the object Used in drawings of machine parts and in working architectural drawings

Oblique Parallel Projection (3/3) Isometric cavaliercabinet Multi-view orthographic

Projection Matrix (1/3) xpypd1xpypd1 xyz1xyz1 = M per/ort /d 0 M per = d M ort = P p (x p,y p,d) = ??? P(x,y,z) d COP z x y

Projection Matrix (2/3) xpyp01xpyp01 xyz1xyz1 = M per/ort /d 1 M per = M ort = P(x,y,z) d P p (x p,y p,0) = ??? COP z x y

Projection Matrix (3/3) P(x,y,z) d P p (x p,y p,0) = ??? COP z x or y Q (a, b, c) 1 0 –a/c da/c 0 1 –b/c db/c 0 0 –d/Q/c d 2 /Q/c+d 0 0 –1/Q/c d/Q/c+1 M general =

Projection of Lines d COP z x y Parametric representation of a line that goes through P(p x, p y, p z ) and has direction c = (c x, c y, c z ) l(t) = P+ct where t  (- , +  ) The projected line is x(t) = d(p x +c x t)/(p z +c z t) y(t) = d(p y +c y t)/(p z +c z t) If the original line is parallel to the projection plane (c z = 0) x(t) = d(p x +c x t)/p z, y(t) = d(p y +c y t)/p z, the slope of the projected line is c y /c x, independent of the position of the original line. The projected lines of parallel lines must be parallel

3D Viewing with OpenGL Viewing transformation: set the position and orientation of the viewpoint Modeling transformation: set the orientation of the model (translate, rotate, scale) Projection transformation: set the view volume and do the projection Viewport transformation: Set the viewport on the computer screen where the scene will be drawn

Matrix Modes Modelview matrix Set the viewpoint and object location by modifying this matrix glMatrixMode(GL_MODELVIEW) If projection matrix is modified Specify the view volume by modifying this matrix glMatrixMode(GL_PROJECTION) If texture matrix is modified glMatrixMode(GL_TEXTURE)

References & External links / zip _computer_graphics_c_version_2ed_-_hearn__baker.pdf Our Book computer_graphics_c_version_2ed