1. 11. Wireframe Perspective Display e-mail: Assoc.Prof.Dr. Ahmet Zafer Şenalp e-mail: azsenalp@gmail.comazsenalp@gmail.com Mechanical Engineering Department Gebze Technical University ME 521 Computer Aided Design

2. 11. Wireframe Perspective Display 11. Wireframe Perspective Display To calculate the position of a point on the display screen which corresponds to a point on some object, object space must be transformed into the eye coordinate system, which has its origin fixed at the viewpoint and its Z e axis pointed in the direction of view. World coordinate (right handed) to eye coordinate system ( change sign of z). choose so that X, Y axes allign Dr. Ahmet Zafer Şenalp ME 521 2 Mechanical Engineering Department, GTU The Eye Coordinate Sysytem:

3. A transformation called the viewing transformation V is used to convert points in object space (x, y, z) to points in the eye coordinate system (x e, y e, z e ). V-transformation matrix Concatenation of several rotations and translations. Dr. Ahmet Zafer Şenalp ME 521 3 Mechanical Engineering Department, GTU 11. Wireframe Perspective Display 11. Wireframe Perspective Display

4. Perspective display can be generated by projecting each point of an object onto the plane of the display screen. Simple Perspective Transformation The coordinates (X s, Y s ) of the projected image of the point P measured in eye coordinates (X e, Y e, Z e ) are easily computed. Considering the Y e, Z e plane: Triangles OQ'P' and OQP are similar, giving: X s and Y s can be converted to dimensionless fractions by dividing the screen size: Dr. Ahmet Zafer Şenalp ME 521 4 Mechanical Engineering Department, GTU 11. Wireframe Perspective Display 11. Wireframe Perspective Display

5. Simple Perspective Transformation or to screen coordinates by including a specification of the location of the image area (viewport): Here: Dr. Ahmet Zafer Şenalp ME 521 5 Mechanical Engineering Department, GTU 11. Wireframe Perspective Display 11. Wireframe Perspective Display

6. Simple Perspective Transformation This transformation is fundamentally different from those for rotation, translation and scaling: it involves dividing by the Z e coordinate value, whereas the others involve only multiplication and addition. Generating a true perspective image requires dividing by the depth of each point. Pespective image of a line can be generated easily by transforming only its endpoints and drawing the line between the two transformed end points. The process of generating a wire-frame perspective display thus involves: a) Retrieving the object-space coordinates of the end points of each line and using viewing transformation equation to obtain the eye coordinates of the endpoints. b) Above Eqn. to find the screen coordinates of each endpoint. c) Vector generator can then generate a line from the endpoint information. If is small aperture will be wide angle If is large, gives narrow aperture like a telephoto lens. Dr. Ahmet Zafer Şenalp ME 521 6 Mechanical Engineering Department, GTU 11. Wireframe Perspective Display 11. Wireframe Perspective Display

7. 3D Clipping 3B Kırpma ekranda görüntülenebilecek (görünür) kısımların belirlenmesi ve görüntü dışı kalanların ayrılmasıdır. The conditions of visibility are: are excluded. clipping coordinates or: (X c, Y c, Z c ): Dr. Ahmet Zafer Şenalp ME 521 7 Mechanical Engineering Department, GTU 11. Wireframe Perspective Display 11. Wireframe Perspective Display