GRAFIKA KOMPUTER ~ M. Ali Fauzi

Drawing 3D Graphics

3D TRANSFORMATION

Transformation Pipeline Vertex Modelview Matrix Projection Perspective Division Viewport Transformation Object Coordinates Eye Clip Normalized device Window GL_MODELVIEW mode glTranslate() glRotate() glScale() glLoadMatrix() glMultMatrix() gluLookAt() GL_PROJECTION mode glOrtho() gluOrtho2D() glFrustum() gluPerspective() glViewport()

Matrix Modes ~ ModelView Matrix (GL_MODELVIEW) These concern model-related operations such as translation, rotation, and scaling, as well as viewing transformations.

THE TRANSFORMATION

Translation The path is represented by a vector, called the translation or shift vector. P' = P + T tx ty tz x’ y’ z’ x y z = + New Position Current Position Translation Vector

Translation Translasi 3D -> 4D Translasi 2D -> 3D Koordinat Asal Koordinat Homogen

Scaling The transformation using Scale Matrix P' = S • P New Position Current Position

Scaling In Homogeneous Coordinate : P' = S • P New Position Scale Matrix Current Position

Rotation For 2D : P' = R . P New Position Rotation Matrix Current Position

Rotation For 2D :

Rotation 2D Rotation about an arbitrary axis (Rotasi pada sembarang sumbu (Xr,Yr) dengan sudut Ө) :

Rotation 3D Rotation, Roll y z x

Rotation 3D Rotation, Yaw y z x

Rotation 3D Rotation, Pitch y z x

sumbu putar sembarang titik (Ax,Ay,Az) Rotation 3D Rotation about an arbitrary axis (Rotasi pada sembarang sumbu (Ax,Ay,Az) dengan sudut Ө) sumbu putar sembarang titik (Ax,Ay,Az) y x z

Shearing 3D Shearing-x Shearing-y

Shearing 3D Shearing-z