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GRAFIKA KOMPUTER ~ M. Ali Fauzi

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Drawing 3D Graphics

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3D TRANSFORMATION

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**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()

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**Matrix Modes ~ ModelView Matrix (GL_MODELVIEW)**

These concern model-related operations such as translation, rotation, and scaling, as well as viewing transformations.

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THE TRANSFORMATION

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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

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

Koordinat Homogen

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

Current Position

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**Scaling In Homogeneous Coordinate : P' = S • P New Position**

Scale Matrix Current Position

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

Current Position

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Rotation For 2D :

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

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Rotation 3D Rotation, Roll y z x

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Rotation 3D Rotation, Yaw y z x

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Rotation 3D Rotation, Pitch y z x

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**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

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Shearing 3D Shearing-x Shearing-y

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Shearing 3D Shearing-z

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