Presentation is loading. Please wait.

Presentation is loading. Please wait.

10. 3D Coordinate Operations Dr. Ahmet Zafer Şenalp Makine Mühendisliği Bölümü Gebze Yüksek Teknoloji.

Similar presentations


Presentation on theme: "10. 3D Coordinate Operations Dr. Ahmet Zafer Şenalp Makine Mühendisliği Bölümü Gebze Yüksek Teknoloji."— Presentation transcript:

1 10. 3D Coordinate Operations Dr. Ahmet Zafer Şenalp Makine Mühendisliği Bölümü Gebze Yüksek Teknoloji Enstitüsü ME 521 Computer Aided Design

2 Introduction Most of the problems needs 3D computer graphics for descrition. For this purpose 3D Trasnformations or coordinate ıperations are used. 3-D Transformations:  Translation  Rotation  Scaling Dr. Ahmet Zafer Şenalp ME GYTE-Makine Mühendisliği Bölümü 10. 3D Coordinate Operations

3 T x, T y, T z are the components of the translation in x, y, z, in object coordinates Dr. Ahmet Zafer Şenalp ME GYTE-Makine Mühendisliği Bölümü 10. 3D Coordinate Operations

4 Through point (0, 0, 0) and about x axis, by the angle  clockwise when looked from +x: Below figure shows +X and –X rotation directions (+y rotation direction) Dr. Ahmet Zafer Şenalp ME GYTE-Makine Mühendisliği Bölümü 10. 3D Coordinate Operations İnitial state +X rotation -X rotation

5 Below figure shows +X +Y, and +Z rotation directions. Dr. Ahmet Zafer Şenalp ME GYTE-Makine Mühendisliği Bölümü 10. 3D Coordinate Operations İnitial state +X rotation +Y rotation +Z rotation

6 Transformation matrices for rotation: Rotation about X axis: Rotation about Y axis: Rotation about Z axis: Dr. Ahmet Zafer Şenalp ME GYTE-Makine Mühendisliği Bölümü 10. 3D Coordinate Operations

7 Transformation matrix for scaling: In below figure mirror images of two objects are onbtained by scaling. Dr. Ahmet Zafer Şenalp ME GYTE-Makine Mühendisliği Bölümü 10. 3D Coordinate Operations

8 Inverse transforms are obtained by placing negative values: Inverse of Translation: Inverse of Rotation abou X: Inverse of Rotation about Y: Inverse of Rotation about Z: Inverse transform of T matrix is represented by T -1. Dr. Ahmet Zafer Şenalp ME GYTE-Makine Mühendisliği Bölümü 10. 3D Coordinate Operations

9 or Concatenation of operations: Dr. Ahmet Zafer Şenalp ME GYTE-Makine Mühendisliği Bölümü 10. 3D Coordinate Operations

10 Performing the procedure must comply with the order of concatenation operations. Below example shows the difference between rotations about first +X and then +Y and the reverse. Dr. Ahmet Zafer Şenalp ME GYTE-Makine Mühendisliği Bölümü 10. 3D Coordinate Operations İnitial state +X rotation İnitial state +Y rotation +X rotation


Download ppt "10. 3D Coordinate Operations Dr. Ahmet Zafer Şenalp Makine Mühendisliği Bölümü Gebze Yüksek Teknoloji."

Similar presentations


Ads by Google