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

Slides:

Advertisements

Similar presentations

TRANSFORMATIONS SPI SPI

Advertisements

ME 521 Computer Aided Design 1. Introduction to CAD

Defining Rotations, Reflections, and Translations

2. Computer Aided Design and Production Process Dr. Ahmet Zafer Şenalp Makine Mühendisliği Bölümü.

Principles of Computer-Aided Design and Manufacturing Second Edition 2004 ISBN Author: Prof. Farid. Amirouche University of Illinois-Chicago.

2. Computer Aided Design and Production Process Assoc.Prof.Dr. Ahmet Zafer Şenalp Mechanical Engineering.

COMPUTER GRAPHICS 2D TRANSFORMATIONS.

8. Stress-Strain Relations

ME 520 Fundamentals of Finite Element Analysis Assoc.Prof.Dr. Ahmet Zafer Şenalp Mechanical Engineering.

11. Wireframe Perspective Display Assoc.Prof.Dr. Ahmet Zafer Şenalp Mechanical Engineering Department.

10. 3D Coordinate Operations Assoc.Prof.Dr. Ahmet Zafer Şenalp Mechanical Engineering Department Gebze.

ME 521 Computer Aided Design Assoc.Dr. Ahmet Zafer Şenalp Mechanical Engineering Department Gebze.

Transformations Moving a shape or object according to prescribed rules to a new position. USE the tracing paper provided to help you understand in the.

8. 2D Coordinate Operations Assoc.Prof.Dr. Ahmet Zafer Şenalp Mechanical Engineering Department Gebze.

Elementary 3D Transformations - a "Graphics Engine" Transformation procedures Transformations of coordinate systems Translation Scaling Rotation.

REFLECTIONS, ROTATIONS AND TRANSLATIONS. Reflections.

Graphics Programming Graphics Programming: Transformations.

Using Matrices to Perform Geometric Transformations

7-Bar Elements in 3-D Space Dr. Ahmet Zafer Şenalp Mechanical Engineering Department Gebze Technical.

2D Geometric Transformations

6-Bar Elements in 2-D Space Dr. Ahmet Zafer Şenalp Mechanical Engineering Department Gebze Technical.

10-Beam Elements in 2-D Space (Plane Frame Element) Dr. Ahmet Zafer Şenalp Mechanical Engineering.

Geometrical Transformations 2 Adapted from Fundamentals of Interactive Computer Graphics, Foley and van Dam, pp , by Geb Thomas.

Computer Graphics 3D Transformations. Translation.

Transformations of Geometric Figures Dr. Shildneck Fall, 2015.

12-Perspective Depth Assoc.Dr. Ahmet Zafer Şenalp Mechanical Engineering Department Gebze Technical.

11. Plastic Anisotropy Assoc.Prof.Dr. Ahmet Zafer Şenalp Mechanical Engineering Department Gebze Technical.

3D Transformation A 3D point (x,y,z) – x,y, and z coordinates

Lecture 5: Introduction to 3D

II-1 Transformations Transformations are needed to: –Position objects defined relative to the origin –Build scenes based on hierarchies –Project objects.

Computer Graphics Lecture 16 Fasih ur Rehman. Last Class Homogeneous transformations Types of Transformations – Linear Transformations – Affine Transformations.

FCC Graficación CAD/CAM 3D Transformations. Contents 1. Translation 2. Scaling 3. Rotation 4. Other Transformations.

Lecture 10 Geometric Transformations In 3D(Three- Dimensional)

4-3 Warm Up Lesson Presentation Lesson Quiz

11. Viewing Transformations

Warm up Identify the transformation ∆RST → ∆XYZ.

3D Transformation.

Computer Graphics 3D Transformations

3D Geometric Transformations

13. Wireframe Perspective Display

DO NOW W ( , ) X ( , ) Y ( , ) Z ( , ) YES NO YES NO YES NO

Lecture 7 Geometric Transformations (Continued)

12. 3D Coordinate Operations

Unit 1 Transformations in the Coordinate Plane

Transformations Example Draw the line Draw 1 at , ,

Transformations in 3 Dimensions CS /28/2018 Dr. Mark L. Hornick

Perform the following transformations on the point (4,−8):

Translations Rotations Reflections Compositions 1 pt 1 pt 1 pt 1 pt

ME 521 Computer Aided Design

4-4 Geometric Transformations with Matrices

Transformations on the coordinate plane

Algebraic Representations of Transformations

TRANSFORMATIONS Translations Reflections Rotations

Rotation: all points in the original figure rotate, or turn, an identical number of degrees around a fixed point.

These are flips, slides, turns, and enlargements/reductions.

Properties or Rules of Transformations

Transformations.

Transformations on the coordinate plane

4-3 Warm Up Lesson Presentation Lesson Quiz

3D transformations Dr Nicolas Holzschuch University of Cape Town

Applications in Coordinate Geometry

Transformations: Translations Rotations Reflections

Transformations with Matrices

Transformations Review

Sept 10, 2013 Transformations Unit 1Review.

Using Matrices to Perform Geometric Transformations

Unit 37 Further Transformations

Warm Up 6.3 Complete the chart for the given counterclockwise rotations about the origin. 90o 180o 270o R(3, -3) S(1, 4) Use.

Congruent Figures Day 2.

Translation in Homogeneous Coordinates

Presentation transcript:

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

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

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

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

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

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

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

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

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

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