Computer Graphics 2 Dimensional, Study notes of Computer Graphics

Download Computer Graphics 2 Dimensional and more Study notes Computer Graphics in PDF only on Docsity!

Graphics

2D Geometric

Transformations

Dr.D.Revathi

Assistant Professor

Department of Information Technology

CGVR Contents ■ Definition & Motivation ■ 2D Geometric Transformation ■ Translation ■ Rotation ■ Scaling ■ Matrix Representation ■ Homogeneous Coordinates ■ Matrix Composition ■ Composite Transformations ■ Pivot-Point Rotation ■ General Fixed-Point Scaling ■ Reflection and Shearing ■ Transformations Between Coordinate Systems

CGVR Example: 2D Geometric Transformation Modeling Coordinates World Coordinates

CGVR Example: 2D Scaling Modeling Coordinates World Coordinates Scale(0.3, 0.3)

CGVR Example: 2D Translation Modeling Coordinates Scale(0.3, 0.3) Rotate(-90) Translate(5, 3) World Coordinates

CGVR Example: 2D Geometric Transformation Modeling Coordinates World Coordinates Again?

CGVR Basic 2D Transformations ■ Translation ■ ■ ■ Scale ■ ■ ■ Rotation ■ ■ ■ Shear ■ ■

CGVR Basic 2D Transformations ■ Translation ■ ■ ■ Scale ■ ■ ■ Rotation ■ ■ ■ Shear ■ ■ Transformations can be combined (with simple algebra)

CGVR Basic 2D Transformations ■ Translation ■ ■ ■ Scale ■ ■ ■ Rotation ■ ■ ■ Shear ■ ■

CGVR Basic 2D Transformations ■ Translation ■ ■ ■ Scale ■ ■ ■ Rotation ■ ■ ■ Shear ■ ■

CGVR Matrix Representation ■ Represent a 2D Transformation by a Matrix ■ Apply the Transformation to a Point Transformation Matrix Point

CGVR Matrix Representation ■ Transformations can be combined by matrix multiplication Matrices are a convenient and efficient way to represent a sequence of transformations Transformation Matrix

CGVR 2×2 Matrices ■ What types of transformations can be represented with a 2×2 matrix? 2D Rotation 2D Shearing

CGVR 2×2 Matrices ■ What types of transformations can be represented with a 2×2 matrix? 2D Mirror over Y axis 2D Mirror over (0,0)