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

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Presentation transcript:

Computer Graphics Lecture 16 Fasih ur Rehman

Last Class Homogeneous transformations Types of Transformations – Linear Transformations – Affine Transformations – Projective Transformations Combining Homogeneous transformations

Today’s Agenda 3D Transforms Inverse Rotation Clipping

3D Transforms The idea of 3D transforms is the same as that of 2D – A 3D point is represented by (x, y, z) – Homogeneous Coordinates are defined as A 4 th Coordinate is added to every 3D point (x, y, z, t) represents (x/t, y/t, z/t) (x, y, z, 0) represents infinity (0, 0, 0, 0) is not allowed

General 3D Homogeneous Transform

Scaling Scaling matrix

Translation Translation matrix

Reflection Reflection Matrix about yz – plane What are other reflection matrices

Other Reflection Matrices

Rotation Rotation about Z – axis

Rotation Rotation about Y – axis

Rotation Rotation about X – axis

Inverse Rotation

Summary 3D Transforms Inverse Rotation Clipping

References Fundamentals of Computer Graphics Third Edition by Peter Shirley and Steve Marschner Interactive Computer Graphics, A Top-down Approach with OpenGL (Sixth Edition) by Edward Angel.