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Computer Graphics Lecture 16 Fasih ur Rehman
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Last Class Homogeneous transformations Types of Transformations – Linear Transformations – Affine Transformations – Projective Transformations Combining Homogeneous transformations
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Today’s Agenda 3D Transforms Inverse Rotation Clipping
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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
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General 3D Homogeneous Transform
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Scaling Scaling matrix
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Translation Translation matrix
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Reflection Reflection Matrix about yz – plane What are other reflection matrices
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Other Reflection Matrices
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Rotation Rotation about Z – axis
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Rotation Rotation about Y – axis
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Rotation Rotation about X – axis
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Inverse Rotation
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Summary 3D Transforms Inverse Rotation Clipping
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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.
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