Lecture 08: Coordinate Transformation II

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Presentation transcript:

Lecture 08: Coordinate Transformation II Topics: Planar coordinate transformation (2D to 2D) 1) Simple affine transformation 2) Complex affine transformation References: Chapter 6 in Noble and Daniel (Applied Linear Algebra, 1977), pp. 177-212

Outlines 3. Planar map transformation (2D to 2D): 3.1 Simple Affine Transformations 3.1.1 Translation: (The translation figure) 3.1.2 Scaling: (The scaling figure) 3.1.3 Rotation: (The rotation figure) What about reflection? (The mirroring figure)

3.2 Complex Affine Transformations 3.2.1 Basic computation: u = a+bx+cy (1) v = d+ex+fy (2) (The Equations and computation figure) 3.2.2 Discussion: 1) What if the relationship is not linear? 2) What if the three points are on a line? (The complex affine spreadsheet figure) 3) What if the points contains errors?