MATH 355 Lecture Notes - Lecture 3: Linear Map, Coordinate System, Euler Angles
16 Mar 2016
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If an eigenvalue is negative then after stretching we should also invert the vector (multiply by negative one, x -> - x ) Theorem: any linear operator (linear transformation of space) is a superposition of stretching, rotation and reflection: superposition: apply the stretching, rotation then reflection (arbitrary order) Example: note e is the old basis and v is the new basis. In general: note: in above, e matrix is identity. Coordinates change via the inverse of the transformation matrix. Applications of coordinate changes to three dimensional graphics. Wants something on euler angles: write an essay about euler angles a few pages. Not extra credit anymore: now we need to project all the objects onto the screen. ", considering three possibilities, 1) orthographic projection, 2) perspective (pinhole) projection, 3) perspective with a lens correction projection. Perspective (pinhole) projection: these can not become blurry, so old special effects looked out of place because they were not blurry like the real objects around them.
