Last updated April 10, 2022

Status: Tags: #cards/math232/unit3 Links: Transformations

Geometrical Transformations

Principles

if tx=ty

• Dilation is when ty>1
• Contraction is when ty<1

Types

Rotation about origin

Linear transformation: When applied to standard basis vectors, we get the f ollowing

• $R_o$ can be multiplied to another vector to find its new position after rotation

Stretching in x or y direction

X

• 
• Use basis vectors to exemplify effects

Y

Shear

Horizontal Shear

• 
• Take first component + s(2nd component)
• Can create paralellogram, idk why

Reflection through origin

Reflection through line instersecting origin

Just confused on how perp = proj? Other than that makes sense

• Parametric (green) found by setting x2= something and finding x1 by moving x2 to RHS
• Identity matrix is just i-2proj since the transformation is just

Procedure ?

• If given linear equation, convert to scalar and plot
• Find vector and normal through the leading variables
  • Vector is slope of y intercept form, y/x
• Find projection of standard basis vectors with n as subscript
• Input into a' equation, identity matrix - combined proj

Backlinks

1

list from Geometrical Transformations AND !outgoing(Geometrical Transformations)

References:

Created:: 2022-01-30 16:54