quartz/content/notes/03-2d-transforms.md

title	tags
03-2d-transforms	lecture cosc342

look into how colours work together

Points lines

• point is 2d location (u,v)
• two points define a line
• a polyline with k segments is a sequence of k+1 points
• a polygon is a polyline where the beginning and ened are the same, we often omit the duplicate point
• points are vectors

[!INFO] polygon and polylines will be specifies in the code

[!INFO] [u v]^T high T indicates vector

coordingate systems

• mathematical
• image based
• matrix based
• 

[!INFO] make sure to check you are using the right coordinate system

transformations

• translation

[!INFO] value of change (delta) for each coordinate. for a shape, apply the transformation to each point

• scaling

• rotation

  • rotate by an abgle about the origin
  • rotation from U towards V, not anti/clockwise
  • [u',v'] = [cos(0) - sin(0), sin(0) cos(0)][u,v]

• inverse

  • inverse of translate is translating by negative
  • inverse of scaling by s is scaling by \frac{1}{s}
  • inverse of rotating by \theta is rotating by -\theta
  • inverse of rotation matrix is its transpose
    • 

• combinations

  • e.g., rotate 45 about (2,1)
    • shift by (-2,-1)
    • rotate by 45
    • shift by (2,1)
    • 

homogenous coordinates

• represent 2D points as 3 points
• all linear transformations become 3x3 matrices
• 

[!DIFFICULT]

homogenous transforms