Mollweide map projection and Newton's method
4 days ago
- #Projection
- #Numerical Methods
- #Cartography
- Karl Brandan Mollweide designed an equal-area map projection mapping Earth to a 2:1 ellipse.
- Latitude lines are unevenly spaced to maintain equal area, requiring numerical solutions for mapping.
- Newton's method is efficient but slows near π/2 due to a double root, requiring modifications.
- A modified Newton's method (m=2) works for exact double roots but may diverge near them.
- Illustration shows Newton's method's performance varies with latitude, especially near π/2.
- Proposed solution involves tuning Newton's method for accuracy and using series inversion near π/2.