MORSE THEORY

Height functions, critical points, and level set topology

SURFACE

LEVEL SET SWEEP

CRITICAL POINTS

TOPOLOGY

Minima (index 0)0
Saddles (index 1)0
Maxima (index 2)0
χ = V−E+F0
Level set comps0
χ = #min − #sad + #max

LEGEND

Minimum (birth)
Saddle (merge/split)
Maximum (death)
━ Current level set