Interactive 2D visualizers for projection-based algorithms that find points in the intersection of two or more sets. Covers the Douglas–Rachford, Peaceman–Rachford, Alternating Projections, and Averaged Projections methods.
Visualize projection methods finding the intersection of two draggable circles. Drag the circles and starting point z₀ to explore how each algorithm traces a path toward a common point. Compare methods side by side and toggle substep arrows to see the underlying projections and reflections.
Find the intersection of multiple convex sets — disks, squares, and triangles — using cyclic projection methods. Add and remove sets freely, drag their centers and resize their boundaries, and compare how DR, AP, PR, and Averaged Projections each converge (or fail to) as the geometry changes.
Douglas-Rachford applied to a nonconvex feasibility problem: Set A is the x-axis and Set B is a finite collection of points. Despite non-convexity, DR's shadow sequence often converges to a point in A ∩ B. Drag the points and starting position, adjust the number of iterations, and watch for cycle detection.
A color-coded heatmap showing which starting point z₀ converges to which intersection, revealing the basins of attraction for the Douglas-Rachford operator. Configure the grid resolution and iteration count, and define custom constraint curves to visualize convergence over non-standard sets.