We present a new Laplacian solver for minimal surfaces—surfaces having a mean curvature of zero everywhere except at some fixed (Dirichlet) boundary conditions. Our solution has two main contributions: First, we provide a robust rasterization technique to transform continuous boundary values (diffusion curves) to a discrete domain. Second, we define a variable stencil size diffusion solver that solves the minimal surface problem. We prove that the solver converges to the right solution, and demonstrate that it is at least as fast as commonly proposed multigrid solvers, but much simpler to implement. It also works for arbitrary image resolutions, as well as 8 bit data. We show examples of robust diffusion curve rendering where our curve rasterization and diffusion solver eliminate the strobing artifacts present in previous methods. We also show results for real-time seamless cloning and stitching of large image panoramas.
- Line and Curve rendering
- Poisson equation
ASJC Scopus subject areas
- Computer Graphics and Computer-Aided Design