3 results
Search Results
Now showing 1 - 3 of 3
Item Singularity-Free Frame Fields for Line Drawing Vectorization(The Eurographics Association and John Wiley & Sons Ltd., 2023) Guțan, Olga; Hegde, Shreya; Berumen, Erick Jimenez; Bessmeltsev, Mikhail; Chien, Edward; Memari, Pooran; Solomon, JustinState-of-the-art methods for line drawing vectorization rely on generated frame fields for robust direction disambiguation, with each of the two axes aligning to different intersecting curve tangents around junctions. However, a common source of topological error for such methods are frame field singularities. To remedy this, we introduce the first frame field optimization framework guaranteed to produce singularity-free fields aligned to a line drawing. We first perform a convex solve for a roughly-aligned orthogonal frame field (cross field), and then comb away its internal singularities with an optimal transport–based matching. The resulting topology of the field is strictly maintained with the machinery of discrete trivial connections in a final, non-convex optimization that allows non-orthogonality of the field, improving smoothness and tangent alignment. Our frame fields can serve as a drop-in replacement for frame field optimizations used in previous work, improving the quality of the final vectorizations.Item Maximum Likelihood Coordinates(The Eurographics Association and John Wiley & Sons Ltd., 2023) Chang, Qingjun; Deng, Chongyang; Hormann, Kai; Memari, Pooran; Solomon, JustinAny point inside a d-dimensional simplex can be expressed in a unique way as a convex combination of the simplex's vertices, and the coefficients of this combination are called the barycentric coordinates of the point. The idea of barycentric coordinates extends to general polytopes with n vertices, but they are no longer unique if n>d+1. Several constructions of such generalized barycentric coordinates have been proposed, in particular for polygons and polyhedra, but most approaches cannot guarantee the non-negativity of the coordinates, which is important for applications like image warping and mesh deformation. We present a novel construction of non-negative and smooth generalized barycentric coordinates for arbitrary simple polygons, which extends to higher dimensions and can include isolated interior points. Our approach is inspired by maximum entropy coordinates, as it also uses a statistical model to define coordinates for convex polygons, but our generalization to non-convex shapes is different and based instead on the project-and-smooth idea of iterative coordinates. We show that our coordinates and their gradients can be evaluated efficiently and provide several examples that illustrate their advantages over previous constructions.Item Quadratic-Attraction Subdivision(The Eurographics Association and John Wiley & Sons Ltd., 2023) Karciauskas, Kestutis; Peters, Jorg; Memari, Pooran; Solomon, JustinThe idea of improving multi-sided piecewise polynomial surfaces, by explicitly prescribing their behavior at a central surface point, allows for decoupling shape finding from enforcing local smoothness constraints. Quadratic-Attraction Subdivision determines the completion of a quadratic expansion at the central point to attract a differentiable subdivision surface towards bounded curvature, with good shape also in-the-large.