2017-11-20, Deussen, Oliver, Spicker, Marc, Zheng, Qian

We propose an adaptive version of Lloyd's optimization method that distributes points based on Voronoi diagrams. Our inspiration is the Linde-Buzo-Gray-Algorithm in vector quantization, which dynamically splits Voronoi cells until a desired number of representative vectors is reached. We reformulate this algorithm by splitting and merging Voronoi cells based on their size, greyscale level, or variance of an underlying input image. The proposed method automatically adapts to various constraints and, in contrast to previous work, requires no good initial point distribution or prior knowledge about the final number of points. Compared to weighted Voronoi stippling the convergence rate is much higher and the spectral and spatial properties are superior. Further, because points are created based on local operations, coherent stipple animations can be produced. Our method is also able to produce good quality point sets in other fields, such as remeshing of geometry, based on local geometric features such as curvature.

2017-09, Zheng, Qian, Fan, Xiaochen, Gong, Minglun, Sharf, Andrei, Deussen, Oliver, Huang, Hui

Flower blooming is a beautiful phenomenon in nature as flowers open in an intricate and complex manner whereas petals bend, stretch and twist under various deformations. Flower petals are typically thin structures arranged in tight configurations with heavy self-occlusions. Thus, capturing and reconstructing spatially and temporally coherent sequences of blooming flowers is highly challenging. Early in the process only exterior petals are visible and thus interior parts will be completely missing in the captured data. Utilizing commercially available 3D scanners, we capture the visible parts of blooming flowers into a sequence of 3D point clouds. We reconstruct the flower geometry and deformation over time using a template-based dynamic tracking algorithm. To track and model interior petals hidden in early stages of the blooming process, we employ an adaptively constrained optimization. Flower characteristics are exploited to track petals both forward and backward in time. Our methods allow us to faithfully reconstruct the flower blooming process of different species. In addition, we provide comparisons with state-of-the-art physical simulation-based approaches and evaluate our approach by using photos of captured real flowers.