Figure 1. Examples of creations realized with DataQuilt, a new interactive authoring tool that allows authors to borrow visual and stylistic elements from raster images and re-purpose them to create custom, pictorial visualizations. Left: a scatterplot of famous paintings by Klimt, showing the date of creation (x-axis) against how much it was sold for in auction (y-axis). Each data point is a spiral-shaped glyph whose texture is mapped to the painting it represents, whereas the Tree of Life painting is used as a decorative background. Middle: a bar chart representing the distance from the sun for the planets of our solar system. Each data point is represented by a space rocket, whose exhaust flames are stretched according to the underlying data. Decorative glyphs (sun, planets) are used for further information and visual appeal. Right: A personal visualization depicting one's coffee intake over a week. The type of coffee (espresso, latte, etc.) is represented by different coffee cups, all extracted from photographs. The orientation of the handle represents the time, whereas size is proportional to the drink size and horizontal position corresponds to the day of the week.
Fig. 1. We introduce a novel geometric multigrid solver for curved surfaces. Our key ingredient is an intrinsic prolongation operator computed via parameterizing the high resolution shape via its coarsened counterpart, visualized using colored triangles. By recursively applying this self-parameterization, we obtain a hierarchy (from left to right) for our multigrid method (e.g., to solve heat geodesics [Crane et al. 2017], far left). ©model by Benoît Rogez under CC BY-NC.This paper introduces a novel geometric multigrid solver for unstructured curved surfaces. Multigrid methods are highly efficient iterative methods for solving systems of linear equations. Despite the success in solving problems defined on structured domains, generalizing multigrid to unstructured curved domains remains a challenging problem. The critical missing ingredient is a prolongation operator to transfer functions across different multigrid levels. We propose a novel method for computing the prolongation for triangulated surfaces based on intrinsic geometry, enabling an efficient geometric multigrid solver for curved surfaces. Our surface multigrid solver achieves better convergence than existing multigrid methods. Compared to direct solvers, our solver is orders of magnitude faster. We evaluate our method on many geometry processing applications and a wide variety of complex shapes with and without boundaries. By simply replacing the direct solver, we upgrade existing algorithms to interactive frame rates, and shift the computational bottleneck away from solving linear systems.
We present a novel approach to enrich arbitrary rig animations with elastodynamic secondary effects. Unlike previous methods which pit rig displacements and physical forces as adversaries against each other, we advocate that physics should complement artists' intentions. We propose optimizing for elastodynamic displacements in the subspace orthogonal to displacements that can be created by the rig. This ensures that the additional dynamic motions do not undo the rig animation. The complementary space is high-dimensional, algebraically constructed without manual oversight, and capable of rich high-frequency dynamics. Unlike prior tracking methods, we do not require extra painted weights, segmentation into fixed and free regions or tracking clusters. Our method is agnostic to the physical model and plugs into non-linear FEM simulations, geometric as-rigid-as-possible energies, or mass-spring models. Our method does not require a particular type of rig and adds secondary effects to skeletal animations, cage-based deformations, wire deformers, motion capture data, and rigid-body simulations.
ARAP surface modeling co-rotational elasticity ICP registration camera alignment Figure 1: Least-squares rotation fitting is a core low-level subroutine in a number of important high-level tasks in computer graphics, geometry processing, robotics and computer vision.
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