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Computer Graphics Forum (Proc. EUROGRAPHICS 2020)

Error quadrics are a fundamental and powerful building block in many geometry processing algorithms. However, finding the minimizer of a given quadric is in many cases not robust and requires a singular value decomposition or some ad-hoc regularization. While classical error quadrics measure the squared deviation from a set of ground truth planes or polygons, we treat the input data as genuinely uncertain information and embed error quadrics in a probabilistic setting ("probabilistic quadrics") where the optimal point minimizes the expected squared error. We derive closed form solutions for the popular plane and triangle quadrics subject to (spatially varying, anisotropic) Gaussian noise. Probabilistic quadrics can be minimized robustly by solving a simple linear system - 50x faster than SVD. We show that probabilistic quadrics have superior properties in tasks like decimation and isosurface extraction since they favor more uniform triangulations and are more tolerant to noise while still maintaining feature sensitivity. A broad spectrum of applications can directly benefit from our new quadrics as a drop-in replacement which we demonstrate with mesh smoothing via filtered quadrics and non-linear subdivision surfaces.

IEEE Computer Graphics and Applications

Digitalization of 3D objects and scenes using modern depth sensors and high-resolution RGB cameras enables the preservation of human cultural artifacts at an unprecedented level of detail. Interactive visualization of these large datasets, however, is challenging without degradation in visual fidelity. A common solution is to fit the dataset into available video memory by downsampling and compression. The achievable reproduction accuracy is thereby limited for interactive scenarios, such as immersive exploration in Virtual Reality (VR). This degradation in visual realism ultimately hinders the effective communication of human cultural knowledge. This article presents a method to render 3D scan datasets with minimal loss of visual fidelity. A point-based rendering approach visualizes scan data as a dense splat cloud. For improved surface approximation of thin and sparsely sampled objects, we propose oriented 3D ellipsoids as rendering primitives. To render massive texture datasets, we present a virtual texturing system that dynamically loads required image data. It is paired with a single-pass page prediction method that minimizes visible texturing artifacts. Our system renders a challenging dataset in the order of 70 million points and a texture size of 1.2 terabytes consistently at 90 frames per second in stereoscopic VR.

SIGGRAPH 2019

The generation of quad meshes based on surface parametrization techniques has proven to be a versatile approach. These techniques quantize an initial seamless parametrization so as to obtain an integer grid map implying a pure quad mesh. State-of-the-art methods following this approach have to assume that the surface to be meshed either has no boundary, or has a boundary which the resulting mesh is supposed to be aligned to. In a variety of applications this is not desirable and non-boundary-aligned meshes or grid-parametrizations are preferred. We thus present a technique to robustly generate integer grid maps which are either boundary-aligned, non-boundary-aligned, or partially boundary-aligned, just as required by different applications. We thereby generalize previous work to this broader setting. This enables the reliable generation of trimmed quad meshes with partial elements along the boundary, preferable in various scenarios, from tiled texturing over design and modeling to fabrication and architecture, due to fewer constraints and hence higher overall mesh quality and other benefits in terms of aesthetics and flexibility.