A quadrilateral rendering primitive

The only surface primitives that are supported by common graphics hardware are triangles and more complex shapes have to be triangulated before being sent to the rasterizer. Even quadrilaterals, which are frequently used in many applications, are rendered as a pair of triangles after splitting them along either diagonal. This creates an undesirable C1 -discontinuity that is visible in the shading or texture signal. We propose a new method that overcomes this drawback and is designed to be implemented in hardware as a new rasterizer. It processes a potentially non-planar quadrilateral directly without any splitting and interpolates attributes smoothly inside the quadrilateral. This interpolation is based on a recent generalization of barycentric coordinates that we adapted to handle perspective correction and situations in which a quadrilateral is partially behind the point of view.The only surface primitives that are supported by common graphics hardware are triangles and more complex shapes have to be triangulated before being sent to the rasterizer. Even quadrilaterals, which are frequently used in many applications, are rendered as a pair of triangles after splitting them along either diagonal. This creates an undesirable C1-discontinuity that is visible in the shading or texture signal. We propose a new method that overcomes this drawback and is designed to be implemented in hardware as a new rasterizer. It processes a potentially non-planar quadrilateral directly without any splitting and interpolates attributes smoothly inside the quadrilateral. This interpolation is based on a recent generalization of barycentric coordinates that we adapted to handle perspective correction and situations in which a quadrilateral is partially behind the point of view. \ua9 The Eurographics Association 2004

Non-uniform interpolatory subdivision schemes with improved smoothness

Subdivision schemes are used to generate smooth curves or surfaces by iteratively refining an initial control polygon or mesh. We focus on univariate, linear, binary subdivision schemes, where the vertices of the refined polygon are computed as linear combinations of the current neighbouring vertices. In the classical stationary setting, there are just two such subdivision rules, which are used throughout all subdivision steps to construct the new vertices with even and odd indices, respectively. These schemes are well understood and many tools have been developed for deriving their properties, including the smoothness of the limit curves. For non-stationary schemes, the subdivision rules are not fixed and can be different in each subdivision step. Non-uniform schemes are even more general, as they allow the subdivision rules to be different for every new vertex that is generated by the scheme. The properties of non-stationary and non-uniform schemes are usually derived by relating the scheme to a corresponding stationary scheme and then exploiting the fact that the properties of the stationary scheme carry over under certain proximity conditions. In particular, this approach can be used to show that the limit curves of a non-stationary or non-uniform scheme are as smooth as those of a corresponding stationary scheme. In this paper we show that non-uniform subdivision schemes have the potential to generate limit curves that are smoother than those of stationary schemes with the same support size of the subdivision rule. For that, we derive interpolatory 2-point and 4-point schemes that generate C-1 and C-2 limit curves, respectively. These values of smoothness exceed the smoothness of classical interpolating schemes with the same support size by one. (C) 2022 The Author(s). Published by Elsevier B.V

PolyCube-Maps

Standard texture mapping of real-world meshes suffers from the presence of seams that need to be introduced in order to avoid excessive distortions and to make the topology of the mesh compatible to the one of the texture domain. In contrast, cube maps provide a mechanism that could be used for seamless texture mapping with low distortion, but only if the object roughly resembles a cube. We extend this concept to arbitrary meshes by using as texture domain the surface of a polycube whose shape is similar to that of the given mesh. Our approach leads to a seamless texture mapping method that is simple enough to be implemented in currently available graphics hardware

Mean value coordinates–based caricature and expression synthesis

We present a novel method for caricature synthesis based on mean value coordinates (MVC). Our method can be applied to any single frontal face image to learn a specified caricature face pair for frontal and 3D caricature synthesis. This technique only requires one or a small number of exemplar pairs and a natural frontal face image training set, while the system can transfer the style of the exemplar pair across individuals. Further exaggeration can be fulfilled in a controllable way. Our method is further applied to facial expression transfer, interpolation, and exaggeration, which are applications of expression editing. Additionally, we have extended our approach to 3D caricature synthesis based on the 3D version of MVC. With experiments we demonstrate that the transferred expressions are credible and the resulting caricatures can be characterized and recognized

A quadrilateral rendering primitive

The only surface primitives that are supported by common graphics hardware are triangles and more complex shapes have to be triangulated before being sent to the rasterizer. Even quadrilaterals, which are frequently used in many applications, are rendered as a pair of triangles after splitting them along either diagonal. This creates an undesirable C1-discontinuity that is visible in the shading or texture signal. We propose a new method that overcomes this drawback and is designed to be implemented in hardware as a new rasterizer. It processes a potentially non-planar quadrilateral directly without any splitting and interpolates attributes smoothly inside the quadrilateral. This interpolation is based on a recent generalization of barycentric coordinates that we adapted to handle perspective correction and situations in which a quadrilateral is partially behind the point of view. \ua9 The Eurographics Association 2004

On Landau theory and symmetric energy landscapes for phase transitions

The aim of this presentation is the development of a general approach for modelling the global complex energy landscapes of phase transitions. For the sake of clarity and brevity the exposition is restricted to martensitic phase transition (i.e., diffusionless phase transitions in crystalline solids). The methods, however, are more broadly applicable. Explicit energy functions are derived for the cubic-to-tetragonal phase transition, where data are fitted for InTl. Another example is given for the cubic-to-monoclinic transition in CuZnAl. The resulting energies are defined globally, in a piecewise manner. We use splines that are twice continuously differentiable to ensure sufficient smoothness. The modular (piecewise) technique advocated here allows for modelling elastic moduli, energy barriers and other characteristics independent of each other. (C) 2007 Elsevier Ltd. All rights reserved

Simple quad domains for field aligned mesh parametrization

We present a method for the global parametrization of meshes that preserves alignment to a cross field in input while obtaining a parametric domain made of few coarse axis-aligned rectangular patches, which form an abstract base complex without T-junctions. The method is based on the topological simplification of the cross field in input, followed by global smoothing

Unwind: Interactive Fish Straightening

The ScanAllFish project is a large-scale effort to scan all the world's 33,100 known species of fishes. It has already generated thousands of volumetric CT scans of fish species which are available on open access platforms such as the Open Science Framework. To achieve a scanning rate required for a project of this magnitude, many specimens are grouped together into a single tube and scanned all at once. The resulting data contain many fish which are often bent and twisted to fit into the scanner. Our system, Unwind, is a novel interactive visualization and processing tool which extracts, unbends, and untwists volumetric images of fish with minimal user interaction. Our approach enables scientists to interactively unwarp these volumes to remove the undesired torque and bending using a piecewise-linear skeleton extracted by averaging isosurfaces of a harmonic function connecting the head and tail of each fish. The result is a volumetric dataset of a individual, straight fish in a canonical pose defined by the marine biologist expert user. We have developed Unwind in collaboration with a team of marine biologists: Our system has been deployed in their labs, and is presently being used for dataset construction, biomechanical analysis, and the generation of figures for scientific publication

Automatic 3D facial model and texture reconstruction from range scans

This paper presents a fully automatic approach to fitting a generic facial model to detailed range scans of human faces to reconstruct 3D facial models and textures with no manual intervention (such as specifying landmarks). A Scaling Iterative Closest Points (SICP) algorithm is introduced to compute the optimal rigid registrations between the generic model and the range scans with different sizes. And then a new template-fitting method, formulated in an optmization framework of minimizing the physically based elastic energy derived from thin shells, faithfully reconstructs the surfaces and the textures from the range scans and yields dense point correspondences across the reconstructed facial models. Finally, we demonstrate a facial expression transfer method to clone facial expressions from the generic model onto the reconstructed facial models by using the deformation transfer technique