Computer Graphics

Over a decade after the original ARAP Paper was published, we found a derivation of the continous energy presented by Chao et. al. using a discontinous transformation function. This perspective helped us to understand the flaws of the original energy. We where able to fix the problem of divergence and the problem of asymetries in the results of Chao et. al.

In the footsteps of the original paper, this work will also be presented at the SGP (within the International Graphics Summit 2023).

More info at the project page.

We show how shadow mapping, a method for approximating visibility in real-time graphics, can be made differentiable. Our central observation is that pre-filtered shadow mapping, in combination with differentiable rasterizers, permits the efficient generation of shadow derivatives. In gradient-based optimizations, differentiable rasterizers with shadow mapping can be an efficient alternative to differentiable ray tracing. The paper has been accepted to CVPR 2023. Additional information, including a presentation video and the source code, can be found on the project page.

We developed a normal driven stylization tool. The set of preferred normals can be chosen arbitrarily from the Gauss sphere, including semi-discrete sets to model preference for cylinder- or cone-like shapes. The resulting paper has been accepted for presentation at this year’s Symposium on Geometry Processing. We created a project web site. where you can find more information like the presentation video and code.

A common operation in geometry processing is solving symmetric and positive semi-definite systems on a subset of a mesh with conditions for the vertices at the boundary of the region. This is commonly done by setting up the linear system for the sub-mesh, factorizing the system (potentially applying preordering to improve sparseness of the factors), and then solving by back-substitution. This approach suffers from a comparably high setup cost for each local operation. We propose to reuse factorizations defined on the full mesh to solve linear problems on sub-meshes. We show how an update on sparse matrices can be performed in a particularly efficient way to obtain the factorization of the operator on a sun-mesh significantly outperforming general factor updates and complete refactorization. We analyze the resulting speedup for a variety of situations and demonstrate that our method outperforms factorization of a new matrix by a factor of up to 10 while never being slower in our experiments.

See our project page for more details.

Mass market digital manufacturing devices are severely limited in accuracy and material, resulting in a significant gap between the appearance of the virtual and the real shape. In imaging as well as rendering of shapes, it is common to enhance features so that they are more apparent. We provide an approach for feature enhancement that directly operates on the geometry of a given shape, with particular focus on improving the visual appearance for 3D printing. The technique is based on unsharp masking, modified to handle arbitrary free-form geometry in a stable, efficient way, without causing large scale deformation. On a series of manufactured shapes we show how features are lost as size of the object decreases, and how our technique can compensate for this. We evaluate this effect in a human subject experiment and find significant preference for modified geometry.

We present an approach to alter the perceived appearance of physical objects by controlling their surrounding space. Many real-world objects cannot easily be equipped with displays or actuators in order to change their shape. While common approaches such as projection mapping enable changing the appearance of objects without modifying them, certain surface properties (e. g. highly reflective or transparent surfaces) can make employing these techniques difficult. In this work, we present a conceptual design exploration on how the appearance of an object can be changed by solely altering the space around it, rather than the object itself. In a proof-of-concept implementation, we place objects onto a tabletop display and track them together with users to display perspective-corrected 3D graphics for augmentation. This enables controlling properties such as the perceived size, color, or shape of objects. We characterize the design space of our approach and demonstrate potential applications. For example, we change the contour of a wallet to notify users when their bank account is debited. We envision our approach to gain in importance with increasing ubiquity of display surfaces.

Please see our project page for more details.

Slicing is the procedure necessary to prepare a shape for layered manufacturing. There are degrees of freedom in this process, such as the starting point of the slicing sequence and the thickness of each slice. The choice of these parameters influences the manufacturing process and its result: the number of slices significantly affects the time needed for manufacturing, while their thickness affects the error. Assuming a discrete setting, we measure the error as the number of voxels that are incorrectly assigned due to slicing. We provide an algorithm that generates, for a given set of available slice heights and a shape, a slicing that is provably optimal. By optimal we mean that the algorithm generates sequences with minimal error for any possible number of slices. The algorithm is fast and flexible, it can accommodate a user driven importance modulation of the error function and allows the interactive exploration of the desired quality/time tradeoff.
We can demonstrate the practical importance of our optimization on several 3D-printed results.

The technical background is described in a paper that now appeared in ACM TOG.

We present physical interfaces that change their appearance through controlled transparency. These transparency-controlled physical interfaces are well suited for applications where communication through optical appearance is sufficient, such as ambient display scenarios. They transition between perceived shapes within milliseconds, require no mechanically moving parts and consume little energy. We build 3D physical interfaces with individually controllable parts by laser cutting and folding a single sheet of transparency-controlled material. We explore the benefits of transparency-controlled physical interfaces by characterizing their design space and showcase four physical prototypes.

Please see our project page for more details.

Our work was featured on Fast Company Co.Design, Vice Motherboard and Futurism.

We investigate human viewing behavior on physical realizations of 3D objects. Using an eye tracker with scene camera and fiducial markers we are able to gather fixations on the surface of the presented stimuli. This data is used to validate assumptions regarding visual saliency so far only experimentally analyzed using flat stimuli. We provide a way to compare fixation sequences from different subjects as well as a model for generating test sequences of fixations unrelated to the stimuli. This way we can show that human observers agree in their fixations for the same object under similar viewing conditions – as expected based on similar results for flat stimuli. We also develop a simple procedure to validate computational models for visual saliency of 3D objects and use it to show that popular models of mesh salience based on the center surround patterns fail to predict fixations.

Please see our project page for more details.

Panono’s panoramic camera, originally developed as a thesis work by CG alumnus Jonas Pfeil is now in it’s second revision and has been selected one of the 36 coolest gadgets in 2014 by CNN.

Prof. Alexa receives the Outstanding Technical Contributions Award of Eurographics. The award is “given each year to an individual in computer graphics to highlight some outstanding technical achievement.”

The award has been presented at the yearly main conference of Eurographics, which took place in Strasbourg, France this year.

Prominently featured in an episode of The Simpson was CG alumnus Andy Nealen’s game, Osmos: Milhouse had his iPad stolen on “The Simpsons.” When he finds it in Bart’s possession and begins to confront him, he is entranced by “the music of this bubble game.”

Jonas Pfeil, alumnus of the CG group, is turning his thesis work into a product: panono – a panoramic ball camera. Right now they are running a crowd-funding campaign on indiegogo and he appeared at TV Total, a popular late night talk show.

Prof. Alexa had been elected to chair the technical program of SIGGRAPH 2013. SIGGRAPH regularly gathers thousands of scientists and professionals in the visual effects industry, and its technical program is the most prestigious and selective in the field. On the left, he opens the fast forward, a 30 second presentation for each of the accepted papers.

Most additive manufacturing technologies work by layering, i.e. slicing the shape and then generating each slice independently. This introduces an anisotropy into the process, often as different accuracies in the tangential and normal directions, but also in terms of other parameters such as build speed or tensile strength and strain. We model this as an anisotropic cubic element. Our approach then finds a compromise between modeling each part of the shape individually in the best possible direction and using one direction for the whole shape part. In particular, we compute an orthogonal basis and consider only the three basis vectors as slice normals (i.e. fabrication directions). Then we optimize a decomposition of the shape along this basis so that each part can be consistently sliced along one of the basis vectors.

In simulation, we show that this approach is superior to slicing the whole shape in one direction, only. It also has clear benefits if the shape is larger than the build volume of the available equipment.

We introduce an algorithm and representation for fabricating 3D shape abstractions using mutually intersecting planar cut-outs. The planes have prefabricated slits at their intersections and are assembled by sliding them together. Based on an analysis of construction rules, we propose an extended binary space partitioning tree as an efficient representation of such cardboard models which allows us to quickly evaluate the feasibility of newly added planar elements. The complexity of insertion order quickly increases with the number of planar elements and manual analysis becomes intractable. We provide tools for generating cardboard sculptures with guaranteed constructibility.

Watch video | Download paper