I am a PhD candidate working in Prof. Marc Alexa's Computer Graphics group at TU Berlin. Prior I optained a Diploma (Master equivalent) from Humboldt University of Berlin. Before starting my PhD I spent 6 months in Prof. Wojciech Matusik's Computational Fabrication Group group at MIT. In 2015 I interned at Disney Research Boston supervised by David Levin.

My research interests span geometry processing, computational fabrication and sparse linear solvers.

Philipp Herholz,
Marc Alexa

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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.

Andreas Fender,
Philipp Herholz,
Marc Alexa and
Joerg Mueller

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We present OptiSpace, a system for the automated placement of perspectively corrected projection mapping content. We analyze the geometry of physical surfaces and the viewing behavior of users over time using depth cameras. Our system measures user view behavior and simulates a virtual projection mapping scene users would see if content were placed in a particular way. OptiSpace evaluates the simulated scene according to perceptual criteria, including visibility and visual quality of virtual content. Finally, based on these evaluations, it optimizes content placement, using a two-phase procedure involving adaptive sampling and the covariance matrix adaptation algorithm. With our proposed architecture, projection mapping applications are developed without any knowledge of the physical layouts of the target environments. Applications can be deployed in different uncontrolled environments, such as living rooms and office spaces.

Philipp Herholz,
Timothy A. Davis and
Marc Alexa

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Computing solutions to linear systems is a fundamental building block of many geometry processing algorithms. In many cases the Cholesky factorization of the system matrix is computed to subsequently solve the system, possibly for many right-hand sides, using forward and back substitution. We demonstrate how to exploit sparsity in both the right-hand side and the set of desired solution values to obtain significant speedups. The method is easy to implement and potentially useful in any scenarios where linear problems have to be solved locally. We show that this technique is useful for geometry processing operations, in particular we consider the solution of diffusion problems. All problems profit significantly from sparse computations in terms of runtime, which we demonstrate by providing timings for a set of numerical experiments.

Andreas Fender,
David Lindlbauer,
Philipp Herholz,
Marc Alexa and
Joerg Mueller

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We present HeatSpace, a system that records and empirically analyzes user behavior in a space and automatically suggests positions and sizes for new displays. The system uses depth cameras to capture 3D geometry and usersâ€™ perspectives over time. To derive possible display placements, it calculates volumetric heatmaps describing geometric persistence and planarity of structures inside the space. It evaluates visibility of display poses by calculating a volumetric heatmap describing occlusions, position within usersâ€™ field of view, and viewing angle. Optimal display size is calculated through a heatmap of average viewing distance. Based on the heatmaps and user constraints we sample the space of valid display placements and jointly optimize their positions. This can be useful when installing displays in multi-display environments such as meeting rooms, offices, and train stations.

Philipp Herholz, Sebastian Koch,
Tamy Boubekeur and
Marc Alexa

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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.

Philipp Herholz, Felix Haase and Marc Alexa

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We define Voronoi cells and centroids based on heat diffusion. These heat cells and heat centroids coincide with the common definitions in Euclidean spaces. On curved surfaces they compare favorably with definitions based on geodesics: they are smooth and can be computed in a stable way with a single linear solve. We analyze the numerics of this approach and can show that diffusion diagrams converge quadratically against the smooth case under mesh refinement, which is better than other common discretization of distance measures in curved spaces. By factorizing the system matrix in a preprocess, computing Voronoi diagrams or centroids amounts to just back-substitution. We show how to localize this operation so that the complexity is linear in the size of the cells and not the underlying mesh. We provide several example applications that show how to benefit from this approach.

Philipp Herholz,
Wojciech Matusik and
Marc Alexa

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We consider the problem of manufacturing free-form geometry with classical manufacturing techniques, such as mold casting or 3-axis milling. We determine a set of constraints that are necessary for manufacturability and then decompose and, if necessary, deform the shape to satisfy the constraints per segment. We show that many objects can be generated from a small number of (mold-)pieces if some deformation is acceptable. We provide examples of actual molds and the resulting manufactured objects.

Philipp Herholz,
Jan Eric Kyprianidis and
Marc Alexa

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A discrete Laplace-Beltrami operator is called perfect if it possesses all the important properties of its smooth counterpart. It is known which triangle meshes admit perfect Laplace operators and how to fix any other mesh by changing the combinatorics. We extend the characterization of meshes that admit perfect Laplacians to general polygon meshes. More importantly, we provide an algorithm that computes a perfect Laplace operator for any polygon mesh without changing the combinatorics, although, possibly changing the embedding. We evaluate this algorithm and demonstrate it at applications.

Philipp Herholz,
Marc Alexa and
Wojciech Matusik

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We consider the problem of manufacturing free-form geometry with classical fabrication techniques such as mold casting or milling. We derive a set of constraints that guarantee manufacturability. A combined deformation and segmentation algorithm yields parts that satisfy the constraints. Our main observation is that allowing some deformation significantly reduces the number of resulting parts and, thus, extends the range of shapes that can be generated in practice. Examples of actual molds and the resulting manufactured shapes for several well-known meshes demonstrate our claims.