Barbara Cutler

Stable real-time deformations

The linear strain measures that are commonly used in real-time animations of deformable objects yield fast and stable simulations. However, they are not suitable for large deformations. Recently, more realistic results have been achieved in computer graphics by using Greens non-linear strain tensor, but the non-linearity makes the simulation more costly and introduces numerical problems.In this paper, we present a new simulation technique that is stable and fast like linear models, but without the disturbing artifacts that occur with large deformations. As a precomputation step, a linear stiffness matrix is computed for the system. At every time step of the simulation, we compute a tensor field that describes the local rotations of all the vertices in the mesh. This field allows us to compute the elastic forces in a non-rotated reference frame while using the precomputed stiffness matrix. The method can be applied to both finite element models and mass-spring systems. Our approach provides robustness, speed, and a realistic appearance in the simulation of large deformations.

A procedural approach to authoring solid models

We present a procedural approach to authoring layered, solid models. Using a simple scripting language, we define the internal structure of a volume from one or more input meshes. Sculpting and simulation operators are applied within the context of the language to shape and modify the model. Our framework treats simulation as a modeling operator rather than simply as a tool for animation, thereby suggesting a new paradigm for modeling as well as a new level of abstraction for interacting with simulation environments.Capturing real-world effects with standard modeling techniques is extremely challenging. Our key contribution is a concise procedural approach for seamlessly building and modifying complex solid geometry. We present an implementation of our language using a flexible tetrahedral representation. We show a variety of complex objects modeled in our system using tools that interface with finite element method and particle system simulations.

Simplification and improvement of tetrahedral models for simulation

Most 3D mesh generation techniques require simplification and mesh improvement stages to prepare a tetrahedral model for efficient simulation. We have developed an algorithm that both reduces the number of tetrahedra in the model to permit interactive manipulation and removes the most poorly shaped tetrahedra to allow for stable physical simulations such as the finite element method. The initial tetrahedral model may be composed of several different materials representing internal structures. Our approach targets the elimination of poorly-shaped elements while simplifying the model using edge collapses and other mesh operations, such as vertex smoothing, tetrahedral swaps, and vertex addition. We present the results of our algorithm on a variety of inputs, including models with more than a million tetrahedra. In practice, our algorithm reliably reduces meshes to contain only tetrahedra that meet specified shape requirements, such as the minimum solid angle.

Robust Adaptive 3-D Segmentation of Vessel Laminae From Fluorescence Confocal Microscope Images and Parallel GPU Implementation

This paper presents robust 3-D algorithms to segment vasculature that is imaged by labeling laminae, rather than the lumenal volume. The signal is weak, sparse, noisy, nonuniform, low-contrast, and exhibits gaps and spectral artifacts, so adaptive thresholding and Hessian filtering based methods are not effective. The structure deviates from a tubular geometry, so tracing algorithms are not effective. We propose a four step approach. The first step detects candidate voxels using a robust hypothesis test based on a model that assumes Poisson noise and locally planar geometry. The second step performs an adaptive region growth to extract weakly labeled and fine vessels while rejecting spectral artifacts. To enable interactive visualization and estimation of features such as statistical confidence, local curvature, local thickness, and local normal, we perform the third step. In the third step, we construct an accurate mesh representation using marching tetrahedra, volume-preserving smoothing, and adaptive decimation algorithms. To enable topological analysis and efficient validation, we describe a method to estimate vessel centerlines using a ray casting and vote accumulation algorithm which forms the final step of our algorithm. Our algorithm lends itself to parallel processing, and yielded an 8× speedup on a graphics processor (GPU). On synthetic data, our meshes had average error per face (EPF) values of (0.1-1.6) voxels per mesh face for peak signal-to-noise ratios from (110-28 dB). Separately, the error from decimating the mesh to less than 1% of its original size, the EPF was less than 1 voxel/face. When validated on real datasets, the average recall and precision values were found to be 94.66% and 94.84%, respectively.

Constrained planar remeshing for architecture

Material limitations and fabrication costs generally run at odds with the creativity of architectural design, producing a wealth of challenging computational geometry problems. We have developed an algorithm for solving an important class of fabrication constraints: those associated with planar construction materials such as glass or plywood. Starting with a complex curved input shape, defined as a NURBS or subdivision surface, we use an iterative clustering method to remesh the surface into planar panels following a cost function that is adjusted by the designer. We solved several challenging connectivity issues to ensure that the topology of the resulting mesh matches that of the input surface. The algorithm described in this paper has been implemented and developed in conjunction with an architectural design seminar. How the participants incorporated this tool into their design process was considered. Their important feedback led to key algorithmic and implementation insights as well as many exciting ideas for future exploration. This prototype tool has potential to impact not only architectural design, but also the engineering for general fabrication problems.

Global Illumination Compensation for Spatially Augmented Reality

When projectors are used to display images on complex, non‐planar surface geometry, indirect illumination between the surfaces will disrupt the final appearance of this imagery, generally increasing brightness, decreasing contrast, and washing out colors. In this paper we predict through global illumination simulation this unintentional indirect component and solve for the optimal compensated projection imagery that will minimize the difference between the desired imagery and the actual total illumination in the resulting physical scene. Our method makes use of quadratic programming to minimize this error within the constraints of the physical system, namely, that negative light is physically impossible. We demonstrate our compensation optimization in both computer simulation and physical validation within a table‐top spatially augmented reality system. We present an application of these results for visualization of interior architectural illumination. To facilitate interactive modifications to the scene geometry and desired appearance, our system is accelerated with a CUDA implementation of the QP optimization method.

Parallel ODETLAP for terrain compression and reconstruction

We introduce a parallel approximation of an Over-determined Laplacian Partial Differential Equation solver (ODETLAP) applied to the compression and restoration of terrain data used for Geographical Information Systems (GIS). ODETLAP can be used to reconstruct a compressed elevation map, or to generate a dense regular grid from airborne Light Detection and Ranging (LIDAR) point cloud data. With previous methods, the time to execute ODETLAP does not scale well with the size of the input elevation map, resulting in running times that are prohibitively long for large data sets. Our algorithm divides the data set into patches, runs ODETLAP on each patch, and then merges the patches together. This method gives two distinct speed improvements. First, we provide scalability by reducing the complexity such that the execution time grows almost linearly with the size of the input, even when run on a single processor. Second, we are able to calculate ODETLAP on the patches concurrently in a parallel or distributed environment. Our new patch-based implementation takes 2 seconds to run ODETLAP on an 800 x 800 elevation map using 128 processors, while the original version of ODETLAP takes nearly 10 minutes on a single processor (271 times longer). We demonstrate the effectiveness of the new algorithm by running it on data sets as large as 16000 x 16000 on a cluster of computers. We also discuss our preliminary results from running on an IBM Blue Gene/L system with 32,768 processors.

A Spatially Augmented Reality Sketching Interface for Architectural Daylighting Design

We present an application of interactive global illumination and spatially augmented reality to architectural daylight modeling that allows designers to explore alternative designs and new technologies for improving the sustainability of their buildings. Images of a model in the real world, captured by a camera above the scene, are processed to construct a virtual 3D model. To achieve interactive rendering rates, we use a hybrid rendering technique, leveraging radiosity to simulate the interreflectance between diffuse patches and shadow volumes to generate per-pixel direct illumination. The rendered images are then projected on the real model by four calibrated projectors to help users study the daylighting illumination. The virtual heliodon is a physical design environment in which multiple designers, a designer and a client, or a teacher and students can gather to experience animated visualizations of the natural illumination within a proposed design by controlling the time of day, season, and climate. Furthermore, participants may interactively redesign the geometry and materials of the space by manipulating physical design elements and see the updated lighting simulation.

Surface compression using over-determined Laplacian approximation

We describe a surface compression technique to lossily compress elevation datasets. Our approach first approximates the uncompressed terrain using an over-determined system of linear equations based on the Laplacian partial differential equation. Then the approximation is refined with respect to the uncompressed terrain using an error metric. These two steps work alternately until we find an approximation that is good enough. We then further compress the result to achieve a better overall compression ratio. We present experiments and measurements using different metrics and our method gives convincing results.

Efficient viewshed computation on terrain in external memory

The recent availability of detailed geographic data permits terrain applications to process large areas at high resolution. However the required massive data processing presents significant challenges, demanding algorithms optimized for both data movement and computation. One such application is viewshed computation, that is, to determine all the points visible from a given point p. In this paper, we present an efficient algorithm to compute viewsheds on terrain stored in external memory. In the usual case where the observer’s radius of interest is smaller than the terrain size, the algorithm complexity is θ(scan(n2)) where n2 is the number of points in an n × n DEM and scan(n2) is the minimum number of I/O operations required to read n2 contiguous items from external memory. This is much faster than existing published algorithms.