Showing papers on "Marching tetrahedra published in 2007"

Isosurface stuffing: fast tetrahedral meshes with good dihedral angles

Abstract: The isosurface stuffing algorithm fills an isosurface with a uniformly sized tetrahedral mesh whose dihedral angles are bounded between 10.7° and 164.8°, or (with a change in parameters) between 8.9° and 158.8°. The algorithm is whip fast, numerically robust, and easy to implement because, like Marching Cubes, it generates tetrahedra from a small set of precomputed stencils. A variant of the algorithm creates a mesh with internal grading: on the boundary, where high resolution is generally desired, the elements are fine and uniformly sized, and in the interior they may be coarser and vary in size. This combination of features makes isosurface stuffing a powerful tool for dynamic fluid simulation, large-deformation mechanics, and applications that require interactive remeshing or use objects defined by smooth implicit surfaces. It is the first algorithm that rigorously guarantees the suitability of tetrahedra for finite element methods in domains whose shapes are substantially more challenging than boxes. Our angle bounds are guaranteed by a computer-assisted proof. If the isosurface is a smooth 2-manifold with bounded curvature, and the tetrahedra are sufficiently small, then the boundary of the mesh is guaranteed to be a geometrically and topologically accurate approximation of the isosurface.

Screen space meshes

Abstract: We present a simple yet powerful approach for the generation and rendering of surfaces defined by the boundary of a three-dimensional point cloud. First, a depth map plus internal and external silhouettes of the surface are generated in screen space. These are used to construct a 2D screen space triangle mesh with a new technique that is derived from Marching Squares. The resulting mesh is transformed back to 3D world space for the computation of occlusions, reflections, refraction, and other shading effects. One of the main applications for screen space meshes is the visualization of Lagrangian, particle-based fluids models. Our new method has several advantages over the full 3D Marching Cubes approach. The algorithm only generates surface where it is visible, view-dependent level of detail comes for free, and interesting visual effects are possible by filtering in screen space.

Construction of Simplified Boundary Surfaces from Serial-sectioned Metal Micrographs

Abstract: We present a method for extracting boundary surfaces from segmented cross-section image data. We use a constrained Potts model to interpolate an arbitrary number of region boundaries between segmented images. This produces a segmented volume from which we extract a triangulated boundary surface using well-known marching tetrahedra methods. This surface contains staircase-like artifacts and an abundance of unnecessary triangles. We describe an approach that addresses these problems with a voxel-accurate simplification algorithm that reduces surface complexity by an order of magnitude. Our boundary interpolation and simplification methods are novel contributions to the study of surface extraction from segmented cross-sections. We have applied our method to construct polycrystal grain boundary surfaces from micrographs of a sample of the metal tantalum.

Topology Preserving Marching Cubes-like Algorithms on the Face-Centered Cubic Grid

Abstract: The well-known marching cubes algorithm is modified to apply to the face-centered cubic (fee) grid. Thus, the local configurations that are considered when extracting the local surface patches are not cubic anymore. This paper presents three different partitionings of the fee grid to be used for the local configurations. The three candidates are evaluated theoretically and experimentally and compared with the original marching cubes algorithm. It is proved that the reconstructed surface is topologically equivalent to the surface of the original object when the surface of the original object that is digitized is smooth and a sufficiently dense fee grid is used.

Converting CSG models into meshed B-Rep models using euler operators and propagation based marching cubes

Abstract: The purpose of this work is to define a new algorithm for converting a CSG representation into a B-Rep representation. Usually this conversion is done determining the union, intersection or difference from two B-Rep represented solids. Due to the lack of explicit representation of surface boundaries, CSG models must be converted into B-Rep solid models when a description based on polygonal mesh is required. A potential solution is to convert a CSG model into a voxel based volume representation and then construct a B-Rep solid model. This method is called CSG voxelization, conceptually it is a set membership classification problem with respect to the CSG object for all sampling points in a volume space. Marching cubes algorithms create a simple mesh that is enough for visualization purposes. However, when engineering processes are involved, a solid model is necessary. A solid ensures that all triangles in the mesh are consistently oriented and define a closed surface. It is proposed in this work an algorithm for converting CSG models into triangulated solid models through propagation based marching cubes algorithm. Three main new concepts are used in the algorithm: open boundary, B-Rep/CSG Voxelization mapping and constructive triangulation of active cells. The triangles supplied by the marching cubes algorithm need not be coherently oriented; the algorithm itself finds the correct orientation for the supplied triangles. The proposed algorithm restricts the exploration to the space occupied by the solid's boundary. Differently from normal marching cubes algorithms that explore the complete sampled space.

Prism Parallax Occlusion Mapping with Accurate Silhouette Generation

Abstract: Per-pixel displacement mapping algorithms such as [Policarpo et al. 2005; Tatarchuk 2006] became very popular recently as they can take advantage of the parallel nature of programmable GPU pipelines and render detailed surfaces at highly interactive rates. These approaches exhibit pleasing visual quality and render motion parallax effects, however, most of them suffer from lack of correct silhouettes. We perform ray-surface intersection in a volume given by prisms extruded from the input mesh triangles in the direction of the normal. The displaced surface is embedded in the volume of these prisms, bounded by a top and a bottom triangle and three bilinear patches (slabs). [Hirche et al. 2004] propose to triangulate the slabs and split the prisms into three tetrahedra. A consistent triangulation of adjacent prisms ensures that no gaps between tetrahedra exist and no tetrahedra overlap. Ray marching through tetrahedra is then straightforward as texture gradients (for marching along the ray) can be computed per tetrahedron.

Polygonisation of disjoint implicit surfaces by the adaptive edge spinning algorithm

Abstract: This paper presents an adaptive method for polygonisation of implicit surfaces. The method is based on the shape of triangles and the accuracy of resulting approximation. The main advantages of the triangulation presented are simplicity and the stable features that can be used for the next expansion. The presented algorithm is based on the surface tracking scheme, and it is compared with other algorithms that are based on the similar principle, such as the Marching cubes and the Marching triangles algorithms. Moreover, the technique for detection of more disjoint implicit surfaces in a defined area is also presented. The algorithm is not limited to a given polygonisation method, but then its use is possible for all other surface approaches that need a starting point at the beginning.

Polygonisation of disjoint implicit surfaces by the adaptive edge spinning algorithm of implicit objects

Abstract: This paper presents an adaptive method for polygonisation of implicit surfaces. The method is based on the shape of triangles and the accuracy of resulting approximation. The main advantages of the triangulation presented are simplicity and the stable features that can be used for the next expansion. The presented algorithm is based on the surface tracking scheme, and it is compared with other algorithms that are based on the similar principle, such as the Marching cubes and the Marching triangles algorithms. Moreover, the technique for detection of more disjoint implicit surfaces in a defined area is also presented. The algorithm is not limited to a given polygonisation method, but then its use is possible for all other surface approaches that need a starting point at the beginning.

Data perturbation for fewer triangles in marching tetrahedra

Abstract: A simple efficient method is proposed to reduce the total number of triangles in an isosurface extraction method based on tetrahedral decomposition. We slightly perturb the input volumetric data so that useless small and thin triangles are removed. The perturbed volumetric data contain the exact isovalues from which a mesh is extracted. Since the proposed method is a pre-process of an isosurface extraction, it is not necessary to modify the mesh structure unlike the other similar methods.

MTCut: GPU-based Marching Tetra Cuts

Abstract: Isosurface construction and rendering based on tetrahedral grids has been adequately implemented on programmable graphics hardware. In this paper we present MTCut: a volume cutting algorithm that is able to cut isosurfaces obtained by a Marching Tetrahedra algorithm on volume data. It does not require a tetrahedal representation and runs in real time for complex meshes of up to 1.8M triangles. Our algorithm takes as input the isosurface to be cut, and produces the cut geometry in response to the user interaction with a haptic device. The result is a watertight manifold model that can be interactively recovered back to CPU upon user request.

Mesh fusion using a new and improved implicit vector field surface representation

Abstract: In this paper we propose a new and improved implicit vector field surface representation to perform mesh fusion in the reconstruction process of 3D objects from scanned data. This new representation is an extension of the implicit scalar field distance function of a mesh. We show our new vector field function is more accurate than the classic scalar field function by comparing both representations with an error metric evaluation. We adapt the fusion process previously performed on the scalar representation to this new implicit vector field function. The Marching Cube triangulation algorithm is also adapted to our new vector representation to correctly reconstruct the resulting explicit surface after fusion. Results show that using this new vector field representation, our mesh fusion and mesh triangulation algorithm designs outperform the previous processes based on the implicit scalar field function representation.