Matching Items (3)
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- All Subjects: Curves on surfaces
- Creators: Farin, Gerald
Description
Quad-dominant (QD) meshes, i.e., three-dimensional, 2-manifold polygonal meshes comprising mostly four-sided faces (i.e., quads), are a popular choice for many applications such as polygonal shape modeling, computer animation, base meshes for spline and subdivision surface, simulation, and architectural design. This thesis investigates the topic of connectivity control, i.e., exploring different choices of mesh connectivity to represent the same 3D shape or surface. One key concept of QD mesh connectivity is the distinction between regular and irregular elements: a vertex with valence 4 is regular; otherwise, it is irregular. In a similar sense, a face with four sides is regular; otherwise, it is irregular. For QD meshes, the placement of irregular elements is especially important since it largely determines the achievable geometric quality of the final mesh.
Traditionally, the research on QD meshes focuses on the automatic generation of pure quadrilateral or QD meshes from a given surface. Explicit control of the placement of irregular elements can only be achieved indirectly. To fill this gap, in this thesis, we make the following contributions. First, we formulate the theoretical background about the fundamental combinatorial properties of irregular elements in QD meshes. Second, we develop algorithms for the explicit control of irregular elements and the exhaustive enumeration of QD mesh connectivities. Finally, we demonstrate the importance of connectivity control for QD meshes in a wide range of applications.
Traditionally, the research on QD meshes focuses on the automatic generation of pure quadrilateral or QD meshes from a given surface. Explicit control of the placement of irregular elements can only be achieved indirectly. To fill this gap, in this thesis, we make the following contributions. First, we formulate the theoretical background about the fundamental combinatorial properties of irregular elements in QD meshes. Second, we develop algorithms for the explicit control of irregular elements and the exhaustive enumeration of QD mesh connectivities. Finally, we demonstrate the importance of connectivity control for QD meshes in a wide range of applications.
ContributorsPeng, Chi-Han (Author) / Wonka, Peter (Thesis advisor) / Maciejewski, Ross (Committee member) / Farin, Gerald (Committee member) / Razdan, Anshuman (Committee member) / Arizona State University (Publisher)
Created2014
Description
The Dual Marching Tetrahedra algorithm is a generalization of the Dual Marching Cubes algorithm, used to build a boundary surface around points which have been assigned a particular scalar density value, such as the data produced by and Magnetic Resonance Imaging or Computed Tomography scanner. This boundary acts as a skin between points which are determined to be "inside" and "outside" of an object. However, the DMT is vague in regards to exactly where each vertex of the boundary should be placed, which will not necessarily produce smooth results. Mesh smoothing algorithms which ignore the DMT data structures may distort the output mesh so that it could incorrectly include or exclude density points. Thus, an algorithm is presented here which is designed to smooth the output mesh, while obeying the underlying data structures of the DMT algorithm.
ContributorsJohnson, Sean (Author) / Farin, Gerald (Thesis advisor) / Richa, Andrea (Committee member) / Nallure Balasubramanian, Vineeth (Committee member) / Arizona State University (Publisher)
Created2011
Description
Mostly, manufacturing tolerance charts are used these days for manufacturing tolerance transfer but these have the limitation of being one dimensional only. Some research has been undertaken for the three dimensional geometric tolerances but it is too theoretical and yet to be ready for operator level usage. In this research, a new three dimensional model for tolerance transfer in manufacturing process planning is presented that is user friendly in the sense that it is built upon the Coordinate Measuring Machine (CMM) readings that are readily available in any decent manufacturing facility. This model can take care of datum reference change between non orthogonal datums (squeezed datums), non-linearly oriented datums (twisted datums) etc. Graph theoretic approach based upon ACIS, C++ and MFC is laid out to facilitate its implementation for automation of the model. A totally new approach to determining dimensions and tolerances for the manufacturing process plan is also presented. Secondly, a new statistical model for the statistical tolerance analysis based upon joint probability distribution of the trivariate normal distributed variables is presented. 4-D probability Maps have been developed in which the probability value of a point in space is represented by the size of the marker and the associated color. Points inside the part map represent the pass percentage for parts manufactured. The effect of refinement with form and orientation tolerance is highlighted by calculating the change in pass percentage with the pass percentage for size tolerance only. Delaunay triangulation and ray tracing algorithms have been used to automate the process of identifying the points inside and outside the part map. Proof of concept software has been implemented to demonstrate this model and to determine pass percentages for various cases. The model is further extended to assemblies by employing convolution algorithms on two trivariate statistical distributions to arrive at the statistical distribution of the assembly. Map generated by using Minkowski Sum techniques on the individual part maps is superimposed on the probability point cloud resulting from convolution. Delaunay triangulation and ray tracing algorithms are employed to determine the assembleability percentages for the assembly.
ContributorsKhan, M Nadeem Shafi (Author) / Phelan, Patrick E (Thesis advisor) / Montgomery, Douglas C. (Committee member) / Farin, Gerald (Committee member) / Roberts, Chell (Committee member) / Henderson, Mark (Committee member) / Arizona State University (Publisher)
Created2011