A highly interactive three dimensional mesh generator

Computer Graphics Forum, 2011

1998

ACM Transactions on Graphics, 2011

The construction of polygonal meshes remains a complex task in Computer Graphics, taking tens of thousands of individual operations over several hours of modeling time. The complexity of modeling in terms of number of operations and time makes it difficult for artists to understand all details of how meshes are constructed. We present MeshFlow, an interactive system for visualizing mesh construction sequences. MeshFlow hierarchically clusters mesh editing operations to provide viewers with an overview of the model construction while still allowing them to view more details on demand. We base our clustering on an analysis of the frequency of repeated operations and implement it using substituting regular expressions. By filtering operations based on either their type or which vertices they affect, MeshFlow also ensures that viewers can interactively focus on the relevant parts of the modeling process. Automatically generated graphical annotations visualize the clustered operations. We have tested MeshFlow by visualizing five mesh sequences each taking a few hours to model, and we found it to work well for all. We have also evaluated MeshFlow with a case study using modeling students. We conclude that our system provides useful visualizations that are found to be more helpful than video or document-form instructions in understanding mesh construction. Contributions. We believe that by combining automatically generated annotations with the functionality for overview, detail-ondemand, and focus, MeshFlow has the benefits of both video and document tutorials. We have validated this intuition by asking eight subjects to compare MeshFlow with traditional tutorials, finding that our tool is highly preferable. To the best of our knowledge, MeshFlow is the first system to support this type of interactive visualization of mesh construction sequences. Design-workflow Visualization. Our system for interactively visualizing mesh construction sequences is inspired by several re-

1998

We investigate a new way to represent arbitrary triangle meshes. We prove that a large class of triangle meshes, called normal triangle meshes, can be represented by a subdivision tree, where each subdivision is one of four elementary subdivision types. We also show how to partition an arbitrary triangle mesh into a small set of normal meshes. The subdivision tree representation can be used to encode mesh connectivity information. Our theoretical analysis shows that such a coding scheme is very promising. surfaces in R 3. For details about these terms and related information, readers may refer to topology textbooks, such as 8]. De nition 1 The Euclidean distance between x = (x 1 ; :::; x n) and y = (y 1 ; :::; y n) in R n is given by kx yk = q (x 1 y 1) 2 + ::: + (x n y n) 2 De nition 2 A topological space is a set X with a collection B of subsets N X, called neighborhoods, such that every point is in some neighborhood, i.e., 8x 2 X; 9N 2 B such that x 2 N N 1 ; N 2 2 B with x 2 N 1 \ N 2 ; 9N 3 2 B such that x 2 N 3 N 1 \ N 2. The set, B, of all neighborhoods is called a basis for the topology on X. De nition 3 Two topological spaces A and B are homeomorphic if there is a continuous invertible function f : A ! B with continuous inverse f 1 : B ! A. Such a function f is called a homeomorphism. De nition 4 An n-cell is a set whose interior is homeomorphic to the n-dimensional disc D n = fx 2 R n : kxk < 1g with the additional property that its boundary must be divided into a nite number of lower-dimensional cells, called the faces of the n-cell. A 0-dimensional cell is a point. A 1-dimensional cell is a line segment. A 2-dimensional cell is a triangle. A 3-dimensional cell is a tetrahedron. De nition 5 A complex K is a nite set of cells, K = f : is a cellg such that: if is a cell in K, then all faces of are elements of K. if and are cells in K, then Int() \ Int() = ;.

2008

Computational scientists are frequently confronted with a choice: implement algorithms using high-level abstractions, such as matrices and mesh entities, for BIOGRAPHICAL SKETCH Brian graduated from Carnegie Mellon University in 1998, where he majored in Computer Science and minored in Mathematics. He worked under Andrew Grimshaw at the University of Virginia and graduated with a Master of Computer Science in 2002. He spent the prior year as a visiting research assistant under Jay Lepreau at the University of Utah. He received a Master of Science degree in Electrical and Computer Engineering from Cornell University in 2006, while working with Sally McKee. His minor field of concentration was Physics. Additionally, Brian spent time during the summers of 2004, 2005, and 2006 working with Dan Quinlan at Lawrence Livermore National Laboratory. iii To my mother, father, and sister, Nicole, who supported and encouraged me through each of the many bends in my studies.