An introduction to splines for use in computer graphics & geometric modeling
An introduction to splines for use in computer graphics & geometric modeling
The simplest subdivision scheme for smoothing polyhedra
ACM Transactions on Graphics (TOG)
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Semiregular Pentagonal Subdivisions
SMI '04 Proceedings of the Shape Modeling International 2004
Remeshing Schemes for Semi-Regular Tilings
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
Computation of rotation minimizing frames
ACM Transactions on Graphics (TOG)
Chaos and Graphics: Truchet curves and surfaces
Computers and Graphics
ACM SIGGRAPH 2009 papers
A wave-based anisotropic quadrangulation method
ACM SIGGRAPH 2010 papers
Single-Cycle Plain-Woven Objects
SMI '10 Proceedings of the 2010 Shape Modeling International Conference
Continuous line drawings via the traveling salesman problem
Operations Research Letters
CAe '12 Proceedings of the Eighth Annual Symposium on Computational Aesthetics in Graphics, Visualization, and Imaging
CAe '12 Proceedings of the Eighth Annual Symposium on Computational Aesthetics in Graphics, Visualization, and Imaging
Introduction: Foreword to the special section on expressive graphics
Computers and Graphics
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In this work, we present the concept of ''Hamiltonian cycle art'' that is based on the fact that any mesh surface can be converted to a single closed 3D curve. These curves are constructed by connecting the centers of every two neighboring triangles in the Hamiltonian triangle strips. We call these curves surface covering since they follow the shape of the mesh surface by meandering over it like a river. We show that these curves can be used to create wire sculptures and duotone (two-color painted) surfaces. To obtain surface covering wire sculptures we have developed two methods to construct corresponding 3D wires from surface covering curves. The first method constructs equal diameter wires. The second method creates wires with varying diameter and can produce wires that densely cover the mesh surface. For duotone surfaces, we have developed a method to obtain surface covering curves that can divide any given mesh surface into two regions that can be painted in two different colors. These curves serve as a boundary that define two visually interlocked regions in the surface. We have implemented this method by mapping appropriate textures to each face of the initial mesh. The resulting textured surfaces look aesthetically pleasing since they closely resemble planar TSP (traveling salesmen problem) art and Truchet-like curves.