To facilitate the construction of constraint-based user interface applications, researchers have proposed various constraint satisfaction methods and constraint solvers. A prime use of constraints in this field is to automatically maintain geometric layouts of graphical objects. Read moreĬonstraints have been playing an important role in the user interface field since its infancy. Thus, less precision is re- quired, the amount of interaction is unrelated to the complexity of the boundary, and users do not need to search for a view of the model in which a cut can be made. Unlike approaches based on scissoring, the user loosely strokes within the body of each de- sired region, and the system computes optimal boundaries between regions via minimum-cost graph cut. A major contribution of our work is our fast, graph cut-based in- teractive surface segmentation algorithm. transfer is formulated as synthesis with a novel surface-based adap- tation of graph cuts, the source and target regions need not match in size or shape, and details can be geometric, textural or even user- defined in nature. The source may be elsewhere on the target sur- face, on another surface altogether, or even part of an image. The user selects a source re- gion and a target region, and the system transfers detail from the source to the target. Our system allows easy detail reuse from existing 3D models or images.
We present a novel technique for surface modelling by example called surfacing by numbers. An alternative definition of the thermostatic manifold is obtained as a Lagrange submanifold defined by the symplectic two-form associated to the Gibbs contact one-form. The relationship of the graph of the thermodynamic energy function and the graph of the thermostatic energy function is defined by a cross-section of a vector bundle. Equilibrium or non-equilibrium processes are paths on the corresponding portions of the graph. The graph of the generalized function contains the thermostatic system as a Legendre submanifold. Homogeneous thermodynamics is geometrically represented in a contact manifold by a codimension one submanifold which is locally the graph of the generalized energy function, ϕ but an extended contact structure applies to non-equlibrium thermodynamics as well. The reason is that the thermodynamics is based – as Gibbs has explicitly proclaimed – on a rather complicted mathematical theory, on the contact geometry”. Arnold (1990) has stated, “Every mathematician knows that it is impossible to understand any elementary course in thermodynamics. Thermodynamics is easier to understand if it is put in a geometric context. N-point metric space M, the weight of the MST of every connected SDG for M is O(logn) Specifically, we demonstrate that for any Furthermore, our upper bound extends to arbitrary metric spaces and, in particular, it applies to any of the normed spaces ℓp In this paper we generalize the upper bound of Abu-Affash et al. A natural question that arises is whether this surprising upper bound of can be generalized for wider families of metric spaces, such as high-dimensional Euclidean spaces. However, the upper bound proof of relies heavily on basic geometric properties of constant-dimensional Euclidean spaces, and does not extend to Euclidean spaces of super-constant dimension. w(MST(M)), and that this bound is tight.networks.Ību-Affash, Aschner, Carmi and Katz (SWAT 2010, ) showed that for any n-point 2-dimensional Euclidean space M, the weight of the MST of every connected SDG for M is O(logn) SDGs are often used to model wireless communication. The symmetric disk graph (henceforth, SDG) that corresponds to M and r is the undirected graph over V whose edge set includes an edge (u,v) if both r(u) and r(v) are no smaller than δ(u,v). The part that I failed to emphasize: there is a proposition in Diestel which says that every face of a 2-connected graph is bounded by a cycle - however, there is a note in my lecture notes that the fact that $F$ is bounded by a cycle can be proven without this.Consider an n-point metric space M = (V,δ), and a transmission range assignment r: V → ℝ + that maps each point v ∈ V to the disk of radius r(v) around it. This image is impossible, I assume, because there is a cycle of odd length here but this is an example where the boundary of the unbounded face of a planar graph is not a cycle. I know that every bounded face must be bounded by a cycle, but I don't know that the unbounded face is bounded by a cycle. Now, the part that's unclear to me is the conculsion that $F$ must be bounded by a cycle. I'm reading a proof of the fact that $K_$, and since $v-e+f=2$, $v=6$, $e=9$, we have $f=5$, and so $9 \geq 10$, which is a contradiction.