The (negative) Torricelli triangle T1(ABC) of a nondegenerate (positively oriented) triangle ABC is defined to be the triangle A1B1C1, where ABC1, BCA1, and CAB1 are the equilateral triangles drawn outwardly on the sides of ABC. It is known that not every triangle is the Torricelli triangle of some initial triangle, and triangles that are not Torricelli triangles are characterized in [28]. In t...

In this paper, we enlarge the language of triangle algebra by addinga unary operation that describes properties of a state. Thesestructure algebras are called state triangle algebra. The vitalproperties of these algebras are given. The notion of state interval-valued residuated lattice (IVRL)-filters are introduced and givesome examples and properties of them are given. ...

We have considered flat Friedmann-Robertson-Walker (FRW) model of the universe and reviewed modified Chaplygin gas as fluid source. Associated with scalar field model, we determined Hubble parameter a generating function in terms field. Instead hyperbolic function, taken Jacobi elliptic Abel obtained Chaplygin-Jacobi (MCJG) Chaplygin-Abel (MCAG) equation states, respectively. Next, assumed that...

We mainly study Max TSP with two objective functions. We propose an algorithm which returns a single Hamiltonian cycle with performance guarantee on both objectives. The algorithm is analysed in three cases. When both (resp. at least one) objective function(s) fulfill(s) the triangle inequality, the approximation ratio is 5 12 − ε ≈ 0.41 (resp. 3 8 − ε). When the triangle inequality is not assu...

The quad/triangular subdivision, whose control net and refined meshes consist of both quads and triangles, provides better visual quality of subdivision surfaces. While some theoretical results such as polynomial reproduction and smoothness analysis of quad/triangle schemes have been obtained in the literature, some issues such as the basis functions at quad/triangle vertices and design of inte...

Fractal objects like Sierpinski triangle and Fern have very high visual complexity and low storage-information content. For generating computer graphic images and compression of such objects, Iterated Function Systems (IFS) {[3] , [1]} are recently being used. The main problem in fractal encoding using IFS is large amount of time taken for the compression of the fractal object. Our endeavor in ...

In this work we introduce a new method for representing and evolving snakes that are constrained to lie on a prescribed surface (triangle mesh). The new representation allows to automatically adapt the snake resolution to the surface tesselation and does not need any (unstable) back-projection operations. Furthermore, it enables efficient and robust collision detection and gives us complete con...

In this paper we introduce a simple and efficient scheme for encoding the connectivity and the stripification of a triangle mesh. Since generating a good set of triangle strips is a hard problem, it is desirable to do this just once and store the computed strips with the triangle mesh. However, no previously reported mesh encoding scheme is designed to include triangle strip information into th...