Exact_predicates_exact_constructions_kernel_with_sqrtbut the number type is a model of conceptFieldWithSqrt Exact_predicates_exact_constructions_kernel_with_kth_rootbut the number type is a model of conceptFieldWithKthRoot Exact_predicates_exact_constructions_kernel_with_root_ofbut the num...
Based on the simple and well understood concept of subfields in a finite field, the technique called 'field reduction' has proved to be a very useful and powerful tool in finite geometry. In this paper we elaborate on this technique. Field reduction for projective and polar spaces is ...
Dynamic segmentation is the process of computing the map locations of events stored and managed in an event table along route features and displaying them on a map. The term dynamic segmentation is derived from the concept that line features need not be split (in other words, segmented) each ...
CGAL, theComputational Geometry Algorithms Library, is written in C++ and consists of three major parts. The first part is the kernel, which consists of constant-size non-modifiable geometric primitive objects and operations on these objects. The objects are represented both as stand-alone classes ...
Linear referencing provides you with a two-fold solution: an intuitive way to model relative locations along linear features, and associate multiple sets of attributes to portions of linear features. ArcGIS Proprovides the tools that will assist you in creating, editing, and analyzing the data requ...
Here are some examples to solidify the concept: ⟨4−5⟩+⟨3,10⟩=⟨7,5⟩,⟨0,2,1⟩+⟨−6,8,−1⟩=⟨−6,10,0⟩,and⟨9,2⟩+⟨4,5⟩+⟨−7,−4⟩=⟨6,3⟩. However, the sum ⟨a,b⟩+⟨x,y,z⟩ is not defined. Geometrically...
In this section, we begin by reviewing the concept of mapping in general as a way of leading into linear mappings, which are functions from one linear space to another. We then show how matrices are used to represent linear mappings. 2.7.1 MAPPINGS IN GENERAL The basic idea of a function...
As an illustration of the concept introduced above, let us consider a coupled two-reservoir system with no external forcing (Fig. 4-6). The dynamic behavior of this system is governed by the two differential equations Sign in to download full-size image Fig. 4-6. A coupled two-reservoir...
Linear approximation is a concept that introduces calculus to help evaluate the values of functions in a domain, without actually involving the geometry of the function. It is the process of finding the equation of a tangent line to a function at a point and using it to approximate values of...
The book develops these fundamental concepts in 2D and 3D with a strong emphasis on geometric understanding before presenting the general (n-dimensional) concept. The book does not employ a theorem/proof structure, and it spends very little time on tedious, by-hand calculations (e.g., ...