Search results
Results from the WOW.Com Content Network
The Z-ordering can be used to efficiently build a quadtree (2D) or octree (3D) for a set of points. [5] [6] The basic idea is to sort the input set according to Z-order.Once sorted, the points can either be stored in a binary search tree and used directly, which is called a linear quadtree, [7] or they can be used to build a pointer based quadtree.
Let (x, y, z) be the standard Cartesian coordinates, and (ρ, θ, φ) the spherical coordinates, with θ the angle measured away from the +Z axis (as , see conventions in spherical coordinates). As φ has a range of 360° the same considerations as in polar (2 dimensional) coordinates apply whenever an arctangent of it is taken. θ has a range ...
A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. [1] In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly.
Curve fitting [1] [2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [3] possibly subject to constraints. [ 4 ] [ 5 ] Curve fitting can involve either interpolation , [ 6 ] [ 7 ] where an exact fit to the data is required, or smoothing , [ 8 ] [ 9 ] in which a "smooth ...
graph-tool is a Python module for manipulation and statistical analysis of graphs (AKA networks). The core data structures and algorithms of graph-tool are implemented in C++ , making extensive use of metaprogramming , based heavily on the Boost Graph Library . [ 1 ]
UV texturing is an alternative to projection mapping (e.g., using any pair of the model's X, Y, Z coordinates or any transformation of the position); it only maps into a texture space rather than into the geometric space of the object. The rendering computation uses the UV texture coordinates to determine how to paint the three-dimensional surface.
Parallel Coordinates were popularised again 87 years later by Alfred Inselberg [5] in 1985 and systematically developed as a coordinate system starting from 1977. Some important applications are in collision avoidance algorithms for air traffic control (1987—3 USA patents), data mining (USA patent), computer vision (USA patent), Optimization ...
By definition, if a particle with no forces acting on it has its position expressed in an inertial coordinate system, (x 1, x 2, x 3, t), then there it will have no acceleration (d 2 x j /dt 2 = 0). [15] In this context, a coordinate system can fail to be "inertial" either due to non-straight time axis or non-straight space axes (or both).