his paper provides a tutorial and survey of methods for parameterizing
surfaces with a view to applications in geometric modelling and computer graphics.
We gather various concepts from di® erential geometry which are relevant to surface
mapping and use them to understand the strengths and weaknesses of the many
methods for parameterizing piecewise linear surfaces and their relationship to one
another.
This demo nstrates the use of the reversible jump MCMC algorithm for neural networks. It uses a hierarchical full Bayesian model for neural networks. This model treats the model dimension (number of neurons), model parameters, regularisation parameters and noise parameters as random variables that need to be estimated. The derivations and proof of geometric convergence are presented, in detail, in: Christophe Andrieu, Nando de Freitas and Arnaud Doucet. Robust Full Bayesian Learning for Neural Networks. Technical report CUED/F-INFENG/TR 343, Cambridge University Department of Engineering, May 1999. After downloading the file, type "tar -xf rjMCMC.tar" to uncompress it. This creates the directory rjMCMC containing the required m files. Go to this directory, load matlab5 and type "rjdemo1". In the header of the demo file, one can select to monitor the simulation progress (with par.doPlot=1) and modify the simulation parameters.
韓國(guó)Yunjin Lee的博士論文，包含了她讀博期間的主要研究成果，包括Mesh Scissoring: Contour-Based Segmentation，Mesh Parameterization Using Virtual Boundaries，geometric Snakes for 3D Meshes，Mean Shift for 3D Meshes
In an electromagnetic cloak based on a transformation approach, reduced sets of
material properties are generally favored due to their easier implementation in reality,
although a seemingly inevitable drawback of undesired reflection exists in such cloaks.
Here we suggest using high-order transformations to create smooth moduli at the outer
boundary of the cloak, therefore completely eliminating the detrimental scattering
within the limit of geometric optics. We apply this scheme to a non-magnetic
cylindrical cloak and demonstrate that the scattered field is reduced substantially in a
cloak with optimal quadratic transformation as compared to its linear counterpart.
We obtained the energy transport velocity distribution for a three dimensional ideal cloak
explicitly. Near the operation frequency, the energy transport velocity has rather peculiar
distribution. The velocity along a line joining the origin of the cloak is a constant, while
the velocity approaches zero at the inner boundary of the cloak. A ray pointing right into
the origin of the cloak will experience abrupt changes of velocities when it impinges on the
inner surface of the cloak. This peculiar distribution causes long time delays for beams
passing through the ideal cloak within a geometric optics description.
An example case is considered to price an option at a maturity of T years - prices are simulated for geometric brownian motion process at 2*T maturity, and Brownian Bridge is used to obtain prices at T maturity. Finally option prices are compared to Black Scholes values to verify results
This book is about 3D math, the study of the mathematics behind the geometry of a 3D world. 3D
math is related to computational geometry, which deals with solving geometric problems algorithmically.
3D math and computational geometry have applications in a wide variety of fields that use computers to model or reason about the world in 3D, such as graphics, games, simulation,
robotics, virtual reality, and cinematography.
This book covers theory and practice in C++.
Matlab 畫(huà)三維立體圖形
The aim of geom3d library is to handle and visualize 3D geometric primitives
such as points, lines, planes, polyhedra... It provides low-level functions
for manipulating 3D geometric primitives, making easier the development of more
complex geometric algorithms.
Some features of the library are:
- creation of various shapes (3D points, 3D lines, planes, polyhedra...)
through an intuitive syntax.
Ex: createPlane(p1, p2, p3) to create a plane through 3 points.
- derivation of new shapes: intersection between 2 planes, intersection between
a plane and a line, between a sphere and a line...
- functions for 3D polygons and polyhedra. Polyhedra use classical vertex-faces
arrays (face array contain indices of vertices), and support faces with any
number of vertices. Some basic models are provided (createOctaedron,
createCubeoctaedron...), as well as some computation (like faceNormal or
centroid)
- manipulation of planar transformation. Ex.:
ROT = createRotationOx(THETA);
P2 = transformPoint3d(P1, ROT);
- direct drawing of shapes with specialized functions. Clipping is performed
automatically for infinite shapes such as lines or rays. Ex:
drawPoint3d([50 50 25; 20 70 10], 'ro'); % draw some points
drawLine3d([X0 Y0 Z0 DX DY DZ]); % clip and draw straight line
Some functions require the geom2d package.
Additional help is provided in geom3d/Contents.m file, as well as summary files
like 'points3d.m' or 'lines3d.m'.
