利用现代计算技术，解决几何，渲染以及模拟问题的工程科学

实例

指向内存位置的表达式被称为左值（lvalue）表达式

变量声明只在编译时有它的意义，在程序连接时编译器需要实际的变量声明

带有静态存储持续时间的变量会被隐式初始化为 NULL

Currently, voxels are used in many scientific disciplines to quickly determine volumetric data. For example, in Voxel-based morphometry, researchers can compare the differences in concentration of brain tissue using voxels. Geologists often use voxel modeling techniques to model geological features like terrain and elevation. More broadly, scientists can use voxel-based modeling to visualize and measure the volume of anything from fluids to green spaces in urban centers. Voxels are also useful in simulation techniques that require modeling of individual particles, as is the case of smart material simulation.

There are other approaches to doing AMR than using quadtrees. For example, you could do longest-edge bisection or red-green refinement for triangles

the distance functions for basic primitives, plus the formulas for combining them together for building more complex shapes, as well as some distortion functions that you can use to shape your objects

how to compute SDFs and raymarch more complex objects such as recursive primitives, fractals or acceleration struture based meshes

To learn how to apply the Marching Cubes algorithm in 3d here. Or if you want to jump ahead to an improved technique checkout Dual Contouring.

to know which the edges are that we have intersections with so that we can start adding triangles.

The algorithm begins by determining the configuration of the cube, by comparing the value of our cube at every corner vertex with the isosurface level. 1 2 3 4 5 6 7 8 9 int cubeIndex = 0; if (cubeValues[0] < isolevel) cubeIndex |= 1; if (cubeValues[1] < isolevel) cubeIndex |= 2; if (cubeValues[2] < isolevel) cubeIndex |= 4; if (cubeValues[3] < isolevel) cubeIndex |= 8; if (cubeValues[4] < isolevel) cubeIndex |= 16; if (cubeValues[5] < isolevel) cubeIndex |= 32; if (cubeValues[6] < isolevel) cubeIndex |= 64; if (cubeValues[7] < isolevel) cubeIndex |= 128;

space structuressuch as space truss consist of a large number of structural members, whichcan easily achieve much more complicate geometry through changingthe number of members, the orientation of the members, and the locationof the members.

Lax–Friedrichs method

or the unknown u i n + 1 , {\displaystyle u_{i}^{n+1},}

boundary conditions

discrete differential geometry

Three main types of nonlinear PDEs are semilinear PDEs, quasilinear PDEs, and fully nonlinear PDEs.

A PDE is called linear if it is linear in the unknown and its derivatives

Hamiltonian

[\s\S] 匹配所有。\s 是匹配所有空白符，包括换行，\S 非空白符，不包括换行。

minimizing ||e||2||e||2||\boldsymbol{e}||^2 implies that ee\boldsymbol{e} is orthogonal to any vector vv\boldsymbol{v} in the space VVV

method of approximation

Three types of approximation principles are covered: 1) the least squares method, 2) the L2L2L_2 projection or Galerkin method, and 3) interpolation or collocation.

integration by parts, boundary conditions, and coordinate mappings

where ψi(x)ψi(x){\psi}_i(x) are prescribed functions and c0,…,cNc0,…,cNc_0,\ldots,c_N are unknown coefficients to be determined

在拉压试验中，试件会被拉长或者缩短，伸长量用△L表示（负值代表缩短）。为了方便对不同长度的试件进行对比，我们将伸长量（△L）除以试件初始长度（L0），记为“应变”（Strain ε）。

为了方便对不同尺寸试件的力学性能进行对比，将单位面积上受到的力作为统一的量化指标，即“应力”（Stress σ）。

The only remaining possibility for a suitable grid generator is to avoid non-Delaunay elements for hybrid grid generators or to use tetrahedras only

The center of the circumsphere is the intersection of all bisecting planes of the edges.

he did a marvelous thing by creating the field of differential equations by allowing us to reformulate the problems of natural sciences to geometrical problems of curves in plane and surfaces in space.

Self Capacitance

There are two types of stresses acting on each face of an element namely,Axial stress ( – normal): acting perpendicular to the face.Shear Stress (): acting in two components on each face.

Departure from classical Rayleigh Ritz Method leads to FEM. The two departures are:Trial functions are defined for sub-domains.Generally, the use of values of space variable at the nodes as unknowns.

Classical Rayleigh Ritz Method is a method of finding displacements at various nodes based on the theorem of minimum potential energy.

This concept of minimum total potential energy is nothing but can be called as the special case of the virtual work principle.

Principal of Virtual work and minimum PE is a particular form of Variational Procedure only.

在左边单元划分最密区域，有应力集中现象（如裂纹问题的奇异解现象），所以又有相应的高级理论（比如non-local theory）来指导这部分的单元应力应变计算。结构被选择性地离散，和高级理论构成了有限元发展的主要研究方向。

这个输出值取决于一个或多个函数（输入）在一整个路径上的积分而非像一般函数一样取决于离散的变量。

检验函数的一种自然选择是 x(t)x(t)x(t) 展开时使用的基底函数 1,t1,t2{1, t^1, t^2}{1, t^1, t^2} , 求解

其中重复指标N意味着求和， uN(e)u_N ^{(e)}u_N ^{(e)} 表示子域(element)节点N上的值，并且 ΦN(e)\Phi_{N}^{(e)}\Phi_{N}^{(e)} 称为子域(element)试探函数(trial functions ),或称为插值函数(interpolation functions)、形状函数( shape functions)或基函数( basis functions).

假设变量 u(e)(x)u ^{(e)} (x)u ^{(e)} (x) 是 xxx 的线性函数

把信号进行傅里叶级数分解后，把不需要频率成分去除，即可达到滤波的作用

任意周期函数都可以分解成若干个三角函数的叠加

Gate level extraction just means that you treat the gates (standard cells) as black boxes and extract the parasitics for the interconnect; often this is done from a DEF description of the layout. Transistor level extraction would be combined with LVS and would extract the devices and all the parasitics around the devices too as well as the interconnect.

Circuits operate all at once, parallelism is easy. If you want sequences of things you have to build a sequencer first (like a state machine).

电池或电源来说，如果我们规定其电动势的方向为电源内部负极指向正极的方向，那么： 电动势方向和绕行方向相同：升压电动势方向和绕行方向相反：降压

o retrieve the current value of the parameter par, use the variable:par.value

无论整数做//除法还是取余数，结果永远是整数，所以，整数运算结果永远是精确的。

执行b = a，解释器创建了变量b，并把b指向a指向的字符串'ABC'：

Orbitals are the regions of space in which electrons are most likely to be found

結構：BJT、JFET、IGFET (MOSFET)、IGBT等。

固體電子元件在應用時比較容易出現靜電放電現象。

一個邏輯閘包含20個電晶體，而2012年一個高級的微處理器使用的電晶體數量達14億個。

電晶體一般都有三個極，其中一極兼任輸入及輸出端子，(B)基極不能做輸出，(C)集極不能做輸入之外，其餘兩個極組成輸入及輸出對。

可以用於放大、開關、穩壓、訊號調變和許多其他功能

電晶體基於輸入的電流或電壓，改變輸出端的阻抗，從而控制通過輸出端的電流，因此電晶體可以作為電流開關，而因為電晶體輸出信號的功率可以大於輸入信號的功率，因此電晶體可以作為電子放大器。

Kelvin technique

It is a measure of the lateral resistance through a thin square of material, i.e. the resistance between opposite sides of a square

The procedure for taking C-V measurements involves the application of DC bias voltages across the capacitor while making the measurements with an AC signal

令牌可以是关键字、标识符、常量、字符串值，或者是一个符号