61 Matching Annotations
  1. Jan 2024
    1. 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

      几何,渲染,模拟

    1. 实例

      声明,定义,初始化: 1. 在被使用前被声明?在使用的位置之外? 2. 定义,和使用的位置紧挨着? 3. 初始化: 赋初值?

    2. 指向内存位置的表达式被称为左值(lvalue)表达式

      表达式:变量、函数、数学表达式?

    3. 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

      变量声明在不同阶段

    4. 带有静态存储持续时间的变量会被隐式初始化为 NULL
  2. Nov 2023
    1. 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.

      voxel modeling applications

  3. Sep 2023
    1. There are other approaches to doing AMR than using quadtrees. For example, you could do longest-edge bisection or red-green refinement for triangles

      adaptive meshing

  4. Aug 2023
    1. 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

      basic primitives with distortion functions to shape complex objects

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

      calculate SDF for complex objects

  5. Jul 2023
    1. 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.
    1. to know which the edges are that we have intersections with so that we can start adding triangles.

      Second step: confirm with edge is intersected

    2. 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;

      First step: confirm the cubic configuration

  6. May 2023
    1. 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.

      space structures

    Annotators

  7. Apr 2023
    1. Lax–Friedrichs method

      The forward time scheme seems slightly different

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

      which one is the numerical dissipation term

    3. boundary conditions

      how many boundary condtions are needed to confirm the solution to a partial differential equation?

    1. discrete differential geometry

      The formulation uses concepts from the nascent field of discrete differential geometry

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

      Three types of nonlinear equations

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

      where ai and f are functions of the independent variables x and y only. (Often the mixed-partial derivatives uxy and uyx will be equated, but this is not required for the discussion of linearity.) If the ai are constants (independent of x and y) then the PDE is called linear with constant coefficients. If f is zero everywhere then the linear PDE is homogeneous, otherwise it is inhomogeneous.

  8. Jan 2023
    1. [\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。

      vim里[\S\s]匹配所有的s和S

  9. Oct 2022
    1. 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

      orthogonal to space vector to minimize

    2. method of approximation
      1. finding ci such that the difference u−f, measured in some norm, is minimized
      2. find u such that the error u−f is orthogonal to the space where we seek u
    1. 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.

      approximation=? interpolation

    2. integration by parts, boundary conditions, and coordinate mappings

      Core topics in FEM

    3. 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

      actually Cn is the unknow function. but it's in a discritized form by point value

    1. 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)。

      采用应变而不采用绝对变形量的原因

    2. 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)。

      采用应力而不是力的原因

  10. Sep 2022
    1. The only remaining possibility for a suitable grid generator is to avoid non-Delaunay elements for hybrid grid generators or to use tetrahedras only

      Tetrahedra can avoid the problem above?

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

      can all the intersection plane cross at a single point?

    1. 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.

      The solution to physical problems is curve in plane or surface in space, geometry.

    1. 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.

      Forces in elesticity problem

    1. 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.

      Rayleigh Ritz Method --> Finite Element Method

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

      Rayleigh Ritz Method

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

      virtual work principle-->minimum total potential ennergy

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

      only variational Procedure uses virtual work and minimum PE?

    1. 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。

      选择性离散,自动meshing?

    1. 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。

      取决于路径积分

    1. 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

      ?

    1. 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).

      FEM插值函数

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

      为什么是坐标的线性函数?

  11. Aug 2022
    1. 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

      傅里叶转换在通信中的应用

    2. 任意周期函数都可以分解成若干个三角函数的叠加

      傅里叶变换的理论基础

    1. 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.

      extraction

  12. www.zerotoasiccourse.com www.zerotoasiccourse.com
    1. 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).

      design #ic_component

  13. Jul 2022
    1. 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

      电池

  14. Apr 2022
    1. o retrieve the current value of the parameter par, use the variable:par.value

      how to get the parameter value

    1. 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。

      永远是精确的?

    2. 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':

      利用变量名给变量赋值,相当于将变量指向变量名所指向的值的内存地址

  15. Nov 2021
    1. 結構:BJT、JFET、IGFET (MOSFET)、IGBT等。

      晶体管的结构

    2. 固體電子元件在應用時比較容易出現靜電放電現象。

      ESD is important

    3. 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。

      一个逻辑闸包含20个transistor?

    4. 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。
    5. 可以用於放大、開關、穩壓、訊號調變和許多其他功能
    6. 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。
  16. Oct 2021
    1. Kelvin technique

      measurement of sheet resistance

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

      sheet resistance definition

  17. Sep 2021
    1. 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

      appiy a DC bias voltage first then input a AC signal?

    1. 令牌可以是关键字、标识符、常量、字符串值,或者是一个符号

      c语言程序语句的组成部分