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<!DOCTYPE html>
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<div class="row mx-auto index-card">
<div class="col-12 col-md-12 mx-auto index-info">
<a class="index-header" href="/2022/04/15/C++PrefectForward/">Prefect Forward 实现</a>
<a href="/2022/04/15/C++PrefectForward/" class="index-excerpt">
<div>Prefect Forward 实现 涉及到模板偏特化、万能引用、引用折叠、模板类型推导
1. Move reference 利用模板偏特化，去除引用，保证返回一个不带引用的类型
template<typename T>
struct RemoveReference
{
using type=T;
RemoveReference()
</div>
</a>
<div class="index-btm post-metas">
<div class="post-meta mr-3">
<i class="iconfont icon-date"></i> 2022-04-15
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<div class="post-meta mr-3">
<i class="iconfont icon-category"></i>
<a href="/categories/C/">C++</a>
</div>
<div class="post-meta">
<i class="iconfont icon-tags"></i>
<a href="/tags/Prefect-Forward/">Prefect Forward</a>
</div>
</div>
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<div class="row mx-auto index-card">
<div class="col-12 col-md-12 mx-auto index-info">
<a class="index-header" href="/2021/09/30/C++PCH%E6%8F%90%E5%8D%87%E7%BC%96%E8%AF%91%E9%80%9F%E5%BA%A6/">C++ PCH提升编译速度</a>
<a href="/2021/09/30/C++PCH%E6%8F%90%E5%8D%87%E7%BC%96%E8%AF%91%E9%80%9F%E5%BA%A6/" class="index-excerpt">
<div>C++ PCH流程
创建pch.h,pch.cpp
//pch.h
#ifndef __PCH_H__
#define __PCH_H__
//include your header file (not likely to change)
//...
//...
#endif
//pch.cpp
#include "pch.h"
在vs项目属性中C/C++的预编译头中设置</div>
</a>
<div class="index-btm post-metas">
<div class="post-meta mr-3">
<i class="iconfont icon-date"></i> 2021-09-30
</div>
<div class="post-meta mr-3">
<i class="iconfont icon-category"></i>
<a href="/categories/C/">C++</a>
</div>
<div class="post-meta">
<i class="iconfont icon-tags"></i>
<a href="/tags/%E7%BC%96%E8%AF%91/">编译</a>
</div>
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<a class="index-header" href="/2021/03/17/2020-03-09-Singularity-Constrained-Octahedral-Fields-for-Hexahedral-Meshing/">Singularity-Constrained Octahedral Fields for Hexahedral Meshing</a>
<a href="/2021/03/17/2020-03-09-Singularity-Constrained-Octahedral-Fields-for-Hexahedral-Meshing/" class="index-excerpt">
<div>1.概括  枚举了所有六面体网格中关于边的度的局部属性；推广了Hopf-Poincare index formula至octahedral fields;设计了一个通过求解非线性整形优化从一个预输入的奇异结构图生成一个优化后的octahedral field的算法。
2.拓扑关系2.1 Local Topology of Eages
$$
\operatorname{</div>
</a>
<div class="index-btm post-metas">
<div class="post-meta mr-3">
<i class="iconfont icon-date"></i> 2021-03-17
</div>
<div class="post-meta mr-3">
<i class="iconfont icon-category"></i>
<a href="/categories/%E7%AC%94%E8%AE%B0/">笔记</a>
</div>
<div class="post-meta">
<i class="iconfont icon-tags"></i>
<a href="/tags/%E6%A0%87%E6%9E%B6%E5%9C%BA/">标架场</a>
</div>
</div>
</div>
</div>
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<div class="col-12 col-md-12 mx-auto index-info">
<a class="index-header" href="/2020/10/30/2020-10-30-Algebraic-Representations-for-Volumetric-Frame-Fields(%E4%B8%80)/">Algebraic Representations for Volumetric Frame Fields(一)</a>
<a href="/2020/10/30/2020-10-30-Algebraic-Representations-for-Volumetric-Frame-Fields(%E4%B8%80)/" class="index-excerpt">
<div>1.解空间  定义映射\rho:SO(3)\to SO(9),定义线性算子H \in \mathbb{R}^{9\times 9}投影至\mathbb{R}^9的子空间（即在八面体群作用下具有不变性的空间）
H=\frac{1}{|O|}\sum_{o \in O}\rho(o)由于
\rho\left(o^{\prime}\right) H=\frac{1}{|\math</div>
</a>
<div class="index-btm post-metas">
<div class="post-meta mr-3">
<i class="iconfont icon-date"></i> 2020-10-30
</div>
<div class="post-meta mr-3">
<i class="iconfont icon-category"></i>
<a href="/categories/%E7%AC%94%E8%AE%B0/">笔记</a>
</div>
<div class="post-meta">
<i class="iconfont icon-tags"></i>
<a href="/tags/%E6%A0%87%E6%9E%B6%E5%9C%BA/">标架场</a>
</div>
</div>
</div>
</div>
<div class="row mx-auto index-card">
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<a class="index-header" href="/2020/10/09/2020-10-09-Greens-identities/">Green's Identities And Boundary Element Method</a>
<a href="/2020/10/09/2020-10-09-Greens-identities/" class="index-excerpt">
<div>1.高维分部积分  回忆下最基本的分部积分
\begin{array}{c}
\int u(x) v^{\prime}(x) d x=u(x) v(x)-\int u^{\prime}(x) v(x) d x \\
\int u d v=u v-\int v d u
\end{array}  对于高维，无非是多了基底，对每个基的方向使用分部积分
\beg</div>
</a>
<div class="index-btm post-metas">
<div class="post-meta mr-3">
<i class="iconfont icon-date"></i> 2020-10-09
</div>
<div class="post-meta mr-3">
<i class="iconfont icon-category"></i>
<a href="/categories/%E7%AC%94%E8%AE%B0/">笔记</a>
</div>
<div class="post-meta">
<i class="iconfont icon-tags"></i>
<a href="/tags/math/">math</a>
</div>
</div>
</div>
</div>
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<a class="index-header" href="/2020/10/07/2020-10-07-Boundary-Element-Octahedral-Fields-in-Volumes/">Boundary Element Octahedral Fields in Volumes</a>
<a href="/2020/10/07/2020-10-07-Boundary-Element-Octahedral-Fields-in-Volumes/" class="index-excerpt">
<div>1.概括  将3D中的标架场描述为Octahedral Fields：三维中所有旋转构成群特殊正交群SO(3),但由于若只用向量表示，一个标架可有24个表示，其恰构成好八面体群O，因此若想唯一的标识标架，应该为SO(3)/O，而球谐基函数恰好可为其作代数表示。不同的是采用了边界元的思想，故而在求解中输入的网格只需要边界即可，如三角形网格，而不再是四面体网格。同时对于约束问题，之</div>
</a>
<div class="index-btm post-metas">
<div class="post-meta mr-3">
<i class="iconfont icon-date"></i> 2020-10-07
</div>
<div class="post-meta mr-3">
<i class="iconfont icon-category"></i>
<a href="/categories/%E7%AC%94%E8%AE%B0/">笔记</a>
</div>
<div class="post-meta">
<i class="iconfont icon-tags"></i>
<a href="/tags/%E6%A0%87%E6%9E%B6%E5%9C%BA/">标架场</a>
</div>
</div>
</div>
</div>
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<a class="index-header" href="/2020/09/17/2020-09-17-Practical-3D-Frame-Field-Generation-3D/">Practical 3D Frame Field Generation-3D</a>
<a href="/2020/09/17/2020-09-17-Practical-3D-Frame-Field-Generation-3D/" class="index-excerpt">
<div>  作者在前文的2d形式下引入的基函数其实是傅里叶基底，而在3d下，根据《Boundary aligned smooth 3D cross-frame field》的启发，使用了球谐函数作为基函数。不同的是该文使用了不同的多项式x^4+y^4+z^4来在球上展开。（而前文是x^2y^2+y^2z^2+z^2x^2，其实优化后式子是一样的）
二、3D1. 标架表示 &e</div>
</a>
<div class="index-btm post-metas">
<div class="post-meta mr-3">
<i class="iconfont icon-date"></i> 2020-09-17
</div>
<div class="post-meta mr-3">
<i class="iconfont icon-category"></i>
<a href="/categories/%E7%AC%94%E8%AE%B0/">笔记</a>
</div>
<div class="post-meta">
<i class="iconfont icon-tags"></i>
<a href="/tags/%E6%A0%87%E6%9E%B6%E5%9C%BA/">标架场</a>
</div>
</div>
</div>
</div>
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<a class="index-header" href="/2020/09/16/2020-09-16-Boundary-Aligned-Smooth-3D-Cross-Frame-Field/">Boundary Aligned Smooth 3D Cross-Frame Field</a>
<a href="/2020/09/16/2020-09-16-Boundary-Aligned-Smooth-3D-Cross-Frame-Field/" class="index-excerpt">
<div>标架表示方法  3d标架存在24个方向（坐标轴有6个选择，垂直它的有4种，即6x4=24种），为了表述两个相邻标架的差异，采用基函数来表示四面体网格面上的标架，而不是采用以前的使用vector pair来表示（避免了混合整数规划问题）,该文首先提出了采用球谐函数作为基函数来描述标架,从而可以通过积分来描述标架的差异并据此定义能量函数来优化 ，最后使用L-BFGS来光滑标架场，该</div>
</a>
<div class="index-btm post-metas">
<div class="post-meta mr-3">
<i class="iconfont icon-date"></i> 2020-09-16
</div>
<div class="post-meta mr-3">
<i class="iconfont icon-category"></i>
<a href="/categories/%E7%AC%94%E8%AE%B0/">笔记</a>
</div>
<div class="post-meta">
<i class="iconfont icon-tags"></i>
<a href="/tags/%E6%A0%87%E6%9E%B6%E5%9C%BA/">标架场</a>
</div>
</div>
</div>
</div>
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<a class="index-header" href="/2020/09/16/2020-09-16-Paper-Introduction/">Paper Introduction</a>
<a href="/2020/09/16/2020-09-16-Paper-Introduction/" class="index-excerpt">
<div>1. 标架场《Instant field-aligned meshes》-2015  采用局部的高斯赛德尔迭代来求解表面网格的标架场和位置场，其在局部直接暴力比较（搜索空间其实很小，以4-Rosy为例，只有16）两个标架的不同来进行优化，并用多分辨率层次法（Multiresolution hierarchy）来避免陷入局部解，该方法速度快，鲁棒性好。笔记1，笔记2
Wenzel</div>
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<i class="iconfont icon-date"></i> 2020-09-16
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<a href="/categories/%E7%AC%94%E8%AE%B0/">笔记</a>
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<a href="/tags/%E8%AE%BA%E6%96%87%E7%AE%80%E4%BB%8B/">论文简介</a>
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<a class="index-header" href="/2020/09/14/2020-09-14-Practical-3D-Frame-Field-Generation-2D/">Practical 3D Frame Field Generation-2D</a>
<a href="/2020/09/14/2020-09-14-Practical-3D-Frame-Field-Generation-2D/" class="index-excerpt">
<div>  该论文以基函数来描述标架，首先说明了该方法在2D下的可行性，然后拓展到3D形式。3D形式延续《Boundary aligned smooth 3D cross-frame field》中使用球谐函数作为基函数，不同的是该文使用了不同的多项式x^4+y^4+z^4来在球上展开，并重新定义了目标函数，优化了求解，速度和质量都得到提升。
一、 2D1.定义  </div>
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<i class="iconfont icon-date"></i> 2020-09-14
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<a href="/categories/%E7%AC%94%E8%AE%B0/">笔记</a>
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<a href="/tags/%E6%A0%87%E6%9E%B6%E5%9C%BA/">标架场</a>
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