What is the problem addressed by the paper? How to represent smooth shapes? How to smooth surfaces? How to process rangescanned meshes? How to improv normal and boundary continuity? image credit Alexa, et al. What is the approach used to resolve the problem? In differential geometry, a smooth surface is characterized by the existence of smooth…
[Summary] The One Hundred Year Study on Artificial Intelligence: An Enduring Study on AI and its Influence on People and Society
Today, technical fellow and director at Microsoft, Dr. Horvitz gave a lecture on The One Hundred Year Study on Artificial Intelligence: An Enduring Study on AI and its Influence on People and Society; I am also fortunate to have a lunch together with Eric. He has presented an update on the One Hundred Year Study on AI, described…
FisherYates Shuffle
The correct way to do a shuffle is to choose a random other index to fill in the current index, which is uniform:
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function getRandom(floor, ceiling) { return Math.floor(Math.random() * (ceiling  floor + 1)) + floor; } function shuffle(theArray) { // if it's 1 or 0 items, just return if (theArray.length <= 1) return; // walk through from beginning to end for (var indexWeAreChoosingFor = 0; indexWeAreChoosingFor < theArray.length; indexWeAreChoosingFor++) { // choose a random notyetplaced item to place there // (could also be the item currently in that spot) // must be an item AFTER the current item, because the stuff // before has all already been placed var randomChoiceIndex = getRandom(indexWeAreChoosingFor, theArray.length  1); // place our random choice in the spot by swapping var valueAtIndexWeChoseFor = theArray[indexWeAreChoosingFor]; theArray[indexWeAreChoosingFor] = theArray[randomChoiceIndex]; theArray[randomChoiceIndex] = valueAtIndexWeChoseFor; } } 
Also, you may need a uniform random generator in C++:
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#include <random> std::random_device rd; std::mt19937 mt(rd()); std::uniform_real_distribution<double> uniform_random(0.0, 1.0); // use as sample = uniform_random(mt); 
Protected: Optimization Using SumtoProduct Identities
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Likert Scale and Paired TTest Are Not Good Friends
Nonparametric Tests Unfortunately, it’s the first time that I learnt that Likert scale cannot be used together with ttest. According to my favorite Stat Wiki by Prof. Koji Yatani, Roughly speaking, there are two cases in which you want to use nonparametric test: Ordinal data: If your data are ordinal (like the results from Likertscale…
What are PCA and FLA / LDA?
PCA The main idea of PCA is to seek the most accurate data representation in a lower dimensional space. For a formal definition, according to Wikipedia, Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of…
What is P value?
P value is the probability that you are wrong if you reject the null hypothesis. or P value is the probability that you get equal or worse result if your experiment is right… or according to Wikipedia: For example, if you propose a hypothesis that Trump has more positive tweets than Hillary has, the your…
N Queens Problem Revisit using Bit Operations
Finally, I have some time to revisit the N queens problem using bit operations. The following functions could solve 11 queens in 1 second:
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class Solution { public: vector<vector<string>> solveNQueens(int n) { NQresult.clear(); NQpath.clear(); NQn = n; NQtotal = 0; bitNQueens(0, 0, 0); cout << NQtotal << endl; return NQresult; } private: /** [Q..... row = 101010 ..Q... ld = 100100 ....Q. rd = 000111 ......] or = 101111 pos = 010000 => p = (010000) & (110000) = 010000 => pos = 0; [Q..... row = 111010 ..Q... ld = 011000 ....Q. rd = 000111 .Q....] **/ vector<vector<string>> NQresult; vector<int> NQpath; int NQtotal; int NQn; void addNQueenSolution() { vector<string> v; for (int i = 0; i < NQn; ++i) v.push_back(string(NQn, '.')); for (int i = 0; i < NQn; ++i) { v[i][NQpath[i]] = 'Q'; //cout << v[i] << endl; } //cout << endl; NQresult.push_back(v); } // col: whether this col is occupied // ld: left diagnal for the current row // rd: right diagnal for the current row void bitNQueens(int col, int ld, int rd) { int allOccupied = (1 << NQn)  1; if (col == allOccupied) { ++NQtotal; addNQueenSolution(); return; } int pos = allOccupied & (~(col  ld  rd)); while (pos != 0) { int p = pos & (pos); // which way to go pos = pos  p; // get the rightmost 1 of position position NQpath.push_back(p == 1 ? 0 : (int)round(log(p) / log(2))); bitNQueens(col + p, (ld + p) << 1, (rd + p) >> 1); NQpath.pop_back(); } } }; 
So far to me, this is the most efficient algorithm for N queens. The code is mostly selfexplenary. Please comment if anything cannot be understood.
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// col: whether this col is occupied // ld: left diagnal for the current row // rd: right diagnal for the current row 
Simplest and Fatest GLSL Edge Detection using Fwidth
Yesterday, I read 834144373’s ShaderToy code which did Edge Detection in 97 chars, it was really simple and fast:
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void mainImage(out vec4 o, vec2 u) { o = o  length(fwidth(texture2D(iChannel0,u/iResolution.xy)))*3.; } 
However, the result is astonishingly good: Let’s expand the code a little bit:
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void mainImage(out vec4 fragColor, vec2 fragCoord) { vec2 uv = fragCoord / iResolution.xy; fragColor = length(fwidth(texture2D(iChannel0, uv))) * vec4(3.); } 
According to OpenGL manual: fwidth means abs(dFdx(p)) + abs(dFdy(p)) and fwidthFine is equivalent to abs(dFdxFine(p)) + abs(dFdyFine(p)). One can use a sigmoid function to increase the…
How to Measure Execution Time in C++ 11
Here are my code snippets to measure execution time in C++ as a DebugTimer:
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#pragma once #include <map> #include <string> #include <chrono> #include <iostream> using namespace std; #define DEBUG_TIMER_ON static class DebugTimer { private: static map<string, chrono::steady_clock::time_point> Map; public: static void Begin(string label = ""); static void End(string label = ""); }; 
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#include "DebugTimer.h" map<string, chrono::steady_clock::time_point> DebugTimer::Map; void DebugTimer::Begin(string label) { #ifdef DEBUG_TIMER_ON Map[label] = chrono::steady_clock::now(); #endif // DEBUG_TIMER_ON } void DebugTimer::End(string label) { #ifdef DEBUG_TIMER_ON auto end = chrono::steady_clock::now(); auto diff = end  Map[label]; cout << "[" << label << "]\t" << chrono::duration <double, milli>(diff).count() << " ms" << endl; #endif // DEBUG_TIMER_ON } 
It’s a static class so it’s very easy to use:
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DebugTimer::Begin("your_label"); // your_function DebugTimer::End("your_label"); 
That’s it!
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