http://alecjacobson.com/art/digital/

http://alecjacobson.com/art/

## Archive for July, 2010

### statutet

Saturday, July 31st, 2010### Contiguous United States of America

Saturday, July 31st, 2010### 40 close

Saturday, July 24th, 2010### 40

Saturday, July 24th, 2010### Real time tester

Thursday, July 22nd, 2010

I’ve adapted an old applet to function as a real time tester. The idea being that you hear a new graphics algorithm is “real-time” or “interactive” because it runs in only “59ms” per frame, but your internal clock isn’t accurate enough to really know what that feels like. Here you can specify the simulated “solve” time and drag around the bezier curve as if hard-core math is going on between frames.

### Extracting entries at multiple indices from std::vectors in c++, from zipped matrices

Tuesday, July 20th, 2010As a naturally follow up to my last post, I have extended my C++ implementation of matlab like array indexing to work for “zipped matrices”. I often store matrices zipped into std::vectors, column-wise. Now I can access them like how I do in matlab. Suppose in matlab I had:

```
A = [10,11,12;13,14,15];
```

You could then suck out a re-ordered block of rows and columns of the matrix by calling:

```
B = A([1],[3,2]);
```

Revealing:

```
B =
12 11
```

This is especially convenient for chopping up and reordering rows and columns in linear systems.

I can do this same sort of indexing with C++, the caveat being that I have to pass the number of columns as a third argument. For now, I think I would rather do this than have it be a field of the SmartMatrix.

```
#include <vector>
#include <stdio.h>
template<typename T>
class SmartMatrix: public std::vector<T>{
public:
// act like operator[]
T operator()(
size_t _row,
size_t _col,
size_t number_of_columns){
return (*this)[_row*number_of_columns+_col];
}
// act like matlab operator()
SmartMatrix<T> operator()(
std::vector<size_t>& row_positions,
std::vector<size_t>& column_positions,
size_t number_of_columns){
SmartMatrix<T> sub;
sub.resize(row_positions.size()*column_positions.size());
size_t sub_i = 0;
for(
std::vector<size_t>::iterator rpit = row_positions.begin();
rpit != row_positions.end();
rpit++,sub_i++){
size_t sub_j = 0;
for(
std::vector<size_t>::iterator cpit = column_positions.begin();
cpit != column_positions.end();
cpit++,sub_j++){
sub[sub_i*column_positions.size() + sub_j] =
(*this)[(*rpit)*number_of_columns + (*cpit)];
}
}
return sub;
}
};
int main(){
SmartMatrix<int> A;
size_t cols_in_A = 3;
size_t rows_in_A = 2;
A.push_back(10);
A.push_back(11);
A.push_back(12);
A.push_back(13);
A.push_back(14);
A.push_back(15);
A.push_back(16);
printf("A=\n");
for(int i=0;i<rows_in_A;i++){
for(int j=0;j<cols_in_A;j++)
printf("%d ",A[i*cols_in_A+j]);
printf("\n");
}
printf("\nA[%d,%d]=%d\n",0,2,A(0,2,cols_in_A));
// make some list of indices
std::vector<size_t> sub_row_indices;
sub_row_indices.push_back(0);
std::vector<size_t> sub_column_indices;
sub_column_indices.push_back(2);
sub_column_indices.push_back(1);
// use operator() to extract entries at those indices
SmartMatrix<int> B = A(sub_row_indices,sub_column_indices,cols_in_A);
printf("\nB = A([ ");
for(int i =0;i<sub_row_indices.size();i++)
printf("%d ",(int)sub_row_indices[i]);
printf("],[ ");
for(int i =0;i<sub_column_indices.size();i++)
printf("%d ",(int)sub_column_indices[i]);
printf("]);\n\n");
printf("B=\n");
for(int i=0;i<sub_row_indices.size();i++){
for(int j=0;j<sub_column_indices.size();j++)
printf("%d ",B[i*sub_column_indices.size()+j]);
printf("\n");
}
return 0;
}
```

Which should output:

```
A=
10 11 12
13 14 15
A[0,2]=12
B = A([ 0 ],[ 2 1 ]);
B=
12 11
```

### Extracting entries at multiple indices from std::vectors in c++

Tuesday, July 20th, 2010I’ve been doing some C++ coding, working with matrices. In a previous project it was convenient to think of our systems in block form. This translates easily into matlab’s indexing. So say you have in matlab:

```
a = [10,11,12,13,14,15];
```

Then you can extract elements 1,3,5 (remember matlab is one-indexed) by calling

```
b = a([1,3,5]);
```

which reveals

```
b =
10 12 14
```

So in C++, I’ve made my first attempt at useful templating to extend the std::vector class to have this feature. It is no where near implemented the full features of matlab’s operator(), but it seems to do this particular feature correctly.

```
#include <vector>
#include <stdio.h>
template<typename T>
class SmartVector : public std::vector<T>{
public:
// act like operator[]
T operator()(size_t _Pos){
return (*this)[_Pos];
}
// act like matlab operator()
SmartVector<T> operator()(std::vector<size_t>& positions){
SmartVector<T> sub;
sub.resize(positions.size());
size_t sub_i = 0;
for(
std::vector<size_t>::iterator pit = positions.begin();
pit != positions.end();
pit++,sub_i++){
sub[sub_i] = (*this)[*pit];
}
return sub;
}
};
int main(){
// make some vector
SmartVector<int> a;
a.push_back(10);
a.push_back(11);
a.push_back(12);
a.push_back(13);
a.push_back(14);
a.push_back(15);
for(int i =0;i<a.size();i++)
printf("a[%d] = %d\n",i,a[i]);
// make some list of indices
std::vector<size_t> sub_indices;
sub_indices.push_back(0);
sub_indices.push_back(2);
sub_indices.push_back(4);
// use operator() to extract entries at those indices
SmartVector<int> b = a(sub_indices);
printf("\nb = a([ ");
for(int i =0;i<sub_indices.size();i++)
printf("%d ",(int)sub_indices[i]);
printf("]);\n\n");
for(int i =0;i<b.size();i++)
printf("b[%d] = %d\n",i,b[i]);
return 0;
}
```

Then if you run ./main you should see:

```
a[0] = 10
a[1] = 11
a[2] = 12
a[3] = 13
a[4] = 14
a[5] = 15
b = a([ 0 2 4 ]);
b[0] = 10
b[1] = 12
b[2] = 14
```

### Boston T map, single image iphone app

Sunday, July 18th, 2010I made this app to test my new make your own single image iphone app feature. Like all single image apps made with the new feature, this app is fully cached when you add it to your iphone’s homescreen. So that means that you can use it in the subway when you don’t have internet connection.

### Academic site

Sunday, July 18th, 2010I have *finally* put up a separate academic site: http://cs.nyu.edu/~jacobson. There I’ll list publications, project pages, research interests and various work/school related addresses.

### mixed fem google images search

Sunday, July 18th, 2010I was mindlessly searching on google for “mixed fem”, as in “Mixed Finite Elements Method”, and when I switched to searching images I was surprised by the results:

Textbook covers, heat maps, marijuana and semi-nude wrestling. See for yourself!