virtual studio 구현: cross ratio test

cross ratio test


Try #1. pi 값 이용

pi = 3.14159265358979323846264338327950288...
pi 값을 이용하여 cross ratio를 구해 보면, 다음과 같이 나온다.

// cross ratio test 
// to design a pattern to be used in real-time virtual studio
// lym 2010-02-25

#include <iostream>
#include <cstring>
using namespace std;


int main (int argc, char * const argv[]) {
   
    string pi ("314159265358979323846264338327950288");
//    cout << "The size of str is " << pi.size() << endl;
    int number = pi.size();
   
    int p[number];
    for( int n = 0; n < number; n++ )
    {
        p[n] = (pi[n]) - 48 + 1;
        cout << p[n] << " ";
    }
    cout << endl;   

    int a = 0;
    int b = 0;
    int c = 0;
    int d = 0;
    double cross_ratio = 0.0;
   
    for( int n = 0; n < number-3; n++ )
    {
//        cout << "n = " << n << endl;
       
        a = p[n];
        b = a + p[n+1];
        c = b + p[n+2];
        d = c + p[n+3];

//        cout << "a=" << a << " b=" << b << " c=" << c << " d=" << d << endl;

        cross_ratio = double( (c-a)*(d-b) ) / double( (d-a)*(c-b) );
       
//        cout << "cross ratio = " << cross_ratio << endl;
        printf("cross ratio = %f\n", cross_ratio);
    }
       
    return 0;
}

cross ratio = 1.088889
cross ratio = 2.153846
cross ratio = 1.185185
cross ratio = 1.094737
cross ratio = 2.166667
cross ratio = 1.160714
cross ratio = 1.274510
cross ratio = 1.562500
cross ratio = 1.315789
cross ratio = 1.266667
cross ratio = 1.266667
cross ratio = 1.446429
cross ratio = 1.145455
cross ratio = 1.441176
cross ratio = 1.484848
cross ratio = 1.421875
cross ratio = 1.123457
cross ratio = 1.600000
cross ratio = 1.142857
cross ratio = 1.960784
cross ratio = 1.142857
cross ratio = 1.350000
cross ratio = 1.384615
cross ratio = 1.529412
cross ratio = 1.104575
cross ratio = 1.421875
cross ratio = 1.711111
cross ratio = 1.178571
cross ratio = 1.200000
cross ratio = 1.098039
cross ratio = 2.800000
cross ratio = 1.230769
cross ratio = 1.142857

다른 식 적용

cross ratio = 0.040000
cross ratio = 0.666667
cross ratio = 0.107143
cross ratio = 0.064935
cross ratio = 0.613636
cross ratio = 0.113636
cross ratio = 0.204545
cross ratio = 0.390625
cross ratio = 0.230769
cross ratio = 0.203620
cross ratio = 0.205882
cross ratio = 0.316406
cross ratio = 0.109375
cross ratio = 0.300000
cross ratio = 0.360000
cross ratio = 0.290909
cross ratio = 0.090909
cross ratio = 0.400000
cross ratio = 0.100000
cross ratio = 0.562500
cross ratio = 0.100000
cross ratio = 0.257143
cross ratio = 0.285714
cross ratio = 0.363636
cross ratio = 0.074380
cross ratio = 0.290909
cross ratio = 0.466667
cross ratio = 0.125000
cross ratio = 0.156250

Try #2. swPark_2000rti: 43p: figure 7의 cross ratio 값들로 패턴의 그리드 (격자 위치)를 역추산
 
40개의 수직선에 대한 37개의 cross ratio :
0.47, 0.11, 0.32, 0.17, 0.44, 0.08, 0.42, 0.25, 0.24, 0.13, 0.46, 0.18, 0.19, 0.29, 0.21, 0.37, 0.16, 0.38, 0.23, 0.09, 0.37, 0.26, 0.31, 0.18, 0.30, 0.15, 0.39, 0.16, 0.32, 0.27, 0.20, 0.28, 0.39, 0.12, 0.23, 0.28, 0.35
20개의 수평선에 대한 17개의 cross ratio :
0.42, 0.13, 0.32, 0.16, 0.49, 0.08, 0.40, 0.20, 0.29, 0.19, 0.37, 0.13, 0.26, 0.38, 0.21, 0.16, 0.42

/* Test: pattern design in implementing a virtual studio
 to design grid lines using cross-ratio as represented in "swPark_2000rti": (16)
 C(x1,x2,x3,x4) = (x2-x1)(x4-x3) / (x4-x2)(x3-x1)
 based on two plots in figure 7, 439p
 2010, lym
 */
 
#include <iostream>
using namespace std;

int main (int argc, char * const argv[]) {

    // ref. swPark_2000rti: 43p: figure 7
    // 37 consecutive cross-ratios for 40 vertical lines
    double crossratio_vertical[] = { 0.47, 0.11, 0.32, 0.17, 0.44, 0.08, 0.42, 0.25, 0.24, 0.13,
        0.46, 0.18, 0.19, 0.29, 0.21, 0.37, 0.16, 0.38, 0.23, 0.09, 0.37, 0.26, 0.31, 0.18,
    0.30, 0.15, 0.39, 0.16, 0.32, 0.27, 0.20, 0.28, 0.39, 0.12, 0.23, 0.28, 0.35 };   
    // 17 consecutive cross-ratios for 20 horizontal lines
    double crossratio_horizontal[] = { 0.42, 0.13, 0.32, 0.16, 0.49, 0.08, 0.40, 0.20, 0.29, 0.19,
    0.37, 0.13, 0.26, 0.38, 0.21, 0.16, 0.42 };
   
    cout << "# of cross-ratios in vertical lines = " << sizeof(crossratio_vertical) / sizeof(double) << endl;
    cout << "# of cross-ratios in horizontal lines = " << sizeof(crossratio_horizontal) / sizeof(double) << endl;

    // initialize grid lines of the pattern
    double x[40] = { 0.0 }; // 40 vertical lines
    double y[20] = { 0.0 }; // 20 horizontal lines
    double r = 0.0; // cross ratio of 4 consecutive lines
    double a,b,c,d; // temporary variables to be used in calculating a cross ratio 

    // set the positions of the first three vertical lines
    x[0] = 1.0;
    x[1] = x[0] + 1.0;
    x[2] = x[1] + 2.0;
   
    // set the positions of the first three horizontal lines
    y[0] = 1.0;
    y[1] = y[0] + 2.0;
    y[2] = y[1] + 1.0;
   
    // for vertical lines
    int number = 40;
    cout << endl << "x[0]=" << x[0] << "  x[1]=" << x[1] << "  x[2]=" << x[2] << endl;
    for( int n = 0; n < number-3; n++ )
    {
//        cout << "n = " << n << endl;
       
        r = crossratio_vertical[n];
 /*       a = x[n];
        b = x[n+1];
        c = x[n+2];
       
//        cout << "a=" << a << " b=" << b << " c=" << c << " ratio =" << r;
       
        d = ( (b-a)*c - (c-a)*b*r ) / ( (b-a) - (c-a)*r ) ;
       
//        cout << "  ==> d= " << d << endl;
   
        x[n+3] = d;
*/   
        double son = (x[n+1]-x[n])*x[n+2] - r*(x[n+2]-x[n])*x[n+1];
        double mom = x[n+1] - x[n] - r*(x[n+2]-x[n]);
        x[n+3] = son / mom;
       
        cout << "x[" << n+3 << "]=" << x[n+3] << "  ";
    }
    return 0;
}

뭥미?????

# of cross-ratios in vertical lines = 37
# of cross-ratios in horizontal lines = 17

x[0]=1  x[1]=2  x[2]=4
x[3]=-2.87805  x[4]=-1.42308  x[5]=-0.932099  x[6]=-0.787617  x[7]=-0.596499  x[8]=-0.55288  x[9]=-0.506403  x[10]=-0.456778  x[11]=-0.407892  x[12]=-0.390887  x[13]=-0.363143  x[14]=-0.338174  x[15]=-0.324067  x[16]=-0.312345  x[17]=-0.305022  x[18]=-0.293986  x[19]=-0.286594  x[20]=-0.273759  x[21]=-0.251966  x[22]=-0.244977  x[23]=-0.238299  x[24]=-0.231391  x[25]=-0.219595  x[26]=-0.20838  x[27]=-0.192558  x[28]=-0.183594  x[29]=-0.16952  x[30]=-0.159689  x[31]=-0.147983  x[32]=-0.131036  x[33]=-0.114782  x[34]=-0.0950305  x[35]=0.0303307  x[36]=0.964201  x[37]=-0.959599  x[38]=-0.519287  x[39]=-0.356521