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# For nonzero <math>p_k</math>, <math>u = \frac{q_k}{p_k}</math> gives the intersection point.
# For each line, calculate <math>u_1</math> and <math>u_2</math>. For <math>u_1</math>, look at boundaries for which <math>p_k < 0</math> (i.e. outside to inside). Take <math>u_1</math> to be the largest among <math>\left\{ 0,\frac{q_k}{p_k} \right\}</math>. For <math>u_2</math>, look at boundaries for which <math>p_k > 0</math> (i.e. inside to outside). Take <math>u_2</math> to be the minimum of <math>\left\{ 1, \frac{q_k}{p_k} \right\}</math>. If <math>u_1 > u_2</math>, the line is outside and therefore rejected.
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C++ implementation of Liang Barsky
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void liangBarsky(double x1, double y1, double x2, double y2)
{
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3,10
double dx = x2 - x1, dy = y2 - y1;
double u1 = 0.0, u2 = 1.0;
double p[5],q[5];
p[1] = -dx;
p[2] = dx;
p[3] = -dy;
p[4] = dy;
q[1] = x1 - xmin;
q[2] = xmax - x1;
q[3] = y1 - ymin;
q[4] = ymax - y1;
for(int i = 1; i<=4 ; i++)
{
if(p[i]==0 && q[i]<0)
return;
}
double r;
for(int i = 1 ; i<=4 ; i++)
{
r = q[i]/p[i];
if(p[i]<0)
u1 = u1>r?u1:r;
if(p[i]>0)
u2 = u2<r?u2:r;
}
if(u2<1.0)
{
x2 = x1 + u2*dx;
y2 = x1 + u2*dy;
}
if(u1>0.0)
{
x1 = x1 + u1*dx;
y1 = y1 + u1*dy;
}
drawLine(x0, y0, x1, y1);
}
==See also==
Algorithms used for the same purpose:
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