Please help me implement clip.cpp in c$++$: #include

#include

#include

#include

#include "vec.h$"$

static std::random$\_$device rd;

static std::mt$19937$ mt$($rd$())$;

static std::uniform$\_$real$\_$distribution$<>$ dist$(0,1)$;

inline double get$\_$rand$()\{$return dist$($mt$)$;$\}$

static std::uniform$\_$int$\_$distribution idist$(0,$ std::mt$19937$::max$())$;

inline unsigned rand$\_$int$()\{$return idist$($mt$)$;$\}$

template void fill$\_$rand$($vec& u$,$double a$,$double b$)$

$\{$

for$($int i$=0$;i Clip$($const Triangle& tri$)$;

inline bool in$($const vec$4$& p$)$

$\{$

for$($int i$=0$;i$<3$;i$++)$

if$($std::abs$($p$[$i$])>1\mathrm{.}00001*$p$[3])$

return false;

return true;

$\}$

inline vec$3$ to$\_$vec$3($const vec$4$& p$)$

$\{$

return vec$3($p$[0],$p$[1],$p$[2])/$p$[3]$;

$\}$

inline bool pt$\_$in$\_$tri$($const Triangle& t$,$ const vec$4$& p$)$

$\{$

vec$3$ ta$=$to$\_$vec$3($t$.$A$),$u$=$to$\_$vec$3($t$.$B$)-$ta$,$v$=$to$\_$vec$3($t$.$C$)-$ta$,$w$=$to$\_$vec$3($p$)-$ta;

vec$3$ n$=$cross$($u$,$v$)$;

double a$=$dot$($w$,$cross$($v$,$n$))/$dot$($n$,$n$)$;

double b$=$dot$($w$,$cross$($n$,$u$))/$dot$($n$,$n$)$;

double c$=$std::abs$($dot$($n$,$w$))$;

return c$<1$e$-4$ && a$>=-1$e$-4$ && b$>=-1$e$-4$ && a$+$b$<=1+1$e$-4$;

$\}$

int main$($int argc, char$*$ argv$[])$

$\{$

bool pass $=$ true;

for$($int i$=0$;i$<1000$;i$++)$

$\{$

Triangle it;

fill$\_$rand$($it$)$;

auto ct$=$Clip$($it$)$;

$//$ Make sure the clipped triangles lie entirely inside the clipping volume.

for$($const auto& t:ct$)$

$\{$

if$(!$in$($t$.$A$)||!$in$($t$.$B$)||!$in$($t$.$C$))$

$\{$

std::cout $<<$ "vertex of clipped triangle is outside clipping volume" $<<$ std::endl;

std::cout $<<$ "input $"<<$ it$.$A $<<""<<$ it$.$B $<<""<<$ it$.$C $<<$ std::endl;

std::cout $<<$ "output $"<<$ t$.$A $<<""<<$ t$.$B $<<""<<$ t$.$C $<<$ std::endl;

pass $=$ false;

break;

$\}$

$\}$

if$(!$pass$)$ break;

$//$ Sample a bunch of points on the original triangle and discard the

$//$ ones that are not in the clipping volume. Verify that the rest lie

$//$ inside some clipped triangle.

for$($int j$=0$;j$<100$;j$++)$

$\{$

double a$=$get$\_$rand$()*\mathrm{.}9+0\mathrm{.}05,$b$=($get$\_$rand$()*\mathrm{.}9+0\mathrm{.}05)*(1-$a$)$;

vec$4$ pt$=$it$.$A$+$a$*($it$.$B$-$it$.$A$)+$b$*($it$.$C$-$it$.$A$)$;

if$(!$in$($pt$))$ continue;

bool ok$=$false;

for$($const auto& t:ct$)$

if$($pt$\_$in$\_$tri$($t$,$pt$))$

ok$=$true;

if$(!$ok$)$

$\{$

std::cout $<<$ "point $"<<$ pt $<<"$ is inside original triangle and inside clipping volume but not inside any of the clipped triangles."$<$