GEODE_COLD GEODE_PURE static inline bool triangle_oriented_sentinels(Perturbed2 x0, Perturbed2 x1, Perturbed2 x2) {
// Move large sentinels last
bool parity = 0;
COMPARATOR(0,1)
COMPARATOR(1,2)
COMPARATOR(0,1)
// Triangle orientation tests reduce to segment vs. direction and direction vs. direction when infinities are involved
return parity ^ (!is_sentinel(x1) ? segment_to_direction_oriented(x0,x1,x2) // one sentinel
: directions_oriented( x1,x2)); // two or three sentinels
}
// Test whether an edge containing sentinels is Delaunay
GEODE_COLD GEODE_PURE static inline bool is_delaunay_sentinels(Perturbed2 x0, Perturbed2 x1, Perturbed2 x2, Perturbed2 x3) {
// Unfortunately, the sentinels need to be at infinity for purposes of Delaunay testing, and our SOS predicates
// don't support infinities. Therefore, we need some case analysis. First, we move all the sentinels to the end,
// sorted in decreasing order of index. Different sentinels will be placed at different orders of infinity,
// with earlier indices further away, so our order will place larger infinities last.
bool parity = 0;
COMPARATOR(0,1)
COMPARATOR(2,3)
COMPARATOR(0,2)
COMPARATOR(1,3)
COMPARATOR(1,2)
if (!is_sentinel(x2)) // One infinity: A finite circle contains infinity iff it is inside out, so we reduce to an orientation test
return parity^triangle_oriented(x0,x1,x2);
else if (!is_sentinel(x1)) // Two infinities: also an orientation test, but with the last point at infinity
return parity^segment_to_direction_oriented(x0,x1,x2);
else // Three infinities: the finite point no longer matters.
return parity^directions_oriented(x1,x2);
}
void EXPR_TAIL(void){
/*expr_tail = comparator simpexpr | epsilon*/
switch(l){
case EQ: case NEQ: case LEQ: case GEQ: case LSS: case GRT: COMPARATOR(); SIMPEXPR(); return;
case ')': case ';': case ',' /*follow(EXPR_TAIL)*/: return;
default: StdError(__func__);
}
}
