point: p
fan : | p – c | <= r, ( α<=θ<=β, r >= 0)
method(1): w = p – c
if ( w^2 > r^2 ) return outside;
assume: p1 = (r*cosα + c.x, r*sinα + c.y)
p2 = (r*cosβ + c.x, r*sinβ + c.y)
u = p1 – c
v = p2 – c
here: | u | = | v | = r, (u & v is 2 edges of the fan)
if ( r> 0 )
return inside;
method(2): w = p – c
if ( w^2 > r^2 ) return outside;
assume: β –α <= π
u = p1 – c
v = p2 – c
nu.x = -u.y;
nu.y = u.x;
if ( nu•w > 0 ) return outside;
nv.x = v.y;
nv.y = -v.x;
if ( nv•w > 0 ) return outside;
return inside;
if (β–α > π) invert the above result;
aabb: a (inf->infimum, sup->
supremum
)aabb: b
if ( a.inf.x > b.sup.x || a.inf.y > b.sup.y || a.inf.z > b.sup.z
|| a.sup.x < b.inf.x || a.sup.y < b.inf.y || a.sup.z < b.inf.z )
return intersectant;
point: p
aabb: a
if ( p.x >= a.inf.x && p.x <= a.sup.x
&& p.y >= a.inf.y && p.y <= a.sup.y
&& p.z >= a.inf.z && p.z <= a.sup.z )
return outside;
point in convex polyhedron
point: p
convex polyhedron: plane 0, plane 1, … plane n-1 (n>=3)
plane i: (pi, ni) (ni points outside of the convex polyhedron) (i >= 0 && i < n)
for ( i = n; i-- > 0; )
}return inside;
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