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didnt read it. I've seen less complex functions work and not work neagtive-wise,
depending on the sytem. handle negs, int() instead of floor() in POV should
solve the neg issue
#macro round(f,n)
#local c = floor(pow(10.0,n));
#local d = 0.5 / c;
#local d = d + abs(f);
#local d = d * c;
#local d=floor(d);
#local d = d/c;
#if (f < 0.0) #local d = d * -1; #end
(dd)
#end
functions rain overkill mode:
#macro incenter(A,B,C)
#local a = C*vlength(A-B);
#local b = A*vlength(B-C);
#local c = B*vlength(C-A);
#local d = vlength(A-B)+
vlength(B-C)+
vlength(C-A);
#local result = (a+b+c)/d;
result
#end
#macro centroid(A,B,C)
#local result = (A+B+C)/3;
result
#end
#macro circumcenter(A,B,C)
#local a = vlength(A-B);
#local b = vlength(B-C);
#local c = vlength(C-A);
#local sp = (a+b+c)*0.5;
#local cosineR = ((b*b + c*c - a*a)/(2*b*c))*
a*b*c/(4*sqrt(sp*(sp-a)*(sp-b)*(sp-c))); //circumradius(A,B,C);
#local mp = (A+B)/2; //midpoint(A,B)
#local result = mp+(vnormalize(vcross(A-mp,vcross(C-B,A-B)))*cosineR);
result
/* "walks" to cCenter in 3D.
Algebra core step=cos(angle)*R.
Input order irrelevant since both (A-mp)
and norm vectors reverse in sync */
#end
#macro outcenter(A,B,C)
circumcenter(A,B,C)
#end
#macro ccenter(A,B,C)
circumcenter(A,B,C)
#end
#macro orthocenter(A,B,C)
#local a = vlength(A-B);
#local b = vlength(B-C);
#local c = vlength(C-A);
#local sp = (a+b+c)*0.5;
#local cosineR = ((b*b + c*c - a*a)/(2*b*c))*
a*b*c/(4*sqrt(sp*(sp-a)*(sp-b)*(sp-c))); //outeradius(a,b,c);
#local mp = (A+B)/2; //midpoint(A,B)
#local cc = mp+(vnormalize(vcross(A-mp,vcross(C-B,A-B)))*cosineR);
#local result = ((A-cc)+(B-cc)+(C-cc)) + cc;
result
#end
#macro inner_radius(A,B,C)
#local a = vlength(A-B);
#local b = vlength(B-C);
#local c = vlength(C-A);
#local result = 0.5*sqrt(((b+c-a)*(c+a-b)*(a+b-c)) / (a+b+c));
result
#end
#macro tetrahedron_volume(A,B,C,D)
#local result = abs(vdot(D-A,vcross(D-B,D-C))) / 6;
result
#end
#macro pyramid_volume(A,B,C,D,E)
// perimeter order for 1st 4 points
#local result =
tetrahedron_volume(A,B,C,E) + tetrahedron_volume(A,C,D,E);
result
#end
#macro triangle_area(A,B,C)
//2D .z must be 0
#local result = abs((B.x*A.y - A.x*B.y)+
(C.x*B.y - B.x*C.y)+
(A.x*C.y - C.x*A.y)) / 2;
result
#end
#declare inneradius = function(a,b,c) {
//(3 lens)
0.5*sqrt(((b+c-a)*(c+a-b)*(a+b-c)) / (a+b+c))
}
#macro circumradius(A,B,C)
#local a = vlength(A-B);
#local b = vlength(B-C);
#local c = vlength(C-A);
#local result = a*b*c/(4*sqrt(((a+b+c)/2)*(((a+b+c)/2)-a)*
(((a+b+c)/2)-b)*(((a+b+c)/2)-c)));
result
#end
#declare outeradius = function(a,b,c) {
//(3 lens)
a*b*c/(4*sqrt(((a+b+c)/2)*(((a+b+c)/2)-a)*(((a+b+c)/2)-b)*(((a+b+c)/2)-c)))
//(a*b*c) / (4*sss_area(a,b,c))
}
#declare sas_area = function(s,a,s2) {
0.5 * s * sin(a) * s2
}
#declare sas_cos = function(s,a,s2) {
sqrt((pow(s,2)+pow(s2,2))-2*s*s2*cos(a))
} // Side Angle Side - solve length of missing side
#declare sas_height = function(s,a,s2) {
s*sin(a)*s2/sqrt((pow(s,2)+pow(s2,2))-2*s*s2*cos(a))
//sas_area(s,a,s2) / (sas_cos(s,a,s2) * 0.5)
} // SAS height to missing side
#declare bh_area = function(b,h) {
//(base,height)
0.5 * b * h
}
#declare sss_height = function(a,b,c) {
sqrt(((a+b+c)/2)*(((a+b+c)/2)-a)*(((a+b+c)/2)-b)*(((a+b+c)/2)-c))/(b*0.5)
//sss_area(a,b,c) / (b * 0.5)
} // height to side2
#declare sss_area = function(a,b,c) {
//semi perimeter
sqrt(((a+b+c)/2)*(((a+b+c)/2)-a)*(((a+b+c)/2)-b)*(((a+b+c)/2)-c))
}
#declare vmyv = function {
//function that returns a vector
transform {
rotate <0, 0, 0>
scale 1
}
}
#declare aas_sin = function(a,b,s) {
sin(b) * (s / sin(a))
} // AAS solve opposing side of angle2 (b)
#declare asa_sin = function(a,s,b) {
sin(b) * (s / sin(pi-(a+b)))
} // ASA solve opposing side of angle2 (b)
#declare sss_cos = function(a,b,c) {
acos((pow(a,2)+pow(c,2)-pow(b,2))/(2*a*c))
} // SSS solve angle opposite side2 (b)
// if (pow(a,2)+pow(c,2)-pow(b,2))/(2*a*c) < 0 obtuse
#declare ssa_acute = function(s,s2,a) {
asin(s2*sin(a)/s)
} // SSA solve angle opposite side2
/*
alias sss_area2 {
; (3 lens)
return $calc(0.5 * ($1 + $2 + $3) * $inneradius($1,$2,$3))
}
alias sss_area3 {
; (3 lens)
return $calc(($1 * $2 * $3) / (4 * $circumradius($1,$2,$3)))
}*/
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povray