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/*
* Implementation of the techniques described in †.
*
* † Tom Duff, James Burgess, Per Christensen, Christophe Hery, Andrew
* Kensler, Max Liani, and Ryusuke Villemin, Building an Orthonormal
* Basis, Revisited, Journal of Computer Graphics Techniques (JCGT), vol. 6,
* no. 1, 1-8, 2017. Available online at http://jcgt.org/published/0006/01/01/
*/
#include <u.h>
#include <libc.h>
typedef struct Vec Vec;
struct Vec {
double x, y, z;
};
vlong t0;
Vec
Vect(double x, double y, double z)
{
return (Vec){x, y, z};
}
void
frisvadONB(Vec b[3])
{
double p, q;
if(b[0].z < -0.9999999){ /* handle singularity */
b[1] = Vect(0, -1, 0);
b[2] = Vect(-1, 0, 0);
return;
}
p = 1/(1 + b[0].z);
q = -b[0].x*b[0].y*p;
b[1] = Vect(1 - b[0].x*b[0].x*p, q, -b[0].x);
b[2] = Vect(q, 1 - b[0].y*b[0].y*p, -b[0].y);
}
void
revisedONB(Vec b[3])
{
double p, q;
if(b[0].z < 0){
p = 1/(1 - b[0].z);
q = b[0].x*b[0].y*p;
b[1] = Vect(1 - b[0].x*b[0].x*p, -q, b[0].x);
b[2] = Vect(q, b[0].y*b[0].y*p - 1, -b[0].y);
return;
}
p = 1/(1 + b[0].z);
q = -b[0].x*b[0].y*p;
b[1] = Vect(1 - b[0].x*b[0].x*p, q, -b[0].x);
b[2] = Vect(q, 1 - b[0].y*b[0].y*p, -b[0].y);
}
void
revisedaONB(Vec b[3])
{
double p, q, σ;
σ = b[0].z >= 0 ? 1 : -1;
p = -1/(σ + b[0].z);
q = b[0].x*b[0].y*p;
b[1] = Vect(1 + σ*b[0].x*b[0].x*p, σ*q, -σ*b[0].x);
b[2] = Vect(q, σ + b[0].y*b[0].y*p, -b[0].y);
}
void
usage(void)
{
fprint(2, "usage: %s x y z\n", argv0);
exits("usage");
}
void
main(int argc, char *argv[])
{
Vec b[3];
int i;
ARGBEGIN{
default: usage();
}ARGEND;
if(argc != 3)
usage();
b[0].x = strtod(argv[0], nil);
b[0].y = strtod(argv[1], nil);
b[0].z = strtod(argv[2], nil);
//b[0] = Vect(0.00038527316, 0.00038460016, -0.99999988079);
t0 = nsec();
frisvadONB(b);
print("Frisvad's (took %lldns)\n", nsec()-t0);
for(i = 0; i < nelem(b); i++)
print("\tB%d [%g %g %g]\n", i+1, b[i].x, b[i].y, b[i].z);
t0 = nsec();
revisedONB(b);
print("Revised (took %lldns)\n", nsec()-t0);
for(i = 0; i < nelem(b); i++)
print("\tB%d [%g %g %g]\n", i+1, b[i].x, b[i].y, b[i].z);
t0 = nsec();
revisedaONB(b);
print("Revised Adv. (took %lldns)\n", nsec()-t0);
for(i = 0; i < nelem(b); i++)
print("\tB%d [%g %g %g]\n", i+1, b[i].x, b[i].y, b[i].z);
exits(nil);
}
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