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#include "cube.h"
static inline double det2x2(double a, double b, double c, double d) { return a*d - b*c; }
static inline double det3x3(double a1, double a2, double a3,
double b1, double b2, double b3,
double c1, double c2, double c3)
{
return a1 * det2x2(b2, b3, c2, c3)
- b1 * det2x2(a2, a3, c2, c3)
+ c1 * det2x2(a2, a3, b2, b3);
}
bool matrix4::invert(const matrix4 &m, double mindet)
{
double a1 = m.a.x, a2 = m.a.y, a3 = m.a.z, a4 = m.a.w,
b1 = m.b.x, b2 = m.b.y, b3 = m.b.z, b4 = m.b.w,
c1 = m.c.x, c2 = m.c.y, c3 = m.c.z, c4 = m.c.w,
d1 = m.d.x, d2 = m.d.y, d3 = m.d.z, d4 = m.d.w,
det1 = det3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4),
det2 = -det3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4),
det3 = det3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4),
det4 = -det3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4),
det = a1*det1 + b1*det2 + c1*det3 + d1*det4;
if(fabs(det) < mindet) return false;
double invdet = 1/det;
a.x = det1 * invdet;
a.y = det2 * invdet;
a.z = det3 * invdet;
a.w = det4 * invdet;
b.x = -det3x3(b1, b3, b4, c1, c3, c4, d1, d3, d4) * invdet;
b.y = det3x3(a1, a3, a4, c1, c3, c4, d1, d3, d4) * invdet;
b.z = -det3x3(a1, a3, a4, b1, b3, b4, d1, d3, d4) * invdet;
b.w = det3x3(a1, a3, a4, b1, b3, b4, c1, c3, c4) * invdet;
c.x = det3x3(b1, b2, b4, c1, c2, c4, d1, d2, d4) * invdet;
c.y = -det3x3(a1, a2, a4, c1, c2, c4, d1, d2, d4) * invdet;
c.z = det3x3(a1, a2, a4, b1, b2, b4, d1, d2, d4) * invdet;
c.w = -det3x3(a1, a2, a4, b1, b2, b4, c1, c2, c4) * invdet;
d.x = -det3x3(b1, b2, b3, c1, c2, c3, d1, d2, d3) * invdet;
d.y = det3x3(a1, a2, a3, c1, c2, c3, d1, d2, d3) * invdet;
d.z = -det3x3(a1, a2, a3, b1, b2, b3, d1, d2, d3) * invdet;
d.w = det3x3(a1, a2, a3, b1, b2, b3, c1, c2, c3) * invdet;
return true;
}
bool raysphereintersect(const vec ¢er, float radius, const vec &o, const vec &ray, float &dist)
{
vec c(center);
c.sub(o);
float v = c.dot(ray),
inside = radius*radius - c.squaredlen();
if(inside<0 && v<0) return false;
float d = inside + v*v;
if(d<0) return false;
dist = v - sqrt(d);
return true;
}
bool rayboxintersect(const vec &b, const vec &s, const vec &o, const vec &ray, float &dist, int &orient)
{
loop(d, 3) if(ray[d])
{
int dc = ray[d]<0 ? 1 : 0;
float pdist = (b[d]+s[d]*dc - o[d]) / ray[d];
vec v(ray);
v.mul(pdist).add(o);
if(v[R[d]] >= b[R[d]] && v[R[d]] <= b[R[d]]+s[R[d]]
&& v[C[d]] >= b[C[d]] && v[C[d]] <= b[C[d]]+s[C[d]])
{
dist = pdist;
orient = 2*d+dc;
return true;
}
}
return false;
}
bool linecylinderintersect(const vec &from, const vec &to, const vec &start, const vec &end, float radius, float &dist)
{
vec d(end), m(from), n(to);
d.sub(start);
m.sub(start);
n.sub(from);
float md = m.dot(d),
nd = n.dot(d),
dd = d.squaredlen();
if(md < 0 && md + nd < 0) return false;
if(md > dd && md + nd > dd) return false;
float nn = n.squaredlen(),
mn = m.dot(n),
a = dd*nn - nd*nd,
k = m.squaredlen() - radius*radius,
c = dd*k - md*md;
if(fabs(a) < 0.005f)
{
if(c > 0) return false;
if(md < 0) dist = -mn / nn;
else if(md > dd) dist = (nd - mn) / nn;
else dist = 0;
return true;
}
else if(c > 0)
{
float b = dd*mn - nd*md,
discrim = b*b - a*c;
if(discrim < 0) return false;
dist = (-b - sqrtf(discrim)) / a;
}
else dist = 0;
float offset = md + dist*nd;
if(offset < 0)
{
if(nd <= 0) return false;
dist = -md / nd;
if(k + dist*(2*mn + dist*nn) > 0) return false;
}
else if(offset > dd)
{
if(nd >= 0) return false;
dist = (dd - md) / nd;
if(k + dd - 2*md + dist*(2*(mn-nd) + dist*nn) > 0) return false;
}
return dist >= 0 && dist <= 1;
}
extern const vec2 sincos360[721] =
{
vec2(1.00000000, 0.00000000), vec2(0.99984770, 0.01745241), vec2(0.99939083, 0.03489950), vec2(0.99862953, 0.05233596), vec2(0.99756405, 0.06975647), vec2(0.99619470, 0.08715574), // 0
vec2(0.99452190, 0.10452846), vec2(0.99254615, 0.12186934), vec2(0.99026807, 0.13917310), vec2(0.98768834, 0.15643447), vec2(0.98480775, 0.17364818), vec2(0.98162718, 0.19080900), // 6
vec2(0.97814760, 0.20791169), vec2(0.97437006, 0.22495105), vec2(0.97029573, 0.24192190), vec2(0.96592583, 0.25881905), vec2(0.96126170, 0.27563736), vec2(0.95630476, 0.29237170), // 12
vec2(0.95105652, 0.30901699), vec2(0.94551858, 0.32556815), vec2(0.93969262, 0.34202014), vec2(0.93358043, 0.35836795), vec2(0.92718385, 0.37460659), vec2(0.92050485, 0.39073113), // 18
vec2(0.91354546, 0.40673664), vec2(0.90630779, 0.42261826), vec2(0.89879405, 0.43837115), vec2(0.89100652, 0.45399050), vec2(0.88294759, 0.46947156), vec2(0.87461971, 0.48480962), // 24
vec2(0.86602540, 0.50000000), vec2(0.85716730, 0.51503807), vec2(0.84804810, 0.52991926), vec2(0.83867057, 0.54463904), vec2(0.82903757, 0.55919290), vec2(0.81915204, 0.57357644), // 30
vec2(0.80901699, 0.58778525), vec2(0.79863551, 0.60181502), vec2(0.78801075, 0.61566148), vec2(0.77714596, 0.62932039), vec2(0.76604444, 0.64278761), vec2(0.75470958, 0.65605903), // 36
vec2(0.74314483, 0.66913061), vec2(0.73135370, 0.68199836), vec2(0.71933980, 0.69465837), vec2(0.70710678, 0.70710678), vec2(0.69465837, 0.71933980), vec2(0.68199836, 0.73135370), // 42
vec2(0.66913061, 0.74314483), vec2(0.65605903, 0.75470958), vec2(0.64278761, 0.76604444), vec2(0.62932039, 0.77714596), vec2(0.61566148, 0.78801075), vec2(0.60181502, 0.79863551), // 48
vec2(0.58778525, 0.80901699), vec2(0.57357644, 0.81915204), vec2(0.55919290, 0.82903757), vec2(0.54463904, 0.83867057), vec2(0.52991926, 0.84804810), vec2(0.51503807, 0.85716730), // 54
vec2(0.50000000, 0.86602540), vec2(0.48480962, 0.87461971), vec2(0.46947156, 0.88294759), vec2(0.45399050, 0.89100652), vec2(0.43837115, 0.89879405), vec2(0.42261826, 0.90630779), // 60
vec2(0.40673664, 0.91354546), vec2(0.39073113, 0.92050485), vec2(0.37460659, 0.92718385), vec2(0.35836795, 0.93358043), vec2(0.34202014, 0.93969262), vec2(0.32556815, 0.94551858), // 66
vec2(0.30901699, 0.95105652), vec2(0.29237170, 0.95630476), vec2(0.27563736, 0.96126170), vec2(0.25881905, 0.96592583), vec2(0.24192190, 0.97029573), vec2(0.22495105, 0.97437006), // 72
vec2(0.20791169, 0.97814760), vec2(0.19080900, 0.98162718), vec2(0.17364818, 0.98480775), vec2(0.15643447, 0.98768834), vec2(0.13917310, 0.99026807), vec2(0.12186934, 0.99254615), // 78
vec2(0.10452846, 0.99452190), vec2(0.08715574, 0.99619470), vec2(0.06975647, 0.99756405), vec2(0.05233596, 0.99862953), vec2(0.03489950, 0.99939083), vec2(0.01745241, 0.99984770), // 84
vec2(0.00000000, 1.00000000), vec2(-0.01745241, 0.99984770), vec2(-0.03489950, 0.99939083), vec2(-0.05233596, 0.99862953), vec2(-0.06975647, 0.99756405), vec2(-0.08715574, 0.99619470), // 90
vec2(-0.10452846, 0.99452190), vec2(-0.12186934, 0.99254615), vec2(-0.13917310, 0.99026807), vec2(-0.15643447, 0.98768834), vec2(-0.17364818, 0.98480775), vec2(-0.19080900, 0.98162718), // 96
vec2(-0.20791169, 0.97814760), vec2(-0.22495105, 0.97437006), vec2(-0.24192190, 0.97029573), vec2(-0.25881905, 0.96592583), vec2(-0.27563736, 0.96126170), vec2(-0.29237170, 0.95630476), // 102
vec2(-0.30901699, 0.95105652), vec2(-0.32556815, 0.94551858), vec2(-0.34202014, 0.93969262), vec2(-0.35836795, 0.93358043), vec2(-0.37460659, 0.92718385), vec2(-0.39073113, 0.92050485), // 108
vec2(-0.40673664, 0.91354546), vec2(-0.42261826, 0.90630779), vec2(-0.43837115, 0.89879405), vec2(-0.45399050, 0.89100652), vec2(-0.46947156, 0.88294759), vec2(-0.48480962, 0.87461971), // 114
vec2(-0.50000000, 0.86602540), vec2(-0.51503807, 0.85716730), vec2(-0.52991926, 0.84804810), vec2(-0.54463904, 0.83867057), vec2(-0.55919290, 0.82903757), vec2(-0.57357644, 0.81915204), // 120
vec2(-0.58778525, 0.80901699), vec2(-0.60181502, 0.79863551), vec2(-0.61566148, 0.78801075), vec2(-0.62932039, 0.77714596), vec2(-0.64278761, 0.76604444), vec2(-0.65605903, 0.75470958), // 126
vec2(-0.66913061, 0.74314483), vec2(-0.68199836, 0.73135370), vec2(-0.69465837, 0.71933980), vec2(-0.70710678, 0.70710678), vec2(-0.71933980, 0.69465837), vec2(-0.73135370, 0.68199836), // 132
vec2(-0.74314483, 0.66913061), vec2(-0.75470958, 0.65605903), vec2(-0.76604444, 0.64278761), vec2(-0.77714596, 0.62932039), vec2(-0.78801075, 0.61566148), vec2(-0.79863551, 0.60181502), // 138
vec2(-0.80901699, 0.58778525), vec2(-0.81915204, 0.57357644), vec2(-0.82903757, 0.55919290), vec2(-0.83867057, 0.54463904), vec2(-0.84804810, 0.52991926), vec2(-0.85716730, 0.51503807), // 144
vec2(-0.86602540, 0.50000000), vec2(-0.87461971, 0.48480962), vec2(-0.88294759, 0.46947156), vec2(-0.89100652, 0.45399050), vec2(-0.89879405, 0.43837115), vec2(-0.90630779, 0.42261826), // 150
vec2(-0.91354546, 0.40673664), vec2(-0.92050485, 0.39073113), vec2(-0.92718385, 0.37460659), vec2(-0.93358043, 0.35836795), vec2(-0.93969262, 0.34202014), vec2(-0.94551858, 0.32556815), // 156
vec2(-0.95105652, 0.30901699), vec2(-0.95630476, 0.29237170), vec2(-0.96126170, 0.27563736), vec2(-0.96592583, 0.25881905), vec2(-0.97029573, 0.24192190), vec2(-0.97437006, 0.22495105), // 162
vec2(-0.97814760, 0.20791169), vec2(-0.98162718, 0.19080900), vec2(-0.98480775, 0.17364818), vec2(-0.98768834, 0.15643447), vec2(-0.99026807, 0.13917310), vec2(-0.99254615, 0.12186934), // 168
vec2(-0.99452190, 0.10452846), vec2(-0.99619470, 0.08715574), vec2(-0.99756405, 0.06975647), vec2(-0.99862953, 0.05233596), vec2(-0.99939083, 0.03489950), vec2(-0.99984770, 0.01745241), // 174
vec2(-1.00000000, 0.00000000), vec2(-0.99984770, -0.01745241), vec2(-0.99939083, -0.03489950), vec2(-0.99862953, -0.05233596), vec2(-0.99756405, -0.06975647), vec2(-0.99619470, -0.08715574), // 180
vec2(-0.99452190, -0.10452846), vec2(-0.99254615, -0.12186934), vec2(-0.99026807, -0.13917310), vec2(-0.98768834, -0.15643447), vec2(-0.98480775, -0.17364818), vec2(-0.98162718, -0.19080900), // 186
vec2(-0.97814760, -0.20791169), vec2(-0.97437006, -0.22495105), vec2(-0.97029573, -0.24192190), vec2(-0.96592583, -0.25881905), vec2(-0.96126170, -0.27563736), vec2(-0.95630476, -0.29237170), // 192
vec2(-0.95105652, -0.30901699), vec2(-0.94551858, -0.32556815), vec2(-0.93969262, -0.34202014), vec2(-0.93358043, -0.35836795), vec2(-0.92718385, -0.37460659), vec2(-0.92050485, -0.39073113), // 198
vec2(-0.91354546, -0.40673664), vec2(-0.90630779, -0.42261826), vec2(-0.89879405, -0.43837115), vec2(-0.89100652, -0.45399050), vec2(-0.88294759, -0.46947156), vec2(-0.87461971, -0.48480962), // 204
vec2(-0.86602540, -0.50000000), vec2(-0.85716730, -0.51503807), vec2(-0.84804810, -0.52991926), vec2(-0.83867057, -0.54463904), vec2(-0.82903757, -0.55919290), vec2(-0.81915204, -0.57357644), // 210
vec2(-0.80901699, -0.58778525), vec2(-0.79863551, -0.60181502), vec2(-0.78801075, -0.61566148), vec2(-0.77714596, -0.62932039), vec2(-0.76604444, -0.64278761), vec2(-0.75470958, -0.65605903), // 216
vec2(-0.74314483, -0.66913061), vec2(-0.73135370, -0.68199836), vec2(-0.71933980, -0.69465837), vec2(-0.70710678, -0.70710678), vec2(-0.69465837, -0.71933980), vec2(-0.68199836, -0.73135370), // 222
vec2(-0.66913061, -0.74314483), vec2(-0.65605903, -0.75470958), vec2(-0.64278761, -0.76604444), vec2(-0.62932039, -0.77714596), vec2(-0.61566148, -0.78801075), vec2(-0.60181502, -0.79863551), // 228
vec2(-0.58778525, -0.80901699), vec2(-0.57357644, -0.81915204), vec2(-0.55919290, -0.82903757), vec2(-0.54463904, -0.83867057), vec2(-0.52991926, -0.84804810), vec2(-0.51503807, -0.85716730), // 234
vec2(-0.50000000, -0.86602540), vec2(-0.48480962, -0.87461971), vec2(-0.46947156, -0.88294759), vec2(-0.45399050, -0.89100652), vec2(-0.43837115, -0.89879405), vec2(-0.42261826, -0.90630779), // 240
vec2(-0.40673664, -0.91354546), vec2(-0.39073113, -0.92050485), vec2(-0.37460659, -0.92718385), vec2(-0.35836795, -0.93358043), vec2(-0.34202014, -0.93969262), vec2(-0.32556815, -0.94551858), // 246
vec2(-0.30901699, -0.95105652), vec2(-0.29237170, -0.95630476), vec2(-0.27563736, -0.96126170), vec2(-0.25881905, -0.96592583), vec2(-0.24192190, -0.97029573), vec2(-0.22495105, -0.97437006), // 252
vec2(-0.20791169, -0.97814760), vec2(-0.19080900, -0.98162718), vec2(-0.17364818, -0.98480775), vec2(-0.15643447, -0.98768834), vec2(-0.13917310, -0.99026807), vec2(-0.12186934, -0.99254615), // 258
vec2(-0.10452846, -0.99452190), vec2(-0.08715574, -0.99619470), vec2(-0.06975647, -0.99756405), vec2(-0.05233596, -0.99862953), vec2(-0.03489950, -0.99939083), vec2(-0.01745241, -0.99984770), // 264
vec2(-0.00000000, -1.00000000), vec2(0.01745241, -0.99984770), vec2(0.03489950, -0.99939083), vec2(0.05233596, -0.99862953), vec2(0.06975647, -0.99756405), vec2(0.08715574, -0.99619470), // 270
vec2(0.10452846, -0.99452190), vec2(0.12186934, -0.99254615), vec2(0.13917310, -0.99026807), vec2(0.15643447, -0.98768834), vec2(0.17364818, -0.98480775), vec2(0.19080900, -0.98162718), // 276
vec2(0.20791169, -0.97814760), vec2(0.22495105, -0.97437006), vec2(0.24192190, -0.97029573), vec2(0.25881905, -0.96592583), vec2(0.27563736, -0.96126170), vec2(0.29237170, -0.95630476), // 282
vec2(0.30901699, -0.95105652), vec2(0.32556815, -0.94551858), vec2(0.34202014, -0.93969262), vec2(0.35836795, -0.93358043), vec2(0.37460659, -0.92718385), vec2(0.39073113, -0.92050485), // 288
vec2(0.40673664, -0.91354546), vec2(0.42261826, -0.90630779), vec2(0.43837115, -0.89879405), vec2(0.45399050, -0.89100652), vec2(0.46947156, -0.88294759), vec2(0.48480962, -0.87461971), // 294
vec2(0.50000000, -0.86602540), vec2(0.51503807, -0.85716730), vec2(0.52991926, -0.84804810), vec2(0.54463904, -0.83867057), vec2(0.55919290, -0.82903757), vec2(0.57357644, -0.81915204), // 300
vec2(0.58778525, -0.80901699), vec2(0.60181502, -0.79863551), vec2(0.61566148, -0.78801075), vec2(0.62932039, -0.77714596), vec2(0.64278761, -0.76604444), vec2(0.65605903, -0.75470958), // 306
vec2(0.66913061, -0.74314483), vec2(0.68199836, -0.73135370), vec2(0.69465837, -0.71933980), vec2(0.70710678, -0.70710678), vec2(0.71933980, -0.69465837), vec2(0.73135370, -0.68199836), // 312
vec2(0.74314483, -0.66913061), vec2(0.75470958, -0.65605903), vec2(0.76604444, -0.64278761), vec2(0.77714596, -0.62932039), vec2(0.78801075, -0.61566148), vec2(0.79863551, -0.60181502), // 318
vec2(0.80901699, -0.58778525), vec2(0.81915204, -0.57357644), vec2(0.82903757, -0.55919290), vec2(0.83867057, -0.54463904), vec2(0.84804810, -0.52991926), vec2(0.85716730, -0.51503807), // 324
vec2(0.86602540, -0.50000000), vec2(0.87461971, -0.48480962), vec2(0.88294759, -0.46947156), vec2(0.89100652, -0.45399050), vec2(0.89879405, -0.43837115), vec2(0.90630779, -0.42261826), // 330
vec2(0.91354546, -0.40673664), vec2(0.92050485, -0.39073113), vec2(0.92718385, -0.37460659), vec2(0.93358043, -0.35836795), vec2(0.93969262, -0.34202014), vec2(0.94551858, -0.32556815), // 336
vec2(0.95105652, -0.30901699), vec2(0.95630476, -0.29237170), vec2(0.96126170, -0.27563736), vec2(0.96592583, -0.25881905), vec2(0.97029573, -0.24192190), vec2(0.97437006, -0.22495105), // 342
vec2(0.97814760, -0.20791169), vec2(0.98162718, -0.19080900), vec2(0.98480775, -0.17364818), vec2(0.98768834, -0.15643447), vec2(0.99026807, -0.13917310), vec2(0.99254615, -0.12186934), // 348
vec2(0.99452190, -0.10452846), vec2(0.99619470, -0.08715574), vec2(0.99756405, -0.06975647), vec2(0.99862953, -0.05233596), vec2(0.99939083, -0.03489950), vec2(0.99984770, -0.01745241), // 354
vec2(1.00000000, 0.00000000), vec2(0.99984770, 0.01745241), vec2(0.99939083, 0.03489950), vec2(0.99862953, 0.05233596), vec2(0.99756405, 0.06975647), vec2(0.99619470, 0.08715574), // 360
vec2(0.99452190, 0.10452846), vec2(0.99254615, 0.12186934), vec2(0.99026807, 0.13917310), vec2(0.98768834, 0.15643447), vec2(0.98480775, 0.17364818), vec2(0.98162718, 0.19080900), // 366
vec2(0.97814760, 0.20791169), vec2(0.97437006, 0.22495105), vec2(0.97029573, 0.24192190), vec2(0.96592583, 0.25881905), vec2(0.96126170, 0.27563736), vec2(0.95630476, 0.29237170), // 372
vec2(0.95105652, 0.30901699), vec2(0.94551858, 0.32556815), vec2(0.93969262, 0.34202014), vec2(0.93358043, 0.35836795), vec2(0.92718385, 0.37460659), vec2(0.92050485, 0.39073113), // 378
vec2(0.91354546, 0.40673664), vec2(0.90630779, 0.42261826), vec2(0.89879405, 0.43837115), vec2(0.89100652, 0.45399050), vec2(0.88294759, 0.46947156), vec2(0.87461971, 0.48480962), // 384
vec2(0.86602540, 0.50000000), vec2(0.85716730, 0.51503807), vec2(0.84804810, 0.52991926), vec2(0.83867057, 0.54463904), vec2(0.82903757, 0.55919290), vec2(0.81915204, 0.57357644), // 390
vec2(0.80901699, 0.58778525), vec2(0.79863551, 0.60181502), vec2(0.78801075, 0.61566148), vec2(0.77714596, 0.62932039), vec2(0.76604444, 0.64278761), vec2(0.75470958, 0.65605903), // 396
vec2(0.74314483, 0.66913061), vec2(0.73135370, 0.68199836), vec2(0.71933980, 0.69465837), vec2(0.70710678, 0.70710678), vec2(0.69465837, 0.71933980), vec2(0.68199836, 0.73135370), // 402
vec2(0.66913061, 0.74314483), vec2(0.65605903, 0.75470958), vec2(0.64278761, 0.76604444), vec2(0.62932039, 0.77714596), vec2(0.61566148, 0.78801075), vec2(0.60181502, 0.79863551), // 408
vec2(0.58778525, 0.80901699), vec2(0.57357644, 0.81915204), vec2(0.55919290, 0.82903757), vec2(0.54463904, 0.83867057), vec2(0.52991926, 0.84804810), vec2(0.51503807, 0.85716730), // 414
vec2(0.50000000, 0.86602540), vec2(0.48480962, 0.87461971), vec2(0.46947156, 0.88294759), vec2(0.45399050, 0.89100652), vec2(0.43837115, 0.89879405), vec2(0.42261826, 0.90630779), // 420
vec2(0.40673664, 0.91354546), vec2(0.39073113, 0.92050485), vec2(0.37460659, 0.92718385), vec2(0.35836795, 0.93358043), vec2(0.34202014, 0.93969262), vec2(0.32556815, 0.94551858), // 426
vec2(0.30901699, 0.95105652), vec2(0.29237170, 0.95630476), vec2(0.27563736, 0.96126170), vec2(0.25881905, 0.96592583), vec2(0.24192190, 0.97029573), vec2(0.22495105, 0.97437006), // 432
vec2(0.20791169, 0.97814760), vec2(0.19080900, 0.98162718), vec2(0.17364818, 0.98480775), vec2(0.15643447, 0.98768834), vec2(0.13917310, 0.99026807), vec2(0.12186934, 0.99254615), // 438
vec2(0.10452846, 0.99452190), vec2(0.08715574, 0.99619470), vec2(0.06975647, 0.99756405), vec2(0.05233596, 0.99862953), vec2(0.03489950, 0.99939083), vec2(0.01745241, 0.99984770), // 444
vec2(0.00000000, 1.00000000), vec2(-0.01745241, 0.99984770), vec2(-0.03489950, 0.99939083), vec2(-0.05233596, 0.99862953), vec2(-0.06975647, 0.99756405), vec2(-0.08715574, 0.99619470), // 450
vec2(-0.10452846, 0.99452190), vec2(-0.12186934, 0.99254615), vec2(-0.13917310, 0.99026807), vec2(-0.15643447, 0.98768834), vec2(-0.17364818, 0.98480775), vec2(-0.19080900, 0.98162718), // 456
vec2(-0.20791169, 0.97814760), vec2(-0.22495105, 0.97437006), vec2(-0.24192190, 0.97029573), vec2(-0.25881905, 0.96592583), vec2(-0.27563736, 0.96126170), vec2(-0.29237170, 0.95630476), // 462
vec2(-0.30901699, 0.95105652), vec2(-0.32556815, 0.94551858), vec2(-0.34202014, 0.93969262), vec2(-0.35836795, 0.93358043), vec2(-0.37460659, 0.92718385), vec2(-0.39073113, 0.92050485), // 468
vec2(-0.40673664, 0.91354546), vec2(-0.42261826, 0.90630779), vec2(-0.43837115, 0.89879405), vec2(-0.45399050, 0.89100652), vec2(-0.46947156, 0.88294759), vec2(-0.48480962, 0.87461971), // 474
vec2(-0.50000000, 0.86602540), vec2(-0.51503807, 0.85716730), vec2(-0.52991926, 0.84804810), vec2(-0.54463904, 0.83867057), vec2(-0.55919290, 0.82903757), vec2(-0.57357644, 0.81915204), // 480
vec2(-0.58778525, 0.80901699), vec2(-0.60181502, 0.79863551), vec2(-0.61566148, 0.78801075), vec2(-0.62932039, 0.77714596), vec2(-0.64278761, 0.76604444), vec2(-0.65605903, 0.75470958), // 486
vec2(-0.66913061, 0.74314483), vec2(-0.68199836, 0.73135370), vec2(-0.69465837, 0.71933980), vec2(-0.70710678, 0.70710678), vec2(-0.71933980, 0.69465837), vec2(-0.73135370, 0.68199836), // 492
vec2(-0.74314483, 0.66913061), vec2(-0.75470958, 0.65605903), vec2(-0.76604444, 0.64278761), vec2(-0.77714596, 0.62932039), vec2(-0.78801075, 0.61566148), vec2(-0.79863551, 0.60181502), // 498
vec2(-0.80901699, 0.58778525), vec2(-0.81915204, 0.57357644), vec2(-0.82903757, 0.55919290), vec2(-0.83867057, 0.54463904), vec2(-0.84804810, 0.52991926), vec2(-0.85716730, 0.51503807), // 504
vec2(-0.86602540, 0.50000000), vec2(-0.87461971, 0.48480962), vec2(-0.88294759, 0.46947156), vec2(-0.89100652, 0.45399050), vec2(-0.89879405, 0.43837115), vec2(-0.90630779, 0.42261826), // 510
vec2(-0.91354546, 0.40673664), vec2(-0.92050485, 0.39073113), vec2(-0.92718385, 0.37460659), vec2(-0.93358043, 0.35836795), vec2(-0.93969262, 0.34202014), vec2(-0.94551858, 0.32556815), // 516
vec2(-0.95105652, 0.30901699), vec2(-0.95630476, 0.29237170), vec2(-0.96126170, 0.27563736), vec2(-0.96592583, 0.25881905), vec2(-0.97029573, 0.24192190), vec2(-0.97437006, 0.22495105), // 522
vec2(-0.97814760, 0.20791169), vec2(-0.98162718, 0.19080900), vec2(-0.98480775, 0.17364818), vec2(-0.98768834, 0.15643447), vec2(-0.99026807, 0.13917310), vec2(-0.99254615, 0.12186934), // 528
vec2(-0.99452190, 0.10452846), vec2(-0.99619470, 0.08715574), vec2(-0.99756405, 0.06975647), vec2(-0.99862953, 0.05233596), vec2(-0.99939083, 0.03489950), vec2(-0.99984770, 0.01745241), // 534
vec2(-1.00000000, 0.00000000), vec2(-0.99984770, -0.01745241), vec2(-0.99939083, -0.03489950), vec2(-0.99862953, -0.05233596), vec2(-0.99756405, -0.06975647), vec2(-0.99619470, -0.08715574), // 540
vec2(-0.99452190, -0.10452846), vec2(-0.99254615, -0.12186934), vec2(-0.99026807, -0.13917310), vec2(-0.98768834, -0.15643447), vec2(-0.98480775, -0.17364818), vec2(-0.98162718, -0.19080900), // 546
vec2(-0.97814760, -0.20791169), vec2(-0.97437006, -0.22495105), vec2(-0.97029573, -0.24192190), vec2(-0.96592583, -0.25881905), vec2(-0.96126170, -0.27563736), vec2(-0.95630476, -0.29237170), // 552
vec2(-0.95105652, -0.30901699), vec2(-0.94551858, -0.32556815), vec2(-0.93969262, -0.34202014), vec2(-0.93358043, -0.35836795), vec2(-0.92718385, -0.37460659), vec2(-0.92050485, -0.39073113), // 558
vec2(-0.91354546, -0.40673664), vec2(-0.90630779, -0.42261826), vec2(-0.89879405, -0.43837115), vec2(-0.89100652, -0.45399050), vec2(-0.88294759, -0.46947156), vec2(-0.87461971, -0.48480962), // 564
vec2(-0.86602540, -0.50000000), vec2(-0.85716730, -0.51503807), vec2(-0.84804810, -0.52991926), vec2(-0.83867057, -0.54463904), vec2(-0.82903757, -0.55919290), vec2(-0.81915204, -0.57357644), // 570
vec2(-0.80901699, -0.58778525), vec2(-0.79863551, -0.60181502), vec2(-0.78801075, -0.61566148), vec2(-0.77714596, -0.62932039), vec2(-0.76604444, -0.64278761), vec2(-0.75470958, -0.65605903), // 576
vec2(-0.74314483, -0.66913061), vec2(-0.73135370, -0.68199836), vec2(-0.71933980, -0.69465837), vec2(-0.70710678, -0.70710678), vec2(-0.69465837, -0.71933980), vec2(-0.68199836, -0.73135370), // 582
vec2(-0.66913061, -0.74314483), vec2(-0.65605903, -0.75470958), vec2(-0.64278761, -0.76604444), vec2(-0.62932039, -0.77714596), vec2(-0.61566148, -0.78801075), vec2(-0.60181502, -0.79863551), // 588
vec2(-0.58778525, -0.80901699), vec2(-0.57357644, -0.81915204), vec2(-0.55919290, -0.82903757), vec2(-0.54463904, -0.83867057), vec2(-0.52991926, -0.84804810), vec2(-0.51503807, -0.85716730), // 594
vec2(-0.50000000, -0.86602540), vec2(-0.48480962, -0.87461971), vec2(-0.46947156, -0.88294759), vec2(-0.45399050, -0.89100652), vec2(-0.43837115, -0.89879405), vec2(-0.42261826, -0.90630779), // 600
vec2(-0.40673664, -0.91354546), vec2(-0.39073113, -0.92050485), vec2(-0.37460659, -0.92718385), vec2(-0.35836795, -0.93358043), vec2(-0.34202014, -0.93969262), vec2(-0.32556815, -0.94551858), // 606
vec2(-0.30901699, -0.95105652), vec2(-0.29237170, -0.95630476), vec2(-0.27563736, -0.96126170), vec2(-0.25881905, -0.96592583), vec2(-0.24192190, -0.97029573), vec2(-0.22495105, -0.97437006), // 612
vec2(-0.20791169, -0.97814760), vec2(-0.19080900, -0.98162718), vec2(-0.17364818, -0.98480775), vec2(-0.15643447, -0.98768834), vec2(-0.13917310, -0.99026807), vec2(-0.12186934, -0.99254615), // 618
vec2(-0.10452846, -0.99452190), vec2(-0.08715574, -0.99619470), vec2(-0.06975647, -0.99756405), vec2(-0.05233596, -0.99862953), vec2(-0.03489950, -0.99939083), vec2(-0.01745241, -0.99984770), // 624
vec2(-0.00000000, -1.00000000), vec2(0.01745241, -0.99984770), vec2(0.03489950, -0.99939083), vec2(0.05233596, -0.99862953), vec2(0.06975647, -0.99756405), vec2(0.08715574, -0.99619470), // 630
vec2(0.10452846, -0.99452190), vec2(0.12186934, -0.99254615), vec2(0.13917310, -0.99026807), vec2(0.15643447, -0.98768834), vec2(0.17364818, -0.98480775), vec2(0.19080900, -0.98162718), // 636
vec2(0.20791169, -0.97814760), vec2(0.22495105, -0.97437006), vec2(0.24192190, -0.97029573), vec2(0.25881905, -0.96592583), vec2(0.27563736, -0.96126170), vec2(0.29237170, -0.95630476), // 642
vec2(0.30901699, -0.95105652), vec2(0.32556815, -0.94551858), vec2(0.34202014, -0.93969262), vec2(0.35836795, -0.93358043), vec2(0.37460659, -0.92718385), vec2(0.39073113, -0.92050485), // 648
vec2(0.40673664, -0.91354546), vec2(0.42261826, -0.90630779), vec2(0.43837115, -0.89879405), vec2(0.45399050, -0.89100652), vec2(0.46947156, -0.88294759), vec2(0.48480962, -0.87461971), // 654
vec2(0.50000000, -0.86602540), vec2(0.51503807, -0.85716730), vec2(0.52991926, -0.84804810), vec2(0.54463904, -0.83867057), vec2(0.55919290, -0.82903757), vec2(0.57357644, -0.81915204), // 660
vec2(0.58778525, -0.80901699), vec2(0.60181502, -0.79863551), vec2(0.61566148, -0.78801075), vec2(0.62932039, -0.77714596), vec2(0.64278761, -0.76604444), vec2(0.65605903, -0.75470958), // 666
vec2(0.66913061, -0.74314483), vec2(0.68199836, -0.73135370), vec2(0.69465837, -0.71933980), vec2(0.70710678, -0.70710678), vec2(0.71933980, -0.69465837), vec2(0.73135370, -0.68199836), // 672
vec2(0.74314483, -0.66913061), vec2(0.75470958, -0.65605903), vec2(0.76604444, -0.64278761), vec2(0.77714596, -0.62932039), vec2(0.78801075, -0.61566148), vec2(0.79863551, -0.60181502), // 678
vec2(0.80901699, -0.58778525), vec2(0.81915204, -0.57357644), vec2(0.82903757, -0.55919290), vec2(0.83867057, -0.54463904), vec2(0.84804810, -0.52991926), vec2(0.85716730, -0.51503807), // 684
vec2(0.86602540, -0.50000000), vec2(0.87461971, -0.48480962), vec2(0.88294759, -0.46947156), vec2(0.89100652, -0.45399050), vec2(0.89879405, -0.43837115), vec2(0.90630779, -0.42261826), // 690
vec2(0.91354546, -0.40673664), vec2(0.92050485, -0.39073113), vec2(0.92718385, -0.37460659), vec2(0.93358043, -0.35836795), vec2(0.93969262, -0.34202014), vec2(0.94551858, -0.32556815), // 696
vec2(0.95105652, -0.30901699), vec2(0.95630476, -0.29237170), vec2(0.96126170, -0.27563736), vec2(0.96592583, -0.25881905), vec2(0.97029573, -0.24192190), vec2(0.97437006, -0.22495105), // 702
vec2(0.97814760, -0.20791169), vec2(0.98162718, -0.19080900), vec2(0.98480775, -0.17364818), vec2(0.98768834, -0.15643447), vec2(0.99026807, -0.13917310), vec2(0.99254615, -0.12186934), // 708
vec2(0.99452190, -0.10452846), vec2(0.99619470, -0.08715574), vec2(0.99756405, -0.06975647), vec2(0.99862953, -0.05233596), vec2(0.99939083, -0.03489950), vec2(0.99984770, -0.01745241), // 714
vec2(1.00000000, 0.00000000) // 720
};
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