}
}
-vector cliptoplane(vector v, vector p)
-{
- return v - (v * p) * p;
-}
-
-vector solve_cubic_pq(float p, float q)
-{
- float D, u, v, a;
- D = q*q/4.0 + p*p*p/27.0;
- if(D < 0)
- {
- // irreducibilis
- a = 1.0/3.0 * acos(-q/2.0 * sqrt(-27.0/(p*p*p)));
- u = sqrt(-4.0/3.0 * p);
- // a in range 0..pi/3
- // cos(a)
- // cos(a + 2pi/3)
- // cos(a + 4pi/3)
- return
- u *
- (
- '1 0 0' * cos(a + 2.0/3.0*M_PI)
- +
- '0 1 0' * cos(a + 4.0/3.0*M_PI)
- +
- '0 0 1' * cos(a)
- );
- }
- else if(D == 0)
- {
- // simple
- if(p == 0)
- return '0 0 0';
- u = 3*q/p;
- v = -u/2;
- if(u >= v)
- return '1 1 0' * v + '0 0 1' * u;
- else
- return '0 1 1' * v + '1 0 0' * u;
- }
- else
- {
- // cardano
- u = cbrt(-q/2.0 + sqrt(D));
- v = cbrt(-q/2.0 - sqrt(D));
- return '1 1 1' * (u + v);
- }
-}
-vector solve_cubic_abcd(float a, float b, float c, float d)
-{
- // y = 3*a*x + b
- // x = (y - b) / 3a
- float p, q;
- vector v;
- p = (9*a*c - 3*b*b);
- q = (27*a*a*d - 9*a*b*c + 2*b*b*b);
- v = solve_cubic_pq(p, q);
- v = (v - b * '1 1 1') * (1.0 / (3.0 * a));
- if(a < 0)
- v += '1 0 -1' * (v_z - v_x); // swap x, z
- return v;
-}
-
-vector findperpendicular(vector v)
-{
- vector p;
- p_x = v_z;
- p_y = -v_x;
- p_z = v_y;
- return normalize(cliptoplane(p, v));
-}
-
-vector W_CalculateProjectileSpread(vector forward, float spread)
-{
- float sigma;
- vector v1 = '0 0 0', v2;
- float dx, dy, r;
- float sstyle;
- spread *= g_weaponspreadfactor;
- if(spread <= 0)
- return forward;
- sstyle = autocvar_g_projectiles_spread_style;
-
- if(sstyle == 0)
- {
- // this is the baseline for the spread value!
- // standard deviation: sqrt(2/5)
- // density function: sqrt(1-r^2)
- return forward + randomvec() * spread;
- }
- else if(sstyle == 1)
- {
- // same thing, basically
- return normalize(forward + cliptoplane(randomvec() * spread, forward));
- }
- else if(sstyle == 2)
- {
- // circle spread... has at sigma=1 a standard deviation of sqrt(1/2)
- sigma = spread * 0.89442719099991587855; // match baseline stddev
- v1 = findperpendicular(forward);
- v2 = cross(forward, v1);
- // random point on unit circle
- dx = random() * 2 * M_PI;
- dy = sin(dx);
- dx = cos(dx);
- // radius in our dist function
- r = random();
- r = sqrt(r);
- return normalize(forward + (v1 * dx + v2 * dy) * r * sigma);
- }
- else if(sstyle == 3) // gauss 3d
- {
- sigma = spread * 0.44721359549996; // match baseline stddev
- // note: 2D gaussian has sqrt(2) times the stddev of 1D, so this factor is right
- v1 = forward;
- v1_x += gsl_ran_gaussian(sigma);
- v1_y += gsl_ran_gaussian(sigma);
- v1_z += gsl_ran_gaussian(sigma);
- return v1;
- }
- else if(sstyle == 4) // gauss 2d
- {
- sigma = spread * 0.44721359549996; // match baseline stddev
- // note: 2D gaussian has sqrt(2) times the stddev of 1D, so this factor is right
- v1_x = gsl_ran_gaussian(sigma);
- v1_y = gsl_ran_gaussian(sigma);
- v1_z = gsl_ran_gaussian(sigma);
- return normalize(forward + cliptoplane(v1, forward));
- }
- else if(sstyle == 5) // 1-r
- {
- sigma = spread * 1.154700538379252; // match baseline stddev
- v1 = findperpendicular(forward);
- v2 = cross(forward, v1);
- // random point on unit circle
- dx = random() * 2 * M_PI;
- dy = sin(dx);
- dx = cos(dx);
- // radius in our dist function
- r = random();
- r = solve_cubic_abcd(-2, 3, 0, -r) * '0 1 0';
- return normalize(forward + (v1 * dx + v2 * dy) * r * sigma);
- }
- else if(sstyle == 6) // 1-r^2
- {
- sigma = spread * 1.095445115010332; // match baseline stddev
- v1 = findperpendicular(forward);
- v2 = cross(forward, v1);
- // random point on unit circle
- dx = random() * 2 * M_PI;
- dy = sin(dx);
- dx = cos(dx);
- // radius in our dist function
- r = random();
- r = sqrt(1 - r);
- r = sqrt(1 - r);
- return normalize(forward + (v1 * dx + v2 * dy) * r * sigma);
- }
- else if(sstyle == 7) // (1-r) (2-r)
- {
- sigma = spread * 1.224744871391589; // match baseline stddev
- v1 = findperpendicular(forward);
- v2 = cross(forward, v1);
- // random point on unit circle
- dx = random() * 2 * M_PI;
- dy = sin(dx);
- dx = cos(dx);
- // radius in our dist function
- r = random();
- r = 1 - sqrt(r);
- r = 1 - sqrt(r);
- return normalize(forward + (v1 * dx + v2 * dy) * r * sigma);
- }
- else
- error("g_projectiles_spread_style must be 0 (sphere), 1 (flattened sphere), 2 (circle), 3 (gauss 3D), 4 (gauss plane), 5 (linear falloff), 6 (quadratic falloff), 7 (stronger falloff)!");
- return '0 0 0';
- /*
- * how to derive falloff functions:
- * rho(r) := (2-r) * (1-r);
- * a : 0;
- * b : 1;
- * rhor(r) := r * rho(r);
- * cr(t) := integrate(rhor(r), r, a, t);
- * scr(t) := integrate(rhor(r) * r^2, r, a, t);
- * variance : scr(b) / cr(b);
- * solve(cr(r) = rand * cr(b), r), programmmode:false;
- * sqrt(0.4 / variance), numer;
- */
-}
-
#if 0
float mspercallsum;
float mspercallsstyle;
}
mspercallsum -= gettime(GETTIME_HIRES);
#endif
- dir = W_CalculateProjectileSpread(dir, spread);
+ dir = W_CalculateSpread(dir, spread, g_weaponspreadfactor, autocvar_g_projectiles_spread_style);
#if 0
mspercallsum += gettime(GETTIME_HIRES);
mspercallcount += 1;
projects / xonotic / xonotic-data.pk3dir.git / blobdiff