First cut at a turbulence model for YASim. It's a

perlin/scale-invariant vector field implemented as a 2D lookup table.
Seems to work OK, but needs testing and feedback.

src/FDM/YASim/FGFDM.cpp

@@ -48,6 +48,10 @@ FGFDM::FGFDM()
     // should probably be settable, but there are very few aircraft
     // who trim their approaches using things other than elevator.
     _airplane.setElevatorControl(parseAxis("/controls/flight/elevator-trim"));
+
+    // FIXME: read seed from somewhere?
+    int seed = 0;
+    _turb = new Turbulence(10, seed);
 }
 
 FGFDM::~FGFDM()
@@ -97,6 +101,8 @@ void FGFDM::init()
     // This has a nasty habit of being false at startup.  That's not
     // good.
     fgSetBool("/controls/gear/gear-down", true);
+
+    _airplane.getModel()->setTurbulence(_turb);
 }
 
 // Not the worlds safest parser.  But it's short & sweet.
@@ -308,6 +314,9 @@ void FGFDM::getExternalInput(float dt)
 {
     char buf[256];
 
+    _turb->setMagnitude(fgGetFloat("/environment/turbulence/magnitude-norm"));
+    _turb->update(dt, fgGetFloat("/environment/turbulence/rate-hz"));
+
     // The control axes
     ControlMap* cm = _airplane.getControlMap();
     cm->reset();

src/FDM/YASim/FGFDM.hpp

@@ -43,6 +43,7 @@ private:
     void parseWeight(XMLAttributes* a);
     void parsePropeller(XMLAttributes* a);
     bool eq(const char* a, const char* b);
+    bool caseeq(const char* a, const char* b);
     char* dup(const char* s);
     int attri(XMLAttributes* atts, char* attr);
     int attri(XMLAttributes* atts, char* attr, int def); 
@@ -53,6 +54,9 @@ private:
     // The core Airplane object we manage.
     Airplane _airplane;
 
+    // Aerodynamic turbulence model
+    Turbulence* _turb;
+
     // The list of "axes" that we expect to find as input.  These are
     // typically property names.
     Vector _axes;

src/FDM/YASim/Makefile.am

@@ -29,7 +29,8 @@ SHARED_SOURCE_FILES = \
         Surface.cpp Surface.hpp \
         Thruster.cpp Thruster.hpp \
         Vector.hpp \
-        Wing.cpp Wing.hpp
+        Wing.cpp Wing.hpp \
+        Turbulence.cpp Turbulence.hpp
 
 noinst_LIBRARIES = libYASim.a
 

src/FDM/YASim/Math.cpp

@@ -60,6 +60,11 @@ float Math::atan2(float y, float x)
     return (float)::atan2(y, x);
 }
 
+double Math::floor(double x)
+{
+    return ::floor(x);
+}
+
 double Math::abs(double f)
 {
     return ::fabs(f);

src/FDM/YASim/Math.hpp

@@ -32,6 +32,7 @@ public:
     static double cos(double f);
     static double tan(double f);
     static double atan2(double y, double x);
+    static double floor(double x);
 
     // Some 3D vector stuff.  In all cases, it is permissible for the
     // "out" vector to be the same as one of the inputs.

src/FDM/YASim/Model.cpp

@@ -53,6 +53,7 @@ Model::Model()
 
     _agl = 0;
     _crashed = false;
+    _turb = 0;
 }
 
 Model::~Model()
@@ -427,9 +428,24 @@ float Model::localGround(State* s, float* out)
 // specified aircraft velocity.
 void Model::localWind(float* pos, State* s, float* out)
 {
-    // Most of the input is in global coordinates.  Fix that.
+    float tmp[3], lwind[3], lrot[3], lv[3];
-    float lwind[3], lrot[3], lv[3];
+
-    Math::vmul33(s->orient, _wind, lwind);
+    // Get a global coordinate for our local position, and calculate
+    // turbulence.
+    // FIXME: modify turbulence for altitude, attenuating the vertical
+    // component near the ground.
+    if(_turb) {
+        double gpos[3];
+        Math::tmul33(s->orient, pos, tmp);
+        for(int i=0; i<3; i++) gpos[i] = s->pos[i] + tmp[i];
+        _turb->getTurbulence(gpos, lwind);
+        Math::add3(_wind, lwind, lwind);
+    } else {
+        Math::set3(_wind, lwind);
+    }
+
+    // Convert to local coordinates
+    Math::vmul33(s->orient, lwind, lwind);
     Math::vmul33(s->orient, s->rot, lrot);
     Math::vmul33(s->orient, s->v, lv);
 

src/FDM/YASim/Model.hpp

@@ -5,6 +5,7 @@
 #include "RigidBody.hpp"
 #include "BodyEnvironment.hpp"
 #include "Vector.hpp"
+#include "Turbulence.hpp"
 
 namespace yasim {
 
@@ -25,6 +26,8 @@ public:
     RigidBody* getBody();
     Integrator* getIntegrator();
 
+    void setTurbulence(Turbulence* turb) { _turb = turb; }
+
     State* getState();
     void setState(State* s);
 
@@ -76,6 +79,8 @@ private:
     Integrator _integrator;
     RigidBody _body;
 
+    Turbulence* _turb;
+
     Vector _thrusters;
     Vector _surfaces;
     Vector _rotorparts;

src/FDM/YASim/Surface.cpp

@@ -202,7 +202,6 @@ void Surface::calcForce(float* v, float rho, float* out, float* torque)
     out[1] *= _cy;
 
     // Diddle the induced drag
-    float IDMUL = 0.5;
     Math::mul3(-1*_inducedDrag*out[2]*lwind[2], lwind, lwind);
     Math::add3(lwind, out, out);
 

src/FDM/YASim/Turbulence.cpp

@@ -0,0 +1,271 @@
+#include "Turbulence.hpp"
+#include "Math.hpp"
+
+namespace yasim {
+// Typical velocity spectrum: MIN 0.017 MAX 0.72 AVG 0.30 RMS 0.33
+
+// Maximum conceivable turbulence flow, in m/s.  In practice, most
+// generated turbulence fields top out at about 70% of this number.
+const float MAX_TURBULENCE = 20;
+
+// How many generations are "meaningful" (i.e., not part of the normal
+// wind computation).  Decreasing this number will reallocate
+// bandwidth to the higher frequency components.
+const int MEANINGFUL_GENS = 9;
+
+static const float FT2M = 0.3048;
+
+// 8 x 32 s-box used by hashrand.  Read out of /dev/random on my Linux
+// box; not analyzed for linearity or coverage issues.
+static unsigned int SBOX[] = {
+    0x0a881716, 0x20daa8ee, 0x61eb7d78, 0x46164e74, 0x39ab9d9d, 0x633a33f6,
+    0x437c821d, 0x60a66f29, 0xc4ae45ab, 0x9a5cb3ce, 0x4a43606a, 0x56802c3c,
+    0xe40d5e25, 0xa0297f41, 0x0457671e, 0xf167ab77, 0x571276db, 0x8b644e02,
+    0xd5cfc592, 0x2331bfa2, 0xf9dfe7c1, 0xce9e7583, 0xfb133c29, 0x951c31c9,
+    0x8e61b24e, 0xddf37570, 0x938c3b72, 0xaf907468, 0x98b77ac7, 0xe6edd515,
+    0xa01f3600, 0xeafea5ad, 0x83fcce08, 0xe2e9fa9d, 0xd87727bb, 0x1945ea4c,
+    0x831d295f, 0xa796ed85, 0xaa907b24, 0x69b25f12, 0xd4b27868, 0xdcde40f5,
+    0x0e9e6def, 0x348a4702, 0x298389c8, 0xce405b63, 0x2e36d5a3, 0xf0569882,
+    0x3beb3219, 0xf2366b9a, 0x69576cca, 0xd2725b8b, 0x6016d6f3, 0x728142ca,
+    0x448b9f47, 0xe600cd4e, 0xac45d524, 0x0e32531b, 0x425d7b55, 0xc65cd9dc,
+    0x58d7f9f1, 0x19f49822, 0x6786f2d3, 0x57844748, 0x523de4a3, 0x01079655,
+    0x6dccea89, 0xb59278f2, 0x13a27e83, 0x19bcfc69, 0x4cff4bf5, 0xb18a3441,
+    0x1e235c5e, 0xa1b47a42, 0x3bee8a5a, 0xa0962594, 0xa9b1ce4c, 0xb00399c8,
+    0x83749847, 0x42c666e7, 0x08b81e57, 0xf7eee24b, 0x66720817, 0x3983f5f8,
+    0x4999a817, 0x94fabd7a, 0x7aa775ef, 0xf6c1adcb, 0x5f32a695, 0x813ecf7e,
+    0x66615fd5, 0xc0012e15, 0x051dd97e, 0xe6ee2803, 0x2449663c, 0x4024d59c,
+    0xcb70a774, 0xacd3db94, 0x1845484e, 0xc803ef3c, 0x0662876f, 0x8794fe30,
+    0xf0f0d16a, 0x41c065b8, 0xff9d5fc7, 0xa4237394, 0x8656614d, 0x26be5da9,
+    0xb32bc625, 0xf215cc58, 0xc1e21848, 0xb97fe9fc, 0xbb28ef04, 0xde88eb23,
+    0xe0623033, 0xa3df9e9c, 0xe9b95887, 0x3a4ab03b, 0x1cba812e, 0x174b4b37,
+    0x0074d24b, 0xe5668d09, 0xf11a070a, 0x2884252b, 0x911149ea, 0x20dab459,
+    0x89573d33, 0x68c2711d, 0x2b8e9781, 0xf007567b, 0x9761c8fa, 0x574d3a4e,
+    0xa2ac28dd, 0x924f2211, 0xb0a91028, 0x83a90487, 0xf22cf6f8, 0x17a5dcfe,
+    0x10497534, 0x27dd1316, 0x94a34815, 0x276e11ee, 0xead1d779, 0x0bfd4f20,
+    0x45f2228f, 0x35d21bf8, 0x121336c0, 0x43a6538b, 0x55e950dc, 0x88a80871,
+    0xfda9f61e, 0x5c76d120, 0x2eb8338f, 0x5193bb8e, 0x30a6995c, 0x500505a8,
+    0x7b214f6a, 0x6a74558d, 0x040d0716, 0x4452846b, 0xd0a0e838, 0xead282e0,
+    0x6bc6465c, 0xcb4ab107, 0xab990ed7, 0x72a1fe7b, 0x06901fdf, 0x18f90739,
+    0x8cd2b861, 0xaea9d40c, 0x2dcf7c18, 0x45979e8a, 0x10393f0d, 0x3209d7c9,
+    0x2c71378f, 0x908a692a, 0xc0e63b24, 0x05de3118, 0xfc974436, 0x1be44823,
+    0x03de2f3d, 0x66cfb6e4, 0x52727bfc, 0xa7b93651, 0xd7b9035f, 0xfac28d33,
+    0x59bb4457, 0xeede4004, 0x175ad747, 0x7808d123, 0xc9c97de8, 0x0c26ca26,
+    0x75e62e96, 0xc8376e97, 0xf2ee6baa, 0x6a885f88, 0x352f92ab, 0x4143f4a4,
+    0xb1cca58c, 0xe8fbea94, 0x5c306621, 0xfbe64c32, 0xa1ed285d, 0xca7395cf,
+    0x4eed31a5, 0x31e39fee, 0x7951c585, 0x23434811, 0xfc103036, 0xef001b3c,
+    0x499f5f34, 0x5f7f38f4, 0x0206d8c5, 0xcc3ee4f1, 0xbc0b485c, 0x4e4f5829,
+    0x05ee6e6d, 0xc82d5353, 0x44892bec, 0x22984b53, 0x8a6374d1, 0x0850c3f9,
+    0x0c06ae88, 0x2dfdc126, 0xd1edacdc, 0x1d8dbd39, 0xdeff2db8, 0xd557278d,
+    0x7e9e3740, 0x49a1ecb5, 0x43f7b391, 0x50b6b9ef, 0x46b9b8f8, 0xd3f5f6d2,
+    0x8d453b88, 0xc0ba5333, 0x5ab92e37, 0x6e7620a4, 0x8eb9795a, 0x30355a84,
+    0xf5e4ad33, 0x7d0b4df2, 0xe0f3e2a1, 0xa466f0e6, 0x39a19c9a, 0x1b284524,
+    0x854f8b3b, 0x02d10b6c, 0x44fb5d9d, 0x60c29fec, 0xda35244a, 0xb5ce6653,
+    0xfd8356ad, 0xff88d46b, 0x23fd1d16, 0xdc0be23c };
+
+// Random hash function on 32 bit integers.  Works by XORing the input
+// word with s-box values looked up from each input byte.  This is
+// pretty much the simplest "good" hash function of this type.  The
+// instruction count is very low; depending on cache behavior with the
+// 1024 byte s-box table, it may or may not be the fastest.
+inline unsigned int Turbulence::hashrand(unsigned int i)
+{
+    i ^= SBOX[(i>> 0) & 0xff]; 
+    i ^= SBOX[(i>> 8) & 0xff]; 
+    i ^= SBOX[(i>>16) & 0xff]; 
+    i ^= SBOX[(i>>24) & 0xff];
+    return i;
+}
+
+// 32 bit integer to [0:1] (safe with 64 bit ints)
+static inline float i2fu(unsigned int i) { return (1.0/0xffffffffu) * i; }
+
+// 32 bit integer to [-1:1] (safe with 64 bit ints)
+static inline float i2fs(unsigned int i) { return 2 * i2fu(i) - 1; }
+
+// Similar conversions, for 8 bit unsigned bytes
+static inline float c2fu(unsigned char c) { return (c+0.5)*(1.0/256); }
+static inline unsigned char f2cu(float f) {
+    int c = (int)(f * 256);
+    return c == 256 ? 255 : c;
+}
+
+inline void Turbulence::turblut(int x, int y, float* out)
+{
+    x = x >= _sz ? x - _sz : x;
+    y = y >= _sz ? y - _sz : y;
+
+    unsigned char* turb = _data + 3*(y*_sz+x);
+    out[0] = c2fu(turb[0]) * (_x1 - _x0) + _x0;
+    out[1] = c2fu(turb[1]) * (_y1 - _y0) + _y0;
+    out[2] = c2fu(turb[2]) * (_z1 - _z0) + _z0;
+}
+
+void Turbulence::update(double dt, double rate)
+{
+    // Assume a normal rate is 2 unit/sec.  This will cause the
+    // highest frequency turbulence component to arrive at 1 Hz.
+    _currTime += 2 * dt * rate;
+    if(_currTime > _sz) _currTime -= _sz;
+}
+
+void Turbulence::getTurbulence(double* loc, float* turbOut)
+{
+    // Convert to integer 2D coordinates; wrap to [0:_sz].
+    double a = loc[0] + loc[2];
+    double b = loc[1] + _currTime;
+    a -= _sz * Math::floor(a * (1.0/_sz));
+    b -= _sz * Math::floor(b * (1.0/_sz));
+    int x = (int)Math::floor(a);
+    int y = (int)Math::floor(b);
+
+    // Convert to fractional interpolation factors
+    a -= x;
+    b -= y;
+
+    // Do the lookups
+    float turb00[3], turb10[3], turb01[3], turb11[3];
+    turblut(x,     y, turb00);
+    turblut(x+1,   y, turb10);
+    turblut(x,   y+1, turb01);
+    turblut(x+1, y+1, turb11);
+
+    // Interpolate, add in units
+    float mag = _mag * _mag * MAX_TURBULENCE;
+    for(int i=0; i<3; i++) {
+        float avg0 = (1-a)*turb00[i] + a*turb01[i];
+        float avg1 = (1-a)*turb10[i] + a*turb11[i];
+        turbOut[i] = mag * ((1-b)*avg0 + b*avg1);
+    }
+}
+
+// Associates a random number in the range [-1:1] with a given lattice
+// point.
+float Turbulence::lattice(unsigned int x, unsigned int y)
+{
+    return i2fs(hashrand((((_seed << _gens) | x) << _gens) | y));
+}
+
+// Returns a scale for a vector that normalizes it into a sphere (as
+// opposed to cube) space.  This prevents the overscaling of the
+// "corner" vectors you get from choosing three random turbulence
+// components.
+float Turbulence::cubenorm(float x, float y, float z)
+{
+    x = x < 0 ? -x : x;
+    y = y < 0 ? -y : y;
+    z = z < 0 ? -z : z;
+    float max = ((x > y) && (x > z)) ? x : ((y > z) ? y : z);
+    return max/Math::sqrt(x*x + y*y + z*z);
+}
+
+Turbulence::~Turbulence()
+{
+    delete[] _data;
+}
+
+Turbulence::Turbulence(int gens, int seed)
+{
+    _gens = gens;
+    _sz = 1 << (_gens - 1);
+    _seed = seed;
+    _mag = 1;
+    _x0 = _x1 = _y0 = _y1 = _z0 = _z1 = 0;
+    _currTime = 0;
+
+    float* xbuf = new float[_sz*_sz];
+    float* ybuf = new float[_sz*_sz];
+    float* zbuf = new float[_sz*_sz];
+
+    mkimg(xbuf, _sz);
+    _seed++;
+    mkimg(ybuf, _sz);
+    _seed++;
+    mkimg(zbuf, _sz);
+
+    // "Normalize" them to proper spherical magnitudes, and calculate
+    // range information for the packing.
+    for(int i=0; i<_sz*_sz; i++) {
+        float n = cubenorm(xbuf[i], ybuf[i], zbuf[i]);
+        xbuf[i] *= n;
+        ybuf[i] *= n;
+        zbuf[i] *= n;
+
+        _x0 = xbuf[i] < _x0 ? xbuf[i] : _x0;
+        _x1 = xbuf[i] > _x1 ? xbuf[i] : _x1;
+        _y0 = ybuf[i] < _y0 ? ybuf[i] : _y0;
+        _y1 = ybuf[i] > _y1 ? ybuf[i] : _y1;
+        _z0 = zbuf[i] < _z0 ? zbuf[i] : _z0;
+        _z1 = zbuf[i] > _z1 ? zbuf[i] : _z1;
+    }
+    
+    // Pack into 3 byte tuples for storage.
+    _data = new unsigned char[3*_sz*_sz];
+    for(int i=0; i<_sz*_sz; i++) {
+        float x = xbuf[i], y = ybuf[i], z = zbuf[i];
+        unsigned char* tuple = _data + 3*i;
+        tuple[0] = f2cu((x - _x0) / (_x1 - _x0));
+        tuple[1] = f2cu((y - _y0) / (_y1 - _y0));
+        tuple[2] = f2cu((z - _z0) / (_z1 - _z0));
+    }
+
+    delete[] xbuf;
+    delete[] ybuf;
+    delete[] zbuf;
+}
+
+// "Integer" turbulence function.  Takes coordinates in the range
+// [0:1] expressed as a fraction of 2^32 (works with 64 bit ints too;
+// it just doesn't use the whole range). The output range is
+// guaranteed to be within [-1:1], with a typical output range of +/-
+// 0.6 or so.
+float Turbulence::iturb(unsigned int x, unsigned int y)
+{
+    float amplitude = 0.5; // start here, so it all sums to ~1.0
+    float total = 0;
+    int wrapmax = 2;
+    int startgen = _gens - MEANINGFUL_GENS;
+    for(int g=startgen; g<_gens; g++) {
+        int xl = x >> (32 - g); // lattice coordinates
+        int yl = y >> (32 - g);
+        float xfrac = i2fu(x << g); // interpolation fractions
+        float yfrac = i2fu(y << g);
+        xfrac = xfrac*xfrac*(3 - 2*xfrac); // ... as cubics
+        yfrac = yfrac*yfrac*(3 - 2*yfrac);
+
+#define WRAP(a) (a) >= wrapmax ? 0 : (a)
+        float p00 = lattice(WRAP(xl),   WRAP(yl)); // lattice values
+        float p01 = lattice(WRAP(xl),   WRAP(yl+1));
+        float p10 = lattice(WRAP(xl+1), WRAP(yl));
+        float p11 = lattice(WRAP(xl+1), WRAP(yl+1));
+#undef WRAP
+
+        float p0 = p00 * (1-yfrac) + p01 * yfrac;
+        float p1 = p10 * (1-yfrac) + p11 * yfrac;
+        float p = p0 * (1-xfrac) + p1 * xfrac;
+        total += p * amplitude;
+        amplitude *= 0.5;
+        wrapmax *= 2;
+    }
+    return total;
+}
+
+// Converts "real" turbulence coordinates expressed in the range
+// [0:_sz] (modulo) to integers and runs them through iturb().
+float Turbulence::fturb(double a, double b)
+{
+    a *= 1.0 / _sz;
+    b *= 1.0 / _sz;
+    a -= Math::floor(a);
+    b -= Math::floor(b);
+    return iturb((unsigned int)(a * 4294967296.0),
+                 (unsigned int)(b * 4294967296.0));
+}
+
+void Turbulence::mkimg(float* buf, int sz)
+{
+    for(int y=0; y<sz; y++)
+        for(int x=0; x<sz; x++)
+            buf[y*sz+x] = fturb(x + 0.5, y + 0.5);
+}
+
+}; // namespace yasim

src/FDM/YASim/Turbulence.hpp

@@ -0,0 +1,30 @@
+namespace yasim {
+
+class Turbulence {
+public:
+    Turbulence(int gens, int seed);
+    ~Turbulence();
+    void update(double dt, double rate);
+    void setMagnitude(double mag) { _mag = mag; }
+    void getTurbulence(double* loc, float* turbOut);
+
+private:
+    unsigned int hashrand(unsigned int i);
+    float lattice(unsigned int x, unsigned int y);
+    float iturb(unsigned int x, unsigned int y);
+    float fturb(double a, double b);
+    void mkimg(float* buf, int sz);
+    float cubenorm(float x, float y, float z);
+    void turblut(int x, int y, float* out);
+
+    int _gens;
+    int _sz;
+    int _seed;
+
+    double _currTime;
+    double _mag;
+    float _x0, _x1, _y0, _y1, _z0, _z1;
+    unsigned char* _data;
+};
+
+}; // namespace yasim

src/FDM/YASim/YASim.cxx

@@ -1,3 +1,4 @@
+
 #include <simgear/debug/logstream.hxx>
 #include <simgear/math/sg_geodesy.hxx>
 #include <simgear/misc/sg_path.hxx>