// actions.cpp
//
// Copyright 1997-1998 by David K. McAllister
//
// I used code Copyright 1997 by Jonathan P. Leech
// as an example in implenting this.
//
// This file implements the dynamics of particle actions.

#include "general.h"
#include <float.h>
#include <iostream>

#define SQRT2PI 2.506628274631000502415765284811045253006
#define ONEOVERSQRT2PI (1. / SQRT2PI)

// To offset [0 .. 1] vectors to [-.5 .. .5]
static pVector vHalf(0.5, 0.5, 0.5);

static inline pVector RandVec()
{
    return pVector(drand48(), drand48(), drand48());
}

// Return a random number with a normal distribution.
static inline float NRand(float sigma = 1.0f)
{
#define ONE_OVER_SIGMA_EXP (1.0f / 0.7975f)

    if(sigma == 0) return 0;

    float y;
    do
    {
        y = -logf(drand48());
    }
    while(drand48() > expf(-fsqr(y - 1.0f)*0.5f));

    if(rand() & 0x1)
        return y * sigma * ONE_OVER_SIGMA_EXP;
    else
        return -y * sigma * ONE_OVER_SIGMA_EXP;
}

void PAAvoid::Execute(ParticleGroup *group)
{
    float magdt = magnitude * dt;

    switch(position.type)
    {
    case PDPlane:
        {
            if(look_ahead < P_MAXFLOAT)
            {
                for(int i = 0; i < group->p_count; i++)
                {
                    Particle &m = group->list[i];

                    // p2 stores the plane normal (the a,b,c of the plane eqn).
                    // Old and new distances: dist(p,plane) = n * p + d
                    // radius1 stores -n*p, which is d.
                    float dist = m.pos * position.p2 + position.radius1;

                    if(dist < look_ahead)
                    {
                        float vm = m.vel.length();
                        pVector Vn = m.vel / vm;
                        // float dot = Vn * position.p2;

                        pVector tmp = (position.p2 * (magdt / (dist*dist+epsilon))) + Vn;
                        m.vel = tmp * (vm / tmp.length());
                    }
                }
            }
            else
            {
                for(int i = 0; i < group->p_count; i++)
                {
                    Particle &m = group->list[i];

                    // p2 stores the plane normal (the a,b,c of the plane eqn).
                    // Old and new distances: dist(p,plane) = n * p + d
                    // radius1 stores -n*p, which is d.
                    float dist = m.pos * position.p2 + position.radius1;

                    float vm = m.vel.length();
                    pVector Vn = m.vel / vm;
                    // float dot = Vn * position.p2;

                    pVector tmp = (position.p2 * (magdt / (dist*dist+epsilon))) + Vn;
                    m.vel = tmp * (vm / tmp.length());
                }
            }
        }
        break;
    case PDRectangle:
        {
            // Compute the inverse matrix of the plane basis.
            pVector &u = position.u;
            pVector &v = position.v;

            // The normalized bases are needed inside the loop.
            pVector un = u / position.radius1Sqr;
            pVector vn = v / position.radius2Sqr;

            // w = u cross v
            float wx = u.y*v.z-u.z*v.y;
            float wy = u.z*v.x-u.x*v.z;
            float wz = u.x*v.y-u.y*v.x;

            float det = 1/(wz*u.x*v.y-wz*u.y*v.x-u.z*wx*v.y-u.x*v.z*wy+v.z*wx*u.y+u.z*v.x*wy);

            pVector s1((v.y*wz-v.z*wy), (v.z*wx-v.x*wz), (v.x*wy-v.y*wx));
            s1 *= det;
            pVector s2((u.y*wz-u.z*wy), (u.z*wx-u.x*wz), (u.x*wy-u.y*wx));
            s2 *= -det;

            // See which particles bounce.
            for(int i = 0; i < group->p_count; i++)
            {
                Particle &m = group->list[i];

                // See if particle's current and next positions cross plane.
                // If not, couldn't bounce, so keep going.
                pVector pnext(m.pos + m.vel * dt * look_ahead);

                // p2 stores the plane normal (the a,b,c of the plane eqn).
                // Old and new distances: dist(p,plane) = n * p + d
                // radius1 stores -n*p, which is d.
                float distold = m.pos * position.p2 + position.radius1;
                float distnew = pnext * position.p2 + position.radius1;

                // Opposite signs if product < 0
                // There is no faster way to do this.
                if(distold * distnew >= 0)
                    continue;

                float nv = position.p2 * m.vel;
                float t = -distold / nv;

                // Actual intersection point p(t) = pos + vel t
                pVector phit(m.pos + m.vel * t);

                // Offset from origin in plane, p - origin
                pVector offset(phit - position.p1);

                // Dot product with basis vectors of old frame
                // in terms of new frame gives position in uv frame.
                float upos = offset * s1;
                float vpos = offset * s2;

                // Did it cross plane outside triangle?
                if(upos < 0 || vpos < 0 || upos > 1 || vpos > 1)
                    continue;

                // A hit! A most palpable hit!
                // Compute distance to the three edges.
                pVector uofs = (un * (un * offset)) - offset;
                float udistSqr = uofs.length2();
                pVector vofs = (vn * (vn * offset)) - offset;
                float vdistSqr = vofs.length2();

                pVector foffset((u + v) - offset);
                pVector fofs = (un * (un * foffset)) - foffset;
                float fdistSqr = fofs.length2();
                pVector gofs = (un * (un * foffset)) - foffset;
                float gdistSqr = gofs.length2();

                pVector S;
                if(udistSqr <= vdistSqr && udistSqr <= fdistSqr
                        && udistSqr <= gdistSqr) S = uofs;
                else if(vdistSqr <= fdistSqr && vdistSqr <= gdistSqr) S = vofs;
                else if(fdistSqr <= gdistSqr) S = fofs;
                else S = gofs;

                S.normalize();

                // We now have a vector to safety.
                float vm = m.vel.length();
                pVector Vn = m.vel / vm;

                // Blend S into V.
                pVector tmp = (S * (magdt / (t*t+epsilon))) + Vn;
                m.vel = tmp * (vm / tmp.length());
            }
        }
        break;
    case PDTriangle:
        {
            // Compute the inverse matrix of the plane basis.
            pVector &u = position.u;
            pVector &v = position.v;

            // The normalized bases are needed inside the loop.
            pVector un = u / position.radius1Sqr;
            pVector vn = v / position.radius2Sqr;

            // f is the third (non-basis) triangle edge.
            pVector f = v - u;
            pVector fn(f);
            fn.normalize();

            // w = u cross v
            float wx = u.y*v.z-u.z*v.y;
            float wy = u.z*v.x-u.x*v.z;
            float wz = u.x*v.y-u.y*v.x;

            float det = 1/(wz*u.x*v.y-wz*u.y*v.x-u.z*wx*v.y-u.x*v.z*wy+v.z*wx*u.y+u.z*v.x*wy);

            pVector s1((v.y*wz-v.z*wy), (v.z*wx-v.x*wz), (v.x*wy-v.y*wx));
            s1 *= det;
            pVector s2((u.y*wz-u.z*wy), (u.z*wx-u.x*wz), (u.x*wy-u.y*wx));
            s2 *= -det;

            // See which particles bounce.
            for(int i = 0; i < group->p_count; i++)
            {
                Particle &m = group->list[i];

                // See if particle's current and next positions cross plane.
                // If not, couldn't bounce, so keep going.
                pVector pnext(m.pos + m.vel * dt * look_ahead);

                // p2 stores the plane normal (the a,b,c of the plane eqn).
                // Old and new distances: dist(p,plane) = n * p + d
                // radius1 stores -n*p, which is d.
                float distold = m.pos * position.p2 + position.radius1;
                float distnew = pnext * position.p2 + position.radius1;

                // Opposite signs if product < 0
                // Is there a faster way to do this?
                if(distold * distnew >= 0)
                    continue;

                float nv = position.p2 * m.vel;
                float t = -distold / nv;

                // Actual intersection point p(t) = pos + vel t
                pVector phit(m.pos + m.vel * t);

                // Offset from origin in plane, p - origin
                pVector offset(phit - position.p1);

                // Dot product with basis vectors of old frame
                // in terms of new frame gives position in uv frame.
                float upos = offset * s1;
                float vpos = offset * s2;

                // Did it cross plane outside triangle?
                if(upos < 0 || vpos < 0 || (upos + vpos) > 1)
                    continue;

                // A hit! A most palpable hit!
                // Compute distance to the three edges.
                pVector uofs = (un * (un * offset)) - offset;
                float udistSqr = uofs.length2();
                pVector vofs = (vn * (vn * offset)) - offset;
                float vdistSqr = vofs.length2();
                pVector foffset(offset - u);
                pVector fofs = (fn * (fn * foffset)) - foffset;
                float fdistSqr = fofs.length2();
                pVector S;
                if(udistSqr <= vdistSqr && udistSqr <= fdistSqr) S = uofs;
                else if(vdistSqr <= fdistSqr) S = vofs;
                else S = fofs;

                S.normalize();

                // We now have a vector to safety.
                float vm = m.vel.length();
                pVector Vn = m.vel / vm;

                // Blend S into V.
                pVector tmp = (S * (magdt / (t*t+epsilon))) + Vn;
                m.vel = tmp * (vm / tmp.length());
            }
        }
        break;
    case PDDisc:
        {
            float r1Sqr = fsqr(position.radius1);
            float r2Sqr = fsqr(position.radius2);

            // See which particles bounce.
            for(int i = 0; i < group->p_count; i++)
            {
                Particle &m = group->list[i];

                // See if particle's current and next positions cross plane.
                // If not, couldn't bounce, so keep going.
                pVector pnext(m.pos + m.vel * dt * look_ahead);

                // p2 stores the plane normal (the a,b,c of the plane eqn).
                // Old and new distances: dist(p,plane) = n * p + d
                // radius1 stores -n*p, which is d. radius1Sqr stores d.
                float distold = m.pos * position.p2 + position.radius1Sqr;
                float distnew = pnext * position.p2 + position.radius1Sqr;

                // Opposite signs if product < 0
                // Is there a faster way to do this?
                if(distold * distnew >= 0)
                    continue;

                // Find position at the crossing point by parameterizing
                // p(t) = pos + vel * t
                // Solve dist(p(t),plane) = 0 e.g.
                // n * p(t) + D = 0 ->
                // n * p + t (n * v) + D = 0 ->
                // t = -(n * p + D) / (n * v)
                // Could factor n*v into distnew = distold + n*v and save a bit.
                // Safe since n*v != 0 assured by quick rejection test.
                // This calc is indep. of dt because we have established that it
                // will hit before dt. We just want to know when.
                float nv = position.p2 * m.vel;
                float t = -distold / nv;

                // Actual intersection point p(t) = pos + vel t
                pVector phit(m.pos + m.vel * t);

                // Offset from origin in plane, phit - origin
                pVector offset(phit - position.p1);

                float rad = offset.length2();

                if(rad > r1Sqr || rad < r2Sqr)
                    continue;

                // A hit! A most palpable hit!
                pVector S = offset;
                S.normalize();

                // We now have a vector to safety.
                float vm = m.vel.length();
                pVector Vn = m.vel / vm;

                // Blend S into V.
                pVector tmp = (S * (magdt / (t*t+epsilon))) + Vn;
                m.vel = tmp * (vm / tmp.length());
            }
        }
        break;
    case PDSphere:
        {
            float rSqr = position.radius1 * position.radius1;

            // See which particles are aimed toward the sphere.
            for(int i = 0; i < group->p_count; i++)
            {
                Particle &m = group->list[i];

                // First do a ray-sphere intersection test and
                // see if it's soon enough.
                // Can I do this faster without t?
                float vm = m.vel.length();
                pVector Vn = m.vel / vm;

                pVector L = position.p1 - m.pos;
                float v = L * Vn;

                float disc = rSqr - (L * L) + v * v;
                if(disc < 0)
                    continue; // I'm not heading toward it.

                // Compute length for second rejection test.
                float t = v - sqrtf(disc);
                if(t < 0 || t > (vm * look_ahead))
                    continue;

                // Get a vector to safety.
                pVector C = Vn ^ L;
                C.normalize();
                pVector S = Vn ^ C;

                // Blend S into V.
                pVector tmp = (S * (magdt / (t*t+epsilon))) + Vn;
                m.vel = tmp * (vm / tmp.length());
            }
        }
        break;
    default:
        break;
    }
}

void PABounce::Execute(ParticleGroup *group)
{
    switch(position.type)
    {
    case PDTriangle:
        {
            // Compute the inverse matrix of the plane basis.
            pVector &u = position.u;
            pVector &v = position.v;

            // w = u cross v
            float wx = u.y*v.z-u.z*v.y;
            float wy = u.z*v.x-u.x*v.z;
            float wz = u.x*v.y-u.y*v.x;

            float det = 1/(wz*u.x*v.y-wz*u.y*v.x-u.z*wx*v.y-u.x*v.z*wy+v.z*wx*u.y+u.z*v.x*wy);

            pVector s1((v.y*wz-v.z*wy), (v.z*wx-v.x*wz), (v.x*wy-v.y*wx));
            s1 *= det;
            pVector s2((u.y*wz-u.z*wy), (u.z*wx-u.x*wz), (u.x*wy-u.y*wx));
            s2 *= -det;

            // See which particles bounce.
            for(int i = 0; i < group->p_count; i++)
            {
                Particle &m = group->list[i];

                // See if particle's current and next positions cross plane.
                // If not, couldn't bounce, so keep going.
                pVector pnext(m.pos + m.vel * dt);

                // p2 stores the plane normal (the a,b,c of the plane eqn).
                // Old and new distances: dist(p,plane) = n * p + d
                // radius1 stores -n*p, which is d.
                float distold = m.pos * position.p2 + position.radius1;
                float distnew = pnext * position.p2 + position.radius1;

                // Opposite signs if product < 0
                // Is there a faster way to do this?
                if(distold * distnew >= 0)
                    continue;

                // Find position at the crossing point by parameterizing
                // p(t) = pos + vel * t
                // Solve dist(p(t),plane) = 0 e.g.
                // n * p(t) + D = 0 ->
                // n * p + t (n * v) + D = 0 ->
                // t = -(n * p + D) / (n * v)
                // Could factor n*v into distnew = distold + n*v and save a bit.
                // Safe since n*v != 0 assured by quick rejection test.
                // This calc is indep. of dt because we have established that it
                // will hit before dt. We just want to know when.
                float nv = position.p2 * m.vel;
                float t = -distold / nv;

                // Actual intersection point p(t) = pos + vel t
                pVector phit(m.pos + m.vel * t);

                // Offset from origin in plane, p - origin
                pVector offset(phit - position.p1);

                // Dot product with basis vectors of old frame
                // in terms of new frame gives position in uv frame.
                float upos = offset * s1;
                float vpos = offset * s2;

                // Did it cross plane outside triangle?
                if(upos < 0 || vpos < 0 || (upos + vpos) > 1)
                    continue;

                // A hit! A most palpable hit!

                // Compute tangential and normal components of velocity
                pVector vn(position.p2 * nv); // Normal Vn = (V.N)N
                pVector vt(m.vel - vn); // Tangent Vt = V - Vn

                // Compute new velocity heading out:
                // Don't apply friction if tangential velocity < cutoff
                if(vt.length2() <= cutoffSqr)
                    m.vel = vt - vn * resilience;
                else
                    m.vel = vt * oneMinusFriction - vn * resilience;
            }
        }
        break;
    case PDDisc:
        {
            float r1Sqr = fsqr(position.radius1);
            float r2Sqr = fsqr(position.radius2);

            // See which particles bounce.
            for(int i = 0; i < group->p_count; i++)
            {
                Particle &m = group->list[i];

                // See if particle's current and next positions cross plane.
                // If not, couldn't bounce, so keep going.
                pVector pnext(m.pos + m.vel * dt);

                // p2 stores the plane normal (the a,b,c of the plane eqn).
                // Old and new distances: dist(p,plane) = n * p + d
                // radius1 stores -n*p, which is d. radius1Sqr stores d.
                float distold = m.pos * position.p2 + position.radius1Sqr;
                float distnew = pnext * position.p2 + position.radius1Sqr;

                // Opposite signs if product < 0
                // Is there a faster way to do this?
                if(distold * distnew >= 0)
                    continue;

                // Find position at the crossing point by parameterizing
                // p(t) = pos + vel * t
                // Solve dist(p(t),plane) = 0 e.g.
                // n * p(t) + D = 0 ->
                // n * p + t (n * v) + D = 0 ->
                // t = -(n * p + D) / (n * v)
                // Could factor n*v into distnew = distold + n*v and save a bit.
                // Safe since n*v != 0 assured by quick rejection test.
                // This calc is indep. of dt because we have established that it
                // will hit before dt. We just want to know when.
                float nv = position.p2 * m.vel;
                float t = -distold / nv;

                // Actual intersection point p(t) = pos + vel t
                pVector phit(m.pos + m.vel * t);

                // Offset from origin in plane, phit - origin
                pVector offset(phit - position.p1);

                float rad = offset.length2();

                if(rad > r1Sqr || rad < r2Sqr)
                    continue;

                // A hit! A most palpable hit!

                // Compute tangential and normal components of velocity
                pVector vn(position.p2 * nv); // Normal Vn = (V.N)N
                pVector vt(m.vel - vn); // Tangent Vt = V - Vn

                // Compute new velocity heading out:
                // Don't apply friction if tangential velocity < cutoff
                if(vt.length2() <= cutoffSqr)
                    m.vel = vt - vn * resilience;
                else
                    m.vel = vt * oneMinusFriction - vn * resilience;
            }
        }
        break;
    case PDPlane:
        {
            // See which particles bounce.
            for(int i = 0; i < group->p_count; i++)
            {
                Particle &m = group->list[i];

                // See if particle's current and next positions cross plane.
                // If not, couldn't bounce, so keep going.
                pVector pnext(m.pos + m.vel * dt);

                // p2 stores the plane normal (the a,b,c of the plane eqn).
                // Old and new distances: dist(p,plane) = n * p + d
                // radius1 stores -n*p, which is d.
                float distold = m.pos * position.p2 + position.radius1;
                float distnew = pnext * position.p2 + position.radius1;

                // Opposite signs if product < 0
                if(distold * distnew >= 0)
                    continue;

                // Compute tangential and normal components of velocity
                float nmag = m.vel * position.p2;
                pVector vn(position.p2 * nmag); // Normal Vn = (V.N)N
                pVector vt(m.vel - vn); // Tangent Vt = V - Vn

                // Compute new velocity heading out:
                // Don't apply friction if tangential velocity < cutoff
                if(vt.length2() <= cutoffSqr)
                    m.vel = vt - vn * resilience;
                else
                    m.vel = vt * oneMinusFriction - vn * resilience;
            }
        }
        break;
    case PDRectangle:
        {
            // Compute the inverse matrix of the plane basis.
            pVector &u = position.u;
            pVector &v = position.v;

            // w = u cross v
            float wx = u.y*v.z-u.z*v.y;
            float wy = u.z*v.x-u.x*v.z;
            float wz = u.x*v.y-u.y*v.x;

            float det = 1/(wz*u.x*v.y-wz*u.y*v.x-u.z*wx*v.y-u.x*v.z*wy+v.z*wx*u.y+u.z*v.x*wy);

            pVector s1((v.y*wz-v.z*wy), (v.z*wx-v.x*wz), (v.x*wy-v.y*wx));
            s1 *= det;
            pVector s2((u.y*wz-u.z*wy), (u.z*wx-u.x*wz), (u.x*wy-u.y*wx));
            s2 *= -det;

            // See which particles bounce.
            for(int i = 0; i < group->p_count; i++)
            {
                Particle &m = group->list[i];

                // See if particle's current and next positions cross plane.
                // If not, couldn't bounce, so keep going.
                pVector pnext(m.pos + m.vel * dt);

                // p2 stores the plane normal (the a,b,c of the plane eqn).
                // Old and new distances: dist(p,plane) = n * p + d
                // radius1 stores -n*p, which is d.
                float distold = m.pos * position.p2 + position.radius1;
                float distnew = pnext * position.p2 + position.radius1;

                // Opposite signs if product < 0
                if(distold * distnew >= 0)
                    continue;

                // Find position at the crossing point by parameterizing
                // p(t) = pos + vel * t
                // Solve dist(p(t),plane) = 0 e.g.
                // n * p(t) + D = 0 ->
                // n * p + t (n * v) + D = 0 ->
                // t = -(n * p + D) / (n * v)
                float t = -distold / (position.p2 * m.vel);

                // Actual intersection point p(t) = pos + vel t
                pVector phit(m.pos + m.vel * t);

                // Offset from origin in plane, p - origin
                pVector offset(phit - position.p1);

                // Dot product with basis vectors of old frame
                // in terms of new frame gives position in uv frame.
                float upos = offset * s1;
                float vpos = offset * s2;

                // Crossed plane outside bounce region if !(0<=[uv]pos<=1)
                if(upos < 0 || upos > 1 || vpos < 0 || vpos > 1)
                    continue;

                // A hit! A most palpable hit!

                // Compute tangential and normal components of velocity
                float nmag = m.vel * position.p2;
                pVector vn(position.p2 * nmag); // Normal Vn = (V.N)N
                pVector vt(m.vel - vn); // Tangent Vt = V - Vn

                // Compute new velocity heading out:
                // Don't apply friction if tangential velocity < cutoff
                if(vt.length2() <= cutoffSqr)
                    m.vel = vt - vn * resilience;
                else
                    m.vel = vt * oneMinusFriction - vn * resilience;
            }
        }
        break;
    case PDSphere:
        {
            // Sphere that particles bounce off
            // The particles are always forced out of the sphere.
            for(int i = 0; i < group->p_count; i++)
            {
                Particle &m = group->list[i];

                // See if particle's next position is inside domain.
                // If so, bounce it.
                pVector pnext(m.pos + m.vel * dt);

                if(position.Within(pnext))
                {
                    // See if we were inside on previous timestep.
                    bool pinside = position.Within(m.pos);

                    // Normal to surface. This works for a sphere. Isn't
                    // computed quite right, should extrapolate particle
                    // position to surface.
                    pVector n(m.pos - position.p1);
                    n.normalize();

                    // Compute tangential and normal components of velocity
                    float nmag = m.vel * n;

                    pVector vn(n * nmag); // Normal Vn = (V.N)N
                    pVector vt = m.vel - vn; // Tangent Vt = V - Vn

                    if(pinside)
                    {
                        // Previous position was inside. If normal component of
                        // velocity points in, reverse it. This effectively
                        // repels particles which would otherwise be trapped
                        // in the sphere.
                        if(nmag < 0)
                            m.vel = vt - vn;
                    }
                    else
                    {
                        // Previous position was outside -> particle will cross
                        // surface boundary. Reverse normal component of velocity,
                        // and apply friction (if Vt >= cutoff) and resilience.

                        // Compute new velocity heading out:
                        // Don't apply friction if tangential velocity < cutoff
                        if(vt.length2() <= cutoffSqr)
                            m.vel = vt - vn * resilience;
                        else
                            m.vel = vt * oneMinusFriction - vn * resilience;
                    }
                }
            }
        }
    default:
        break;
    }
}

// Set the secondary position of each particle to be its position.
void PACallActionList::Execute(ParticleGroup *group)
{
    pCallActionList(action_list_num);
}

// Set the secondary position of each particle to be its position.
void PACopyVertexB::Execute(ParticleGroup *group)
{
    int i;

    if(copy_pos)
    {
        for(i = 0; i < group->p_count; i++)
        {
            Particle &m = group->list[i];
            m.posB = m.pos;
        }
    }

    if(copy_vel)
    {
        for(i = 0; i < group->p_count; i++)
        {
            Particle &m = group->list[i];
            m.velB = m.vel;
        }
    }
}

// Dampen velocities
void PADamping::Execute(ParticleGroup *group)
{
    // This is important if dt is != 1.
    pVector one(1,1,1);
    pVector scale(one - ((one - damping) * dt));

    for(int i = 0; i < group->p_count; i++)
    {
        Particle &m = group->list[i];
        float vSqr = m.vel.length2();

        if(vSqr >= vlowSqr && vSqr <= vhighSqr)
        {
            m.vel.x *= scale.x;
            m.vel.y *= scale.y;
            m.vel.z *= scale.z;
        }
    }
}

// Exert force on each particle away from explosion center
void PAExplosion::Execute(ParticleGroup *group)
{
    float radius = velocity * age;
    float magdt = magnitude * dt;
    float oneOverSigma = 1.0f / stdev;
    float inexp = -0.5f*fsqr(oneOverSigma);
    float outexp = ONEOVERSQRT2PI * oneOverSigma;

    for(int i = 0; i < group->p_count; i++)
    {
        Particle &m = group->list[i];

        // Figure direction to particle.
        pVector dir(m.pos - center);
        float distSqr = dir.length2();
        float dist = sqrtf(distSqr);
        float DistFromWaveSqr = fsqr(radius - dist);

        float Gd = exp(DistFromWaveSqr * inexp) * outexp;

        m.vel += dir * (Gd * magdt / (dist * (distSqr + epsilon)));
    }

    age += dt;
}

// Follow the next particle in the list
void PAFollow::Execute(ParticleGroup *group)
{
    float magdt = magnitude * dt;
    float max_radiusSqr = max_radius * max_radius;

    if(max_radiusSqr < P_MAXFLOAT)
    {
        for(int i = 0; i < group->p_count - 1; i++)
        {
            Particle &m = group->list[i];

            // Accelerate toward the particle after me in the list.
            pVector tohim(group->list[i+1].pos - m.pos); // tohim = p1 - p0
            float tohimlenSqr = tohim.length2();

            if(tohimlenSqr < max_radiusSqr)
            {
                // Compute force exerted between the two bodies
                m.vel += tohim * (magdt / (sqrtf(tohimlenSqr) * (tohimlenSqr + epsilon)));
            }
        }
    }
    else
    {
        for(int i = 0; i < group->p_count - 1; i++)
        {
            Particle &m = group->list[i];

            // Accelerate toward the particle after me in the list.
            pVector tohim(group->list[i+1].pos - m.pos); // tohim = p1 - p0
            float tohimlenSqr = tohim.length2();

            // Compute force exerted between the two bodies
            m.vel += tohim * (magdt / (sqrtf(tohimlenSqr) * (tohimlenSqr + epsilon)));
        }
    }
}

// Inter-particle gravitation
void PAGravitate::Execute(ParticleGroup *group)
{
    float magdt = magnitude * dt;
    float max_radiusSqr = max_radius * max_radius;

    if(max_radiusSqr < P_MAXFLOAT)
    {
        for(int i = 0; i < group->p_count; i++)
        {
            Particle &m = group->list[i];

            // Add interactions with other particles
            for(int j = i + 1; j < group->p_count; j++)
            {
                Particle &mj = group->list[j];

                pVector tohim(mj.pos - m.pos); // tohim = p1 - p0
                float tohimlenSqr = tohim.length2();

                if(tohimlenSqr < max_radiusSqr)
                {
                    // Compute force exerted between the two bodies
                    pVector acc(tohim * (magdt / (sqrtf(tohimlenSqr) * (tohimlenSqr + epsilon))));

                    m.vel += acc;
                    mj.vel -= acc;
                }
            }
        }
    }
    else
    {
        for(int i = 0; i < group->p_count; i++)
        {
            Particle &m = group->list[i];

            // Add interactions with other particles
            for(int j = i + 1; j < group->p_count; j++)
            {
                Particle &mj = group->list[j];

                pVector tohim(mj.pos - m.pos); // tohim = p1 - p0
                float tohimlenSqr = tohim.length2();

                // Compute force exerted between the two bodies
                pVector acc(tohim * (magdt / (sqrtf(tohimlenSqr) * (tohimlenSqr + epsilon))));

                m.vel += acc;
                mj.vel -= acc;
            }
        }
    }
}

// Acceleration in a constant direction
void PAGravity::Execute(ParticleGroup *group)
{
    pVector ddir(direction * dt);

    for(int i = 0; i < group->p_count; i++)
    {
        // Step velocity with acceleration
        group->list[i].vel += ddir;
    }
}

// Accelerate particles along a line
void PAJet::Execute(ParticleGroup *group)
{
    float magdt = magnitude * dt;
    float max_radiusSqr = max_radius * max_radius;

    if(max_radiusSqr < P_MAXFLOAT)
    {
        for(int i = 0; i < group->p_count; i++)
        {
            Particle &m = group->list[i];

            // Figure direction to particle.
            pVector dir(m.pos - center);

            // Distance to jet (force drops as 1/r^2)
            // Soften by epsilon to avoid tight encounters to infinity
            float rSqr = dir.length2();

            if(rSqr < max_radiusSqr)
            {
                pVector accel;
                acc.Generate(accel);

                // Step velocity with acceleration
                m.vel += accel * (magdt / (rSqr + epsilon));
            }
        }
    }
    else
    {
        for(int i = 0; i < group->p_count; i++)
        {
            Particle &m = group->list[i];

            // Figure direction to particle.
            pVector dir(m.pos - center);

            // Distance to jet (force drops as 1/r^2)
            // Soften by epsilon to avoid tight encounters to infinity
            float rSqr = dir.length2();

            pVector accel;
            acc.Generate(accel);

            // Step velocity with acceleration
            m.vel += accel * (magdt / (rSqr + epsilon));
        }
    }
}

// Get rid of older particles
void PAKillOld::Execute(ParticleGroup *group)
{
    // Must traverse list in reverse order so Remove will work
    for(int i = group->p_count-1; i >= 0; i--)
    {
        Particle &m = group->list[i];

        if(!((m.age < age_limit) ^ kill_less_than))
            group->Remove(i);
    }
}

// Match velocity to near neighbors
void PAMatchVelocity::Execute(ParticleGroup *group)
{
    float magdt = magnitude * dt;
    float max_radiusSqr = max_radius * max_radius;

    if(max_radiusSqr < P_MAXFLOAT)
    {
        for(int i = 0; i < group->p_count; i++)
        {
            Particle &m = group->list[i];

            // Add interactions with other particles
            for(int j = i + 1; j < group->p_count; j++)
            {
                Particle &mj = group->list[j];

                pVector tohim(mj.pos - m.pos); // tohim = p1 - p0
                float tohimlenSqr = tohim.length2();

                if(tohimlenSqr < max_radiusSqr)
                {
                    // Compute force exerted between the two bodies
                    pVector acc(mj.vel * (magdt / (tohimlenSqr + epsilon)));

                    m.vel += acc;
                    mj.vel -= acc;
                }
            }
        }
    }
    else
    {
        for(int i = 0; i < group->p_count; i++)
        {
            Particle &m = group->list[i];

            // Add interactions with other particles
            for(int j = i + 1; j < group->p_count; j++)
            {
                Particle &mj = group->list[j];

                pVector tohim(mj.pos - m.pos); // tohim = p1 - p0
                float tohimlenSqr = tohim.length2();

                // Compute force exerted between the two bodies
                pVector acc(mj.vel * (magdt / (tohimlenSqr + epsilon)));

                m.vel += acc;
                mj.vel -= acc;
            }
        }
    }
}

void PAMove::Execute(ParticleGroup *group)
{
    // Step particle positions forward by dt, and age the particles.
    for(int i = 0; i < group->p_count; i++)
    {
        Particle &m = group->list[i];

        m.age += dt;
        m.pos += m.vel * dt;
    }
}

// Accelerate particles towards a line
void PAOrbitLine::Execute(ParticleGroup *group)
{
    float magdt = magnitude * dt;
    float max_radiusSqr = max_radius * max_radius;

    if(max_radiusSqr < P_MAXFLOAT)
    {
        for(int i = 0; i < group->p_count; i++)
        {
            Particle &m = group->list[i];

            // Figure direction to particle from base of line.
            pVector f(m.pos - p);

            pVector w(axis * (f * axis));

            // Direction from particle to nearest point on line.
            pVector into = w - f;

            // Distance to line (force drops as 1/r^2, normalize by 1/r)
            // Soften by epsilon to avoid tight encounters to infinity
            float rSqr = into.length2();

            if(rSqr < max_radiusSqr)
                // Step velocity with acceleration
                m.vel += into * (magdt / (sqrtf(rSqr) + (rSqr + epsilon)));
        }
    }
    else
    {
        // Removed because it causes pipeline stalls.
        for(int i = 0; i < group->p_count; i++)
        {
            Particle &m = group->list[i];

            // Figure direction to particle from base of line.
            pVector f(m.pos - p);

            pVector w(axis * (f * axis));

            // Direction from particle to nearest point on line.
            pVector into = w - f;

            // Distance to line (force drops as 1/r^2, normalize by 1/r)
            // Soften by epsilon to avoid tight encounters to infinity
            float rSqr = into.length2();

            // Step velocity with acceleration
            m.vel += into * (magdt / (sqrtf(rSqr) + (rSqr + epsilon)));
        }
    }
}

// Accelerate particles towards a point
void PAOrbitPoint::Execute(ParticleGroup *group)
{
    float magdt = magnitude * dt;
    float max_radiusSqr = max_radius * max_radius;

    if(max_radiusSqr < P_MAXFLOAT)
    {
        for(int i = 0; i < group->p_count; i++)
        {
            Particle &m = group->list[i];

            // Figure direction to particle.
            pVector dir(center - m.pos);

            // Distance to gravity well (force drops as 1/r^2, normalize by 1/r)
            // Soften by epsilon to avoid tight encounters to infinity
            float rSqr = dir.length2();

            // Step velocity with acceleration
            if(rSqr < max_radiusSqr)
                m.vel += dir * (magdt / (sqrtf(rSqr) + (rSqr + epsilon)));
        }
    }
    else
    {
        // Avoids pipeline stalls.
        for(int i = 0; i < group->p_count; i++)
        {
            Particle &m = group->list[i];

            // Figure direction to particle.
            pVector dir(center - m.pos);

            // Distance to gravity well (force drops as 1/r^2, normalize by 1/r)
            // Soften by epsilon to avoid tight encounters to infinity
            float rSqr = dir.length2();

            // Step velocity with acceleration
            m.vel += dir * (magdt / (sqrtf(rSqr) + (rSqr + epsilon)));
        }
    }
}

// Accelerate in random direction each time step
void PARandomAccel::Execute(ParticleGroup *group)
{
    for(int i = 0; i < group->p_count; i++)
    {
        Particle &m = group->list[i];

        pVector acceleration;
        gen_acc.Generate(acceleration);

        // dt will affect this by making a higher probability of
        // being near the original velocity after unit time. Smaller
        // dt approach a normal distribution instead of a square wave.
        m.vel += acceleration * dt;
    }
}

// Immediately displace position randomly
void PARandomDisplace::Execute(ParticleGroup *group)
{
    for(int i = 0; i < group->p_count; i++)
    {
        Particle &m = group->list[i];

        pVector displacement;
        gen_disp.Generate(displacement);

        // dt will affect this by making a higher probability of
        // being near the original position after unit time. Smaller
        // dt approach a normal distribution instead of a square wave.
        m.pos += displacement * dt;
    }
}

// Immediately assign a random velocity
void PARandomVelocity::Execute(ParticleGroup *group)
{
    for(int i = 0; i < group->p_count; i++)
    {
        Particle &m = group->list[i];

        pVector velocity;
        gen_vel.Generate(velocity);

        // Shouldn't multiply by dt because velocities are
        // invariant of dt. How should dt affect this?
        m.vel = velocity;
    }
}

#if 0
// Produce coefficients of a velocity function v(t)=at^2 + bt + c
// satisfying initial x(0)=x0,v(0)=v0 and desired x(t)=xf,v(t)=vf,
// where x = x(0) + integrate(v(T),0,t)
static inline void _pconstrain(float x0, float v0, float xf, float vf,
                               float t, float *a, float *b, float *c)
{
    *c = v0;
    *b = 2 * (-t*vf - 2*t*v0 + 3*xf - 3*x0) / (t * t);
    *a = 3 * (t*vf + t*v0 - 2*xf + 2*x0) / (t * t * t);
}
#endif

// Over time, restore particles to initial positions
// Put all particles on the surface of a statue, explode the statue,
// and then suck the particles back to the original position. Cool!
void PARestore::Execute(ParticleGroup *group)
{
    if(time_left <= 0)
    {
        for(int i = 0; i < group->p_count; i++)
        {
            Particle &m = group->list[i];

            // Already constrained, keep it there.
            m.pos = m.posB;
            m.vel = pVector(0,0,0);
        }
    }
    else
    {
        float t = time_left;
        float dtSqr = dt * dt;
        float tSqrInv2dt = dt * 2.0f / (t * t);
        float tCubInv3dtSqr = dtSqr * 3.0f / (t * t * t);

        for(int i = 0; i < group->p_count; i++)
        {
#if 1
            Particle &m = group->list[i];

            // Solve for a desired-behavior velocity function in each axis
            // _pconstrain(m.pos.x, m.vel.x, m.posB.x, 0., timeLeft, &a, &b, &c);

            // Figure new velocity at next timestep
            // m.vel.x = a * dtSqr + b * dt + c;

            float b = (-2*t*m.vel.x + 3*m.posB.x - 3*m.pos.x) * tSqrInv2dt;
            float a = (t*m.vel.x - m.posB.x - m.posB.x + m.pos.x + m.pos.x) * tCubInv3dtSqr;

            // Figure new velocity at next timestep
            m.vel.x += a + b;

            b = (-2*t*m.vel.y + 3*m.posB.y - 3*m.pos.y) * tSqrInv2dt;
            a = (t*m.vel.y - m.posB.y - m.posB.y + m.pos.y + m.pos.y) * tCubInv3dtSqr;

            // Figure new velocity at next timestep
            m.vel.y += a + b;

            b = (-2*t*m.vel.z + 3*m.posB.z - 3*m.pos.z) * tSqrInv2dt;
            a = (t*m.vel.z - m.posB.z - m.posB.z + m.pos.z + m.pos.z) * tCubInv3dtSqr;

            // Figure new velocity at next timestep
            m.vel.z += a + b;
#else
            Particle &m = group->list[i];

            // XXX Optimize this.
            // Solve for a desired-behavior velocity function in each axis
            float a, b, c; // Coefficients of velocity function needed

            _pconstrain(m.pos.x, m.vel.x, m.posB.x, 0.,
                        timeLeft, &a, &b, &c);

            // Figure new velocity at next timestep
            m.vel.x = a * dtSqr + b * dt + c;

            _pconstrain(m.pos.y, m.vel.y, m.posB.y, 0.,
                        timeLeft, &a, &b, &c);

            // Figure new velocity at next timestep
            m.vel.y = a * dtSqr + b * dt + c;

            _pconstrain(m.pos.z, m.vel.z, m.posB.z, 0.,
                        timeLeft, &a, &b, &c);

            // Figure new velocity at next timestep
            m.vel.z = a * dtSqr + b * dt + c;

#endif
        }
    }

    time_left -= dt;
}

// Kill particles with positions on wrong side of the specified domain
void PASink::Execute(ParticleGroup *group)
{
    // Must traverse list in reverse order so Remove will work
    for(int i = group->p_count-1; i >= 0; i--)
    {
        Particle &m = group->list[i];

        // Remove if inside/outside flag matches object's flag
        if(!(position.Within(m.pos) ^ kill_inside))
            group->Remove(i);
    }
}

// Kill particles with velocities on wrong side of the specified domain
void PASinkVelocity::Execute(ParticleGroup *group)
{
    // Must traverse list in reverse order so Remove will work
    for(int i = group->p_count-1; i >= 0; i--)
    {
        Particle &m = group->list[i];

        // Remove if inside/outside flag matches object's flag
        if(!(velocity.Within(m.vel) ^ kill_inside))
            group->Remove(i);
    }
}

// Randomly add particles to the system
void PASource::Execute(ParticleGroup *group)
{
    int rate = int(floor(particle_rate * dt));

    // Dither the fraction particle in time.
    if(drand48() < particle_rate * dt - float(rate))
        rate++;

    // Don't emit more than it can hold.
    if(group->p_count + rate > group->max_particles)
        rate = group->max_particles - group->p_count;

    pVector pos, posB, vel, col, siz;

    if(vertexB_tracks)
    {
        for(int i = 0; i < rate; i++)
        {
            position.Generate(pos);
            size.Generate(siz);
            velocity.Generate(vel);
            color.Generate(col);
            float ag = age + NRand(age_sigma);

            group->Add(pos, pos, siz, vel, col, alpha, ag);
        }
    }
    else
    {
        for(int i = 0; i < rate; i++)
        {
            position.Generate(pos);
            positionB.Generate(posB);
            size.Generate(siz);
            velocity.Generate(vel);
            color.Generate(col);
            float ag = age + NRand(age_sigma);

            group->Add(pos, posB, siz, vel, col, alpha, ag);
        }
    }
}

void PASpeedLimit::Execute(ParticleGroup *group)
{
    float min_sqr = min_speed*min_speed;
    float max_sqr = max_speed*max_speed;

    for(int i = 0; i < group->p_count; i++)
    {
        Particle &m = group->list[i];
        float sSqr = m.vel.length2();
        if(sSqr<min_sqr && sSqr)
        {
            float s = sqrtf(sSqr);
            m.vel *= (min_speed/s);
        }
        else if(sSqr>max_sqr)
        {
            float s = sqrtf(sSqr);
            m.vel *= (max_speed/s);
        }
    }
}

// Change color of all particles toward the specified color
void PATargetColor::Execute(ParticleGroup *group)
{
    float scaleFac = scale * dt;

    for(int i = 0; i < group->p_count; i++)
    {
        Particle &m = group->list[i];
        m.color += (color - m.color) * scaleFac;
        m.alpha += (alpha - m.alpha) * scaleFac;
    }
}

// Change sizes of all particles toward the specified size
void PATargetSize::Execute(ParticleGroup *group)
{
    float scaleFac_x = scale.x * dt;
    float scaleFac_y = scale.y * dt;
    float scaleFac_z = scale.z * dt;

    for(int i = 0; i < group->p_count; i++)
    {
        Particle &m = group->list[i];
        pVector dif(size - m.size);
        dif.x *= scaleFac_x;
        dif.y *= scaleFac_y;
        dif.z *= scaleFac_z;
        m.size += dif;
    }
}

// Change velocity of all particles toward the specified velocity
void PATargetVelocity::Execute(ParticleGroup *group)
{
    float scaleFac = scale * dt;

    for(int i = 0; i < group->p_count; i++)
    {
        Particle &m = group->list[i];
        m.vel += (velocity - m.vel) * scaleFac;
    }
}

// Immediately displace position using vortex
// Vortex tip at center, around axis, with magnitude
// and tightness exponent
void PAVortex::Execute(ParticleGroup *group)
{
    float magdt = magnitude * dt;
    float max_radiusSqr = max_radius * max_radius;

    if(max_radiusSqr < P_MAXFLOAT)
    {
        for(int i = 0; i < group->p_count; i++)
        {
            Particle &m = group->list[i];

            // Vector from tip of vortex
            pVector offset(m.pos - center);

            // Compute distance from particle to tip of vortex.
            float rSqr = offset.length2();

            // Don't do anything to particle if too close or too far.
            if(rSqr > max_radiusSqr)
                continue;

            float r = sqrtf(rSqr);

            // Compute normalized offset vector.
            pVector offnorm(offset / r);

            // Construct orthogonal vector frame in which to rotate
            // transformed point around origin
            float axisProj = offnorm * axis; // offnorm . axis

            // Components of offset perpendicular and parallel to axis
            pVector w(axis * axisProj); // parallel component
            pVector u(offnorm - w); // perpendicular component

            // Perpendicular component completing frame:
            pVector v(axis ^ u);

            // Figure amount of rotation
            // Resultant is (cos theta) u + (sin theta) v
            float theta = magdt / (rSqr + epsilon);
            float s = sinf(theta);
            float c = cosf(theta);

            offset = (u * c + v * s + w) * r;

            // Translate back to object space
            m.pos = offset + center;
        }
    }
    else
    {
        for(int i = 0; i < group->p_count; i++)
        {
            Particle &m = group->list[i];

            // Vector from tip of vortex
            pVector offset(m.pos - center);

            // Compute distance from particle to tip of vortex.
            float rSqr = offset.length2();

            float r = sqrtf(rSqr);

            // Compute normalized offset vector.
            pVector offnorm(offset / r);

            // Construct orthogonal vector frame in which to rotate
            // transformed point around origin
            float axisProj = offnorm * axis; // offnorm . axis

            // Components of offset perpendicular and parallel to axis
            pVector w(axis * axisProj); // parallel component
            pVector u(offnorm - w); // perpendicular component

            // Perpendicular component completing frame:
            pVector v(axis ^ u);

            // Figure amount of rotation
            // Resultant is (cos theta) u + (sin theta) v
            float theta = magdt / (rSqr + epsilon);
            float s = sinf(theta);
            float c = cosf(theta);

            offset = (u * c + v * s + w) * r;

            // Translate back to object space
            m.pos = offset + center;
        }
    }
}

////////////////////////////////////////////////////////////////////////////////
// Stuff for the pDomain.

pDomain::pDomain(PDomainEnum dtype, float a0, float a1,
                 float a2, float a3, float a4, float a5,
                 float a6, float a7, float a8)
{
    type = dtype;
    switch(type)
    {
    case PDPoint:
        p1 = pVector(a0, a1, a2);
        break;
    case PDLine:
        {
            p1 = pVector(a0, a1, a2);
            pVector tmp(a3, a4, a5);
            // p2 is vector from p1 to other endpoint.
            p2 = tmp - p1;
        }
        break;
    case PDBox:
        // p1 is the min corner. p2 is the max corner.
        if(a0 < a3)
        {
            p1.x = a0; p2.x = a3;
        }
        else
        {
            p1.x = a3; p2.x = a0;
        }
        if(a1 < a4)
        {
            p1.y = a1; p2.y = a4;
        }
        else
        {
            p1.y = a4; p2.y = a1;
        }
        if(a2 < a5)
        {
            p1.z = a2; p2.z = a5;
        }
        else
        {
            p1.z = a5; p2.z = a2;
        }
        break;
    case PDTriangle:
        {
            p1 = pVector(a0, a1, a2);
            pVector tp2 = pVector(a3, a4, a5);
            pVector tp3 = pVector(a6, a7, a8);

            u = tp2 - p1;
            v = tp3 - p1;

            // The rest of this is needed for bouncing.
            radius1Sqr = u.length();
            pVector tu = u / radius1Sqr;
            radius2Sqr = v.length();
            pVector tv = v / radius2Sqr;

            p2 = tu ^ tv; // This is the non-unit normal.
            p2.normalize(); // Must normalize it.

            // radius1 stores the d of the plane eqn.
            radius1 = -(p1 * p2);
        }
        break;
    case PDRectangle:
        {
            p1 = pVector(a0, a1, a2);
            u = pVector(a3, a4, a5);
            v = pVector(a6, a7, a8);

            // The rest of this is needed for bouncing.
            radius1Sqr = u.length();
            pVector tu = u / radius1Sqr;
            radius2Sqr = v.length();
            pVector tv = v / radius2Sqr;

            p2 = tu ^ tv; // This is the non-unit normal.
            p2.normalize(); // Must normalize it.

            // radius1 stores the d of the plane eqn.
            radius1 = -(p1 * p2);
        }
        break;
    case PDPlane:
        {
            p1 = pVector(a0, a1, a2);
            p2 = pVector(a3, a4, a5);
            p2.normalize(); // Must normalize it.

            // radius1 stores the d of the plane eqn.
            radius1 = -(p1 * p2);
        }
        break;
    case PDSphere:
        p1 = pVector(a0, a1, a2);
        if(a3 > a4)
        {
            radius1 = a3; radius2 = a4;
        }
        else
        {
            radius1 = a4; radius2 = a3;
        }
        radius1Sqr = radius1 * radius1;
        radius2Sqr = radius2 * radius2;
        break;
    case PDCone:
    case PDCylinder:
        {
            // p2 is a vector from p1 to the other end of cylinder.
            // p1 is apex of cone.

            p1 = pVector(a0, a1, a2);
            pVector tmp(a3, a4, a5);
            p2 = tmp - p1;

            if(a6 > a7)
            {
                radius1 = a6; radius2 = a7;
            }
            else
            {
                radius1 = a7; radius2 = a6;
            }
            radius1Sqr = fsqr(radius1);

            // Given an arbitrary nonzero vector n, make two orthonormal
            // vectors u and v forming a frame [u,v,n.normalize()].
            pVector n = p2;
            float p2l2 = n.length2(); // Optimize this.
            n.normalize();

            // radius2Sqr stores 1 / (p2.p2)
            // XXX Used to have an actual if.
            radius2Sqr = p2l2 ? 1.0f / p2l2 : 0.0f;

            // Find a vector orthogonal to n.
            pVector basis(1.0f, 0.0f, 0.0f);
            if(fabs(basis * n) > 0.999)
                basis = pVector(0.0f, 1.0f, 0.0f);

            // Project away N component, normalize and cross to get
            // second orthonormal vector.
            u = basis - n * (basis * n);
            u.normalize();
            v = n ^ u;
        }
        break;
    case PDBlob:
        {
            p1 = pVector(a0, a1, a2);
            radius1 = a3;
            float tmp = 1./radius1;
            radius2Sqr = -0.5f*fsqr(tmp);
            radius2 = ONEOVERSQRT2PI * tmp;
        }
        break;
    case PDDisc:
        {
            p1 = pVector(a0, a1, a2); // Center point
            p2 = pVector(a3, a4, a5); // Normal (not used in Within and Generate)
            p2.normalize();

            if(a6 > a7)
            {
                radius1 = a6; radius2 = a7;
            }
            else
            {
                radius1 = a7; radius2 = a6;
            }

            // Find a vector orthogonal to n.
            pVector basis(1.0f, 0.0f, 0.0f);
            if(fabs(basis * p2) > 0.999)
                basis = pVector(0.0f, 1.0f, 0.0f);

            // Project away N component, normalize and cross to get
            // second orthonormal vector.
            u = basis - p2 * (basis * p2);
            u.normalize();
            v = p2 ^ u;
            radius1Sqr = -(p1 * p2); // D of the plane eqn.
        }
        break;
    }
}

// Determines if pos is inside the domain
bool pDomain::Within(const pVector &pos) const
{
    switch (type)
    {
    case PDBox:
        return !((pos.x < p1.x) || (pos.x > p2.x) ||
                 (pos.y < p1.y) || (pos.y > p2.y) ||
                 (pos.z < p1.z) || (pos.z > p2.z));
    case PDPlane:
        // Distance from plane = n * p + d
        // Inside is the positive half-space.
        return pos * p2 >= -radius1;
    case PDSphere:
        {
            pVector rvec(pos - p1);
            float rSqr = rvec.length2();
            return rSqr <= radius1Sqr && rSqr >= radius2Sqr;
        }
    case PDCylinder:
    case PDCone:
        {
            // This is painful and slow. Might be better to do quick
            // accept/reject tests.
            // Let p2 = vector from base to tip of the cylinder
            // x = vector from base to test point
            // x . p2
            // dist = ------ = projected distance of x along the axis
            // p2. p2 ranging from 0 (base) to 1 (tip)
            //
            // rad = x - dist * p2 = projected vector of x along the base
            // p1 is the apex of the cone.

            pVector x(pos - p1);

            // Check axial distance
            // radius2Sqr stores 1 / (p2.p2)
            float dist = (p2 * x) * radius2Sqr;
            if(dist < 0.0f || dist > 1.0f)
                return false;

            // Check radial distance; scale radius along axis for cones
            pVector xrad = x - p2 * dist; // Radial component of x
            float rSqr = xrad.length2();

            if(type == PDCone)
                return (rSqr <= fsqr(dist * radius1) &&
                        rSqr >= fsqr(dist * radius2));
            else
                return (rSqr <= radius1Sqr && rSqr >= fsqr(radius2));
        }
    case PDBlob:
        {
            pVector x(pos - p1);
            // return exp(-0.5 * xSq * Sqr(oneOverSigma)) * ONEOVERSQRT2PI * oneOverSigma;
            float Gx = expf(x.length2() * radius2Sqr) * radius2;
            return (drand48() < Gx);
        }
    case PDPoint:
    case PDLine:
    case PDRectangle:
    case PDTriangle:
    case PDDisc:
    default:
        return false; // XXX Is there something better?
    }
}

// Generate a random point uniformly distrbuted within the domain
void pDomain::Generate(pVector &pos) const
{
    switch (type)
    {
    case PDPoint:
        pos = p1;
        break;
    case PDLine:
        pos = p1 + p2 * drand48();
        break;
    case PDBox:
        // Scale and translate [0,1] random to fit box
        pos.x = p1.x + (p2.x - p1.x) * drand48();
        pos.y = p1.y + (p2.y - p1.y) * drand48();
        pos.z = p1.z + (p2.z - p1.z) * drand48();
        break;
    case PDTriangle:
        {
            float r1 = drand48();
            float r2 = drand48();
            if(r1 + r2 < 1.0f)
                pos = p1 + u * r1 + v * r2;
            else
                pos = p1 + u * (1.0f-r1) + v * (1.0f-r2);
        }
        break;
    case PDRectangle:
        pos = p1 + u * drand48() + v * drand48();
        break;
    case PDPlane: // How do I sensibly make a point on an infinite plane?
        pos = p1;
        break;
    case PDSphere:
        // Place on [-1..1] sphere
        pos = RandVec() - vHalf;
        pos.normalize();

        // Scale unit sphere pos by [0..r] and translate
        // (should distribute as r^2 law)
        if(radius1 == radius2)
            pos = p1 + pos * radius1;
        else
            pos = p1 + pos * (radius2 + drand48() * (radius1 - radius2));
        break;
    case PDCylinder:
    case PDCone:
        {
            // For a cone, p2 is the apex of the cone.
            float dist = drand48(); // Distance between base and tip
            float theta = drand48() * 2.0f * float(M_PI); // Angle around axis
            // Distance from axis
            float r = radius2 + drand48() * (radius1 - radius2);

            float x = r * cosf(theta); // Weighting of each frame vector
            float y = r * sinf(theta);

            // Scale radius along axis for cones
            if(type == PDCone)
            {
                x *= dist;
                y *= dist;
            }

            pos = p1 + p2 * dist + u * x + v * y;
        }
        break;
    case PDBlob:
        pos.x = p1.x + NRand(radius1);
        pos.y = p1.y + NRand(radius1);
        pos.z = p1.z + NRand(radius1);

        break;
    case PDDisc:
        {
            float theta = drand48() * 2.0f * float(M_PI); // Angle around normal
            // Distance from center
            float r = radius2 + drand48() * (radius1 - radius2);

            float x = r * cosf(theta); // Weighting of each frame vector
            float y = r * sinf(theta);

            pos = p1 + u * x + v * y;
        }
        break;
    default:
        pos = pVector(0,0,0);
    }
}
