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mathlib.c

/*
Copyright (C) 1996-1997 Id Software, Inc.

This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.

*/
// mathlib.c -- math primitives

#include "quakedef.h"

#include <math.h>

vec3_t vec3_origin = {0,0,0};
float ixtable[4096];

/*-----------------------------------------------------------------*/

float m_bytenormals[NUMVERTEXNORMALS][3] =
{
{-0.525731, 0.000000, 0.850651}, {-0.442863, 0.238856, 0.864188},
{-0.295242, 0.000000, 0.955423}, {-0.309017, 0.500000, 0.809017},
{-0.162460, 0.262866, 0.951056}, {0.000000, 0.000000, 1.000000},
{0.000000, 0.850651, 0.525731}, {-0.147621, 0.716567, 0.681718},
{0.147621, 0.716567, 0.681718}, {0.000000, 0.525731, 0.850651},
{0.309017, 0.500000, 0.809017}, {0.525731, 0.000000, 0.850651},
{0.295242, 0.000000, 0.955423}, {0.442863, 0.238856, 0.864188},
{0.162460, 0.262866, 0.951056}, {-0.681718, 0.147621, 0.716567},
{-0.809017, 0.309017, 0.500000}, {-0.587785, 0.425325, 0.688191},
{-0.850651, 0.525731, 0.000000}, {-0.864188, 0.442863, 0.238856},
{-0.716567, 0.681718, 0.147621}, {-0.688191, 0.587785, 0.425325},
{-0.500000, 0.809017, 0.309017}, {-0.238856, 0.864188, 0.442863},
{-0.425325, 0.688191, 0.587785}, {-0.716567, 0.681718, -0.147621},
{-0.500000, 0.809017, -0.309017}, {-0.525731, 0.850651, 0.000000},
{0.000000, 0.850651, -0.525731}, {-0.238856, 0.864188, -0.442863},
{0.000000, 0.955423, -0.295242}, {-0.262866, 0.951056, -0.162460},
{0.000000, 1.000000, 0.000000}, {0.000000, 0.955423, 0.295242},
{-0.262866, 0.951056, 0.162460}, {0.238856, 0.864188, 0.442863},
{0.262866, 0.951056, 0.162460}, {0.500000, 0.809017, 0.309017},
{0.238856, 0.864188, -0.442863}, {0.262866, 0.951056, -0.162460},
{0.500000, 0.809017, -0.309017}, {0.850651, 0.525731, 0.000000},
{0.716567, 0.681718, 0.147621}, {0.716567, 0.681718, -0.147621},
{0.525731, 0.850651, 0.000000}, {0.425325, 0.688191, 0.587785},
{0.864188, 0.442863, 0.238856}, {0.688191, 0.587785, 0.425325},
{0.809017, 0.309017, 0.500000}, {0.681718, 0.147621, 0.716567},
{0.587785, 0.425325, 0.688191}, {0.955423, 0.295242, 0.000000},
{1.000000, 0.000000, 0.000000}, {0.951056, 0.162460, 0.262866},
{0.850651, -0.525731, 0.000000}, {0.955423, -0.295242, 0.000000},
{0.864188, -0.442863, 0.238856}, {0.951056, -0.162460, 0.262866},
{0.809017, -0.309017, 0.500000}, {0.681718, -0.147621, 0.716567},
{0.850651, 0.000000, 0.525731}, {0.864188, 0.442863, -0.238856},
{0.809017, 0.309017, -0.500000}, {0.951056, 0.162460, -0.262866},
{0.525731, 0.000000, -0.850651}, {0.681718, 0.147621, -0.716567},
{0.681718, -0.147621, -0.716567}, {0.850651, 0.000000, -0.525731},
{0.809017, -0.309017, -0.500000}, {0.864188, -0.442863, -0.238856},
{0.951056, -0.162460, -0.262866}, {0.147621, 0.716567, -0.681718},
{0.309017, 0.500000, -0.809017}, {0.425325, 0.688191, -0.587785},
{0.442863, 0.238856, -0.864188}, {0.587785, 0.425325, -0.688191},
{0.688191, 0.587785, -0.425325}, {-0.147621, 0.716567, -0.681718},
{-0.309017, 0.500000, -0.809017}, {0.000000, 0.525731, -0.850651},
{-0.525731, 0.000000, -0.850651}, {-0.442863, 0.238856, -0.864188},
{-0.295242, 0.000000, -0.955423}, {-0.162460, 0.262866, -0.951056},
{0.000000, 0.000000, -1.000000}, {0.295242, 0.000000, -0.955423},
{0.162460, 0.262866, -0.951056}, {-0.442863, -0.238856, -0.864188},
{-0.309017, -0.500000, -0.809017}, {-0.162460, -0.262866, -0.951056},
{0.000000, -0.850651, -0.525731}, {-0.147621, -0.716567, -0.681718},
{0.147621, -0.716567, -0.681718}, {0.000000, -0.525731, -0.850651},
{0.309017, -0.500000, -0.809017}, {0.442863, -0.238856, -0.864188},
{0.162460, -0.262866, -0.951056}, {0.238856, -0.864188, -0.442863},
{0.500000, -0.809017, -0.309017}, {0.425325, -0.688191, -0.587785},
{0.716567, -0.681718, -0.147621}, {0.688191, -0.587785, -0.425325},
{0.587785, -0.425325, -0.688191}, {0.000000, -0.955423, -0.295242},
{0.000000, -1.000000, 0.000000}, {0.262866, -0.951056, -0.162460},
{0.000000, -0.850651, 0.525731}, {0.000000, -0.955423, 0.295242},
{0.238856, -0.864188, 0.442863}, {0.262866, -0.951056, 0.162460},
{0.500000, -0.809017, 0.309017}, {0.716567, -0.681718, 0.147621},
{0.525731, -0.850651, 0.000000}, {-0.238856, -0.864188, -0.442863},
{-0.500000, -0.809017, -0.309017}, {-0.262866, -0.951056, -0.162460},
{-0.850651, -0.525731, 0.000000}, {-0.716567, -0.681718, -0.147621},
{-0.716567, -0.681718, 0.147621}, {-0.525731, -0.850651, 0.000000},
{-0.500000, -0.809017, 0.309017}, {-0.238856, -0.864188, 0.442863},
{-0.262866, -0.951056, 0.162460}, {-0.864188, -0.442863, 0.238856},
{-0.809017, -0.309017, 0.500000}, {-0.688191, -0.587785, 0.425325},
{-0.681718, -0.147621, 0.716567}, {-0.442863, -0.238856, 0.864188},
{-0.587785, -0.425325, 0.688191}, {-0.309017, -0.500000, 0.809017},
{-0.147621, -0.716567, 0.681718}, {-0.425325, -0.688191, 0.587785},
{-0.162460, -0.262866, 0.951056}, {0.442863, -0.238856, 0.864188},
{0.162460, -0.262866, 0.951056}, {0.309017, -0.500000, 0.809017},
{0.147621, -0.716567, 0.681718}, {0.000000, -0.525731, 0.850651},
{0.425325, -0.688191, 0.587785}, {0.587785, -0.425325, 0.688191},
{0.688191, -0.587785, 0.425325}, {-0.955423, 0.295242, 0.000000},
{-0.951056, 0.162460, 0.262866}, {-1.000000, 0.000000, 0.000000},
{-0.850651, 0.000000, 0.525731}, {-0.955423, -0.295242, 0.000000},
{-0.951056, -0.162460, 0.262866}, {-0.864188, 0.442863, -0.238856},
{-0.951056, 0.162460, -0.262866}, {-0.809017, 0.309017, -0.500000},
{-0.864188, -0.442863, -0.238856}, {-0.951056, -0.162460, -0.262866},
{-0.809017, -0.309017, -0.500000}, {-0.681718, 0.147621, -0.716567},
{-0.681718, -0.147621, -0.716567}, {-0.850651, 0.000000, -0.525731},
{-0.688191, 0.587785, -0.425325}, {-0.587785, 0.425325, -0.688191},
{-0.425325, 0.688191, -0.587785}, {-0.425325, -0.688191, -0.587785},
{-0.587785, -0.425325, -0.688191}, {-0.688191, -0.587785, -0.425325},
};

#if 0
unsigned char NormalToByte(const vec3_t n)
{
      int i, best;
      float bestdistance, distance;

      best = 0;
      bestdistance = DotProduct (n, m_bytenormals[0]);
      for (i = 1;i < NUMVERTEXNORMALS;i++)
      {
            distance = DotProduct (n, m_bytenormals[i]);
            if (distance > bestdistance)
            {
                  bestdistance = distance;
                  best = i;
            }
      }
      return best;
}

// note: uses byte partly to force unsigned for the validity check
void ByteToNormal(unsigned char num, vec3_t n)
{
      if (num < NUMVERTEXNORMALS)
            VectorCopy(m_bytenormals[num], n);
      else
            VectorClear(n); // FIXME: complain?
}

// assumes "src" is normalized
void PerpendicularVector( vec3_t dst, const vec3_t src )
{
      // LordHavoc: optimized to death and beyond
      int pos;
      float minelem;

      if (src[0])
      {
            dst[0] = 0;
            if (src[1])
            {
                  dst[1] = 0;
                  if (src[2])
                  {
                        dst[2] = 0;
                        pos = 0;
                        minelem = fabs(src[0]);
                        if (fabs(src[1]) < minelem)
                        {
                              pos = 1;
                              minelem = fabs(src[1]);
                        }
                        if (fabs(src[2]) < minelem)
                              pos = 2;

                        dst[pos] = 1;
                        dst[0] -= src[pos] * src[0];
                        dst[1] -= src[pos] * src[1];
                        dst[2] -= src[pos] * src[2];

                        // normalize the result
                        VectorNormalize(dst);
                  }
                  else
                        dst[2] = 1;
            }
            else
            {
                  dst[1] = 1;
                  dst[2] = 0;
            }
      }
      else
      {
            dst[0] = 1;
            dst[1] = 0;
            dst[2] = 0;
      }
}
#endif


// LordHavoc: like AngleVectors, but taking a forward vector instead of angles, useful!
void VectorVectors(const vec3_t forward, vec3_t right, vec3_t up)
{
      float d;

      right[0] = forward[2];
      right[1] = -forward[0];
      right[2] = forward[1];

      d = DotProduct(forward, right);
      VectorMA(right, -d, forward, right);
      VectorNormalize(right);
      CrossProduct(right, forward, up);
}

void VectorVectorsDouble(const double *forward, double *right, double *up)
{
      double d;

      right[0] = forward[2];
      right[1] = -forward[0];
      right[2] = forward[1];

      d = DotProduct(forward, right);
      VectorMA(right, -d, forward, right);
      VectorNormalize(right);
      CrossProduct(right, forward, up);
}

void RotatePointAroundVector( vec3_t dst, const vec3_t dir, const vec3_t point, float degrees )
{
      float t0, t1;
      float angle, c, s;
      vec3_t vr, vu, vf;

      angle = DEG2RAD(degrees);
      c = cos(angle);
      s = sin(angle);
      VectorCopy(dir, vf);
      VectorVectors(vf, vr, vu);

      t0 = vr[0] *  c + vu[0] * -s;
      t1 = vr[0] *  s + vu[0] *  c;
      dst[0] = (t0 * vr[0] + t1 * vu[0] + vf[0] * vf[0]) * point[0]
             + (t0 * vr[1] + t1 * vu[1] + vf[0] * vf[1]) * point[1]
             + (t0 * vr[2] + t1 * vu[2] + vf[0] * vf[2]) * point[2];

      t0 = vr[1] *  c + vu[1] * -s;
      t1 = vr[1] *  s + vu[1] *  c;
      dst[1] = (t0 * vr[0] + t1 * vu[0] + vf[1] * vf[0]) * point[0]
             + (t0 * vr[1] + t1 * vu[1] + vf[1] * vf[1]) * point[1]
             + (t0 * vr[2] + t1 * vu[2] + vf[1] * vf[2]) * point[2];

      t0 = vr[2] *  c + vu[2] * -s;
      t1 = vr[2] *  s + vu[2] *  c;
      dst[2] = (t0 * vr[0] + t1 * vu[0] + vf[2] * vf[0]) * point[0]
             + (t0 * vr[1] + t1 * vu[1] + vf[2] * vf[1]) * point[1]
             + (t0 * vr[2] + t1 * vu[2] + vf[2] * vf[2]) * point[2];
}

/*-----------------------------------------------------------------*/

// returns the smallest integer greater than or equal to "value", or 0 if "value" is too big
unsigned int CeilPowerOf2(unsigned int value)
{
      unsigned int ceilvalue;

      if (value > (1U << (sizeof(int) * 8 - 1)))
            return 0;

      ceilvalue = 1;
      while (ceilvalue < value)
            ceilvalue <<= 1;

      return ceilvalue;
}


/*-----------------------------------------------------------------*/


void PlaneClassify(mplane_t *p)
{
      // for optimized plane comparisons
      if (p->normal[0] == 1)
            p->type = 0;
      else if (p->normal[1] == 1)
            p->type = 1;
      else if (p->normal[2] == 1)
            p->type = 2;
      else
            p->type = 3;
      // for BoxOnPlaneSide
      p->signbits = 0;
      if (p->normal[0] < 0) // 1
            p->signbits |= 1;
      if (p->normal[1] < 0) // 2
            p->signbits |= 2;
      if (p->normal[2] < 0) // 4
            p->signbits |= 4;
}

int BoxOnPlaneSide(const vec3_t emins, const vec3_t emaxs, const mplane_t *p)
{
      if (p->type < 3)
            return ((emaxs[p->type] >= p->dist) | ((emins[p->type] < p->dist) << 1));
      switch(p->signbits)
      {
      default:
      case 0: return (((p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] + p->normal[2] * emaxs[2]) >= p->dist) | (((p->normal[0] * emins[0] + p->normal[1] * emins[1] + p->normal[2] * emins[2]) < p->dist) << 1));
      case 1: return (((p->normal[0] * emins[0] + p->normal[1] * emaxs[1] + p->normal[2] * emaxs[2]) >= p->dist) | (((p->normal[0] * emaxs[0] + p->normal[1] * emins[1] + p->normal[2] * emins[2]) < p->dist) << 1));
      case 2: return (((p->normal[0] * emaxs[0] + p->normal[1] * emins[1] + p->normal[2] * emaxs[2]) >= p->dist) | (((p->normal[0] * emins[0] + p->normal[1] * emaxs[1] + p->normal[2] * emins[2]) < p->dist) << 1));
      case 3: return (((p->normal[0] * emins[0] + p->normal[1] * emins[1] + p->normal[2] * emaxs[2]) >= p->dist) | (((p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] + p->normal[2] * emins[2]) < p->dist) << 1));
      case 4: return (((p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] + p->normal[2] * emins[2]) >= p->dist) | (((p->normal[0] * emins[0] + p->normal[1] * emins[1] + p->normal[2] * emaxs[2]) < p->dist) << 1));
      case 5: return (((p->normal[0] * emins[0] + p->normal[1] * emaxs[1] + p->normal[2] * emins[2]) >= p->dist) | (((p->normal[0] * emaxs[0] + p->normal[1] * emins[1] + p->normal[2] * emaxs[2]) < p->dist) << 1));
      case 6: return (((p->normal[0] * emaxs[0] + p->normal[1] * emins[1] + p->normal[2] * emins[2]) >= p->dist) | (((p->normal[0] * emins[0] + p->normal[1] * emaxs[1] + p->normal[2] * emaxs[2]) < p->dist) << 1));
      case 7: return (((p->normal[0] * emins[0] + p->normal[1] * emins[1] + p->normal[2] * emins[2]) >= p->dist) | (((p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] + p->normal[2] * emaxs[2]) < p->dist) << 1));
      }
}

#if 0
int BoxOnPlaneSide_Separate(const vec3_t emins, const vec3_t emaxs, const vec3_t normal, const vec_t dist)
{
      switch((normal[0] < 0) | ((normal[1] < 0) << 1) | ((normal[2] < 0) << 2))
      {
      default:
      case 0: return (((normal[0] * emaxs[0] + normal[1] * emaxs[1] + normal[2] * emaxs[2]) >= dist) | (((normal[0] * emins[0] + normal[1] * emins[1] + normal[2] * emins[2]) < dist) << 1));
      case 1: return (((normal[0] * emins[0] + normal[1] * emaxs[1] + normal[2] * emaxs[2]) >= dist) | (((normal[0] * emaxs[0] + normal[1] * emins[1] + normal[2] * emins[2]) < dist) << 1));
      case 2: return (((normal[0] * emaxs[0] + normal[1] * emins[1] + normal[2] * emaxs[2]) >= dist) | (((normal[0] * emins[0] + normal[1] * emaxs[1] + normal[2] * emins[2]) < dist) << 1));
      case 3: return (((normal[0] * emins[0] + normal[1] * emins[1] + normal[2] * emaxs[2]) >= dist) | (((normal[0] * emaxs[0] + normal[1] * emaxs[1] + normal[2] * emins[2]) < dist) << 1));
      case 4: return (((normal[0] * emaxs[0] + normal[1] * emaxs[1] + normal[2] * emins[2]) >= dist) | (((normal[0] * emins[0] + normal[1] * emins[1] + normal[2] * emaxs[2]) < dist) << 1));
      case 5: return (((normal[0] * emins[0] + normal[1] * emaxs[1] + normal[2] * emins[2]) >= dist) | (((normal[0] * emaxs[0] + normal[1] * emins[1] + normal[2] * emaxs[2]) < dist) << 1));
      case 6: return (((normal[0] * emaxs[0] + normal[1] * emins[1] + normal[2] * emins[2]) >= dist) | (((normal[0] * emins[0] + normal[1] * emaxs[1] + normal[2] * emaxs[2]) < dist) << 1));
      case 7: return (((normal[0] * emins[0] + normal[1] * emins[1] + normal[2] * emins[2]) >= dist) | (((normal[0] * emaxs[0] + normal[1] * emaxs[1] + normal[2] * emaxs[2]) < dist) << 1));
      }
}
#endif

void BoxPlaneCorners(const vec3_t emins, const vec3_t emaxs, const mplane_t *p, vec3_t outnear, vec3_t outfar)
{
      if (p->type < 3)
      {
            outnear[0] = outnear[1] = outnear[2] = outfar[0] = outfar[1] = outfar[2] = 0;
            outnear[p->type] = emins[p->type];
            outfar[p->type] = emaxs[p->type];
            return;
      }
      switch(p->signbits)
      {
      default:
      case 0: outnear[0] = emaxs[0];outnear[1] = emaxs[1];outnear[2] = emaxs[2];outfar[0] = emins[0];outfar[1] = emins[1];outfar[2] = emins[2];break;
      case 1: outnear[0] = emins[0];outnear[1] = emaxs[1];outnear[2] = emaxs[2];outfar[0] = emaxs[0];outfar[1] = emins[1];outfar[2] = emins[2];break;
      case 2: outnear[0] = emaxs[0];outnear[1] = emins[1];outnear[2] = emaxs[2];outfar[0] = emins[0];outfar[1] = emaxs[1];outfar[2] = emins[2];break;
      case 3: outnear[0] = emins[0];outnear[1] = emins[1];outnear[2] = emaxs[2];outfar[0] = emaxs[0];outfar[1] = emaxs[1];outfar[2] = emins[2];break;
      case 4: outnear[0] = emaxs[0];outnear[1] = emaxs[1];outnear[2] = emins[2];outfar[0] = emins[0];outfar[1] = emins[1];outfar[2] = emaxs[2];break;
      case 5: outnear[0] = emins[0];outnear[1] = emaxs[1];outnear[2] = emins[2];outfar[0] = emaxs[0];outfar[1] = emins[1];outfar[2] = emaxs[2];break;
      case 6: outnear[0] = emaxs[0];outnear[1] = emins[1];outnear[2] = emins[2];outfar[0] = emins[0];outfar[1] = emaxs[1];outfar[2] = emaxs[2];break;
      case 7: outnear[0] = emins[0];outnear[1] = emins[1];outnear[2] = emins[2];outfar[0] = emaxs[0];outfar[1] = emaxs[1];outfar[2] = emaxs[2];break;
      }
}

void BoxPlaneCorners_Separate(const vec3_t emins, const vec3_t emaxs, const vec3_t normal, vec3_t outnear, vec3_t outfar)
{
      switch((normal[0] < 0) | ((normal[1] < 0) << 1) | ((normal[2] < 0) << 2))
      {
      default:
      case 0: outnear[0] = emaxs[0];outnear[1] = emaxs[1];outnear[2] = emaxs[2];outfar[0] = emins[0];outfar[1] = emins[1];outfar[2] = emins[2];break;
      case 1: outnear[0] = emins[0];outnear[1] = emaxs[1];outnear[2] = emaxs[2];outfar[0] = emaxs[0];outfar[1] = emins[1];outfar[2] = emins[2];break;
      case 2: outnear[0] = emaxs[0];outnear[1] = emins[1];outnear[2] = emaxs[2];outfar[0] = emins[0];outfar[1] = emaxs[1];outfar[2] = emins[2];break;
      case 3: outnear[0] = emins[0];outnear[1] = emins[1];outnear[2] = emaxs[2];outfar[0] = emaxs[0];outfar[1] = emaxs[1];outfar[2] = emins[2];break;
      case 4: outnear[0] = emaxs[0];outnear[1] = emaxs[1];outnear[2] = emins[2];outfar[0] = emins[0];outfar[1] = emins[1];outfar[2] = emaxs[2];break;
      case 5: outnear[0] = emins[0];outnear[1] = emaxs[1];outnear[2] = emins[2];outfar[0] = emaxs[0];outfar[1] = emins[1];outfar[2] = emaxs[2];break;
      case 6: outnear[0] = emaxs[0];outnear[1] = emins[1];outnear[2] = emins[2];outfar[0] = emins[0];outfar[1] = emaxs[1];outfar[2] = emaxs[2];break;
      case 7: outnear[0] = emins[0];outnear[1] = emins[1];outnear[2] = emins[2];outfar[0] = emaxs[0];outfar[1] = emaxs[1];outfar[2] = emaxs[2];break;
      }
}

void BoxPlaneCornerDistances(const vec3_t emins, const vec3_t emaxs, const mplane_t *p, vec_t *outneardist, vec_t *outfardist)
{
      if (p->type < 3)
      {
            *outneardist = emins[p->type] - p->dist;
            *outfardist = emaxs[p->type] - p->dist;
            return;
      }
      switch(p->signbits)
      {
      default:
      case 0: *outneardist = p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] + p->normal[2] * emaxs[2] - p->dist;*outfardist = p->normal[0] * emins[0] + p->normal[1] * emins[1] + p->normal[2] * emins[2] - p->dist;break;
      case 1: *outneardist = p->normal[0] * emins[0] + p->normal[1] * emaxs[1] + p->normal[2] * emaxs[2] - p->dist;*outfardist = p->normal[0] * emaxs[0] + p->normal[1] * emins[1] + p->normal[2] * emins[2] - p->dist;break;
      case 2: *outneardist = p->normal[0] * emaxs[0] + p->normal[1] * emins[1] + p->normal[2] * emaxs[2] - p->dist;*outfardist = p->normal[0] * emins[0] + p->normal[1] * emaxs[1] + p->normal[2] * emins[2] - p->dist;break;
      case 3: *outneardist = p->normal[0] * emins[0] + p->normal[1] * emins[1] + p->normal[2] * emaxs[2] - p->dist;*outfardist = p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] + p->normal[2] * emins[2] - p->dist;break;
      case 4: *outneardist = p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] + p->normal[2] * emins[2] - p->dist;*outfardist = p->normal[0] * emins[0] + p->normal[1] * emins[1] + p->normal[2] * emaxs[2] - p->dist;break;
      case 5: *outneardist = p->normal[0] * emins[0] + p->normal[1] * emaxs[1] + p->normal[2] * emins[2] - p->dist;*outfardist = p->normal[0] * emaxs[0] + p->normal[1] * emins[1] + p->normal[2] * emaxs[2] - p->dist;break;
      case 6: *outneardist = p->normal[0] * emaxs[0] + p->normal[1] * emins[1] + p->normal[2] * emins[2] - p->dist;*outfardist = p->normal[0] * emins[0] + p->normal[1] * emaxs[1] + p->normal[2] * emaxs[2] - p->dist;break;
      case 7: *outneardist = p->normal[0] * emins[0] + p->normal[1] * emins[1] + p->normal[2] * emins[2] - p->dist;*outfardist = p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] + p->normal[2] * emaxs[2] - p->dist;break;
      }
}

void BoxPlaneCornerDistances_Separate(const vec3_t emins, const vec3_t emaxs, const vec3_t normal, vec_t *outneardist, vec_t *outfardist)
{
      switch((normal[0] < 0) | ((normal[1] < 0) << 1) | ((normal[2] < 0) << 2))
      {
      default:
      case 0: *outneardist = normal[0] * emaxs[0] + normal[1] * emaxs[1] + normal[2] * emaxs[2];*outfardist = normal[0] * emins[0] + normal[1] * emins[1] + normal[2] * emins[2];break;
      case 1: *outneardist = normal[0] * emins[0] + normal[1] * emaxs[1] + normal[2] * emaxs[2];*outfardist = normal[0] * emaxs[0] + normal[1] * emins[1] + normal[2] * emins[2];break;
      case 2: *outneardist = normal[0] * emaxs[0] + normal[1] * emins[1] + normal[2] * emaxs[2];*outfardist = normal[0] * emins[0] + normal[1] * emaxs[1] + normal[2] * emins[2];break;
      case 3: *outneardist = normal[0] * emins[0] + normal[1] * emins[1] + normal[2] * emaxs[2];*outfardist = normal[0] * emaxs[0] + normal[1] * emaxs[1] + normal[2] * emins[2];break;
      case 4: *outneardist = normal[0] * emaxs[0] + normal[1] * emaxs[1] + normal[2] * emins[2];*outfardist = normal[0] * emins[0] + normal[1] * emins[1] + normal[2] * emaxs[2];break;
      case 5: *outneardist = normal[0] * emins[0] + normal[1] * emaxs[1] + normal[2] * emins[2];*outfardist = normal[0] * emaxs[0] + normal[1] * emins[1] + normal[2] * emaxs[2];break;
      case 6: *outneardist = normal[0] * emaxs[0] + normal[1] * emins[1] + normal[2] * emins[2];*outfardist = normal[0] * emins[0] + normal[1] * emaxs[1] + normal[2] * emaxs[2];break;
      case 7: *outneardist = normal[0] * emins[0] + normal[1] * emins[1] + normal[2] * emins[2];*outfardist = normal[0] * emaxs[0] + normal[1] * emaxs[1] + normal[2] * emaxs[2];break;
      }
}

void AngleVectors (const vec3_t angles, vec3_t forward, vec3_t right, vec3_t up)
{
      double angle, sr, sp, sy, cr, cp, cy;

      angle = angles[YAW] * (M_PI*2 / 360);
      sy = sin(angle);
      cy = cos(angle);
      angle = angles[PITCH] * (M_PI*2 / 360);
      sp = sin(angle);
      cp = cos(angle);
      if (forward)
      {
            forward[0] = cp*cy;
            forward[1] = cp*sy;
            forward[2] = -sp;
      }
      if (right || up)
      {
            if (angles[ROLL])
            {
                  angle = angles[ROLL] * (M_PI*2 / 360);
                  sr = sin(angle);
                  cr = cos(angle);
                  if (right)
                  {
                        right[0] = -1*(sr*sp*cy+cr*-sy);
                        right[1] = -1*(sr*sp*sy+cr*cy);
                        right[2] = -1*(sr*cp);
                  }
                  if (up)
                  {
                        up[0] = (cr*sp*cy+-sr*-sy);
                        up[1] = (cr*sp*sy+-sr*cy);
                        up[2] = cr*cp;
                  }
            }
            else
            {
                  if (right)
                  {
                        right[0] = sy;
                        right[1] = -cy;
                        right[2] = 0;
                  }
                  if (up)
                  {
                        up[0] = (sp*cy);
                        up[1] = (sp*sy);
                        up[2] = cp;
                  }
            }
      }
}

void AngleVectorsFLU (const vec3_t angles, vec3_t forward, vec3_t left, vec3_t up)
{
      double angle, sr, sp, sy, cr, cp, cy;

      angle = angles[YAW] * (M_PI*2 / 360);
      sy = sin(angle);
      cy = cos(angle);
      angle = angles[PITCH] * (M_PI*2 / 360);
      sp = sin(angle);
      cp = cos(angle);
      if (forward)
      {
            forward[0] = cp*cy;
            forward[1] = cp*sy;
            forward[2] = -sp;
      }
      if (left || up)
      {
            if (angles[ROLL])
            {
                  angle = angles[ROLL] * (M_PI*2 / 360);
                  sr = sin(angle);
                  cr = cos(angle);
                  if (left)
                  {
                        left[0] = sr*sp*cy+cr*-sy;
                        left[1] = sr*sp*sy+cr*cy;
                        left[2] = sr*cp;
                  }
                  if (up)
                  {
                        up[0] = cr*sp*cy+-sr*-sy;
                        up[1] = cr*sp*sy+-sr*cy;
                        up[2] = cr*cp;
                  }
            }
            else
            {
                  if (left)
                  {
                        left[0] = -sy;
                        left[1] = cy;
                        left[2] = 0;
                  }
                  if (up)
                  {
                        up[0] = sp*cy;
                        up[1] = sp*sy;
                        up[2] = cp;
                  }
            }
      }
}

// LordHavoc: calculates pitch/yaw/roll angles from forward and up vectors
void AnglesFromVectors (vec3_t angles, const vec3_t forward, const vec3_t up, qboolean flippitch)
{
      if (forward[0] == 0 && forward[1] == 0)
      {
            if(forward[2] > 0)
            {
                  angles[PITCH] = -M_PI * 0.5;
                  angles[YAW] = up ? atan2(-up[1], -up[0]) : 0;
            }
            else
            {
                  angles[PITCH] = M_PI * 0.5;
                  angles[YAW] = up ? atan2(up[1], up[0]) : 0;
            }
            angles[ROLL] = 0;
      }
      else
      {
            angles[YAW] = atan2(forward[1], forward[0]);
            angles[PITCH] = -atan2(forward[2], sqrt(forward[0]*forward[0] + forward[1]*forward[1]));
            if (up)
            {
                  vec_t cp = cos(angles[PITCH]), sp = sin(angles[PITCH]);
                  vec_t cy = cos(angles[YAW]), sy = sin(angles[YAW]);
                  vec3_t tleft, tup;
                  tleft[0] = -sy;
                  tleft[1] = cy;
                  tleft[2] = 0;
                  tup[0] = sp*cy;
                  tup[1] = sp*sy;
                  tup[2] = cp;
                  angles[ROLL] = -atan2(DotProduct(up, tleft), DotProduct(up, tup));
            }
            else
                  angles[ROLL] = 0;
      }

      // now convert radians to degrees, and make all values positive
      VectorScale(angles, 180.0 / M_PI, angles);
      if (flippitch)
            angles[PITCH] *= -1;
      if (angles[PITCH] < 0) angles[PITCH] += 360;
      if (angles[YAW] < 0) angles[YAW] += 360;
      if (angles[ROLL] < 0) angles[ROLL] += 360;

#if 0
{
      // debugging code
      vec3_t tforward, tleft, tup, nforward, nup;
      VectorCopy(forward, nforward);
      VectorNormalize(nforward);
      if (up)
      {
            VectorCopy(up, nup);
            VectorNormalize(nup);
            AngleVectors(angles, tforward, tleft, tup);
            if (VectorDistance(tforward, nforward) > 0.01 || VectorDistance(tup, nup) > 0.01)
            {
                  Con_Printf("vectoangles('%f %f %f', '%f %f %f') = %f %f %f\n", nforward[0], nforward[1], nforward[2], nup[0], nup[1], nup[2], angles[0], angles[1], angles[2]);
                  Con_Printf("^3But that is '%f %f %f', '%f %f %f'\n", tforward[0], tforward[1], tforward[2], tup[0], tup[1], tup[2]);
            }
      }
      else
      {
            AngleVectors(angles, tforward, tleft, tup);
            if (VectorDistance(tforward, nforward) > 0.01)
            {
                  Con_Printf("vectoangles('%f %f %f') = %f %f %f\n", nforward[0], nforward[1], nforward[2], angles[0], angles[1], angles[2]);
                  Con_Printf("^3But that is '%f %f %f'\n", tforward[0], tforward[1], tforward[2]);
            }
      }
}
#endif
}

#if 0
void AngleMatrix (const vec3_t angles, const vec3_t translate, vec_t matrix[][4])
{
      double angle, sr, sp, sy, cr, cp, cy;

      angle = angles[YAW] * (M_PI*2 / 360);
      sy = sin(angle);
      cy = cos(angle);
      angle = angles[PITCH] * (M_PI*2 / 360);
      sp = sin(angle);
      cp = cos(angle);
      angle = angles[ROLL] * (M_PI*2 / 360);
      sr = sin(angle);
      cr = cos(angle);
      matrix[0][0] = cp*cy;
      matrix[0][1] = sr*sp*cy+cr*-sy;
      matrix[0][2] = cr*sp*cy+-sr*-sy;
      matrix[0][3] = translate[0];
      matrix[1][0] = cp*sy;
      matrix[1][1] = sr*sp*sy+cr*cy;
      matrix[1][2] = cr*sp*sy+-sr*cy;
      matrix[1][3] = translate[1];
      matrix[2][0] = -sp;
      matrix[2][1] = sr*cp;
      matrix[2][2] = cr*cp;
      matrix[2][3] = translate[2];
}
#endif


// LordHavoc: renamed this to Length, and made the normal one a #define
float VectorNormalizeLength (vec3_t v)
{
      float length, ilength;

      length = v[0]*v[0] + v[1]*v[1] + v[2]*v[2];
      length = sqrt (length);

      if (length)
      {
            ilength = 1/length;
            v[0] *= ilength;
            v[1] *= ilength;
            v[2] *= ilength;
      }

      return length;

}


/*
================
R_ConcatRotations
================
*/
void R_ConcatRotations (const float in1[3*3], const float in2[3*3], float out[3*3])
{
      out[0*3+0] = in1[0*3+0] * in2[0*3+0] + in1[0*3+1] * in2[1*3+0] + in1[0*3+2] * in2[2*3+0];
      out[0*3+1] = in1[0*3+0] * in2[0*3+1] + in1[0*3+1] * in2[1*3+1] + in1[0*3+2] * in2[2*3+1];
      out[0*3+2] = in1[0*3+0] * in2[0*3+2] + in1[0*3+1] * in2[1*3+2] + in1[0*3+2] * in2[2*3+2];
      out[1*3+0] = in1[1*3+0] * in2[0*3+0] + in1[1*3+1] * in2[1*3+0] + in1[1*3+2] * in2[2*3+0];
      out[1*3+1] = in1[1*3+0] * in2[0*3+1] + in1[1*3+1] * in2[1*3+1] + in1[1*3+2] * in2[2*3+1];
      out[1*3+2] = in1[1*3+0] * in2[0*3+2] + in1[1*3+1] * in2[1*3+2] + in1[1*3+2] * in2[2*3+2];
      out[2*3+0] = in1[2*3+0] * in2[0*3+0] + in1[2*3+1] * in2[1*3+0] + in1[2*3+2] * in2[2*3+0];
      out[2*3+1] = in1[2*3+0] * in2[0*3+1] + in1[2*3+1] * in2[1*3+1] + in1[2*3+2] * in2[2*3+1];
      out[2*3+2] = in1[2*3+0] * in2[0*3+2] + in1[2*3+1] * in2[1*3+2] + in1[2*3+2] * in2[2*3+2];
}


/*
================
R_ConcatTransforms
================
*/
void R_ConcatTransforms (const float in1[3*4], const float in2[3*4], float out[3*4])
{
      out[0*4+0] = in1[0*4+0] * in2[0*4+0] + in1[0*4+1] * in2[1*4+0] + in1[0*4+2] * in2[2*4+0];
      out[0*4+1] = in1[0*4+0] * in2[0*4+1] + in1[0*4+1] * in2[1*4+1] + in1[0*4+2] * in2[2*4+1];
      out[0*4+2] = in1[0*4+0] * in2[0*4+2] + in1[0*4+1] * in2[1*4+2] + in1[0*4+2] * in2[2*4+2];
      out[0*4+3] = in1[0*4+0] * in2[0*4+3] + in1[0*4+1] * in2[1*4+3] + in1[0*4+2] * in2[2*4+3] + in1[0*4+3];
      out[1*4+0] = in1[1*4+0] * in2[0*4+0] + in1[1*4+1] * in2[1*4+0] + in1[1*4+2] * in2[2*4+0];
      out[1*4+1] = in1[1*4+0] * in2[0*4+1] + in1[1*4+1] * in2[1*4+1] + in1[1*4+2] * in2[2*4+1];
      out[1*4+2] = in1[1*4+0] * in2[0*4+2] + in1[1*4+1] * in2[1*4+2] + in1[1*4+2] * in2[2*4+2];
      out[1*4+3] = in1[1*4+0] * in2[0*4+3] + in1[1*4+1] * in2[1*4+3] + in1[1*4+2] * in2[2*4+3] + in1[1*4+3];
      out[2*4+0] = in1[2*4+0] * in2[0*4+0] + in1[2*4+1] * in2[1*4+0] + in1[2*4+2] * in2[2*4+0];
      out[2*4+1] = in1[2*4+0] * in2[0*4+1] + in1[2*4+1] * in2[1*4+1] + in1[2*4+2] * in2[2*4+1];
      out[2*4+2] = in1[2*4+0] * in2[0*4+2] + in1[2*4+1] * in2[1*4+2] + in1[2*4+2] * in2[2*4+2];
      out[2*4+3] = in1[2*4+0] * in2[0*4+3] + in1[2*4+1] * in2[1*4+3] + in1[2*4+2] * in2[2*4+3] + in1[2*4+3];
}

float RadiusFromBounds (const vec3_t mins, const vec3_t maxs)
{
      vec3_t m1, m2;
      VectorMultiply(mins, mins, m1);
      VectorMultiply(maxs, maxs, m2);
      return sqrt(max(m1[0], m2[0]) + max(m1[1], m2[1]) + max(m1[2], m2[2]));
}

float RadiusFromBoundsAndOrigin (const vec3_t mins, const vec3_t maxs, const vec3_t origin)
{
      vec3_t m1, m2;
      VectorSubtract(mins, origin, m1);VectorMultiply(m1, m1, m1);
      VectorSubtract(maxs, origin, m2);VectorMultiply(m2, m2, m2);
      return sqrt(max(m1[0], m2[0]) + max(m1[1], m2[1]) + max(m1[2], m2[2]));
}

void Mathlib_Init(void)
{
      int a;

      // LordHavoc: setup 1.0f / N table for quick recipricols of integers
      ixtable[0] = 0;
      for (a = 1;a < 4096;a++)
            ixtable[a] = 1.0f / a;
}

#include "matrixlib.h"

void Matrix4x4_Print(const matrix4x4_t *in)
{
      Con_Printf("%f %f %f %f\n%f %f %f %f\n%f %f %f %f\n%f %f %f %f\n"
      , in->m[0][0], in->m[0][1], in->m[0][2], in->m[0][3]
      , in->m[1][0], in->m[1][1], in->m[1][2], in->m[1][3]
      , in->m[2][0], in->m[2][1], in->m[2][2], in->m[2][3]
      , in->m[3][0], in->m[3][1], in->m[3][2], in->m[3][3]);
}

int Math_atov(const char *s, vec3_t out)
{
      int i;
      VectorClear(out);
      if (*s == '\'')
            s++;
      for (i = 0;i < 3;i++)
      {
            while (*s == ' ' || *s == '\t')
                  s++;
            out[i] = atof (s);
            if (out[i] == 0 && *s != '-' && *s != '+' && (*s < '0' || *s > '9'))
                  break; // not a number
            while (*s && *s != ' ' && *s !='\t' && *s != '\'')
                  s++;
            if (*s == '\'')
                  break;
      }
      return i;
}

void BoxFromPoints(vec3_t mins, vec3_t maxs, int numpoints, vec_t *point3f)
{
      int i;
      VectorCopy(point3f, mins);
      VectorCopy(point3f, maxs);
      for (i = 1, point3f += 3;i < numpoints;i++, point3f += 3)
      {
            mins[0] = min(mins[0], point3f[0]);maxs[0] = max(maxs[0], point3f[0]);
            mins[1] = min(mins[1], point3f[1]);maxs[1] = max(maxs[1], point3f[1]);
            mins[2] = min(mins[2], point3f[2]);maxs[2] = max(maxs[2], point3f[2]);
      }
}

// LordHavoc: this has to be done right or you get severe precision breakdown
int LoopingFrameNumberFromDouble(double t, int loopframes)
{
      if (loopframes)
            return (int)(t - floor(t/loopframes)*loopframes);
      else
            return (int)t;
}


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