math.c

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/*
Copyright (C) 1997-2001 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.,
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*/
 
#include "shared/shared.h"
#include "common/math.h"
 
#if USE_CLIENT
 
/*
======
vectoangles2 - this is duplicated in the game DLL, but I need it here.
======
*/
void vectoangles2(const vec3_t value1, vec3_t angles)
{
    float   forward;
    float   yaw, pitch;
 
    if (value1[1] == 0 && value1[0] == 0) {
        yaw = 0;
        if (value1[2] > 0)
            pitch = 90;
        else
            pitch = 270;
    } else {
        if (value1[0])
            yaw = atan2(value1[1], value1[0]) * 180 / M_PI;
        else if (value1[1] > 0)
            yaw = 90;
        else
            yaw = 270;
 
        if (yaw < 0)
            yaw += 360;
 
        forward = sqrt(value1[0] * value1[0] + value1[1] * value1[1]);
        pitch = atan2(value1[2], forward) * 180 / M_PI;
        if (pitch < 0)
            pitch += 360;
    }
 
    angles[PITCH] = -pitch;
    angles[YAW] = yaw;
    angles[ROLL] = 0;
}
 
void MakeNormalVectors(const vec3_t forward, vec3_t right, vec3_t up)
{
    float       d;
 
    // this rotate and negate guarantees a vector
    // not colinear with the original
    right[1] = -forward[0];
    right[2] = forward[1];
    right[0] = forward[2];
 
    d = DotProduct(right, forward);
    VectorMA(right, -d, forward, right);
    VectorNormalize(right);
    CrossProduct(right, forward, up);
}
 
#endif  // USE_CLIENT
 
const vec3_t bytedirs[NUMVERTEXNORMALS] = {
    {-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}, 
};
 
int DirToByte(const vec3_t dir)
{
    int     i, best;
    float   d, bestd;
 
    if (!dir) {
        return 0;
    }
 
    bestd = 0;
    best = 0;
    for (i = 0; i < NUMVERTEXNORMALS; i++) {
        d = DotProduct(dir, bytedirs[i]);
        if (d > bestd) {
            bestd = d;
            best = i;
        }
    }
 
    return best;
}
 
#if 0
void ByteToDir(int index, vec3_t dir)
{
    if (index < 0 || index >= NUMVERTEXNORMALS) {
        Com_Error(ERR_FATAL, "ByteToDir: illegal index");
    }
 
    VectorCopy(bytedirs[index], dir);
}
#endif
 
void SetPlaneType(cplane_t *plane)
{
    vec_t *normal = plane->normal;
 
    if (normal[0] == 1) {
        plane->type = PLANE_X;
        return;
    }
    if (normal[1] == 1) {
        plane->type = PLANE_Y;
        return;
    }
    if (normal[2] == 1) {
        plane->type = PLANE_Z;
        return;
    }
 
    plane->type = PLANE_NON_AXIAL;
}
 
void SetPlaneSignbits(cplane_t *plane)
{
    int bits = 0;
 
    if (plane->normal[0] < 0) {
        bits |= 1;
    }
    if (plane->normal[1] < 0) {
        bits |= 2;
    }
    if (plane->normal[2] < 0) {
        bits |= 4;
    }
 
    plane->signbits = bits;
}
 
/*
==================
BoxOnPlaneSide
 
Returns 1, 2, or 1 + 2
==================
*/
int BoxOnPlaneSide(vec3_t emins, vec3_t emaxs, cplane_t *p)
{
    vec_t   *bounds[2] = { emins, emaxs };
    int     i = p->signbits & 1;
    int     j = (p->signbits >> 1) & 1;
    int     k = (p->signbits >> 2) & 1;
 
#define P(i, j, k) \
    p->normal[0] * bounds[i][0] + \
    p->normal[1] * bounds[j][1] + \
    p->normal[2] * bounds[k][2]
 
    vec_t   dist1 = P(i ^ 1, j ^ 1, k ^ 1);
    vec_t   dist2 = P(i, j, k);
    int     sides = 0;
 
#undef P
 
    if (dist1 >= p->dist)
        sides = BOX_INFRONT;
    if (dist2 < p->dist)
        sides |= BOX_BEHIND;
 
    return sides;
}
 
void RotatePointAroundVector(vec3_t dst, const vec3_t dir, const vec3_t point, float degrees)
{
    vec3_t  matrix[3];
 
    SetupRotationMatrix(matrix, dir, degrees);
 
    dst[0] = DotProduct(matrix[0], point);
    dst[1] = DotProduct(matrix[1], point);
    dst[2] = DotProduct(matrix[2], point);
}
 
/*
==================
SetupRotationMatrix
 
Setup rotation matrix given the normalized direction vector and angle to rotate
around this vector. Adapted from Mesa 3D implementation of _math_matrix_rotate.
==================
*/
void SetupRotationMatrix(vec3_t matrix[3], const vec3_t dir, float degrees)
{
    vec_t   angle, s, c, one_c, xx, yy, zz, xy, yz, zx, xs, ys, zs;
 
    angle = DEG2RAD(degrees);
    s = sin(angle);
    c = cos(angle);
    one_c = 1.0F - c;
 
    xx = dir[0] * dir[0];
    yy = dir[1] * dir[1];
    zz = dir[2] * dir[2];
    xy = dir[0] * dir[1];
    yz = dir[1] * dir[2];
    zx = dir[2] * dir[0];
    xs = dir[0] * s;
    ys = dir[1] * s;
    zs = dir[2] * s;
 
    matrix[0][0] = (one_c * xx) + c;
    matrix[0][1] = (one_c * xy) - zs;
    matrix[0][2] = (one_c * zx) + ys;
 
    matrix[1][0] = (one_c * xy) + zs;
    matrix[1][1] = (one_c * yy) + c;
    matrix[1][2] = (one_c * yz) - xs;
 
    matrix[2][0] = (one_c * zx) - ys;
    matrix[2][1] = (one_c * yz) + xs;
    matrix[2][2] = (one_c * zz) + c;
}
 
 
#if USE_REF
 
#if USE_REF == REF_SOFT
 
void ProjectPointOnPlane(vec3_t dst, const vec3_t p, const vec3_t normal)
{
    float d;
    vec3_t n;
    float inv_denom;
 
    inv_denom = 1.0F / DotProduct(normal, normal);
 
    d = DotProduct(normal, p) * inv_denom;
 
    n[0] = normal[0] * inv_denom;
    n[1] = normal[1] * inv_denom;
    n[2] = normal[2] * inv_denom;
 
    dst[0] = p[0] - d * n[0];
    dst[1] = p[1] - d * n[1];
    dst[2] = p[2] - d * n[2];
}
 
/*
** assumes "src" is normalized
*/
void PerpendicularVector(vec3_t dst, const vec3_t src)
{
    int pos;
    int i;
    float minelem = 1.0F;
    vec3_t tempvec;
 
    /*
    ** find the smallest magnitude axially aligned vector
    */
    for (pos = 0, i = 0; i < 3; i++) {
        if (fabs(src[i]) < minelem) {
            pos = i;
            minelem = fabs(src[i]);
        }
    }
    tempvec[0] = tempvec[1] = tempvec[2] = 0.0F;
    tempvec[pos] = 1.0F;
 
    /*
    ** project the point onto the plane defined by src
    */
    ProjectPointOnPlane(dst, tempvec, src);
 
    /*
    ** normalize the result
    */
    VectorNormalize(dst);
}
 
#endif  // USE_REF == REF_SOFT
 
#endif  // USE_REF