来自上个世纪的传奇 q_math.c 源码展示
经典的快速平方根倒数算法就在其中
此算法首先接收一个32位带符浮点数，然后将之作为一个32位整数看待，将其右移一次（取半），并用十六进制“魔术数字”0x5f3759df减之，如此即可得对输入的浮点数的平方根倒数的首次近似值；而后重新将其作为原来的浮点数，以牛顿迭代法反复迭代，以求出更精确的近似值，直至求出符合精确度要求的近似值。在计算浮点数的平方根倒数的同一精度的近似值时，此算法比直接使用浮点数除法要快四倍。
/*
===========================================================================
Copyright (C) 1999-2005 Id Software, Inc.
This file is part of Quake III Arena source code.
Quake III Arena source code 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.
Quake III Arena source code 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 Foobar; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
===========================================================================
*/
//
// q_math.c -- stateless support routines that are included in each code module
#include "q_shared.h"
vec3_t vec3_origin = {0,0,0};
vec3_t axisDefault[3] = { { 1, 0, 0 }, { 0, 1, 0 }, { 0, 0, 1 } };
vec4_t colorBlack = {0, 0, 0, 1};
vec4_t colorRed = {1, 0, 0, 1};
vec4_t colorGreen = {0, 1, 0, 1};
vec4_t colorBlue = {0, 0, 1, 1};
vec4_t colorYellow = {1, 1, 0, 1};
vec4_t colorMagenta= {1, 0, 1, 1};
vec4_t colorCyan = {0, 1, 1, 1};
vec4_t colorWhite = {1, 1, 1, 1};
vec4_t colorLtGrey = {0.75, 0.75, 0.75, 1};
vec4_t colorMdGrey = {0.5, 0.5, 0.5, 1};
vec4_t colorDkGrey = {0.25, 0.25, 0.25, 1};
vec4_t g_color_table[8] =
{
{0.0, 0.0, 0.0, 1.0},
{1.0, 0.0, 0.0, 1.0},
{0.0, 1.0, 0.0, 1.0},
{1.0, 1.0, 0.0, 1.0},
{0.0, 0.0, 1.0, 1.0},
{0.0, 1.0, 1.0, 1.0},
{1.0, 0.0, 1.0, 1.0},
{1.0, 1.0, 1.0, 1.0},
};
vec3_t bytedirs[NUMVERTEXNORMALS] =
{
{-0.525731f, 0.000000f, 0.850651f}, {-0.442863f, 0.238856f, 0.864188f},
{-0.295242f, 0.000000f, 0.955423f}, {-0.309017f, 0.500000f, 0.809017f},
{-0.162460f, 0.262866f, 0.951056f}, {0.000000f, 0.000000f, 1.000000f},
{0.000000f, 0.850651f, 0.525731f}, {-0.147621f, 0.716567f, 0.681718f},
{0.147621f, 0.716567f, 0.681718f}, {0.000000f, 0.525731f, 0.850651f},
{0.309017f, 0.500000f, 0.809017f}, {0.525731f, 0.000000f, 0.850651f},
{0.295242f, 0.000000f, 0.955423f}, {0.442863f, 0.238856f, 0.864188f},
{0.162460f, 0.262866f, 0.951056f}, {-0.681718f, 0.147621f, 0.716567f},
{-0.809017f, 0.309017f, 0.500000f},{-0.587785f, 0.425325f, 0.688191f},
{-0.850651f, 0.525731f, 0.000000f},{-0.864188f, 0.442863f, 0.238856f},
{-0.716567f, 0.681718f, 0.147621f},{-0.688191f, 0.587785f, 0.425325f},
{-0.500000f, 0.809017f, 0.309017f}, {-0.238856f, 0.864188f, 0.442863f},
{-0.425325f, 0.688191f, 0.587785f}, {-0.716567f, 0.681718f, -0.147621f},
{-0.500000f, 0.809017f, -0.309017f}, {-0.525731f, 0.850651f, 0.000000f},
{0.000000f, 0.850651f, -0.525731f}, {-0.238856f, 0.864188f, -0.442863f},
{0.000000f, 0.955423f, -0.295242f}, {-0.262866f, 0.951056f, -0.162460f},
{0.000000f, 1.000000f, 0.000000f}, {0.000000f, 0.955423f, 0.295242f},
{-0.262866f, 0.951056f, 0.162460f}, {0.238856f, 0.864188f, 0.442863f},
{0.262866f, 0.951056f, 0.162460f}, {0.500000f, 0.809017f, 0.309017f},
{0.238856f, 0.864188f, -0.442863f},{0.262866f, 0.951056f, -0.162460f},
{0.500000f, 0.809017f, -0.309017f},{0.850651f, 0.525731f, 0.000000f},
{0.716567f, 0.681718f, 0.147621f}, {0.716567f, 0.681718f, -0.147621f},
{0.525731f, 0.850651f, 0.000000f}, {0.425325f, 0.688191f, 0.587785f},
{0.864188f, 0.442863f, 0.238856f}, {0.688191f, 0.587785f, 0.425325f},
{0.809017f, 0.309017f, 0.500000f}, {0.681718f, 0.147621f, 0.716567f},
{0.587785f, 0.425325f, 0.688191f}, {0.955423f, 0.295242f, 0.000000f},
{1.000000f, 0.000000f, 0.000000f}, {0.951056f, 0.162460f, 0.262866f},
{0.850651f, -0.525731f, 0.000000f},{0.955423f, -0.295242f, 0.000000f},
{0.864188f, -0.442863f, 0.238856f}, {0.951056f, -0.162460f, 0.262866f},
{0.809017f, -0.309017f, 0.500000f}, {0.681718f, -0.147621f, 0.716567f},
{0.850651f, 0.000000f, 0.525731f}, {0.864188f, 0.442863f, -0.238856f},
{0.809017f, 0.309017f, -0.500000f}, {0.951056f, 0.162460f, -0.262866f},
{0.525731f, 0.000000f, -0.850651f}, {0.681718f, 0.147621f, -0.716567f},
{0.681718f, -0.147621f, -0.716567f},{0.850651f, 0.000000f, -0.525731f},
{0.809017f, -0.309017f, -0.500000f}, {0.864188f, -0.442863f, -0.238856f},
{0.951056f, -0.162460f, -0.262866f}, {0.147621f, 0.716567f, -0.681718f},
{0.309017f, 0.500000f, -0.809017f}, {0.425325f, 0.688191f, -0.587785f},
{0.442863f, 0.238856f, -0.864188f}, {0.587785f, 0.425325f, -0.688191f},
{0.688191f, 0.587785f, -0.425325f}, {-0.147621f, 0.716567f, -0.681718f},
{-0.309017f, 0.500000f, -0.809017f}, {0.000000f, 0.525731f, -0.850651f},
{-0.525731f, 0.000000f, -0.850651f}, {-0.442863f, 0.238856f, -0.864188f},
{-0.295242f, 0.000000f, -0.955423f}, {-0.162460f, 0.262866f, -0.951056f},
{0.000000f, 0.000000f, -1.000000f}, {0.295242f, 0.000000f, -0.955423f},
{0.162460f, 0.262866f, -0.951056f}, {-0.442863f, -0.238856f, -0.864188f},
{-0.309017f, -0.500000f, -0.809017f}, {-0.162460f, -0.262866f, -0.951056f},
{0.000000f, -0.850651f, -0.525731f}, {-0.147621f, -0.716567f, -0.681718f},
{0.147621f, -0.716567f, -0.681718f}, {0.000000f, -0.525731f, -0.850651f},
{0.309017f, -0.500000f, -0.809017f}, {0.442863f, -0.238856f, -0.864188f},
{0.162460f, -0.262866f, -0.951056f}, {0.238856f, -0.864188f, -0.442863f},
{0.500000f, -0.809017f, -0.309017f}, {0.425325f, -0.688191f, -0.587785f},
{0.716567f, -0.681718f, -0.147621f}, {0.688191f, -0.587785f, -0.425325f},
{0.587785f, -0.425325f, -0.688191f}, {0.000000f, -0.955423f, -0.295242f},
{0.000000f, -1.000000f, 0.000000f}, {0.262866f, -0.951056f, -0.162460f},
{0.000000f, -0.850651f, 0.525731f}, {0.000000f, -0.955423f, 0.295242f},
{0.238856f, -0.864188f, 0.442863f}, {0.262866f, -0.951056f, 0.162460f},
{0.500000f, -0.809017f, 0.309017f}, {0.716567f, -0.681718f, 0.147621f},
{0.525731f, -0.850651f, 0.000000f}, {-0.238856f, -0.864188f, -0.442863f},
{-0.500000f, -0.809017f, -0.309017f}, {-0.262866f, -0.951056f, -0.162460f},
{-0.850651f, -0.525731f, 0.000000f}, {-0.716567f, -0.681718f, -0.147621f},
{-0.716567f, -0.681718f, 0.147621f}, {-0.525731f, -0.850651f, 0.000000f},
{-0.500000f, -0.809017f, 0.309017f}, {-0.238856f, -0.864188f, 0.442863f},
{-0.262866f, -0.951056f, 0.162460f}, {-0.864188f, -0.442863f, 0.238856f},
{-0.809017f, -0.309017f, 0.500000f}, {-0.688191f, -0.587785f, 0.425325f},
{-0.681718f, -0.147621f, 0.716567f}, {-0.442863f, -0.238856f, 0.864188f},
{-0.587785f, -0.425325f, 0.688191f}, {-0.309017f, -0.500000f, 0.809017f},
{-0.147621f, -0.716567f, 0.681718f}, {-0.425325f, -0.688191f, 0.587785f},
{-0.162460f, -0.262866f, 0.951056f}, {0.442863f, -0.238856f, 0.864188f},
{0.162460f, -0.262866f, 0.951056f}, {0.309017f, -0.500000f, 0.809017f},
{0.147621f, -0.716567f, 0.681718f}, {0.000000f, -0.525731f, 0.850651f},
{0.425325f, -0.688191f, 0.587785f}, {0.587785f, -0.425325f, 0.688191f},
{0.688191f, -0.587785f, 0.425325f}, {-0.955423f, 0.295242f, 0.000000f},
{-0.951056f, 0.162460f, 0.262866f}, {-1.000000f, 0.000000f, 0.000000f},
{-0.850651f, 0.000000f, 0.525731f}, {-0.955423f, -0.295242f, 0.000000f},
{-0.951056f, -0.162460f, 0.262866f}, {-0.864188f, 0.442863f, -0.238856f},
{-0.951056f, 0.162460f, -0.262866f}, {-0.809017f, 0.309017f, -0.500000f},
{-0.864188f, -0.442863f, -0.238856f}, {-0.951056f, -0.162460f, -0.262866f},
{-0.809017f, -0.309017f, -0.500000f}, {-0.681718f, 0.147621f, -0.716567f},
{-0.681718f, -0.147621f, -0.716567f}, {-0.850651f, 0.000000f, -0.525731f},
{-0.688191f, 0.587785f, -0.425325f}, {-0.587785f, 0.425325f, -0.688191f},
{-0.425325f, 0.688191f, -0.587785f}, {-0.425325f, -0.688191f, -0.587785f},
{-0.587785f, -0.425325f, -0.688191f}, {-0.688191f, -0.587785f, -0.425325f}
};
//==============================================================
int Q_rand( int *seed ) {
*seed = (69069 * *seed + 1);
return *seed;
}
float Q_random( int *seed ) {
return ( Q_rand( seed ) & 0xffff ) / (float)0x10000;
}
float Q_crandom( int *seed ) {
return 2.0 * ( Q_random( seed ) - 0.5 );
}
#ifdef __LCC__
int VectorCompare( const vec3_t v1, const vec3_t v2 ) {
if (v1[0] != v2[0] || v1[1] != v2[1] || v1[2] != v2[2]) {
return 0;
}
return 1;
}
vec_t VectorLength( const vec3_t v ) {
return (vec_t)sqrt (v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
}
vec_t VectorLengthSquared( const vec3_t v ) {
return (v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
}
vec_t Distance( const vec3_t p1, const vec3_t p2 ) {
vec3_t v;
VectorSubtract (p2, p1, v);
return VectorLength( v );
}
vec_t DistanceSquared( const vec3_t p1, const vec3_t p2 ) {
vec3_t v;
VectorSubtract (p2, p1, v);
return v[0]*v[0] + v[1]*v[1] + v[2]*v[2];
}
// fast vector normalize routine that does not check to make sure
// that length != 0, nor does it return length, uses rsqrt approximation
void VectorNormalizeFast( vec3_t v )
{
float ilength;
ilength = Q_rsqrt( DotProduct( v, v ) );
v[0] *= ilength;
v[1] *= ilength;
v[2] *= ilength;
}
void VectorInverse( vec3_t v ){
v[0] = -v[0];
v[1] = -v[1];
v[2] = -v[2];
}
void CrossProduct( const vec3_t v1, const vec3_t v2, vec3_t cross ) {
cross[0] = v1[1]*v2[2] - v1[2]*v2[1];
cross[1] = v1[2]*v2[0] - v1[0]*v2[2];
cross[2] = v1[0]*v2[1] - v1[1]*v2[0];
}
#endif
//=======================================================
signed char ClampChar( int i ) {
if ( i < -128 ) {
return -128;
}
if ( i > 127 ) {
return 127;
}
return i;
}
signed short ClampShort( int i ) {
if ( i < -32768 ) {
return -32768;
}
if ( i > 0x7fff ) {
return 0x7fff;
}
return i;
}
// this isn't a real cheap function to call!
int DirToByte( 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;
}
void ByteToDir( int b, vec3_t dir ) {
if ( b < 0 || b >= NUMVERTEXNORMALS ) {
VectorCopy( vec3_origin, dir );
return;
}
VectorCopy (bytedirs[b], dir);
}
unsigned ColorBytes3 (float r, float g, float b) {
unsigned i;
( (byte *)&i )[0] = r * 255;
( (byte *)&i )[1] = g * 255;
( (byte *)&i )[2] = b * 255;
return i;
}
unsigned ColorBytes4 (float r, float g, float b, float a) {
unsigned i;
( (byte *)&i )[0] = r * 255;
( (byte *)&i )[1] = g * 255;
( (byte *)&i )[2] = b * 255;
( (byte *)&i )[3] = a * 255;
return i;
}
float NormalizeColor( const vec3_t in, vec3_t out ) {
float max;
max = in[0];
if ( in[1] > max ) {
max = in[1];
}
if ( in[2] > max ) {
max = in[2];
}
if ( !max ) {
VectorClear( out );
} else {
out[0] = in[0] / max;
out[1] = in[1] / max;
out[2] = in[2] / max;
}
return max;
}
/*
=====================
PlaneFromPoints
Returns false if the triangle is degenrate.
The normal will point out of the clock for clockwise ordered points
=====================
*/
qboolean PlaneFromPoints( vec4_t plane, const vec3_t a, const vec3_t b, const vec3_t c ) {
vec3_t d1, d2;
VectorSubtract( b, a, d1 );
VectorSubtract( c, a, d2 );
CrossProduct( d2, d1, plane );
if ( VectorNormalize( plane ) == 0 ) {
return qfalse;
}
plane[3] = DotProduct( a, plane );
return qtrue;
}
/*
===============
RotatePointAroundVector
This is not implemented very well...
===============
*/
void RotatePointAroundVector( vec3_t dst, const vec3_t dir, const vec3_t point,
float degrees ) {
float m[3][3];
float im[3][3];
float zrot[3][3];
float tmpmat[3][3];
float rot[3][3];
int i;
vec3_t vr, vup, vf;
float rad;
vf[0] = dir[0];
vf[1] = dir[1];
vf[2] = dir[2];
PerpendicularVector( vr, dir );
CrossProduct( vr, vf, vup );
m[0][0] = vr[0];
m[1][0] = vr[1];
m[2][0] = vr[2];
m[0][1] = vup[0];
m[1][1] = vup[1];
m[2][1] = vup[2];
m[0][2] = vf[0];
m[1][2] = vf[1];
m[2][2] = vf[2];
memcpy( im, m, sizeof( im ) );
im[0][1] = m[1][0];
im[0][2] = m[2][0];
im[1][0] = m[0][1];
im[1][2] = m[2][1];
im[2][0] = m[0][2];
im[2][1] = m[1][2];
memset( zrot, 0, sizeof( zrot ) );
zrot[0][0] = zrot[1][1] = zrot[2][2] = 1.0F;
rad = DEG2RAD( degrees );
zrot[0][0] = cos( rad );
zrot[0][1] = sin( rad );
zrot[1][0] = -sin( rad );
zrot[1][1] = cos( rad );
MatrixMultiply( m, zrot, tmpmat );
MatrixMultiply( tmpmat, im, rot );
for ( i = 0; i < 3; i++ ) {
dst[i] = rot[i][0] * point[0] + rot[i][1] * point[1] + rot[i][2] * point[2];
}
}
/*
===============
RotateAroundDirection
===============
*/
void RotateAroundDirection( vec3_t axis[3], float yaw ) {
// create an arbitrary axis[1]
PerpendicularVector( axis[1], axis[0] );
// rotate it around axis[0] by yaw
if ( yaw ) {
vec3_t temp;
VectorCopy( axis[1], temp );
RotatePointAroundVector( axis[1], axis[0], temp, yaw );
}
// cross to get axis[2]
CrossProduct( axis[0], axis[1], axis[2] );
}
void vectoangles( 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;
}
/*
=================
AnglesToAxis
=================
*/
void AnglesToAxis( const vec3_t angles, vec3_t axis[3] ) {
vec3_t right;
// angle vectors returns "right" instead of "y axis"
AngleVectors( angles, axis[0], right, axis[2] );
VectorSubtract( vec3_origin, right, axis[1] );
}
void AxisClear( vec3_t axis[3] ) {
axis[0][0] = 1;
axis[0][1] = 0;
axis[0][2] = 0;
axis[1][0] = 0;
axis[1][1] = 1;
axis[1][2] = 0;
axis[2][0] = 0;
axis[2][1] = 0;
axis[2][2] = 1;
}
void AxisCopy( vec3_t in[3], vec3_t out[3] ) {
VectorCopy( in[0], out[0] );
VectorCopy( in[1], out[1] );
VectorCopy( in[2], out[2] );
}
void ProjectPointOnPlane( vec3_t dst, const vec3_t p, const vec3_t normal )
{
float d;
vec3_t n;
float inv_denom;
inv_denom = DotProduct( normal, normal );
#ifndef Q3_VM
assert( Q_fabs(inv_denom) != 0.0f ); // bk010122 - zero vectors get here
#endif
inv_denom = 1.0f / inv_denom;
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];
}
/*
================
MakeNormalVectors
Given a normalized forward vector, create two
other perpendicular vectors
================
*/
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);
}
void VectorRotate( vec3_t in, vec3_t matrix[3], vec3_t out )
{
out[0] = DotProduct( in, matrix[0] );
out[1] = DotProduct( in, matrix[1] );
out[2] = DotProduct( in, matrix[2] );
}
//============================================================================
#if !idppc
/*
** float q_rsqrt( float number )
*/
float Q_rsqrt( float number )
{
long i;
float x2, y;
const float threehalfs = 1.5F;
x2 = number * 0.5F;
y = number;
i = * ( long * ) &y; // evil floating point bit level hacking
i = 0x5f3759df - ( i >> 1 ); // what the fuck?
y = * ( float * ) &i;
y = y * ( threehalfs - ( x2 * y * y ) ); // 1st iteration
// y = y * ( threehalfs - ( x2 * y * y ) ); // 2nd iteration, this can be removed
#ifndef Q3_VM
#ifdef __linux__
assert( !isnan(y) ); // bk010122 - FPE?
#endif
#endif
return y;
}
float Q_fabs( float f ) {
int tmp = * ( int * ) &f;
tmp &= 0x7FFFFFFF;
return * ( float * ) &tmp;
}
#endif
//============================================================
/*
===============
LerpAngle
===============
*/
float LerpAngle (float from, float to, float frac) {
float a;
if ( to - from > 180 ) {
to -= 360;
}
if ( to - from < -180 ) {
to += 360;
}
a = from + frac * (to - from);
return a;
}
/*
=================
AngleSubtract
Always returns a value from -180 to 180
=================
*/
float AngleSubtract( float a1, float a2 ) {
float a;
a = a1 - a2;
while ( a > 180 ) {
a -= 360;
}
while ( a < -180 ) {
a += 360;
}
return a;
}
void AnglesSubtract( vec3_t v1, vec3_t v2, vec3_t v3 ) {
v3[0] = AngleSubtract( v1[0], v2[0] );
v3[1] = AngleSubtract( v1[1], v2[1] );
v3[2] = AngleSubtract( v1[2], v2[2] );
}
float AngleMod(float a) {
a = (360.0/65536) * ((int)(a*(65536/360.0)) & 65535);
return a;
}
/*
=================
AngleNormalize360
returns angle normalized to the range [0 <= angle < 360]
=================
*/
float AngleNormalize360 ( float angle ) {
return (360.0 / 65536) * ((int)(angle * (65536 / 360.0)) & 65535);
}
/*
=================
AngleNormalize180
returns angle normalized to the range [-180 < angle <= 180]
=================
*/
float AngleNormalize180 ( float angle ) {
angle = AngleNormalize360( angle );
if ( angle > 180.0 ) {
angle -= 360.0;
}
return angle;
}
/*
=================
AngleDelta
returns the normalized delta from angle1 to angle2
=================
*/
float AngleDelta ( float angle1, float angle2 ) {
return AngleNormalize180( angle1 - angle2 );
}
//============================================================
/*
=================
SetPlaneSignbits
=================
*/
void SetPlaneSignbits (cplane_t *out) {
int bits, j;
// for fast box on planeside test
bits = 0;
for (j=0 ; j<3 ; j++) {
if (out->normal[j] < 0) {
bits |= 1<<j;
}
}
out->signbits = bits;
}
/*
==================
BoxOnPlaneSide
Returns 1, 2, or 1 + 2
// this is the slow, general version
int BoxOnPlaneSide2 (vec3_t emins, vec3_t emaxs, struct cplane_s *p)
{
int i;
float dist1, dist2;
int sides;
vec3_t corners[2];
for (i=0 ; i<3 ; i++)
{
if (p->normal[i] < 0)
{
corners[0][i] = emins[i];
corners[1][i] = emaxs[i];
}
else
{
corners[1][i] = emins[i];
corners[0][i] = emaxs[i];
}
}
dist1 = DotProduct (p->normal, corners[0]) - p->dist;
dist2 = DotProduct (p->normal, corners[1]) - p->dist;
sides = 0;
if (dist1 >= 0)
sides = 1;
if (dist2 < 0)
sides |= 2;
return sides;
}
==================
*/
#if !( (defined __linux__ || __FreeBSD__) && (defined __i386__) && (!defined C_ONLY)) // rb010123
#if defined __LCC__ || defined C_ONLY || !id386 || defined __VECTORC
int BoxOnPlaneSide (vec3_t emins, vec3_t emaxs, struct cplane_s *p)
{
float dist1, dist2;
int sides;
// fast axial cases
if (p->type < 3)
{
if (p->dist <= emins[p->type])
return 1;
if (p->dist >= emaxs[p->type])
return 2;
return 3;
}
// general case
switch (p->signbits)
{
case 0:
dist1 = p->normal[0]*emaxs[0] + p->normal[1]*emaxs[1] + p->normal[2]*emaxs[2];
dist2 = p->normal[0]*emins[0] + p->normal[1]*emins[1] + p->normal[2]*emins[2];
break;
case 1:
dist1 = p->normal[0]*emins[0] + p->normal[1]*emaxs[1] + p->normal[2]*emaxs[2];
dist2 = p->normal[0]*emaxs[0] + p->normal[1]*emins[1] + p->normal[2]*emins[2];
break;
case 2:
dist1 = p->normal[0]*emaxs[0] + p->normal[1]*emins[1] + p->normal[2]*emaxs[2];
dist2 = p->normal[0]*emins[0] + p->normal[1]*emaxs[1] + p->normal[2]*emins[2];
break;
case 3:
dist1 = p->normal[0]*emins[0] + p->normal[1]*emins[1] + p->normal[2]*emaxs[2];
dist2 = p->normal[0]*emaxs[0] + p->normal[1]*emaxs[1] + p->normal[2]*emins[2];
break;
case 4:
dist1 = p->normal[0]*emaxs[0] + p->normal[1]*emaxs[1] + p->normal[2]*emins[2];
dist2 = p->normal[0]*emins[0] + p->normal[1]*emins[1] + p->normal[2]*emaxs[2];
break;
case 5:
dist1 = p->normal[0]*emins[0] + p->normal[1]*emaxs[1] + p->normal[2]*emins[2];
dist2 = p->normal[0]*emaxs[0] + p->normal[1]*emins[1] + p->normal[2]*emaxs[2];
break;
case 6:
dist1 = p->normal[0]*emaxs[0] + p->normal[1]*emins[1] + p->normal[2]*emins[2];
dist2 = p->normal[0]*emins[0] + p->normal[1]*emaxs[1] + p->normal[2]*emaxs[2];
break;
case 7:
dist1 = p->normal[0]*emins[0] + p->normal[1]*emins[1] + p->normal[2]*emins[2];
dist2 = p->normal[0]*emaxs[0] + p->normal[1]*emaxs[1] + p->normal[2]*emaxs[2];
break;
default:
dist1 = dist2 = 0; // shut up compiler
break;
}
sides = 0;
if (dist1 >= p->dist)
sides = 1;
if (dist2 < p->dist)
sides |= 2;
return sides;
}
#else
#pragma warning( disable: 4035 )
__declspec( naked ) int BoxOnPlaneSide (vec3_t emins, vec3_t emaxs, struct cplane_s *p)
{
static int bops_initialized;
static int Ljmptab[8];
__asm {
push ebx
cmp bops_initialized, 1
je initialized
mov bops_initialized, 1
mov Ljmptab[0*4], offset Lcase0
mov Ljmptab[1*4], offset Lcase1
mov Ljmptab[2*4], offset Lcase2
mov Ljmptab[3*4], offset Lcase3
mov Ljmptab[4*4], offset Lcase4
mov Ljmptab[5*4], offset Lcase5
mov Ljmptab[6*4], offset Lcase6
mov Ljmptab[7*4], offset Lcase7
initialized:
mov edx,dword ptr[4+12+esp]
mov ecx,dword ptr[4+4+esp]
xor eax,eax
mov ebx,dword ptr[4+8+esp]
mov al,byte ptr[17+edx]
cmp al,8
jge Lerror
fld dword ptr[0+edx]
fld st(0)
jmp dword ptr[Ljmptab+eax*4]
Lcase0:
fmul dword ptr[ebx]
fld dword ptr[0+4+edx]
fxch st(2)
fmul dword ptr[ecx]
fxch st(2)
fld st(0)
fmul dword ptr[4+ebx]
fld dword ptr[0+8+edx]
fxch st(2)
fmul dword ptr[4+ecx]
fxch st(2)
fld st(0)
fmul dword ptr[8+ebx]
fxch st(5)
faddp st(3),st(0)
fmul dword ptr[8+ecx]
fxch st(1)
faddp st(3),st(0)
fxch st(3)
faddp st(2),st(0)
jmp LSetSides
Lcase1:
fmul dword ptr[ecx]
fld dword ptr[0+4+edx]
fxch st(2)
fmul dword ptr[ebx]
fxch st(2)
fld st(0)
fmul dword ptr[4+ebx]
fld dword ptr[0+8+edx]
fxch st(2)
fmul dword ptr[4+ecx]
fxch st(2)
fld st(0)
fmul dword ptr[8+ebx]
fxch st(5)
faddp st(3),st(0)
fmul dword ptr[8+ecx]
fxch st(1)
faddp st(3),st(0)
fxch st(3)
faddp st(2),st(0)
jmp LSetSides
Lcase2:
fmul dword ptr[ebx]
fld dword ptr[0+4+edx]
fxch st(2)
fmul dword ptr[ecx]
fxch st(2)
fld st(0)
fmul dword ptr[4+ecx]
fld dword ptr[0+8+edx]
fxch st(2)
fmul dword ptr[4+ebx]
fxch st(2)
fld st(0)
fmul dword ptr[8+ebx]
fxch st(5)
faddp st(3),st(0)
fmul dword ptr[8+ecx]
fxch st(1)
faddp st(3),st(0)
fxch st(3)
faddp st(2),st(0)
jmp LSetSides
Lcase3:
fmul dword ptr[ecx]
fld dword ptr[0+4+edx]
fxch st(2)
fmul dword ptr[ebx]
fxch st(2)
fld st(0)
fmul dword ptr[4+ecx]
fld dword ptr[0+8+edx]
fxch st(2)
fmul dword ptr[4+ebx]
fxch st(2)
fld st(0)
fmul dword ptr[8+ebx]
fxch st(5)
faddp st(3),st(0)
fmul dword ptr[8+ecx]
fxch st(1)
faddp st(3),st(0)
fxch st(3)
faddp st(2),st(0)
jmp LSetSides
Lcase4:
fmul dword ptr[ebx]
fld dword ptr[0+4+edx]
fxch st(2)
fmul dword ptr[ecx]
fxch st(2)
fld st(0)
fmul dword ptr[4+ebx]
fld dword ptr[0+8+edx]
fxch st(2)
fmul dword ptr[4+ecx]
fxch st(2)
fld st(0)
fmul dword ptr[8+ecx]
fxch st(5)
faddp st(3),st(0)
fmul dword ptr[8+ebx]
fxch st(1)
faddp st(3),st(0)
fxch st(3)
faddp st(2),st(0)
jmp LSetSides
Lcase5:
fmul dword ptr[ecx]
fld dword ptr[0+4+edx]
fxch st(2)
fmul dword ptr[ebx]
fxch st(2)
fld st(0)
fmul dword ptr[4+ebx]
fld dword ptr[0+8+edx]
fxch st(2)
fmul dword ptr[4+ecx]
fxch st(2)
fld st(0)
fmul dword ptr[8+ecx]
fxch st(5)
faddp st(3),st(0)
fmul dword ptr[8+ebx]
fxch st(1)
faddp st(3),st(0)
fxch st(3)
faddp st(2),st(0)
jmp LSetSides
Lcase6:
fmul dword ptr[ebx]
fld dword ptr[0+4+edx]
fxch st(2)
fmul dword ptr[ecx]
fxch st(2)
fld st(0)
fmul dword ptr[4+ecx]
fld dword ptr[0+8+edx]
fxch st(2)
fmul dword ptr[4+ebx]
fxch st(2)
fld st(0)
fmul dword ptr[8+ecx]
fxch st(5)
faddp st(3),st(0)
fmul dword ptr[8+ebx]
fxch st(1)
faddp st(3),st(0)
fxch st(3)
faddp st(2),st(0)
jmp LSetSides
Lcase7:
fmul dword ptr[ecx]
fld dword ptr[0+4+edx]
fxch st(2)
fmul dword ptr[ebx]
fxch st(2)
fld st(0)
fmul dword ptr[4+ecx]
fld dword ptr[0+8+edx]
fxch st(2)
fmul dword ptr[4+ebx]
fxch st(2)
fld st(0)
fmul dword ptr[8+ecx]
fxch st(5)
faddp st(3),st(0)
fmul dword ptr[8+ebx]
fxch st(1)
faddp st(3),st(0)
fxch st(3)
faddp st(2),st(0)
LSetSides:
faddp st(2),st(0)
fcomp dword ptr[12+edx]
xor ecx,ecx
fnstsw ax
fcomp dword ptr[12+edx]
and ah,1
xor ah,1
add cl,ah
fnstsw ax
and ah,1
add ah,ah
add cl,ah
pop ebx
mov eax,ecx
ret
Lerror:
int 3
}
}
#pragma warning( default: 4035 )
#endif
#endif
/*
=================
RadiusFromBounds
=================
*/
float RadiusFromBounds( const vec3_t mins, const vec3_t maxs ) {
int i;
vec3_t corner;
float a, b;
for (i=0 ; i<3 ; i++) {
a = fabs( mins[i] );
b = fabs( maxs[i] );
corner[i] = a > b ? a : b;
}
return VectorLength (corner);
}
void ClearBounds( vec3_t mins, vec3_t maxs ) {
mins[0] = mins[1] = mins[2] = 99999;
maxs[0] = maxs[1] = maxs[2] = -99999;
}
void AddPointToBounds( const vec3_t v, vec3_t mins, vec3_t maxs ) {
if ( v[0] < mins[0] ) {
mins[0] = v[0];
}
if ( v[0] > maxs[0]) {
maxs[0] = v[0];
}
if ( v[1] < mins[1] ) {
mins[1] = v[1];
}
if ( v[1] > maxs[1]) {
maxs[1] = v[1];
}
if ( v[2] < mins[2] ) {
mins[2] = v[2];
}
if ( v[2] > maxs[2]) {
maxs[2] = v[2];
}
}
vec_t VectorNormalize( vec3_t v ) {
// NOTE: TTimo - Apple G4 altivec source uses double?
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;
}
vec_t VectorNormalize2( const vec3_t v, vec3_t out) {
float length, ilength;
length = v[0]*v[0] + v[1]*v[1] + v[2]*v[2];
length = sqrt (length);
if (length)
{
#ifndef Q3_VM // bk0101022 - FPE related
// assert( ((Q_fabs(v[0])!=0.0f) || (Q_fabs(v[1])!=0.0f) || (Q_fabs(v[2])!=0.0f)) );
#endif
ilength = 1/length;
out[0] = v[0]*ilength;
out[1] = v[1]*ilength;
out[2] = v[2]*ilength;
} else {
#ifndef Q3_VM // bk0101022 - FPE related
// assert( ((Q_fabs(v[0])==0.0f) && (Q_fabs(v[1])==0.0f) && (Q_fabs(v[2])==0.0f)) );
#endif
VectorClear( out );
}
return length;
}
void _VectorMA( const vec3_t veca, float scale, const vec3_t vecb, vec3_t vecc) {
vecc[0] = veca[0] + scale*vecb[0];
vecc[1] = veca[1] + scale*vecb[1];
vecc[2] = veca[2] + scale*vecb[2];
}
vec_t _DotProduct( const vec3_t v1, const vec3_t v2 ) {
return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
}
void _VectorSubtract( const vec3_t veca, const vec3_t vecb, vec3_t out ) {
out[0] = veca[0]-vecb[0];
out[1] = veca[1]-vecb[1];
out[2] = veca[2]-vecb[2];
}
void _VectorAdd( const vec3_t veca, const vec3_t vecb, vec3_t out ) {
out[0] = veca[0]+vecb[0];
out[1] = veca[1]+vecb[1];
out[2] = veca[2]+vecb[2];
}
void _VectorCopy( const vec3_t in, vec3_t out ) {
out[0] = in[0];
out[1] = in[1];
out[2] = in[2];
}
void _VectorScale( const vec3_t in, vec_t scale, vec3_t out ) {
out[0] = in[0]*scale;
out[1] = in[1]*scale;
out[2] = in[2]*scale;
}
void Vector4Scale( const vec4_t in, vec_t scale, vec4_t out ) {
out[0] = in[0]*scale;
out[1] = in[1]*scale;
out[2] = in[2]*scale;
out[3] = in[3]*scale;
}
int Q_log2( int val ) {
int answer;
answer = 0;
while ( ( val>>=1 ) != 0 ) {
answer++;
}
return answer;
}
/*
=================
PlaneTypeForNormal
=================
*/
/*
int PlaneTypeForNormal (vec3_t normal) {
if ( normal[0] == 1.0 )
return PLANE_X;
if ( normal[1] == 1.0 )
return PLANE_Y;
if ( normal[2] == 1.0 )
return PLANE_Z;
return PLANE_NON_AXIAL;
}
*/
/*
================
MatrixMultiply
================
*/
void MatrixMultiply(float in1[3][3], float in2[3][3], float out[3][3]) {
out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] +
in1[0][2] * in2[2][0];
out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] +
in1[0][2] * in2[2][1];
out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] +
in1[0][2] * in2[2][2];
out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] +
in1[1][2] * in2[2][0];
out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] +
in1[1][2] * in2[2][1];
out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] +
in1[1][2] * in2[2][2];
out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] +
in1[2][2] * in2[2][0];
out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] +
in1[2][2] * in2[2][1];
out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] +
in1[2][2] * in2[2][2];
}
void AngleVectors( const vec3_t angles, vec3_t forward, vec3_t right, vec3_t up) {
float angle;
static float sr, sp, sy, cr, cp, cy;
// static to help MS compiler fp bugs
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);
if (forward)
{
forward[0] = cp*cy;
forward[1] = cp*sy;
forward[2] = -sp;
}
if (right)
{
right[0] = (-1*sr*sp*cy+-1*cr*-sy);
right[1] = (-1*sr*sp*sy+-1*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;
}
}
/*
** 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 );
}
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