mirror of
https://github.com/ptitSeb/Serious-Engine
synced 2024-12-25 15:14:51 +01:00
319 lines
10 KiB
C++
319 lines
10 KiB
C++
/* Copyright (c) 2002-2012 Croteam Ltd.
|
|
This program is free software; you can redistribute it and/or modify
|
|
it under the terms of version 2 of the GNU General Public License as published by
|
|
the Free Software Foundation
|
|
|
|
|
|
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 "stdh.h"
|
|
|
|
#include <Engine/Math/Geometry.h>
|
|
|
|
#include <Engine/Math/Functions.h>
|
|
|
|
/////////////////////////////////////////////////////////////////////
|
|
//
|
|
// General functions
|
|
//
|
|
/////////////////////////////////////////////////////////////////////
|
|
|
|
/*
|
|
* Calculate rotation matrix from angles in 3D.
|
|
*/
|
|
/*void operator^=(FLOATmatrix3D &t3dRotation, const ANGLE3D &a3dAngles)
|
|
{
|
|
MakeRotationMatrix(t3dRotation, a3dAngles);
|
|
}
|
|
*/
|
|
|
|
void MakeRotationMatrix(FLOATmatrix3D &t3dRotation, const ANGLE3D &a3dAngles)
|
|
{
|
|
FLOAT fSinH = Sin(a3dAngles(1)); // heading
|
|
FLOAT fCosH = Cos(a3dAngles(1));
|
|
FLOAT fSinP = Sin(a3dAngles(2)); // pitch
|
|
FLOAT fCosP = Cos(a3dAngles(2));
|
|
FLOAT fSinB = Sin(a3dAngles(3)); // banking
|
|
FLOAT fCosB = Cos(a3dAngles(3));
|
|
|
|
t3dRotation(1,1) = fCosH*fCosB+fSinP*fSinH*fSinB;
|
|
t3dRotation(1,2) = fSinP*fSinH*fCosB-fCosH*fSinB;
|
|
t3dRotation(1,3) = fCosP*fSinH;
|
|
t3dRotation(2,1) = fCosP*fSinB;
|
|
t3dRotation(2,2) = fCosP*fCosB;
|
|
t3dRotation(2,3) = -fSinP;
|
|
t3dRotation(3,1) = fSinP*fCosH*fSinB-fSinH*fCosB;
|
|
t3dRotation(3,2) = fSinP*fCosH*fCosB+fSinH*fSinB;
|
|
t3dRotation(3,3) = fCosP*fCosH;
|
|
}
|
|
void MakeRotationMatrixFast(FLOATmatrix3D &t3dRotation, const ANGLE3D &a3dAngles)
|
|
{
|
|
FLOAT fSinH = SinFast(a3dAngles(1)); // heading
|
|
FLOAT fCosH = CosFast(a3dAngles(1));
|
|
FLOAT fSinP = SinFast(a3dAngles(2)); // pitch
|
|
FLOAT fCosP = CosFast(a3dAngles(2));
|
|
FLOAT fSinB = SinFast(a3dAngles(3)); // banking
|
|
FLOAT fCosB = CosFast(a3dAngles(3));
|
|
|
|
t3dRotation(1,1) = fCosH*fCosB+fSinP*fSinH*fSinB;
|
|
t3dRotation(1,2) = fSinP*fSinH*fCosB-fCosH*fSinB;
|
|
t3dRotation(1,3) = fCosP*fSinH;
|
|
t3dRotation(2,1) = fCosP*fSinB;
|
|
t3dRotation(2,2) = fCosP*fCosB;
|
|
t3dRotation(2,3) = -fSinP;
|
|
t3dRotation(3,1) = fSinP*fCosH*fSinB-fSinH*fCosB;
|
|
t3dRotation(3,2) = fSinP*fCosH*fCosB+fSinH*fSinB;
|
|
t3dRotation(3,3) = fCosP*fCosH;
|
|
}
|
|
|
|
/*
|
|
* Calculate inverse rotation matrix from angles in 3D.
|
|
*/
|
|
/*void operator!=(FLOATmatrix3D &t3dRotation, const ANGLE3D &a3dAngles)
|
|
{
|
|
MakeInverseRotationMatrix(t3dRotation, a3dAngles);
|
|
}
|
|
*/
|
|
void MakeInverseRotationMatrix(FLOATmatrix3D &t3dRotation, const ANGLE3D &a3dAngles)
|
|
{
|
|
FLOAT fSinH = Sin(a3dAngles(1)); // heading
|
|
FLOAT fCosH = Cos(a3dAngles(1));
|
|
FLOAT fSinP = Sin(a3dAngles(2)); // pitch
|
|
FLOAT fCosP = Cos(a3dAngles(2));
|
|
FLOAT fSinB = Sin(a3dAngles(3)); // banking
|
|
FLOAT fCosB = Cos(a3dAngles(3));
|
|
|
|
// to make inverse of rotation matrix, we only need to transpose it
|
|
t3dRotation(1,1) = fCosH*fCosB+fSinP*fSinH*fSinB;
|
|
t3dRotation(2,1) = fSinP*fSinH*fCosB-fCosH*fSinB;
|
|
t3dRotation(3,1) = fCosP*fSinH;
|
|
t3dRotation(1,2) = fCosP*fSinB;
|
|
t3dRotation(2,2) = fCosP*fCosB;
|
|
t3dRotation(3,2) = -fSinP;
|
|
t3dRotation(1,3) = fSinP*fCosH*fSinB-fSinH*fCosB;
|
|
t3dRotation(2,3) = fSinP*fCosH*fCosB+fSinH*fSinB;
|
|
t3dRotation(3,3) = fCosP*fCosH;
|
|
}
|
|
void MakeInverseRotationMatrixFast(FLOATmatrix3D &t3dRotation, const ANGLE3D &a3dAngles)
|
|
{
|
|
FLOAT fSinH = SinFast(a3dAngles(1)); // heading
|
|
FLOAT fCosH = CosFast(a3dAngles(1));
|
|
FLOAT fSinP = SinFast(a3dAngles(2)); // pitch
|
|
FLOAT fCosP = CosFast(a3dAngles(2));
|
|
FLOAT fSinB = SinFast(a3dAngles(3)); // banking
|
|
FLOAT fCosB = CosFast(a3dAngles(3));
|
|
|
|
// to make inverse of rotation matrix, we only need to transpose it
|
|
t3dRotation(1,1) = fCosH*fCosB+fSinP*fSinH*fSinB;
|
|
t3dRotation(2,1) = fSinP*fSinH*fCosB-fCosH*fSinB;
|
|
t3dRotation(3,1) = fCosP*fSinH;
|
|
t3dRotation(1,2) = fCosP*fSinB;
|
|
t3dRotation(2,2) = fCosP*fCosB;
|
|
t3dRotation(3,2) = -fSinP;
|
|
t3dRotation(1,3) = fSinP*fCosH*fSinB-fSinH*fCosB;
|
|
t3dRotation(2,3) = fSinP*fCosH*fCosB+fSinH*fSinB;
|
|
t3dRotation(3,3) = fCosP*fCosH;
|
|
}
|
|
|
|
/*
|
|
* Decompose rotation matrix into angles in 3D.
|
|
*/
|
|
// NOTE: for derivation of the algorithm, see mathlib.doc
|
|
void DecomposeRotationMatrixNoSnap(ANGLE3D &a3dAngles, const FLOATmatrix3D &t3dRotation)
|
|
{
|
|
ANGLE &h=a3dAngles(1); // heading
|
|
ANGLE &p=a3dAngles(2); // pitch
|
|
ANGLE &b=a3dAngles(3); // banking
|
|
FLOAT a; // temporary
|
|
|
|
// calculate pitch
|
|
FLOAT f23 = t3dRotation(2,3);
|
|
p = ASin(-f23);
|
|
a = Sqrt(1.0f-f23*f23);
|
|
|
|
// if pitch makes banking beeing the same as heading
|
|
if (a<0.001) {
|
|
// we choose to have banking of 0
|
|
b = 0;
|
|
// and calculate heading for that
|
|
ASSERT(Abs(t3dRotation(2,3))>0.5); // must be around 1, what is far from 0
|
|
h = ATan2(t3dRotation(1,2)/(-t3dRotation(2,3)), t3dRotation(1,1)); // no division by 0
|
|
// otherwise
|
|
} else {
|
|
// calculate banking and heading normally
|
|
b = ATan2(t3dRotation(2,1), t3dRotation(2,2));
|
|
h = ATan2(t3dRotation(1,3), t3dRotation(3,3));
|
|
}
|
|
}
|
|
|
|
void DecomposeRotationMatrix(ANGLE3D &a3dAngles, const FLOATmatrix3D &t3dRotation)
|
|
{
|
|
// decompose the matrix without snapping
|
|
DecomposeRotationMatrixNoSnap(a3dAngles, t3dRotation);
|
|
// snap angles to compensate for errors when converting to and from matrix notation
|
|
Snap(a3dAngles(1), ANGLE_SNAP);
|
|
Snap(a3dAngles(2), ANGLE_SNAP);
|
|
Snap(a3dAngles(3), ANGLE_SNAP);
|
|
}
|
|
|
|
/*void operator^=(ANGLE3D &a3dAngles, const FLOATmatrix3D &t3dRotation) {
|
|
DecomposeRotationMatrix(a3dAngles, t3dRotation);
|
|
}
|
|
*/
|
|
|
|
/*
|
|
* Create direction vector from angles in 3D (ignoring banking).
|
|
*/
|
|
void AnglesToDirectionVector(const ANGLE3D &a3dAngles, FLOAT3D &vDirection)
|
|
{
|
|
// find the rotation matrix from the angles
|
|
FLOATmatrix3D mDirection;
|
|
MakeRotationMatrix(mDirection, a3dAngles);
|
|
// rotate a front oriented vector by the matrix
|
|
vDirection = FLOAT3D(0.0f, 0.0f, -1.0f)*mDirection;
|
|
}
|
|
|
|
/*
|
|
* Create angles in 3D from direction vector(ignoring banking).
|
|
*/
|
|
void DirectionVectorToAnglesNoSnap(const FLOAT3D &vDirection, ANGLE3D &a3dAngles)
|
|
{
|
|
// now calculate the angles
|
|
ANGLE &h = a3dAngles(1);
|
|
ANGLE &p = a3dAngles(2);
|
|
ANGLE &b = a3dAngles(3);
|
|
|
|
const FLOAT &x = vDirection(1);
|
|
const FLOAT &y = vDirection(2);
|
|
const FLOAT &z = vDirection(3);
|
|
|
|
// banking is always irrelevant
|
|
b = 0;
|
|
// calculate pitch
|
|
p = ASin(y);
|
|
|
|
// if y is near +1 or -1
|
|
if (y>0.99 || y<-0.99) {
|
|
// heading is irrelevant
|
|
h = 0;
|
|
// otherwise
|
|
} else {
|
|
// calculate heading
|
|
h = ATan2(-x, -z);
|
|
}
|
|
}
|
|
void DirectionVectorToAngles(const FLOAT3D &vDirection, ANGLE3D &a3dAngles)
|
|
{
|
|
DirectionVectorToAnglesNoSnap(vDirection, a3dAngles);
|
|
|
|
// snap angles to compensate for errors when converting to and from vector notation
|
|
Snap(a3dAngles(1), ANGLE_SNAP);
|
|
Snap(a3dAngles(2), ANGLE_SNAP);
|
|
Snap(a3dAngles(3), ANGLE_SNAP);
|
|
}
|
|
|
|
/* Create angles in 3D from up vector (ignoring objects relative heading).
|
|
(up vector must be normalized!)*/
|
|
void UpVectorToAngles(const FLOAT3D &vY, ANGLE3D &a3dAngles)
|
|
{
|
|
// create any front vector
|
|
FLOAT3D vZ;
|
|
if (Abs(vY(2))>0.5f) {
|
|
vZ = FLOAT3D(1,0,0)*vY;
|
|
} else {
|
|
vZ = FLOAT3D(0,1,0)*vY;
|
|
}
|
|
vZ.Normalize();
|
|
// side vector is cross product
|
|
FLOAT3D vX = vY*vZ;
|
|
vX.Normalize();
|
|
// create the rotation matrix
|
|
FLOATmatrix3D m;
|
|
m(1,1) = vX(1); m(1,2) = vY(1); m(1,3) = vZ(1);
|
|
m(2,1) = vX(2); m(2,2) = vY(2); m(2,3) = vZ(2);
|
|
m(3,1) = vX(3); m(3,2) = vY(3); m(3,3) = vZ(3);
|
|
|
|
// decompose the matrix without snapping
|
|
DecomposeRotationMatrixNoSnap(a3dAngles, m);
|
|
}
|
|
|
|
/*
|
|
* Calculate rotation matrix from angles in 3D.
|
|
*/
|
|
void operator^=(DOUBLEmatrix3D &t3dRotation, const ANGLE3D &a3dAngles) {
|
|
const ANGLE &h=a3dAngles(1); // heading
|
|
const ANGLE &p=a3dAngles(2); // pitch
|
|
const ANGLE &b=a3dAngles(3); // banking
|
|
|
|
t3dRotation(1,1) = Cos(h)*Cos(b)+Sin(p)*Sin(h)*Sin(b);
|
|
t3dRotation(1,2) = Sin(p)*Sin(h)*Cos(b)-Cos(h)*Sin(b);
|
|
t3dRotation(1,3) = Cos(p)*Sin(h);
|
|
t3dRotation(2,1) = Cos(p)*Sin(b);
|
|
t3dRotation(2,2) = Cos(p)*Cos(b);
|
|
t3dRotation(2,3) = -Sin(p);
|
|
t3dRotation(3,1) = Sin(p)*Cos(h)*Sin(b)-Sin(h)*Cos(b);
|
|
t3dRotation(3,2) = Sin(p)*Cos(h)*Cos(b)+Sin(h)*Sin(b);
|
|
t3dRotation(3,3) = Cos(p)*Cos(h);
|
|
}
|
|
|
|
/*
|
|
* Calculate inverse rotation matrix from angles in 3D.
|
|
*/
|
|
void operator!=(DOUBLEmatrix3D &t3dRotation, const ANGLE3D &a3dAngles) {
|
|
const ANGLE &h=a3dAngles(1); // heading
|
|
const ANGLE &p=a3dAngles(2); // pitch
|
|
const ANGLE &b=a3dAngles(3); // banking
|
|
|
|
// to make inverse of rotation matrix, we only need to transpose it
|
|
t3dRotation(1,1) = Cos(h)*Cos(b)+Sin(p)*Sin(h)*Sin(b);
|
|
t3dRotation(2,1) = Sin(p)*Sin(h)*Cos(b)-Cos(h)*Sin(b);
|
|
t3dRotation(3,1) = Cos(p)*Sin(h);
|
|
t3dRotation(1,2) = Cos(p)*Sin(b);
|
|
t3dRotation(2,2) = Cos(p)*Cos(b);
|
|
t3dRotation(3,2) = -Sin(p);
|
|
t3dRotation(1,3) = Sin(p)*Cos(h)*Sin(b)-Sin(h)*Cos(b);
|
|
t3dRotation(2,3) = Sin(p)*Cos(h)*Cos(b)+Sin(h)*Sin(b);
|
|
t3dRotation(3,3) = Cos(p)*Cos(h);
|
|
}
|
|
|
|
/*
|
|
* Decompose rotation matrix into angles in 3D.
|
|
*/
|
|
// NOTE: for derivation of the algorithm, see mathlib.doc
|
|
void operator^=(ANGLE3D &a3dAngles, const DOUBLEmatrix3D &t3dRotation) {
|
|
ANGLE &h=a3dAngles(1); // heading
|
|
ANGLE &p=a3dAngles(2); // pitch
|
|
ANGLE &b=a3dAngles(3); // banking
|
|
DOUBLE a; // temporary
|
|
|
|
// calculate pitch
|
|
p = ASin(-t3dRotation(2,3));
|
|
a = sqrt(1-t3dRotation(2,3)*t3dRotation(2,3));
|
|
|
|
// if pitch makes banking beeing the same as heading
|
|
if (a<0.0001) {
|
|
// we choose to have banking of 0
|
|
b = 0;
|
|
// and calculate heading for that
|
|
ASSERT(Abs(t3dRotation(2,3))>0.5); // must be around 1, what is far from 0
|
|
h = ATan2(t3dRotation(1,2)/(-t3dRotation(2,3)), t3dRotation(1,1)); // no division by 0
|
|
// otherwise
|
|
} else {
|
|
// calculate banking and heading normally
|
|
b = ATan2(t3dRotation(2,1)/a, t3dRotation(2,2)/a);
|
|
h = ATan2(t3dRotation(1,3)/a, t3dRotation(3,3)/a);
|
|
}
|
|
// snap angles to compensate for errors when converting to and from matrix notation
|
|
Snap(h, ANGLE_SNAP);
|
|
Snap(p, ANGLE_SNAP);
|
|
Snap(b, ANGLE_SNAP);
|
|
}
|
|
|