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