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vecmat3.cc
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vecmat3.cc
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/*
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LA: linear algebra C++ interface library
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Copyright (C) 2008-2020 Jiri Pittner <jiri.pittner@jh-inst.cas.cz> or <jiri@pittnerovi.com>
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include "vecmat3.h"
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#include <ctype.h>
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using namespace LA_Vecmat3;
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//cf. https://en.wikipedia.org/wiki/Euler_angles
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template<typename T>
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void euler2rotmat(const Vec3<T> &eul, Mat3<T> a, char *type, bool transpose, bool direction, bool reverse)
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{
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T c2=cos(eul[1]);
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T s2=sin(eul[1]);
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T c1=cos(eul[reverse?2:0]);
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T s1=sin(eul[reverse?2:0]);
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T c3=cos(eul[reverse?0:2]);
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T s3=sin(eul[reverse?0:2]);
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if(direction) {s1= -s1; s2= -s2; s3= -s3;}
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if(tolower(type[0])=='x' && tolower(type[1])=='z' && tolower(type[2])=='x')
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{
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a[0][0]= c2;
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a[0][1]= -c3*s2;
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a[0][2]= s2*s3;
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a[1][0]= c1*s2;
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a[1][1]= c1*c2*c3-s1*s3;
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a[1][2]= -c3*s1-c1*c2*s3;
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a[2][0]= s1*s2;
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a[2][1]= c1*s3+c2*c3*s1;
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a[2][2]= c1*c3-c2*s1*s3;
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}
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if(tolower(type[0])=='x' && tolower(type[1])=='y' && tolower(type[2])=='x')
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{
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a[0][0]= c2;
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a[0][1]= s2*s3;
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a[0][2]= c3*s2;
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a[1][0]= s1*s2;
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a[1][1]= c1*c3-c2*s1*s3;
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a[1][2]= -c1*s3-c2*c3*s1;
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a[2][0]= -c1*s2;
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a[2][1]= c3*s1+c1*c2*s3;
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a[2][2]= c1*c2*c3-s1*s3;
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}
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if(tolower(type[0])=='y' && tolower(type[1])=='x' && tolower(type[2])=='y')
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{
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a[0][0]= c1*c3-c2*s1*s3;
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a[0][1]= s1*s2;
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a[0][2]= c1*s3+c2*c3*s1;
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a[1][0]= s2*s3;
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a[1][1]= c2;
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a[1][2]= -c3*s2;
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a[2][0]= -c3*s1-c1*c2*s3;
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a[2][1]= c1*s2;
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a[2][2]= c1*c2*c3-s1*s3;
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}
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if(tolower(type[0])=='y' && tolower(type[1])=='z' && tolower(type[2])=='y')
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{
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a[0][0]= c1*c2*c3-s1*s3;
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a[0][1]= -c1*s2;
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a[0][2]= c3*s1+c1*c2*s3;
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a[1][0]= c3*s2;
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a[1][1]= c2;
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a[1][2]= s2*s3;
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a[2][0]= -c1*s3;
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a[2][1]= s1*s2;
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a[2][2]= c1*c3-c2*s1*s3;
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}
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if(tolower(type[0])=='z' && tolower(type[1])=='y' && tolower(type[2])=='z')
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{
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a[0][0]= c1*c2*c3-s1*s3;
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a[0][1]= -c3*s1;
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a[0][2]= c1*s2;
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a[1][0]= c1*s3+c2*c3*s1;
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a[1][1]= c1*c3-c2*s1*s3;
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a[1][2]= s1*s2;
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a[2][0]= -c3*s2;
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a[2][1]= s2*s3;
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a[2][2]= c2;
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}
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if(tolower(type[0])=='z' && tolower(type[1])=='x' && tolower(type[2])=='z')
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{
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a[0][0]= c1*c3-c2*s1*s3;
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a[0][1]= -c1*s3-c2*c3*s1;
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a[0][2]= s1*s2;
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a[1][0]= c3*s1+c1*c2*s3;
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a[1][1]= c1*c2*c3-s1*s3;
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a[1][2]= -c1*s2;
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a[2][0]= s2*s3;
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a[2][1]= c3*s2;
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a[2][2]= c2;
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}
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//improper angles Tait-Bryan
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if(tolower(type[0])=='x' && tolower(type[1])=='z' && tolower(type[2])=='y')
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{
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a[0][0]= c2*c3;
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a[0][1]= -s2;
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a[0][2]= c2*s3;
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a[1][0]= s1*s3+c1*c3*s2;
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a[1][1]= c1*c2;
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a[1][2]= c1*s2*s3-c3*s1;
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a[2][0]= c3*s1*s2-c1*s3;
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a[2][1]= c2*s1;
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a[2][2]= c1*c3+s1*s2*s3;
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}
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if(tolower(type[0])=='x' && tolower(type[1])=='y' && tolower(type[2])=='z')
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{
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a[0][0]= c2*c3;
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a[0][1]= -c2*s3;
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a[0][2]= s2;
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a[1][0]= c1*s3+c3*s1*s2;
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a[1][1]= c1*c3-s1*s2*s3;
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a[1][2]= -c2*s1;
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a[2][0]= s1*s3-c1*c3*s2;
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a[2][1]= c3*s1+c1*s2*s3;
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a[2][2]= c1*c2;
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}
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if(tolower(type[0])=='y' && tolower(type[1])=='x' && tolower(type[2])=='z')
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{
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a[0][0]= c1*c3+s1*s2*s3;
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a[0][1]= c3*s1*s2-c1*s3;
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a[0][2]= c2*s1;
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a[1][0]= c2*s3;
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a[1][1]= c2*c3;
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a[1][2]= -s2;
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a[2][0]= c1*s2*s3-c3*s1;
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a[2][1]= c1*c3*s2+s1*s3;
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a[2][2]= c1*c2;
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}
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if(tolower(type[0])=='y' && tolower(type[1])=='z' && tolower(type[2])=='x')
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{
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a[0][0]= c1*c2;
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a[0][1]= s1*s3-c1*c3*s2;
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a[0][2]= c3*s1+c1*s2*s3;
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a[1][0]= s2;
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a[1][1]= c2*c3;
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a[1][2]= -c2*s3;
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a[2][0]= -c2*s1;
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a[2][1]= c1*s3+c3*s1*s2;
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a[2][2]= c1*c3-s1*s2*s3;
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}
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if(tolower(type[0])=='z' && tolower(type[1])=='y' && tolower(type[2])=='x')
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{
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a[0][0]= c1*c2;
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a[0][1]= c1*s2*s3-c3*s1;
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a[0][2]= s1*s2+c1*c3*s2;
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a[1][0]= c2*s1;
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a[1][1]= c1*c3+s1*s2*s3;
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a[1][2]= c3*s1*s2-c1*s3;
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a[2][0]= -s2;
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a[2][1]= c2*s3;
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a[2][2]= c2*c3;
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}
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if(tolower(type[0])=='z' && tolower(type[1])=='x' && tolower(type[2])=='y')
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{
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a[0][0]= c1*c3-s1*s2*s3;
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a[0][1]= -c2*s1;
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a[0][2]= c1*s3+c3*s1*s2;
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a[1][0]= c3*s1+c1*s2*s3;
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a[1][1]= c1*c2;
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a[1][2]= s1*s3-c1*c3*s2;
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a[2][0]= -c2*s3;
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a[2][1]= s2;
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a[2][2]= c2*c3;
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}
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if(transpose) a.transposeme();
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}
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