blob: 1f920f5a8cd4768fe9352b710aaa00087721e021 [file] [log] [blame]
 /* * Quaternion arithmetic: * qadd(q, r) returns q+r * qsub(q, r) returns q-r * qneg(q) returns -q * qmul(q, r) returns q*r * qdiv(q, r) returns q/r, can divide check. * qinv(q) returns 1/q, can divide check. * double qlen(p) returns modulus of p * qunit(q) returns a unit quaternion parallel to q * The following only work on unit quaternions and rotation matrices: * slerp(q, r, a) returns q*(r*q^-1)^a * qmid(q, r) slerp(q, r, .5) * qsqrt(q) qmid(q, (Quaternion){1,0,0,0}) * qtom(m, q) converts a unit quaternion q into a rotation matrix m * mtoq(m) returns a quaternion equivalent to a rotation matrix m */ #include #include #include #include void qtom(Matrix m, Quaternion q){ #ifndef new m[0][0]=1-2*(q.j*q.j+q.k*q.k); m[0][1]=2*(q.i*q.j+q.r*q.k); m[0][2]=2*(q.i*q.k-q.r*q.j); m[0][3]=0; m[1][0]=2*(q.i*q.j-q.r*q.k); m[1][1]=1-2*(q.i*q.i+q.k*q.k); m[1][2]=2*(q.j*q.k+q.r*q.i); m[1][3]=0; m[2][0]=2*(q.i*q.k+q.r*q.j); m[2][1]=2*(q.j*q.k-q.r*q.i); m[2][2]=1-2*(q.i*q.i+q.j*q.j); m[2][3]=0; m[3][0]=0; m[3][1]=0; m[3][2]=0; m[3][3]=1; #else /* * Transcribed from Ken Shoemake's new code -- not known to work */ double Nq = q.r*q.r+q.i*q.i+q.j*q.j+q.k*q.k; double s = (Nq > 0.0) ? (2.0 / Nq) : 0.0; double xs = q.i*s, ys = q.j*s, zs = q.k*s; double wx = q.r*xs, wy = q.r*ys, wz = q.r*zs; double xx = q.i*xs, xy = q.i*ys, xz = q.i*zs; double yy = q.j*ys, yz = q.j*zs, zz = q.k*zs; m[0][0] = 1.0 - (yy + zz); m[1][0] = xy + wz; m[2][0] = xz - wy; m[0][1] = xy - wz; m[1][1] = 1.0 - (xx + zz); m[2][1] = yz + wx; m[0][2] = xz + wy; m[1][2] = yz - wx; m[2][2] = 1.0 - (xx + yy); m[0][3] = m[1][3] = m[2][3] = m[3][0] = m[3][1] = m[3][2] = 0.0; m[3][3] = 1.0; #endif } Quaternion mtoq(Matrix mat){ #ifndef new #define EPS 1.387778780781445675529539585113525e-17 /* 2^-56 */ double t; Quaternion q; q.r=0.; q.i=0.; q.j=0.; q.k=1.; if((t=.25*(1+mat[0][0]+mat[1][1]+mat[2][2]))>EPS){ q.r=sqrt(t); t=4*q.r; q.i=(mat[1][2]-mat[2][1])/t; q.j=(mat[2][0]-mat[0][2])/t; q.k=(mat[0][1]-mat[1][0])/t; } else if((t=-.5*(mat[1][1]+mat[2][2]))>EPS){ q.i=sqrt(t); t=2*q.i; q.j=mat[0][1]/t; q.k=mat[0][2]/t; } else if((t=.5*(1-mat[2][2]))>EPS){ q.j=sqrt(t); q.k=mat[1][2]/(2*q.j); } return q; #else /* * Transcribed from Ken Shoemake's new code -- not known to work */ /* This algorithm avoids near-zero divides by looking for a large * component -- first r, then i, j, or k. When the trace is greater than zero, * |r| is greater than 1/2, which is as small as a largest component can be. * Otherwise, the largest diagonal entry corresponds to the largest of |i|, * |j|, or |k|, one of which must be larger than |r|, and at least 1/2. */ Quaternion qu; double tr, s; tr = mat[0][0] + mat[1][1] + mat[2][2]; if (tr >= 0.0) { s = sqrt(tr + mat[3][3]); qu.r = s*0.5; s = 0.5 / s; qu.i = (mat[2][1] - mat[1][2]) * s; qu.j = (mat[0][2] - mat[2][0]) * s; qu.k = (mat[1][0] - mat[0][1]) * s; } else { int i = 0; if (mat[1][1] > mat[0][0]) i = 1; if (mat[2][2] > mat[i][i]) i = 2; switch(i){ case 0: s = sqrt( (mat[0][0] - (mat[1][1]+mat[2][2])) + mat[3][3] ); qu.i = s*0.5; s = 0.5 / s; qu.j = (mat[0][1] + mat[1][0]) * s; qu.k = (mat[2][0] + mat[0][2]) * s; qu.r = (mat[2][1] - mat[1][2]) * s; break; case 1: s = sqrt( (mat[1][1] - (mat[2][2]+mat[0][0])) + mat[3][3] ); qu.j = s*0.5; s = 0.5 / s; qu.k = (mat[1][2] + mat[2][1]) * s; qu.i = (mat[0][1] + mat[1][0]) * s; qu.r = (mat[0][2] - mat[2][0]) * s; break; case 2: s = sqrt( (mat[2][2] - (mat[0][0]+mat[1][1])) + mat[3][3] ); qu.k = s*0.5; s = 0.5 / s; qu.i = (mat[2][0] + mat[0][2]) * s; qu.j = (mat[1][2] + mat[2][1]) * s; qu.r = (mat[1][0] - mat[0][1]) * s; break; } } if (mat[3][3] != 1.0){ s=1/sqrt(mat[3][3]); qu.r*=s; qu.i*=s; qu.j*=s; qu.k*=s; } return (qu); #endif } Quaternion qadd(Quaternion q, Quaternion r){ q.r+=r.r; q.i+=r.i; q.j+=r.j; q.k+=r.k; return q; } Quaternion qsub(Quaternion q, Quaternion r){ q.r-=r.r; q.i-=r.i; q.j-=r.j; q.k-=r.k; return q; } Quaternion qneg(Quaternion q){ q.r=-q.r; q.i=-q.i; q.j=-q.j; q.k=-q.k; return q; } Quaternion qmul(Quaternion q, Quaternion r){ Quaternion s; s.r=q.r*r.r-q.i*r.i-q.j*r.j-q.k*r.k; s.i=q.r*r.i+r.r*q.i+q.j*r.k-q.k*r.j; s.j=q.r*r.j+r.r*q.j+q.k*r.i-q.i*r.k; s.k=q.r*r.k+r.r*q.k+q.i*r.j-q.j*r.i; return s; } Quaternion qdiv(Quaternion q, Quaternion r){ return qmul(q, qinv(r)); } Quaternion qunit(Quaternion q){ double l=qlen(q); q.r/=l; q.i/=l; q.j/=l; q.k/=l; return q; } /* * Bug?: takes no action on divide check */ Quaternion qinv(Quaternion q){ double l=q.r*q.r+q.i*q.i+q.j*q.j+q.k*q.k; q.r/=l; q.i=-q.i/l; q.j=-q.j/l; q.k=-q.k/l; return q; } double qlen(Quaternion p){ return sqrt(p.r*p.r+p.i*p.i+p.j*p.j+p.k*p.k); } Quaternion slerp(Quaternion q, Quaternion r, double a){ double u, v, ang, s; double dot=q.r*r.r+q.i*r.i+q.j*r.j+q.k*r.k; ang=dot<-1?PI:dot>1?0:acos(dot); /* acos gives NaN for dot slightly out of range */ s=sin(ang); if(s==0) return ang