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/*
* quat - alculate using quaternions of the form: a + bi + cj + dk
*
* Copyright (C) 1999 David I. Bell
*
* Calc is open software; you can redistribute it and/or modify it under
* the terms of the version 2.1 of the GNU Lesser General Public License
* as published by the Free Software Foundation.
*
* Calc 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 Lesser General
* Public License for more details.
*
* A copy of version 2.1 of the GNU Lesser General Public License is
* distributed with calc under the filename COPYING-LGPL. You should have
* received a copy with calc; if not, write to Free Software Foundation, Inc.
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*
* Under source code control: 1990/02/15 01:50:35
* File existed as early as: before 1990
*
* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
*/
/*
* Routines to handle quaternions of the form:
* a + bi + cj + dk
*
* Note: In this module, quaternians are manipulated in the form:
* s + v
* Where s is a scalar and v is a vector of size 3.
*/
obj quat {s, v}; /* definition of the quaternion object */
define quat(a,b,c,d)
{
local obj quat x;
x.s = isnull(a) ? 0 : a;
mat x.v[3];
x.v[0] = isnull(b) ? 0 : b;
x.v[1] = isnull(c) ? 0 : c;
x.v[2] = isnull(d) ? 0 : d;
return x;
}
define quat_print(a)
{
print "quat(" : a.s : ", " : a.v[0] : ", " :
a.v[1] : ", " : a.v[2] : ")" :;
}
define quat_norm(a)
{
return a.s^2 + dp(a.v, a.v);
}
define quat_abs(a, e)
{
return sqrt(a.s^2 + dp(a.v, a.v), e);
}
define quat_conj(a)
{
local obj quat x;
x.s = a.s;
x.v = -a.v;
return x;
}
define quat_add(a, b)
{
local obj quat x;
if (!istype(b, x)) {
x.s = a.s + b;
x.v = a.v;
return x;
}
if (!istype(a, x)) {
x.s = a + b.s;
x.v = b.v;
return x;
}
x.s = a.s + b.s;
x.v = a.v + b.v;
if (x.v)
return x;
return x.s;
}
define quat_sub(a, b)
{
local obj quat x;
if (!istype(b, x)) {
x.s = a.s - b;
x.v = a.v;
return x;
}
if (!istype(a, x)) {
x.s = a - b.s;
x.v = -b.v;
return x;
}
x.s = a.s - b.s;
x.v = a.v - b.v;
if (x.v)
return x;
return x.s;
}
define quat_inc(a)
{
local x;
x = a;
x.s++;
return x;
}
define quat_dec(a)
{
local x;
x = a;
x.s--;
return x;
}
define quat_neg(a)
{
local obj quat x;
x.s = -a.s;
x.v = -a.v;
return x;
}
define quat_mul(a, b)
{
local obj quat x;
if (!istype(b, x)) {
x.s = a.s * b;
x.v = a.v * b;
} else if (!istype(a, x)) {
x.s = b.s * a;
x.v = b.v * a;
} else {
x.s = a.s * b.s - dp(a.v, b.v);
x.v = a.s * b.v + b.s * a.v + cp(a.v, b.v);
}
if (x.v)
return x;
return x.s;
}
define quat_div(a, b)
{
local obj quat x;
if (!istype(b, x)) {
x.s = a.s / b;
x.v = a.v / b;
return x;
}
return a * quat_inv(b);
}
define quat_inv(a)
{
local x, q2;
obj quat x;
q2 = a.s^2 + dp(a.v, a.v);
x.s = a.s / q2;
x.v = a.v / (-q2);
return x;
}
define quat_scale(a, b)
{
local obj quat x;
x.s = scale(a.s, b);
x.v = scale(a.v, b);
return x;
}
define quat_shift(a, b)
{
local obj quat x;
x.s = a.s << b;
x.v = a.v << b;
if (x.v)
return x;
return x.s;
}
if (config("resource_debug") & 3) {
print "obj quat {s, v} defined";
}