linuxcnc-hal-sys 0.1.5

/********************************************************************
* Description: _posemath.c
*    C definitions for pose math library data types and manipulation
*    functions.
*
*   Derived from a work by Fred Proctor & Will Shackleford
*
* Author:
* License: LGPL Version 2
* System: Linux
*    
* Copyright (c) 2004 All rights reserved.
*
* Last change: 
********************************************************************/

#if defined(PM_PRINT_ERROR) && defined(rtai)
#undef PM_PRINT_ERROR
#endif

#if defined(PM_DEBUG) && defined(rtai)
#undef PM_DEBUG
#endif

#ifdef PM_PRINT_ERROR
#define PM_DEBUG		/* have to have debug with printing */
#include <stdio.h>
#include <stdarg.h>
#endif
#include "posemath.h"

#include "rtapi_math.h"
#include <float.h>

#include "sincos.h"

/* global error number */
int pmErrno = 0;

#ifdef PM_PRINT_ERROR

void pmPrintError(const char *fmt, ...)
{
    va_list args;

    va_start(args, fmt);
    vfprintf(stderr, fmt, args);
    va_end(args);
}

/* error printing function */
void pmPerror(const char *s)
{
    char *pmErrnoString;

    switch (pmErrno) {
    case 0:
	/* no error */
	return;

    case PM_ERR:
	pmErrnoString = "unspecified error";
	break;

    case PM_IMPL_ERR:
	pmErrnoString = "not implemented";
	break;

    case PM_NORM_ERR:
	pmErrnoString = "expected normalized value";
	break;

    case PM_DIV_ERR:
	pmErrnoString = "divide by zero";
	break;

    default:
	pmErrnoString = "unassigned error";
	break;
    }

    if (s != 0 && s[0] != 0) {
	fprintf(stderr, "%s: %s\n", s, pmErrnoString);
    } else {
	fprintf(stderr, "%s\n", pmErrnoString);
    }
}

#endif /* PM_PRINT_ERROR */

/* fuzz checker */
#define IS_FUZZ(a,fuzz) (fabs(a) < (fuzz) ? 1 : 0)

/* Pose Math Basis Functions */

/* Scalar functions */

double pmSqrt(double x)
{
    if (x > 0.0) {
	return sqrt(x);
    }

    if (x > SQRT_FUZZ) {
	return 0.0;
    }
#ifdef PM_PRINT_ERROR
    pmPrintError("sqrt of large negative number\n");
#endif

    return 0.0;
}

/* Translation rep conversion functions */

int pmCartSphConvert(PmCartesian const * const v, PmSpherical * const s)
{
    double _r;

    s->theta = atan2(v->y, v->x);
    s->r = pmSqrt(pmSq(v->x) + pmSq(v->y) + pmSq(v->z));
    _r = pmSqrt(pmSq(v->x) + pmSq(v->y));
    s->phi = atan2(_r, v->z);

    return pmErrno = 0;
}

int pmCartCylConvert(PmCartesian const * const v, PmCylindrical * const c)
{
    c->theta = atan2(v->y, v->x);
    c->r = pmSqrt(pmSq(v->x) + pmSq(v->y));
    c->z = v->z;

    return pmErrno = 0;
}

int pmSphCartConvert(PmSpherical const * const s, PmCartesian * const v)
{
    double _r;

    _r = s->r * sin(s->phi);
    v->z = s->r * cos(s->phi);
    v->x = _r * cos(s->theta);
    v->y = _r * sin(s->theta);

    return pmErrno = 0;
}

int pmSphCylConvert(PmSpherical const * const s, PmCylindrical * const c)
{
    c->theta = s->theta;
    c->r = s->r * cos(s->phi);
    c->z = s->r * sin(s->phi);
    return pmErrno = 0;
}

int pmCylCartConvert(PmCylindrical const * const c, PmCartesian * const v)
{
    v->x = c->r * cos(c->theta);
    v->y = c->r * sin(c->theta);
    v->z = c->z;
    return pmErrno = 0;
}

int pmCylSphConvert(PmCylindrical const * const c, PmSpherical * const s)
{
    s->theta = c->theta;
    s->r = pmSqrt(pmSq(c->r) + pmSq(c->z));
    s->phi = atan2(c->z, c->r);
    return pmErrno = 0;
}

/* Rotation rep conversion functions */

int pmAxisAngleQuatConvert(PmAxis axis, double a, PmQuaternion * const q)
{
    double sh;

    a *= 0.5;
    sincos(a, &sh, &(q->s));

    switch (axis) {
    case PM_X:
	q->x = sh;
	q->y = 0.0;
	q->z = 0.0;
	break;

    case PM_Y:
	q->x = 0.0;
	q->y = sh;
	q->z = 0.0;
	break;

    case PM_Z:
	q->x = 0.0;
	q->y = 0.0;
	q->z = sh;
	break;

    default:
#ifdef PM_PRINT_ERROR
	pmPrintError("error: bad axis in pmAxisAngleQuatConvert\n");
#endif
	return -1;
    }

    if (q->s < 0.0) {
	q->s *= -1.0;
	q->x *= -1.0;
	q->y *= -1.0;
	q->z *= -1.0;
    }

    return 0;
}

int pmRotQuatConvert(PmRotationVector const * const r, PmQuaternion * const q)
{
    double sh;

#ifdef PM_DEBUG
    /* make sure r is normalized */
    //FIXME breaks const promise
    PmRotationVector r_raw = *r;
    if (0 != pmRotNorm(&r_raw, r)) {
#ifdef PM_PRINT_ERROR
	pmPrintError
	    ("error: pmRotQuatConvert rotation vector not normalized\n");
#endif
	return pmErrno = PM_NORM_ERR;
    }
#endif

    if (pmClose(r->s, 0.0, QS_FUZZ)) {
	q->s = 1.0;
	q->x = q->y = q->z = 0.0;

	return pmErrno = 0;
    }

    sincos(r->s / 2.0, &sh, &(q->s));

    if (q->s >= 0.0) {
	q->x = r->x * sh;
	q->y = r->y * sh;
	q->z = r->z * sh;
    } else {
	q->s *= -1;
	q->x = -r->x * sh;
	q->y = -r->y * sh;
	q->z = -r->z * sh;
    }

    return pmErrno = 0;
}

int pmRotMatConvert(PmRotationVector const * const r, PmRotationMatrix * const m)
{
    double s, c, omc;

#ifdef PM_DEBUG
    if (!pmRotIsNorm(r)) {
#ifdef PM_PRINT_ERROR
	pmPrintError("Bad vector in pmRotMatConvert\n");
#endif
	return pmErrno = PM_NORM_ERR;
    }
#endif

    sincos(r->s, &s, &c);

    /* from space book */
    m->x.x = c + pmSq(r->x) * (omc = 1 - c);	/* omc = One Minus Cos */
    m->y.x = -r->z * s + r->x * r->y * omc;
    m->z.x = r->y * s + r->x * r->z * omc;

    m->x.y = r->z * s + r->y * r->x * omc;
    m->y.y = c + pmSq(r->y) * omc;
    m->z.y = -r->x * s + r->y * r->z * omc;

    m->x.z = -r->y * s + r->z * r->x * omc;
    m->y.z = r->x * s + r->z * r->y * omc;
    m->z.z = c + pmSq(r->z) * omc;

    return pmErrno = 0;
}

int pmRotZyzConvert(PmRotationVector const * const r, PmEulerZyz * const zyz)
{
#ifdef PM_DEBUG
#ifdef PM_PRINT_ERROR
    pmPrintError("error: pmRotZyzConvert not implemented\n");
#endif
    return pmErrno = PM_IMPL_ERR;
#else
    return PM_IMPL_ERR;
#endif
}

int pmRotZyxConvert(PmRotationVector const * const r, PmEulerZyx * const zyx)
{
    PmRotationMatrix m;
    int r1, r2;

    r1 = pmRotMatConvert(r, &m);
    r2 = pmMatZyxConvert(&m, zyx);

    return pmErrno = r1 || r2 ? PM_NORM_ERR : 0;
}

int pmRotRpyConvert(PmRotationVector const * const r, PmRpy * const rpy)
{
    PmQuaternion q;
    int r1, r2;

    q.s = q.x = q.y = q.z = 0.0;

    r1 = pmRotQuatConvert(r, &q);
    r2 = pmQuatRpyConvert(&q, rpy);

    return r1 || r2 ? pmErrno : 0;
}

int pmQuatRotConvert(PmQuaternion const * const q, PmRotationVector * const r)
{
    double sh;

#ifdef PM_DEBUG
    if (!pmQuatIsNorm(q)) {
#ifdef PM_PRINT_ERROR
	pmPrintError("Bad quaternion in pmQuatRotConvert\n");
#endif
	return pmErrno = PM_NORM_ERR;
    }
#endif
    if (r == 0) {
	return (pmErrno = PM_ERR);
    }

    sh = pmSqrt(pmSq(q->x) + pmSq(q->y) + pmSq(q->z));

    if (sh > QSIN_FUZZ) {
	r->s = 2.0 * atan2(sh, q->s);
	r->x = q->x / sh;
	r->y = q->y / sh;
	r->z = q->z / sh;
    } else {
	r->s = 0.0;
	r->x = 0.0;
	r->y = 0.0;
	r->z = 0.0;
    }

    return pmErrno = 0;
}

int pmQuatMatConvert(PmQuaternion const * const q, PmRotationMatrix * const m)
{
#ifdef PM_DEBUG
    if (!pmQuatIsNorm(q)) {
#ifdef PM_PRINT_ERROR
	pmPrintError("Bad quaternion in pmQuatMatConvert\n");
#endif
	return pmErrno = PM_NORM_ERR;
    }
#endif

    /* from space book where e1=q->x e2=q->y e3=q->z e4=q->s */
    m->x.x = 1.0 - 2.0 * (pmSq(q->y) + pmSq(q->z));
    m->y.x = 2.0 * (q->x * q->y - q->z * q->s);
    m->z.x = 2.0 * (q->z * q->x + q->y * q->s);

    m->x.y = 2.0 * (q->x * q->y + q->z * q->s);
    m->y.y = 1.0 - 2.0 * (pmSq(q->z) + pmSq(q->x));
    m->z.y = 2.0 * (q->y * q->z - q->x * q->s);

    m->x.z = 2.0 * (q->z * q->x - q->y * q->s);
    m->y.z = 2.0 * (q->y * q->z + q->x * q->s);
    m->z.z = 1.0 - 2.0 * (pmSq(q->x) + pmSq(q->y));

    return pmErrno = 0;
}

int pmQuatZyzConvert(PmQuaternion const * const q, PmEulerZyz * const zyz)
{
    PmRotationMatrix m;
    int r1, r2;

    /*! \todo FIXME-- need direct equations */
    r1 = pmQuatMatConvert(q, &m);
    r2 = pmMatZyzConvert(&m, zyz);

    return pmErrno = r1 || r2 ? PM_NORM_ERR : 0;
}

int pmQuatZyxConvert(PmQuaternion const * const q, PmEulerZyx * const zyx)
{
    PmRotationMatrix m;
    int r1, r2;

    /*! \todo FIXME-- need direct equations */
    r1 = pmQuatMatConvert(q, &m);
    r2 = pmMatZyxConvert(&m, zyx);

    return pmErrno = r1 || r2 ? PM_NORM_ERR : 0;
}

int pmQuatRpyConvert(PmQuaternion const * const q, PmRpy * const rpy)
{
    PmRotationMatrix m;
    int r1, r2;

    /*! \todo FIXME-- need direct equations */
    r1 = pmQuatMatConvert(q, &m);
    r2 = pmMatRpyConvert(&m, rpy);

    return pmErrno = r1 || r2 ? PM_NORM_ERR : 0;
}

int pmMatRotConvert(PmRotationMatrix const * const m, PmRotationVector * const r)
{
    PmQuaternion q;
    int r1, r2;

    /*! \todo FIXME-- need direct equations */
    r1 = pmMatQuatConvert(m, &q);
    r2 = pmQuatRotConvert(&q, r);

    return pmErrno = r1 || r2 ? PM_NORM_ERR : 0;
}

int pmMatQuatConvert(PmRotationMatrix const * const m, PmQuaternion * const q)
{
    /* 
       from Stephe's "space" book e1 = (c32 - c23) / 4*e4 e2 = (c13 - c31) /
       4*e4 e3 = (c21 - c12) / 4*e4 e4 = sqrt(1 + c11 + c22 + c33) / 2

       if e4 == 0 e1 = sqrt(1 + c11 - c33 - c22) / 2 e2 = sqrt(1 + c22 - c33
       - c11) / 2 e3 = sqrt(1 + c33 - c11 - c22) / 2 to determine whether to
       take the positive or negative sqrt value since e4 == 0 indicates a
       180* rotation then (0 x y z) = (0 -x -y -z). Thus some generallities
       can be used: 1) find which of e1, e2, or e3 has the largest magnitude
       and leave it pos. 2) if e1 is largest then if c21 < 0 then take the
       negative for e2 if c31 < 0 then take the negative for e3 3) else if e2 
       is largest then if c21 < 0 then take the negative for e1 if c32 < 0
       then take the negative for e3 4) else if e3 is larget then if c31 < 0
       then take the negative for e1 if c32 < 0 then take the negative for e2

       Note: c21 in the space book is m->x.y in this C code */

    double a;

#ifdef PM_DEBUG
    if (!pmMatIsNorm(m)) {
#ifdef PM_PRINT_ERROR
	pmPrintError("Bad matrix in pmMatQuatConvert\n");
#endif
	return pmErrno = PM_NORM_ERR;
    }
#endif

    q->s = 0.5 * pmSqrt(1.0 + m->x.x + m->y.y + m->z.z);

    if (fabs(q->s) > QS_FUZZ) {
	q->x = (m->y.z - m->z.y) / (a = 4 * q->s);
	q->y = (m->z.x - m->x.z) / a;
	q->z = (m->x.y - m->y.x) / a;
    } else {
	q->s = 0;
	q->x = pmSqrt(1.0 + m->x.x - m->y.y - m->z.z) / 2.0;
	q->y = pmSqrt(1.0 + m->y.y - m->x.x - m->z.z) / 2.0;
	q->z = pmSqrt(1.0 + m->z.z - m->y.y - m->x.x) / 2.0;

	if (q->x > q->y && q->x > q->z) {
	    if (m->x.y < 0.0) {
		q->y *= -1;
	    }
	    if (m->x.z < 0.0) {
		q->z *= -1;
	    }
	} else if (q->y > q->z) {
	    if (m->x.y < 0.0) {
		q->x *= -1;
	    }
	    if (m->y.z < 0.0) {
		q->z *= -1;
	    }
	} else {
	    if (m->x.z < 0.0) {
		q->x *= -1;
	    }
	    if (m->y.z < 0.0) {
		q->y *= -1;
	    }
	}
    }

    return pmQuatNorm(q, q);
}

int pmMatZyzConvert(PmRotationMatrix const * const m, PmEulerZyz * const zyz)
{
    zyz->y = atan2(pmSqrt(pmSq(m->x.z) + pmSq(m->y.z)), m->z.z);

    if (fabs(zyz->y) < ZYZ_Y_FUZZ) {
	zyz->z = 0.0;
	zyz->y = 0.0;		/* force Y to 0 */
	zyz->zp = atan2(-m->y.x, m->x.x);
    } else if (fabs(zyz->y - PM_PI) < ZYZ_Y_FUZZ) {
	zyz->z = 0.0;
	zyz->y = PM_PI;		/* force Y to 180 */
	zyz->zp = atan2(m->y.x, -m->x.x);
    } else {
	zyz->z = atan2(m->z.y, m->z.x);
	zyz->zp = atan2(m->y.z, -m->x.z);
    }

    return pmErrno = 0;
}

int pmMatZyxConvert(PmRotationMatrix const * const m, PmEulerZyx * const zyx)
{
    zyx->y = atan2(-m->x.z, pmSqrt(pmSq(m->x.x) + pmSq(m->x.y)));

    if (fabs(zyx->y - PM_PI_2) < ZYX_Y_FUZZ) {
	zyx->z = 0.0;
	zyx->y = PM_PI_2;	/* force it */
	zyx->x = atan2(m->y.x, m->y.y);
    } else if (fabs(zyx->y + PM_PI_2) < ZYX_Y_FUZZ) {
	zyx->z = 0.0;
	zyx->y = -PM_PI_2;	/* force it */
	zyx->x = -atan2(m->y.z, m->y.y);
    } else {
	zyx->z = atan2(m->x.y, m->x.x);
	zyx->x = atan2(m->y.z, m->z.z);
    }

    return pmErrno = 0;
}

int pmMatRpyConvert(PmRotationMatrix const * const m, PmRpy * const rpy)
{
    rpy->p = atan2(-m->x.z, pmSqrt(pmSq(m->x.x) + pmSq(m->x.y)));

    if (fabs(rpy->p - PM_PI_2) < RPY_P_FUZZ) {
	rpy->r = atan2(m->y.x, m->y.y);
	rpy->p = PM_PI_2;	/* force it */
	rpy->y = 0.0;
    } else if (fabs(rpy->p + PM_PI_2) < RPY_P_FUZZ) {
	rpy->r = -atan2(m->y.x, m->y.y);
	rpy->p = -PM_PI_2;	/* force it */
	rpy->y = 0.0;
    } else {
	rpy->r = atan2(m->y.z, m->z.z);
	rpy->y = atan2(m->x.y, m->x.x);
    }

    return pmErrno = 0;
}

int pmZyzRotConvert(PmEulerZyz const * const zyz, PmRotationVector * const r)
{
#ifdef PM_PRINT_ERROR
    pmPrintError("error: pmZyzRotConvert not implemented\n");
#endif
    return pmErrno = PM_IMPL_ERR;
}

int pmZyzQuatConvert(PmEulerZyz const * const zyz, PmQuaternion * const q)
{
    PmRotationMatrix m;
    int r1, r2;

    /*! \todo FIXME-- need direct equations */
    r1 = pmZyzMatConvert(zyz, &m);
    r2 = pmMatQuatConvert(&m, q);

    return pmErrno = r1 || r2 ? PM_NORM_ERR : 0;
}

int pmZyzMatConvert(PmEulerZyz  const * const zyz, PmRotationMatrix * const m)
{
    double sa, sb, sg;
    double ca, cb, cg;

    sa = sin(zyz->z);
    sb = sin(zyz->y);
    sg = sin(zyz->zp);

    ca = cos(zyz->z);
    cb = cos(zyz->y);
    cg = cos(zyz->zp);

    m->x.x = ca * cb * cg - sa * sg;
    m->y.x = -ca * cb * sg - sa * cg;
    m->z.x = ca * sb;

    m->x.y = sa * cb * cg + ca * sg;
    m->y.y = -sa * cb * sg + ca * cg;
    m->z.y = sa * sb;

    m->x.z = -sb * cg;
    m->y.z = sb * sg;
    m->z.z = cb;

    return pmErrno = 0;
}

int pmZyzRpyConvert(PmEulerZyz  const * const zyz, PmRpy * const rpy)
{
#ifdef PM_PRINT_ERROR
    pmPrintError("error: pmZyzRpyConvert not implemented\n");
#endif
    return pmErrno = PM_IMPL_ERR;
}

int pmZyxRotConvert(PmEulerZyx  const * const zyx, PmRotationVector * const r)
{
    PmRotationMatrix m;
    int r1, r2;

    /*! \todo FIXME-- need direct equations */
    r1 = pmZyxMatConvert(zyx, &m);
    r2 = pmMatRotConvert(&m, r);

    return pmErrno = r1 || r2 ? PM_NORM_ERR : 0;
}

int pmZyxQuatConvert(PmEulerZyx  const * const zyx, PmQuaternion * const q)
{
    PmRotationMatrix m;
    int r1, r2;

    /*! \todo FIXME-- need direct equations */
    r1 = pmZyxMatConvert(zyx, &m);
    r2 = pmMatQuatConvert(&m, q);

    return pmErrno = r1 || r2 ? PM_NORM_ERR : 0;
}

int pmZyxMatConvert(PmEulerZyx  const * const zyx, PmRotationMatrix * const m)
{
    double sa, sb, sg;
    double ca, cb, cg;

    sa = sin(zyx->z);
    sb = sin(zyx->y);
    sg = sin(zyx->x);

    ca = cos(zyx->z);
    cb = cos(zyx->y);
    cg = cos(zyx->x);

    m->x.x = ca * cb;
    m->y.x = ca * sb * sg - sa * cg;
    m->z.x = ca * sb * cg + sa * sg;

    m->x.y = sa * cb;
    m->y.y = sa * sb * sg + ca * cg;
    m->z.y = sa * sb * cg - ca * sg;

    m->x.z = -sb;
    m->y.z = cb * sg;
    m->z.z = cb * cg;

    return pmErrno = 0;
}

int pmZyxZyzConvert(PmEulerZyx  const * const zyx, PmEulerZyz * const zyz)
{
#ifdef PM_PRINT_ERROR
    pmPrintError("error: pmZyxZyzConvert not implemented\n");
#endif
    return pmErrno = PM_IMPL_ERR;
}

int pmZyxRpyConvert(PmEulerZyx  const * const zyx, PmRpy * const rpy)
{
#ifdef PM_PRINT_ERROR
    pmPrintError("error: pmZyxRpyConvert not implemented\n");
#endif
    return pmErrno = PM_IMPL_ERR;
}

int pmRpyRotConvert(PmRpy  const * const rpy, PmRotationVector * const r)
{
    PmQuaternion q;
    int r1, r2;

    q.s = q.x = q.y = q.z = 0.0;
    r->s = r->x = r->y = r->z = 0.0;

    r1 = pmRpyQuatConvert(rpy, &q);
    r2 = pmQuatRotConvert(&q, r);

    return r1 || r2 ? pmErrno : 0;
}

int pmRpyQuatConvert(PmRpy  const * const rpy, PmQuaternion * const q)
{
    PmRotationMatrix m;
    int r1, r2;

    /*! \todo FIXME-- need direct equations */
    r1 = pmRpyMatConvert(rpy, &m);
    r2 = pmMatQuatConvert(&m, q);

    return pmErrno = r1 || r2 ? PM_NORM_ERR : 0;
}

int pmRpyMatConvert(PmRpy  const * const rpy, PmRotationMatrix * const m)
{
    double sa, sb, sg;
    double ca, cb, cg;

    sa = sin(rpy->y);
    sb = sin(rpy->p);
    sg = sin(rpy->r);

    ca = cos(rpy->y);
    cb = cos(rpy->p);
    cg = cos(rpy->r);

    m->x.x = ca * cb;
    m->y.x = ca * sb * sg - sa * cg;
    m->z.x = ca * sb * cg + sa * sg;

    m->x.y = sa * cb;
    m->y.y = sa * sb * sg + ca * cg;
    m->z.y = sa * sb * cg - ca * sg;

    m->x.z = -sb;
    m->y.z = cb * sg;
    m->z.z = cb * cg;

    return pmErrno = 0;
}

int pmRpyZyzConvert(PmRpy  const * const rpy, PmEulerZyz * const zyz)
{
#ifdef PM_PRINT_ERROR
    pmPrintError("error: pmRpyZyzConvert not implemented\n");
#endif
    return pmErrno = PM_IMPL_ERR;
}

int pmRpyZyxConvert(PmRpy  const * const rpy, PmEulerZyx * const zyx)
{
#ifdef PM_PRINT_ERROR
    pmPrintError("error: pmRpyZyxConvert not implemented\n");
#endif
    return pmErrno = PM_IMPL_ERR;
}

int pmPoseHomConvert(PmPose const * const p, PmHomogeneous * const h)
{
    int r1;

    h->tran = p->tran;
    r1 = pmQuatMatConvert(&p->rot, &h->rot);

    return pmErrno = r1;
}

int pmHomPoseConvert(PmHomogeneous const * const h, PmPose * const p)
{
    int r1;

    p->tran = h->tran;
    r1 = pmMatQuatConvert(&h->rot, &p->rot);

    return pmErrno = r1;
}

/* PmCartesian functions */

int pmCartCartCompare(PmCartesian const * const v1, PmCartesian const * const v2)
{
    if (fabs(v1->x - v2->x) >= V_FUZZ ||
	fabs(v1->y - v2->y) >= V_FUZZ || fabs(v1->z - v2->z) >= V_FUZZ) {
	return 0;
    }

    return 1;
}

int pmCartCartDot(PmCartesian const * const v1, PmCartesian const * const v2, double *d)
{
    *d = v1->x * v2->x + v1->y * v2->y + v1->z * v2->z;

    return pmErrno = 0;
}

int pmCartCartMult(PmCartesian const * const v1, PmCartesian const * const v2,
        PmCartesian * const out)
{
    out->x = v1->x * v2->x;
    out->y = v1->y * v2->y;
    out->z = v1->z * v2->z;

    return pmErrno = 0;
}

int pmCartCartDiv(PmCartesian const * const v1, PmCartesian const * const v2,
        PmCartesian * const out)
{
    out->x = v1->x / v2->x;
    out->y = v1->y / v2->y;
    out->z = v1->z / v2->z;

    return pmErrno = 0;
}

int pmCartCartCross(PmCartesian const * const v1, PmCartesian const * const v2,
        PmCartesian * const vout)
{
    if (vout == v1 || vout == v2) {
        return pmErrno = PM_IMPL_ERR;
    }
    vout->x = v1->y * v2->z - v1->z * v2->y;
    vout->y = v1->z * v2->x - v1->x * v2->z;
    vout->z = v1->x * v2->y - v1->y * v2->x;

    return pmErrno = 0;
}

int pmCartInfNorm(PmCartesian const * v, double * out)
{
    *out = fmax(fabs(v->x),fmax(fabs(v->y),fabs(v->z)));
    return pmErrno = 0;
}

int pmCartMag(PmCartesian const * const v, double *d)
{
    *d = pmSqrt(pmSq(v->x) + pmSq(v->y) + pmSq(v->z));

    return pmErrno = 0;
}

/** Find square of magnitude of a vector (useful for some calculations to save a sqrt).*/
int pmCartMagSq(PmCartesian const * const v, double *d)
{
    *d = pmSq(v->x) + pmSq(v->y) + pmSq(v->z);

    return pmErrno = 0;
}

int pmCartCartDisp(PmCartesian const * const v1, PmCartesian const * const v2,
        double *d)
{
    *d = pmSqrt(pmSq(v2->x - v1->x) + pmSq(v2->y - v1->y) + pmSq(v2->z - v1->z));

    return pmErrno = 0;
}

int pmCartCartAdd(PmCartesian const * const v1, PmCartesian const * const v2,
        PmCartesian * const vout)
{
    vout->x = v1->x + v2->x;
    vout->y = v1->y + v2->y;
    vout->z = v1->z + v2->z;

    return pmErrno = 0;
}

int pmCartCartSub(PmCartesian const * const v1, PmCartesian const * const v2,
        PmCartesian * const vout)
{
    vout->x = v1->x - v2->x;
    vout->y = v1->y - v2->y;
    vout->z = v1->z - v2->z;

    return pmErrno = 0;
}

int pmCartScalMult(PmCartesian const * const v1, double d, PmCartesian * const vout)
{
    if (v1 != vout) {
        *vout = *v1;
    }
    return pmCartScalMultEq(vout, d);
}

int pmCartScalDiv(PmCartesian const * const v1, double d, PmCartesian * const vout)
{
    if (v1 != vout) {
        *vout = *v1;
    }
    return pmCartScalDivEq(vout, d);
}

int pmCartNeg(PmCartesian const * const v1, PmCartesian * const vout)
{
    if (v1 != vout) {
        *vout = *v1;
    }

    return pmCartNegEq(vout);
}

int pmCartNegEq(PmCartesian * const v1)
{
    v1->x = -v1->x;
    v1->y = -v1->y;
    v1->z = -v1->z;

    return pmErrno = 0;
}

int pmCartInv(PmCartesian const * const v1, PmCartesian * const vout)
{
    if (v1 != vout) {
        *vout = *v1;
    }

    return pmCartInvEq(vout);
}

int pmCartInvEq(PmCartesian * const v)
{
    double size_sq;
    pmCartMagSq(v,&size_sq);

    if (size_sq == 0.0) {
#ifdef PM_PRINT_ERROR
        pmPrintError(&"Zero vector in pmCartInv\n");
#endif
        return pmErrno = PM_NORM_ERR;
    }

    v->x /= size_sq;
    v->y /= size_sq;
    v->z /= size_sq;

    return pmErrno = 0;
}

// This used to be called pmCartNorm.

int pmCartUnit(PmCartesian const * const v, PmCartesian * const vout)
{
    if (vout != v) {
        *vout = *v;
    }
    return pmCartUnitEq(vout);
}

int pmCartAbs(PmCartesian const * const v, PmCartesian * const vout)
{

    vout->x = fabs(v->x);
    vout->y = fabs(v->y);
    vout->z = fabs(v->z);

    return pmErrno = 0;
}

/* Compound assign operator equivalent functions. These are to prevent issues with passing the same variable as both input (const) and output */

int pmCartCartAddEq(PmCartesian * const v, PmCartesian const * const v_add)
{
    v->x += v_add->x;
    v->y += v_add->y;
    v->z += v_add->z;

    return pmErrno = 0;
}

int pmCartCartSubEq(PmCartesian * const v, PmCartesian const * const v_sub)
{
    v->x -= v_sub->x;
    v->y -= v_sub->y;
    v->z -= v_sub->z;

    return pmErrno = 0;
}

int pmCartScalMultEq(PmCartesian * const v, double d)
{

    v->x *= d;
    v->y *= d;
    v->z *= d;

    return pmErrno = 0;
}

int pmCartScalDivEq(PmCartesian * const v, double d)
{

    if (d == 0.0) {
#ifdef PM_PRINT_ERROR
        pmPrintError(&"Divide by 0 in pmCartScalDiv\n");
#endif

        return pmErrno = PM_DIV_ERR;
    }

    v->x /= d;
    v->y /= d;
    v->z /= d;

    return pmErrno = 0;
}

int pmCartUnitEq(PmCartesian * const v)
{
    double size = pmSqrt(pmSq(v->x) + pmSq(v->y) + pmSq(v->z));

    if (size == 0.0) {
#ifdef PM_PRINT_ERROR
        pmPrintError("Zero vector in pmCartUnit\n");
#endif
        return pmErrno = PM_NORM_ERR;
    }

    v->x /= size;
    v->y /= size;
    v->z /= size;

    return pmErrno = 0;
}

/*! \todo This is if 0'd out so we can find all the pmCartNorm calls that should
 be renamed pmCartUnit. 
 Later we'll put this back. */
#if 0

int pmCartNorm(PmCartesian const * const v, PmCartesian * const vout)
{

    vout->x = v->x;
    vout->y = v->y;
    vout->z = v->z;

    return pmErrno = 0;
}
#endif

int pmCartIsNorm(PmCartesian const * const v)
{
    return pmSqrt(pmSq(v->x) + pmSq(v->y) + pmSq(v->z)) - 1.0 < UNIT_VEC_FUZZ ? 1 : 0;
}

int pmCartCartProj(PmCartesian const * const v1, PmCartesian const * const v2, PmCartesian * const vout)
{
    int r1, r2;
    int r3=1;
    double d12;
    double d22;
    
    r1 = pmCartCartDot(v1, v2, &d12);
    r2 = pmCartCartDot(v2, v2, &d22);
    if (!(r1 || r1)){
        r3 = pmCartScalMult(v2, d12/d22, vout);
    }

    return pmErrno = r1 || r2 || r3 ? PM_NORM_ERR : 0;
}

int pmCartPlaneProj(PmCartesian const * const v, PmCartesian const * const normal, PmCartesian * const vout)
{
    int r1, r2;
    PmCartesian par;

    r1 = pmCartCartProj(v, normal, &par);
    r2 = pmCartCartSub(v, &par, vout);

    return pmErrno = r1 || r2 ? PM_NORM_ERR : 0;
}

/* angle-axis functions */

int pmQuatAxisAngleMult(PmQuaternion const * const q, PmAxis axis, double angle,
    PmQuaternion * const pq)
{
    double sh, ch;

#ifdef PM_DEBUG
    if (!pmQuatIsNorm(q)) {
#ifdef PM_PRINT_ERROR
	pmPrintError("error: non-unit quaternion in pmQuatAxisAngleMult\n");
#endif
	return -1;
    }
#endif

    angle *= 0.5;
    sincos(angle, &sh, &ch);

    switch (axis) {
    case PM_X:
	pq->s = ch * q->s - sh * q->x;
	pq->x = ch * q->x + sh * q->s;
	pq->y = ch * q->y + sh * q->z;
	pq->z = ch * q->z - sh * q->y;
	break;

    case PM_Y:
	pq->s = ch * q->s - sh * q->y;
	pq->x = ch * q->x - sh * q->z;
	pq->y = ch * q->y + sh * q->s;
	pq->z = ch * q->z + sh * q->x;
	break;

    case PM_Z:
	pq->s = ch * q->s - sh * q->z;
	pq->x = ch * q->x + sh * q->y;
	pq->y = ch * q->y - sh * q->x;
	pq->z = ch * q->z + sh * q->s;
	break;

    default:
#ifdef PM_PRINT_ERROR
	pmPrintError("error: bad axis in pmQuatAxisAngleMult\n");
#endif
	return -1;
    }

    if (pq->s < 0.0) {
	pq->s *= -1.0;
	pq->x *= -1.0;
	pq->y *= -1.0;
	pq->z *= -1.0;
    }

    return 0;
}

/* PmRotationVector functions */

int pmRotScalMult(PmRotationVector const * const r, double s, PmRotationVector * const rout)
{
    rout->s = r->s * s;
    rout->x = r->x;
    rout->y = r->y;
    rout->z = r->z;

    return pmErrno = 0;
}

int pmRotScalDiv(PmRotationVector const * const r, double s, PmRotationVector * const rout)
{
    if (s == 0.0) {
#ifdef PM_PRINT_ERROR
	pmPrintError("Divide by zero in pmRotScalDiv\n");
#endif

	rout->s = DBL_MAX;
	rout->x = r->x;
	rout->y = r->y;
	rout->z = r->z;

	return pmErrno = PM_NORM_ERR;
    }

    rout->s = r->s / s;
    rout->x = r->x;
    rout->y = r->y;
    rout->z = r->z;

    return pmErrno = 0;
}

int pmRotIsNorm(PmRotationVector const * const r)
{
    if (fabs(r->s) < RS_FUZZ ||
	fabs(pmSqrt(pmSq(r->x) + pmSq(r->y) + pmSq(r->z))) - 1.0 < UNIT_VEC_FUZZ)
    {
	return 1;
    }

    return 0;
}

int pmRotNorm(PmRotationVector const * const r, PmRotationVector * const rout)
{
    double size;

    size = pmSqrt(pmSq(r->x) + pmSq(r->y) + pmSq(r->z));

    if (fabs(r->s) < RS_FUZZ) {
	rout->s = 0.0;
	rout->x = 0.0;
	rout->y = 0.0;
	rout->z = 0.0;

	return pmErrno = 0;
    }

    if (size == 0.0) {
#ifdef PM_PRINT_ERROR
	pmPrintError("error: pmRotNorm size is zero\n");
#endif

	rout->s = 0.0;
	rout->x = 0.0;
	rout->y = 0.0;
	rout->z = 0.0;

	return pmErrno = PM_NORM_ERR;
    }

    rout->s = r->s;
    rout->x = r->x / size;
    rout->y = r->y / size;
    rout->z = r->z / size;

    return pmErrno = 0;
}

/* PmRotationMatrix functions */

int pmMatNorm(PmRotationMatrix const * const m, PmRotationMatrix * const mout)
{
    /*! \todo FIXME */
    *mout = *m;

#ifdef PM_PRINT_ERROR
    pmPrintError("error: pmMatNorm not implemented\n");
#endif
    return pmErrno = PM_IMPL_ERR;
}

int pmMatIsNorm(PmRotationMatrix const * const m)
{
    PmCartesian u;

    pmCartCartCross(&m->x, &m->y, &u);

    return (pmCartIsNorm(&m->x) && pmCartIsNorm(&m->y) && pmCartIsNorm(&m->z) && pmCartCartCompare(&u, &m->z));
}

int pmMatInv(PmRotationMatrix const * const m, PmRotationMatrix * const mout)
{
    /* inverse of a rotation matrix is the transpose */

    mout->x.x = m->x.x;
    mout->x.y = m->y.x;
    mout->x.z = m->z.x;

    mout->y.x = m->x.y;
    mout->y.y = m->y.y;
    mout->y.z = m->z.y;

    mout->z.x = m->x.z;
    mout->z.y = m->y.z;
    mout->z.z = m->z.z;

    return pmErrno = 0;
}

int pmMatCartMult(PmRotationMatrix const * const m, PmCartesian const * const v, PmCartesian * const vout)
{
    vout->x = m->x.x * v->x + m->y.x * v->y + m->z.x * v->z;
    vout->y = m->x.y * v->x + m->y.y * v->y + m->z.y * v->z;
    vout->z = m->x.z * v->x + m->y.z * v->y + m->z.z * v->z;

    return pmErrno = 0;
}

int pmMatMatMult(PmRotationMatrix const * const m1, PmRotationMatrix const * const m2,
    PmRotationMatrix * const mout)
{
    mout->x.x = m1->x.x * m2->x.x + m1->y.x * m2->x.y + m1->z.x * m2->x.z;
    mout->x.y = m1->x.y * m2->x.x + m1->y.y * m2->x.y + m1->z.y * m2->x.z;
    mout->x.z = m1->x.z * m2->x.x + m1->y.z * m2->x.y + m1->z.z * m2->x.z;

    mout->y.x = m1->x.x * m2->y.x + m1->y.x * m2->y.y + m1->z.x * m2->y.z;
    mout->y.y = m1->x.y * m2->y.x + m1->y.y * m2->y.y + m1->z.y * m2->y.z;
    mout->y.z = m1->x.z * m2->y.x + m1->y.z * m2->y.y + m1->z.z * m2->y.z;

    mout->z.x = m1->x.x * m2->z.x + m1->y.x * m2->z.y + m1->z.x * m2->z.z;
    mout->z.y = m1->x.y * m2->z.x + m1->y.y * m2->z.y + m1->z.y * m2->z.z;
    mout->z.z = m1->x.z * m2->z.x + m1->y.z * m2->z.y + m1->z.z * m2->z.z;

    return pmErrno = 0;
}

/* PmQuaternion functions */

int pmQuatQuatCompare(PmQuaternion const * const q1, PmQuaternion const * const q2)
{
#ifdef PM_DEBUG
    if (!pmQuatIsNorm(q1) || !pmQuatIsNorm(q2)) {
#ifdef PM_PRINT_ERROR
	pmPrintError("Bad quaternion in pmQuatQuatCompare\n");
#endif
    }
#endif

    if (fabs(q1->s - q2->s) < Q_FUZZ &&
	fabs(q1->x - q2->x) < Q_FUZZ &&
	fabs(q1->y - q2->y) < Q_FUZZ && fabs(q1->z - q2->z) < Q_FUZZ) {
	return 1;
    }

    /* note (0, x, y, z) = (0, -x, -y, -z) */
    if (fabs(q1->s) >= QS_FUZZ ||
	fabs(q1->x + q2->x) >= Q_FUZZ ||
	fabs(q1->y + q2->y) >= Q_FUZZ || fabs(q1->z + q2->z) >= Q_FUZZ) {
	return 0;
    }

    return 1;
}

int pmQuatMag(PmQuaternion const * const q, double *d)
{
    PmRotationVector r;
    int r1;

    if (0 == d) {
	return (pmErrno = PM_ERR);
    }

    r1 = pmQuatRotConvert(q, &r);
    *d = r.s;

    return pmErrno = r1;
}

int pmQuatNorm(PmQuaternion const * const q1, PmQuaternion * const qout)
{
    double size = pmSqrt(pmSq(q1->s) + pmSq(q1->x) + pmSq(q1->y) + pmSq(q1->z));

    if (size == 0.0) {
#ifdef PM_PRINT_ERROR
	pmPrintError("Bad quaternion in pmQuatNorm\n");
#endif
	qout->s = 1;
	qout->x = 0;
	qout->y = 0;
	qout->z = 0;

	return pmErrno = PM_NORM_ERR;
    }

    if (q1->s >= 0.0) {
	qout->s = q1->s / size;
	qout->x = q1->x / size;
	qout->y = q1->y / size;
	qout->z = q1->z / size;

	return pmErrno = 0;
    } else {
	qout->s = -q1->s / size;
	qout->x = -q1->x / size;
	qout->y = -q1->y / size;
	qout->z = -q1->z / size;

	return pmErrno = 0;
    }
}

int pmQuatInv(PmQuaternion const * const q1, PmQuaternion * const qout)
{
    if (qout == 0) {
	return pmErrno = PM_ERR;
    }

    qout->s = q1->s;
    qout->x = -q1->x;
    qout->y = -q1->y;
    qout->z = -q1->z;

#ifdef PM_DEBUG
    if (!pmQuatIsNorm(q1)) {
#ifdef PM_PRINT_ERROR
	pmPrintError("Bad quaternion in pmQuatInv\n");
#endif
	return pmErrno = PM_NORM_ERR;
    }
#endif

    return pmErrno = 0;
}

int pmQuatIsNorm(PmQuaternion const * const q1)
{
    return (fabs(pmSq(q1->s) + pmSq(q1->x) + pmSq(q1->y) + pmSq(q1->z) - 1.0) <
	UNIT_QUAT_FUZZ);
}

int pmQuatScalMult(PmQuaternion const * const q, double s, PmQuaternion * const qout)
{
    /*! \todo FIXME-- need a native version; this goes through a rotation vector */
    PmRotationVector r;
    int r1, r2, r3;

    r1 = pmQuatRotConvert(q, &r);
    r2 = pmRotScalMult(&r, s, &r);
    r3 = pmRotQuatConvert(&r, qout);

    return pmErrno = (r1 || r2 || r3) ? PM_NORM_ERR : 0;
}

int pmQuatScalDiv(PmQuaternion const * const q, double s, PmQuaternion * const qout)
{
    /*! \todo FIXME-- need a native version; this goes through a rotation vector */
    PmRotationVector r;
    int r1, r2, r3;

    r1 = pmQuatRotConvert(q, &r);
    r2 = pmRotScalDiv(&r, s, &r);
    r3 = pmRotQuatConvert(&r, qout);

    return pmErrno = (r1 || r2 || r3) ? PM_NORM_ERR : 0;
}

int pmQuatQuatMult(PmQuaternion const * const q1, PmQuaternion const * const q2, PmQuaternion * const qout)
{
    if (qout == 0) {
	return pmErrno = PM_ERR;
    }

    qout->s = q1->s * q2->s - q1->x * q2->x - q1->y * q2->y - q1->z * q2->z;

    if (qout->s >= 0.0) {
	qout->x = q1->s * q2->x + q1->x * q2->s + q1->y * q2->z - q1->z * q2->y;
	qout->y = q1->s * q2->y - q1->x * q2->z + q1->y * q2->s + q1->z * q2->x;
	qout->z = q1->s * q2->z + q1->x * q2->y - q1->y * q2->x + q1->z * q2->s;
    } else {
	qout->s *= -1;
	qout->x = -q1->s * q2->x - q1->x * q2->s - q1->y * q2->z + q1->z * q2->y;
	qout->y = -q1->s * q2->y + q1->x * q2->z - q1->y * q2->s - q1->z * q2->x;
	qout->z = -q1->s * q2->z - q1->x * q2->y + q1->y * q2->x - q1->z * q2->s;
    }

#ifdef PM_DEBUG
    if (!pmQuatIsNorm(q1) || !pmQuatIsNorm(q2)) {
#ifdef PM_PRINT_ERROR
	pmPrintError("Bad quaternion in pmQuatQuatMult\n");
#endif
	return pmErrno = PM_NORM_ERR;
    }
#endif

    return pmErrno = 0;
}

int pmQuatCartMult(PmQuaternion const * const q1, PmCartesian const * const v2, PmCartesian * const vout)
{
    PmCartesian c;

    c.x = q1->y * v2->z - q1->z * v2->y;
    c.y = q1->z * v2->x - q1->x * v2->z;
    c.z = q1->x * v2->y - q1->y * v2->x;

    vout->x = v2->x + 2.0 * (q1->s * c.x + q1->y * c.z - q1->z * c.y);
    vout->y = v2->y + 2.0 * (q1->s * c.y + q1->z * c.x - q1->x * c.z);
    vout->z = v2->z + 2.0 * (q1->s * c.z + q1->x * c.y - q1->y * c.x);

#ifdef PM_DEBUG
    if (!pmQuatIsNorm(q1)) {
#ifdef PM_PRINT_ERROR
	pmPrintError(&"Bad quaternion in pmQuatCartMult\n");
#endif
	return pmErrno = PM_NORM_ERR;
    }
#endif

    return pmErrno = 0;
}

/* PmPose functions*/

int pmPosePoseCompare(PmPose const * const p1, PmPose const * const p2)
{
#ifdef PM_DEBUG
    if (!pmQuatIsNorm(&p1->rot) || !pmQuatIsNorm(&p2->rot)) {
#ifdef PM_PRINT_ERROR
	pmPrintError("Bad quaternion in pmPosePoseCompare\n");
#endif
    }
#endif

    return pmErrno = (pmQuatQuatCompare(&p1->rot, &p2->rot) && pmCartCartCompare(&p1->tran, &p2->tran));
}

int pmPoseInv(PmPose const * const p1, PmPose * const p2)
{
    int r1, r2;

#ifdef PM_DEBUG
    if (!pmQuatIsNorm(&p1->rot)) {
#ifdef PM_PRINT_ERROR
	pmPrintError("Bad quaternion in pmPoseInv\n");
#endif
    }
#endif

    r1 = pmQuatInv(&p1->rot, &p2->rot);
    r2 = pmQuatCartMult(&p2->rot, &p1->tran, &p2->tran);

    p2->tran.x *= -1.0;
    p2->tran.y *= -1.0;
    p2->tran.z *= -1.0;

    return pmErrno = (r1 || r2) ? PM_NORM_ERR : 0;
}

int pmPoseCartMult(PmPose const * const p1, PmCartesian const * const v2, PmCartesian * const vout)
{
    int r1, r2;

#ifdef PM_DEBUG
    if (!pmQuatIsNorm(&p1->rot)) {
#ifdef PM_PRINT_ERROR
	pmPrintError(&"Bad quaternion in pmPoseCartMult\n");
#endif
	return pmErrno = PM_NORM_ERR;
    }
#endif

    r1 = pmQuatCartMult(&p1->rot, v2, vout);
    r2 = pmCartCartAdd(&p1->tran, vout, vout);

    return pmErrno = (r1 || r2) ? PM_NORM_ERR : 0;
}

int pmPosePoseMult(PmPose const * const p1, PmPose const * const p2, PmPose * const pout)
{
    int r1, r2, r3;

#ifdef PM_DEBUG
    if (!pmQuatIsNorm(&p1->rot) || !pmQuatIsNorm(&p2->rot)) {
#ifdef PM_PRINT_ERROR
	pmPrintError("Bad quaternion in pmPosePoseMult\n");
#endif
	return pmErrno = PM_NORM_ERR;
    }
#endif

    r1 = pmQuatCartMult(&p1->rot, &p2->tran, &pout->tran);
    r2 = pmCartCartAdd(&p1->tran, &pout->tran, &pout->tran);
    r3 = pmQuatQuatMult(&p1->rot, &p2->rot, &pout->rot);

    return pmErrno = (r1 || r2 || r3) ? PM_NORM_ERR : 0;
}

/* homogeneous transform functions */

int pmHomInv(PmHomogeneous const * const h1, PmHomogeneous * const h2)
{
    int r1, r2;

#ifdef PM_DEBUG
    if (!pmMatIsNorm(&h1->rot)) {
#ifdef PM_PRINT_ERROR
	pmPrintError("Bad rotation matrix in pmHomInv\n");
#endif
    }
#endif

    r1 = pmMatInv(&h1->rot, &h2->rot);
    r2 = pmMatCartMult(&h2->rot, &h1->tran, &h2->tran);

    h2->tran.x *= -1.0;
    h2->tran.y *= -1.0;
    h2->tran.z *= -1.0;

    return pmErrno = (r1 || r2) ? PM_NORM_ERR : 0;
}

/* line functions */

int pmLineInit(PmLine * const line, PmPose const * const start, PmPose const * const end)
{
    int r1 = 0, r2 = 0, r3 = 0, r4 = 0, r5 = 0;
    double tmag = 0.0;
    double rmag = 0.0;
    PmQuaternion startQuatInverse;

    if (0 == line) {
        return (pmErrno = PM_ERR);
    }

    r3 = pmQuatInv(&start->rot, &startQuatInverse);
    if (r3) {
        return r3;
    }

    r4 = pmQuatQuatMult(&startQuatInverse, &end->rot, &line->qVec);
    if (r4) {
        return r4;
    }

    pmQuatMag(&line->qVec, &rmag);
    if (rmag > Q_FUZZ) {
        r5 = pmQuatScalMult(&line->qVec, 1 / rmag, &(line->qVec));
        if (r5) {
            return r5;
        }
    }

    line->start = *start;
    line->end = *end;
    r1 = pmCartCartSub(&end->tran, &start->tran, &line->uVec);
    if (r1) {
        return r1;
    }

    pmCartMag(&line->uVec, &tmag);
    if (IS_FUZZ(tmag, CART_FUZZ)) {
        line->uVec.x = 1.0;
        line->uVec.y = 0.0;
        line->uVec.z = 0.0;
    } else {
        r2 = pmCartUnit(&line->uVec, &line->uVec);
    }
    line->tmag = tmag;
    line->rmag = rmag;
    line->tmag_zero = (line->tmag <= CART_FUZZ);
    line->rmag_zero = (line->rmag <= Q_FUZZ);

    /* return PM_NORM_ERR if uVec has been set to 1, 0, 0 */
    return pmErrno = (r1 || r2 || r3 || r4 || r5) ? PM_NORM_ERR : 0;
}

int pmLinePoint(PmLine const * const line, double len, PmPose * const point)
{
    int r1 = 0, r2 = 0, r3 = 0, r4 = 0;

    if (line->tmag_zero) {
	point->tran = line->end.tran;
    } else {
	/* return start + len * uVec */
	r1 = pmCartScalMult(&line->uVec, len, &point->tran);
	r2 = pmCartCartAdd(&line->start.tran, &point->tran, &point->tran);
    }

    if (line->rmag_zero) {
	point->rot = line->end.rot;
    } else {
	if (line->tmag_zero) {
	    r3 = pmQuatScalMult(&line->qVec, len, &point->rot);
	} else {
	    r3 = pmQuatScalMult(&line->qVec, len * line->rmag / line->tmag,
		&point->rot);
	}
	r4 = pmQuatQuatMult(&line->start.rot, &point->rot, &point->rot);
    }

    return pmErrno = (r1 || r2 || r3 || r4) ? PM_NORM_ERR : 0;
}


/* pure cartesian line functions */

int pmCartLineInit(PmCartLine * const line, PmCartesian const * const start, PmCartesian const * const end)
{
    int r1 = 0, r2 = 0;

    if (0 == line) {
        return (pmErrno = PM_ERR);
    }

    line->start = *start;
    line->end = *end;
    r1 = pmCartCartSub(end, start, &line->uVec);
    if (r1) {
        return r1;
    }

    pmCartMag(&line->uVec, &line->tmag);
    // NOTE: use the same criteria for "zero" length vectors as used by canon
    double max_xyz=0;
    pmCartInfNorm(&line->uVec, &max_xyz);

    if (IS_FUZZ(max_xyz, CART_FUZZ)) {
        line->uVec.x = 1.0;
        line->uVec.y = 0.0;
        line->uVec.z = 0.0;
        line->tmag_zero = 1;
    } else {
        r2 = pmCartUnitEq(&line->uVec);
        line->tmag_zero = 0;
    }

    /* return PM_NORM_ERR if uVec has been set to 1, 0, 0 */
    return pmErrno = (r1 || r2) ? PM_NORM_ERR : 0;
}

int pmCartLinePoint(PmCartLine const * const line, double len, PmCartesian * const point)
{
    int r1 = 0, r2 = 0;

    if (line->tmag_zero) {
        *point = line->end;
    } else {
        /* return start + len * uVec */
        r1 = pmCartScalMult(&line->uVec, len, point);
        r2 = pmCartCartAdd(&line->start, point, point);
    }

    return pmErrno = (r1 || r2) ? PM_NORM_ERR : 0;
}


int pmCartLineStretch(PmCartLine * const line, double new_len, int from_end)
{
    int r1 = 0, r2 = 0;

    if (!line || line->tmag_zero || new_len <= DOUBLE_FUZZ) {
        return PM_ERR;
    }

    if (from_end) {
        // Store the new relative position from end in the start point
        r1 = pmCartScalMult(&line->uVec, -new_len, &line->start);
        // Offset the new start point by the current end point
        r2 = pmCartCartAddEq(&line->start, &line->end);
    } else {
        // Store the new relative position from start in the end point:
        r1 = pmCartScalMult(&line->uVec, new_len, &line->end);
        // Offset the new end point by the current start point
        r2 = pmCartCartAdd(&line->start, &line->end, &line->end);
    }
    line->tmag = new_len;

    return pmErrno = (r1 || r2) ? PM_NORM_ERR : 0;
}

/* circle functions */

/*
  pmCircleInit() takes the defining parameters of a generalized circle
  and sticks them in the structure. It also computes the radius and vectors
  in the plane that are useful for other functions and that don't need
  to be recomputed every time.

  Note that the end can be placed arbitrarily, resulting in a combination of
  spiral and helical motion. There is an overconstraint between the start,
  center, and normal vector: the center vector and start vector are assumed
  to be in the plane defined by the normal vector. If this is not true, then
  it will be made true by moving the center vector onto the plane.
  */
int pmCircleInit(PmCircle * const circle,
        PmCartesian const * const start, PmCartesian const * const end,
        PmCartesian const * const center, PmCartesian const * const normal, int turn)
{
    double dot;
    PmCartesian rEnd;
    PmCartesian v;
    double d;
    int r1;

#ifdef PM_DEBUG
    if (0 == circle) {
#ifdef PM_PRINT_ERROR
        pmPrintError("error: pmCircleInit cirle pointer is null\n");
#endif
        return pmErrno = PM_ERR;
    }
#endif

    /* adjust center */
    pmCartCartSub(start, center, &v);
    r1 = pmCartCartProj(&v, normal, &v);
    if (PM_NORM_ERR == r1) {
        /* bad normal vector-- abort */
#ifdef PM_PRINT_ERROR
        pmPrintError("error: pmCircleInit normal vector is 0\n");
#endif
        return -1;
    }
    pmCartCartAdd(&v, center, &circle->center);

    /* normalize and redirect normal vector based on turns. If turn is less
       than 0, point normal vector in other direction and make turn positive, 
       -1 -> 0, -2 -> 1, etc. */
    pmCartUnit(normal, &circle->normal);
    if (turn < 0) {
        turn = -1 - turn;
        pmCartScalMult(&circle->normal, -1.0, &circle->normal);
    }

    /* radius */
    pmCartCartDisp(start, &circle->center, &circle->radius);

    /* vector in plane of circle from center to start, magnitude radius */
    pmCartCartSub(start, &circle->center, &circle->rTan);
    /* vector in plane of circle perpendicular to rTan, magnitude radius */
    pmCartCartCross(&circle->normal, &circle->rTan, &circle->rPerp);

    /* do rHelix, rEnd */
    pmCartCartSub(end, &circle->center, &circle->rHelix);
    pmCartPlaneProj(&circle->rHelix, &circle->normal, &rEnd);
    pmCartMag(&rEnd, &circle->spiral);
    circle->spiral -= circle->radius;
    pmCartCartSub(&circle->rHelix, &rEnd, &circle->rHelix);
    pmCartUnit(&rEnd, &rEnd);
    pmCartScalMult(&rEnd, circle->radius, &rEnd);

    /* Patch for error spiral end same as spiral center */
    pmCartMag(&rEnd, &d);
    if (d == 0.0) {
        pmCartScalMult(&circle->normal, DOUBLE_FUZZ, &v);
        pmCartCartAdd(&rEnd, &v, &rEnd);
    }
    /* end patch 03-mar-1999 Dirk Maij */

    /* angle */
    pmCartCartDot(&circle->rTan, &rEnd, &dot);
    dot = dot / (circle->radius * circle->radius);
    if (dot > 1.0) {
        circle->angle = 0.0;
    } else if (dot < -1.0) {
        circle->angle = PM_PI;
    } else {
        circle->angle = acos(dot);
    }
    /* now angle is in range 0..PI . Check if cross is antiparallel to
       normal. If so, true angle is between PI..2PI. Need to subtract from
       2PI. */
    pmCartCartCross(&circle->rTan, &rEnd, &v);
    pmCartCartDot(&v, &circle->normal, &d);
    if (d < 0.0) {
        circle->angle = PM_2_PI - circle->angle;
    }

    if (circle->angle > -(CIRCLE_FUZZ) && circle->angle < (CIRCLE_FUZZ)) {
        circle->angle = PM_2_PI;
    }

    /* now add more angle for multi turns */
    if (turn > 0) {
        circle->angle += turn * 2.0 * PM_PI;
    }

    //Default to invalid
/* if 0'ed out while not debugging*/
#if 0
    printf("\n\n");
    printf("pmCircleInit:\n");
    printf(" \t start  : \t{x=%9.9f, y=%9.9f, z=%9.9f}\n",
	start->x, start->y, start->z);
    printf(" \t end    : \t{x=%9.9f, y=%9.9f, z=%9.9f}\n",
	end->x, end->y, end->z);
    printf(" \t center : \t{x=%9.9f, y=%9.9f, z=%9.9f}\n",
	center->x, center->y, center->z);
    printf(" \t normal : \t{x=%9.9f, y=%9.9f, z=%9.9f}\n",
	normal->x, normal->y, normal->z);
    printf(" \t rEnd   : \t{x=%9.9f, y=%9.9f, z=%9.9f}\n",
	rEnd.x, rEnd.y, rEnd.z);
    printf(" \t turn=%d\n", turn);
    printf(" \t dot=%9.9f\n", dot);
    printf(" \t d=%9.9f\n", d);
    printf(" \t circle  \t{angle=%9.9f, radius=%9.9f, spiral=%9.9f}\n",
	circle->angle, circle->radius, circle->spiral);
    printf(" \t circle->normal : \t{x=%9.9f, y=%9.9f, z=%9.9f}\n",
	circle->normal.x, circle->normal.y, circle->normal.z);
    printf(" \t circle->center : \t{x=%9.9f, y=%9.9f, z=%9.9f}\n",
	circle->center.x, circle->center.y, circle->center.z);
    printf(" \t circle->rTan : \t{x=%9.9f, y=%9.9f, z=%9.9f}\n",
	circle->rTan.x, circle->rTan.y, circle->rTan.z);
    printf(" \t circle->rPerp : \t{x=%9.9f, y=%9.9f, z=%9.9f}\n",
	circle->rPerp.x, circle->rPerp.y, circle->rPerp.z);
    printf(" \t circle->rHelix : \t{x=%9.9f, y=%9.9f, z=%9.9f}\n",
            circle->rHelix.x, circle->rHelix.y, circle->rHelix.z);
    printf("\n\n");
#endif

    return pmErrno = 0;
}


/*
  pmCirclePoint() returns the point at the given angle along
  the circle. If the circle is a helix or spiral or combination, the
  point will include interpolation off the actual circle.
  */
int pmCirclePoint(PmCircle const * const circle, double angle, PmCartesian * const point)
{
    PmCartesian par, perp;
    double scale;

#ifdef PM_DEBUG
    if (0 == circle || 0 == point) {
#ifdef PM_PRINT_ERROR
	pmPrintError
	    ("error: pmCirclePoint circle or point pointer is null\n");
#endif
	return pmErrno = PM_ERR;
    }
#endif

    /* compute components rel to center */
    pmCartScalMult(&circle->rTan, cos(angle), &par);
    pmCartScalMult(&circle->rPerp, sin(angle), &perp);

    /* add to get radius vector rel to center */
    pmCartCartAdd(&par, &perp, point);

    /* get scale for spiral, helix interpolation */
    if (circle->angle == 0.0) {
#ifdef PM_PRINT_ERROR
	pmPrintError("error: pmCirclePoint angle is zero\n");
#endif
	return pmErrno = PM_DIV_ERR;
    }
    scale = angle / circle->angle;

    /* add scaled vector in radial dir for spiral */
    pmCartUnit(point, &par);
    pmCartScalMult(&par, scale * circle->spiral, &par);
    pmCartCartAdd(point, &par, point);

    /* add scaled vector in helix dir */
    pmCartScalMult(&circle->rHelix, scale, &perp);
    pmCartCartAdd(point, &perp, point);

    /* add to center vector for final result */
    pmCartCartAdd(&circle->center, point, point);

    return pmErrno = 0;
}

int pmCircleStretch(PmCircle * const circ, double new_angle, int from_end)
{
    if (!circ || new_angle <= DOUBLE_FUZZ) {
        return PM_ERR;
    }

    double mag = 0;
    pmCartMagSq(&circ->rHelix, &mag);
    if ( mag > 1e-6 ) {
        //Can't handle helices
        return PM_ERR;
    }
    //TODO handle spiral?
    if (from_end) {
        //Not implemented yet, way more reprocessing...
        PmCartesian new_start;
        double start_angle = circ->angle - new_angle;
        pmCirclePoint(circ, start_angle, &new_start);
        pmCartCartSub(&new_start, &circ->center, &circ->rTan);
        pmCartCartCross(&circ->normal, &circ->rTan, &circ->rPerp);
        pmCartMag(&circ->rTan, &circ->radius);
    } 
    //Reduce the spiral proportionally
    circ->spiral *= (new_angle / circ->angle);
    // Easy to grow / shrink from start
    circ->angle = new_angle;

    return 0;
}