pmCirclePoint function in c\linuxcnc\src\libnml\posemath\posemath.c

/*
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;
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Question：
For function pmCirclePoint,who can explain it clearly ? it is better that you could draw a figure to us, thank you a lot ！

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

---

what is theroy ?
pmCartScalMult(&circle->rPerp, sin(angle), &perp);

---

what is theroy ?

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

---

what is theroy ?

there is not exact document or figure to introduce this.A little bit regret.

The machine needs X and Y position, as it only can move from point to point.
The Funktion does calculate the X and Y position for a point of a circle and gives that point (X/Y) to the machine that will move to that position.

Explained as simple as possible

Norbert