/**
* Determine the 'jerk' between 2 2D vectors and their speeds. The jerk can be
* used to obtain an acceptable speed for changing directions between moves.
* @param x1 x component of first vector
* @param y1 y component of first vector
* @param F1 feed rate of first move
* @param x2 x component of second vector
* @param y2 y component of second vector
* @param F2 feed rate of second move
*/
int dda_jerk_size_2d_real(int32_t x1, int32_t y1, uint32_t F1, int32_t x2, int32_t y2, uint32_t F2) {
const int maxlen = 10000;
// Normalize vectors so their length will be fixed
// Note: approx_distance is not precise enough and may result in violent direction changes
//sersendf_P(PSTR("Input vectors: (%ld, %ld) and (%ld, %ld)\r\n"),x1,y1,x2,y2);
int32_t len = int_sqrt(x1*x1+y1*y1);
x1 = (x1 * maxlen) / len;
y1 = (y1 * maxlen) / len;
len = int_sqrt(x2*x2+y2*y2);
x2 = (x2 * maxlen) / len;
y2 = (y2 * maxlen) / len;
//sersendf_P(PSTR("Normalized vectors: (%ld, %ld) and (%ld, %ld)\r\n"),x1,y1,x2,y2);
// Now scale the normalized vectors by their speeds
x1 *= F1; y1 *= F1; x2 *= F2; y2 *= F2;
//sersendf_P(PSTR("Speed vectors: (%ld, %ld) and (%ld, %ld)\r\n"),x1,y1,x2,y2);
// The difference between the vectors actually depicts the jerk
x1 -= x2; y1 -= y2;
//sersendf_P(PSTR("Jerk vector: (%ld, %ld)\r\n"),x1,y1);
return approx_distance(x1,y1) / maxlen;
}
void dda_create(DDA *dda, TARGET *target) {
uint32_t distance, c_limit, c_limit_calc;
// initialise DDA to a known state
dda->allflags = 0;
if (debug_flags & DEBUG_DDA)
serial_writestr_P(PSTR("\n{DDA_CREATE: ["));
// we end at the passed target
memcpy(&(dda->endpoint), target, sizeof(TARGET));
dda->x_delta = ABS(target->X - startpoint.X);
dda->y_delta = ABS(target->Y - startpoint.Y);
dda->z_delta = ABS(target->Z - startpoint.Z);
dda->e_delta = ABS(target->E - startpoint.E);
dda->x_direction = (target->X >= startpoint.X)?1:0;
dda->y_direction = (target->Y >= startpoint.Y)?1:0;
dda->z_direction = (target->Z >= startpoint.Z)?1:0;
dda->e_direction = (target->E >= startpoint.E)?1:0;
if (debug_flags & DEBUG_DDA) {
if (dda->x_direction == 0)
serial_writechar('-');
serwrite_uint32(dda->x_delta);
serial_writechar(',');
if (dda->y_direction == 0)
serial_writechar('-');
serwrite_uint32(dda->y_delta);
serial_writechar(',');
if (dda->z_direction == 0)
serial_writechar('-');
serwrite_uint32(dda->z_delta);
serial_writechar(',');
if (dda->e_direction == 0)
serial_writechar('-');
serwrite_uint32(dda->e_delta);
serial_writestr_P(PSTR("] ["));
}
dda->total_steps = dda->x_delta;
if (dda->y_delta > dda->total_steps)
dda->total_steps = dda->y_delta;
if (dda->z_delta > dda->total_steps)
dda->total_steps = dda->z_delta;
if (dda->e_delta > dda->total_steps)
dda->total_steps = dda->e_delta;
if (debug_flags & DEBUG_DDA) {
serial_writestr_P(PSTR("ts:"));
serwrite_uint32(dda->total_steps);
}
if (dda->total_steps == 0) {
dda->nullmove = 1;
}
else {
// get steppers ready to go
steptimeout = 0;
power_on();
dda->x_counter = dda->y_counter = dda->z_counter = dda->e_counter =
-(dda->total_steps >> 1);
// since it's unusual to combine X, Y and Z changes in a single move on reprap, check if we can use simpler approximations before trying the full 3d approximation.
if (dda->z_delta == 0)
distance = approx_distance(dda->x_delta * UM_PER_STEP_X, dda->y_delta * UM_PER_STEP_Y);
else if (dda->x_delta == 0 && dda->y_delta == 0)
distance = dda->z_delta * UM_PER_STEP_Z;
else
distance = approx_distance_3(dda->x_delta * UM_PER_STEP_X, dda->y_delta * UM_PER_STEP_Y, dda->z_delta * UM_PER_STEP_Z);
if (distance < 2)
distance = dda->e_delta * UM_PER_STEP_E;
if (debug_flags & DEBUG_DDA) {
serial_writestr_P(PSTR(",ds:"));
serwrite_uint32(distance);
}
// pre-calculate move speed in millimeter microseconds per step minute for less math in interrupt context
// mm (distance) * 60000000 us/min / step (total_steps) = mm.us per step.min
// note: um (distance) * 60000 == mm * 60000000
// so in the interrupt we must simply calculate
// mm.us per step.min / mm per min (F) = us per step
// break this calculation up a bit and lose some precision because 300,000um * 60000 is too big for a uint32
// calculate this with a uint64 if you need the precision, but it'll take longer so routines with lots of short moves may suffer
// 2^32/6000 is about 715mm which should be plenty
// changed * 10 to * (F_CPU / 100000) so we can work in cpu_ticks rather than microseconds.
// timer.c setTimer() routine altered for same reason
// changed distance * 6000 .. * F_CPU / 100000 to
// distance * 2400 .. * F_CPU / 40000 so we can move a distance of up to 1800mm without overflowing
uint32_t move_duration = ((distance * 2400) / dda->total_steps) * (F_CPU / 40000);
// similarly, find out how fast we can run our axes.
// do this for each axis individually, as the combined speed of two or more axes can be higher than the capabilities of a single one.
c_limit = 0;
c_limit_calc = ( (dda->x_delta * (UM_PER_STEP_X * 2400L)) / dda->total_steps * (F_CPU / 40000) / MAXIMUM_FEEDRATE_X) << 8;
if (c_limit_calc > c_limit)
c_limit = c_limit_calc;
c_limit_calc = ( (dda->y_delta * (UM_PER_STEP_Y * 2400L)) / dda->total_steps * (F_CPU / 40000) / MAXIMUM_FEEDRATE_Y) << 8;
if (c_limit_calc > c_limit)
c_limit = c_limit_calc;
c_limit_calc = ( (dda->z_delta * (UM_PER_STEP_Z * 2400L)) / dda->total_steps * (F_CPU / 40000) / MAXIMUM_FEEDRATE_Z) << 8;
if (c_limit_calc > c_limit)
c_limit = c_limit_calc;
c_limit_calc = ( (dda->e_delta * (UM_PER_STEP_E * 2400L)) / dda->total_steps * (F_CPU / 40000) / MAXIMUM_FEEDRATE_E) << 8;
if (c_limit_calc > c_limit)
c_limit = c_limit_calc;
#ifdef ACCELERATION_REPRAP
// c is initial step time in IOclk ticks
dda->c = (move_duration / startpoint.F) << 8;
if (dda->c < c_limit)
dda->c = c_limit;
dda->end_c = (move_duration / target->F) << 8;
if (dda->end_c < c_limit)
dda->end_c = c_limit;
if (debug_flags & DEBUG_DDA) {
serial_writestr_P(PSTR(",md:"));
serwrite_uint32(move_duration);
serial_writestr_P(PSTR(",c:"));
serwrite_uint32(dda->c >> 8);
}
if (dda->c != dda->end_c) {
uint32_t stF = startpoint.F / 4;
uint32_t enF = target->F / 4;
// now some constant acceleration stuff, courtesy of http://www.embedded.com/columns/technicalinsights/56800129?printable=true
uint32_t ssq = (stF * stF);
uint32_t esq = (enF * enF);
int32_t dsq = (int32_t) (esq - ssq) / 4;
uint8_t msb_ssq = msbloc(ssq);
uint8_t msb_tot = msbloc(dda->total_steps);
// the raw equation WILL overflow at high step rates, but 64 bit math routines take waay too much space
// at 65536 mm/min (1092mm/s), ssq/esq overflows, and dsq is also close to overflowing if esq/ssq is small
// but if ssq-esq is small, ssq/dsq is only a few bits
// we'll have to do it a few different ways depending on the msb locations of each
if ((msb_tot + msb_ssq) <= 30) {
// we have room to do all the multiplies first
if (debug_flags & DEBUG_DDA)
serial_writechar('A');
dda->n = ((int32_t) (dda->total_steps * ssq) / dsq) + 1;
}
else if (msb_tot >= msb_ssq) {
// total steps has more precision
if (debug_flags & DEBUG_DDA)
serial_writechar('B');
dda->n = (((int32_t) dda->total_steps / dsq) * (int32_t) ssq) + 1;
}
else {
// otherwise
if (debug_flags & DEBUG_DDA)
serial_writechar('C');
dda->n = (((int32_t) ssq / dsq) * (int32_t) dda->total_steps) + 1;
}
if (debug_flags & DEBUG_DDA) {
sersendf_P(PSTR("\n{DDA:CA end_c:%lu, n:%ld, md:%lu, ssq:%lu, esq:%lu, dsq:%lu, msbssq:%u, msbtot:%u}\n"),
(long unsigned int)dda->end_c >> 8,
(long int)dda->n,
(long unsigned int)move_duration,
(long unsigned int)ssq,
(long unsigned int)esq,
(long unsigned int)dsq,
msb_ssq,
msb_tot);
}
