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DDA: make a huge comment compact and move it to where it belongs. 

Also clarify the acceleration formula.
This commit is contained in:
Markus Hitter 2013-12-05 21:33:30 +01:00
parent 42ad12fba3
commit 46548dba47
2 changed files with 8 additions and 22 deletions
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26
dda.c
View File

@ -339,25 +339,9 @@ void dda_create(DDA *dda, TARGET *target) {
if (dda->c_min < c_limit)
dda->c_min = c_limit;
/**
Assuming: F is in mm/min, STEPS_PER_M_X is in steps/m, ACCELERATION is in mm/s²
Given:
- Velocity v at time t given acceleration a: v(t) = a*t
- Displacement s at time t given acceleration a: s(t) = 1/2 * a * t²
- Displacement until reaching target velocity v: s = 1/2 * (v² / a)
- Final result: steps needed to reach velocity v given acceleration a:
steps = (STEPS_PER_M_X * F^2) / (7200000 * ACCELERATION)
To keep precision, break up in floating point and integer part:
F^2 * (int)(STEPS_PER_M_X / (7200000 * ACCELERATION))
Note: the floating point part is static so its calculated during compilation.
Note 2: the floating point part will be smaller than one, invert it:
steps = F^2 / (int)((7200000 * ACCELERATION) / STEPS_PER_M_X)
Note 3: As mentioned, setting F to 65535 or larger will overflow the
calculation. Make sure this does not happen.
Note 4: Anyone trying to run their machine at 65535 mm/min > 1m/s is nuts
*/
if (target->F > 65534)
target->F = 65534;
// Lookahead can deal with 16 bits ( = 1092 mm/s), only.
if (target->F > 65535)
target->F = 65535;
// Note: this is inaccurate for several reasons:
// - target->F isn't reverse-calculated from c_limit, so speed
@ -864,8 +848,8 @@ void dda_clock() {
if (dda->n == 0)
move_c = C0;
else
// Explicit formula: sqrt(n + 1) - sqrt(n),
// approximation here: 1 / (2 * sqrt(n)).
// Explicit formula: c0 * (sqrt(n + 1) - sqrt(n)),
// approximation here: c0 * (1 / (2 * sqrt(n))).
move_c = ((C0 >> 8) * int_inv_sqrt(dda->n)) >> 5;
if (move_c < dda->c_min) {

4
dda_maths.h
View File

@ -66,7 +66,9 @@ uint16_t int_inv_sqrt(uint16_t a);
// 2 ^ msbloc(v) >= v
const uint8_t msbloc (uint32_t v);
// Note: the floating point bit is optimized away during compilation
// s = 1/2 * a * t^2, v = a * t ==> s = v^2 / (2 * a)
// 7200000 = 60 * 60 * 1000 * 2 (mm/min -> mm/s, steps/m -> steps/mm, factor 2)
// Note: the floating point bit is optimized away during compilation.
#define ACCELERATE_RAMP_LEN(speed) (((speed)*(speed)) / (uint32_t)((7200000.0f * ACCELERATION) / (float)STEPS_PER_M_X))
// Initialization constant for the ramping algorithm.