More accurate Junction Deviation fast-acos (#17575)
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1 changed files with 16 additions and 3 deletions
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@ -2390,13 +2390,26 @@ bool Planner::_populate_block(block_t * const block, bool split_move,
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sin_theta_d2 = SQRT(0.5f * (1.0f - junction_cos_theta)); // Trig half angle identity. Always positive.
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vmax_junction_sqr = (junction_acceleration * junction_deviation_mm * sin_theta_d2) / (1.0f - sin_theta_d2);
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if (block->millimeters < 1) {
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// Fast acos approximation, minus the error bar to be safe
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const float junction_theta = (RADIANS(-40) * sq(junction_cos_theta) - RADIANS(50)) * junction_cos_theta + RADIANS(90) - 0.18f;
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if (block->millimeters < 1) {
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// Fast acos approximation (max. error +-0.033 rads)
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// Based on MinMax polynomial published by W. Randolph Franklin, see
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// https://wrf.ecse.rpi.edu/Research/Short_Notes/arcsin/onlyelem.html
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// (acos(x) = pi / 2 - asin(x))
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const float neg = junction_cos_theta < 0 ? -1 : 1,
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t = neg * junction_cos_theta,
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asinx = 0.032843707f
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+ t * (-1.451838349f
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+ t * ( 29.66153956f
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+ t * (-131.1123477f
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+ t * ( 262.8130562f
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+ t * (-242.7199627f + t * 84.31466202f) )))),
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junction_theta = RADIANS(90) - neg * asinx;
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// If angle is greater than 135 degrees (octagon), find speed for approximate arc
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if (junction_theta > RADIANS(135)) {
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// NOTE: MinMax acos approximation and thereby also junction_theta top out at pi-0.033, which avoids division by 0
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const float limit_sqr = block->millimeters / (RADIANS(180) - junction_theta) * junction_acceleration;
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NOMORE(vmax_junction_sqr, limit_sqr);
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}
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