// Prepare an arc. theta == start angle, angular_travel == number of radians to go along the arc, // positive angular_travel means clockwise, negative means counterclockwise. Radius == the radius of the // circle in millimeters. axis_1 and axis_2 selects the plane in tool space. // ISSUE: The arc interpolator assumes all axes have the same steps/mm as the X axis. void mc_arc(double theta, double angular_travel, double radius, int axis_1, int axis_2, double feed_rate) { uint32_t radius_steps = round(radius*X_STEPS_PER_MM); mc.mode = MC_MODE_ARC; // Determine angular direction (+1 = clockwise, -1 = counterclockwise) mc.arc.angular_direction = signof(angular_travel); // Calculate the initial position and target position in the local coordinate system of the arc mc.arc.x = round(sin(theta)*radius_steps); mc.arc.y = round(cos(theta)*radius_steps); mc.arc.target_x = trunc(sin(theta+angular_travel)*radius_steps); mc.arc.target_y = trunc(cos(theta+angular_travel)*radius_steps); // Precalculate these values to optimize target detection mc.arc.target_direction_x = signof(mc.arc.target_x)*mc.arc.angular_direction; mc.arc.target_direction_y = signof(mc.arc.target_y)*mc.arc.angular_direction; // The "error" factor is kept up to date so that it is always == (x**2+y**2-radius**2). When error // <0 we are inside the arc, when it is >0 we are outside of the arc, and when it is 0 we // are exactly on top of the arc. mc.arc.error = mc.arc.x*mc.arc.x + mc.arc.y*mc.arc.y - radius_steps*radius_steps; // Because the error-value moves in steps of (+/-)2x+1 and (+/-)2y+1 we save a couple of multiplications // by keeping track of the doubles of the arc coordinates at all times. mc.arc.x2 = 2*mc.arc.x; mc.arc.y2 = 2*mc.arc.y; // Set up a vector with the steppers we are going to use tracing the plane of this arc clear_vector(mc.arc.plane_steppers); mc.arc.plane_steppers[axis_1] = 1; mc.arc.plane_steppers[axis_2] = 1; // And map the local coordinate system of the arc onto the tool axes of the selected plane mc.arc.axis_x = axis_1; mc.arc.axis_y = axis_2; // mm/second -> microseconds/step. Assumes all axes have the same steps/mm as the x axis mc.pace = ONE_MINUTE_OF_MICROSECONDS / (feed_rate * X_STEPS_PER_MM); mc.arc.incomplete = true; } #define check_arc_target \ if ((mc.arc.x * mc.arc.target_direction_y >= \ mc.arc.target_x * mc.arc.target_direction_y) && \ (mc.arc.y * mc.arc.target_direction_x <= \ mc.arc.target_y * mc.arc.target_direction_x)) \ { mc.arc.incomplete = false; } // Internal method used by execute_arc to trace horizontally in the general direction provided by dx and dy void step_arc_along_x(int8_t dx, int8_t dy) { uint32_t diagonal_error; mc.arc.x+=dx; mc.arc.error += 1+mc.arc.x2*dx; mc.arc.x2 += 2*dx; diagonal_error = mc.arc.error + 1 + mc.arc.y2*dy; if(abs(mc.arc.error) >= abs(diagonal_error)) { mc.arc.y += dy; mc.arc.y2 += 2*dy; mc.arc.error = diagonal_error; step_steppers(mc.arc.plane_steppers); // step diagonal } else { step_axis(mc.arc.axis_x); // step straight } check_arc_target; } // Internal method used by execute_arc to trace vertically in the general direction provided by dx and dy void step_arc_along_y(int8_t dx, int8_t dy) { uint32_t diagonal_error; mc.arc.y+=dy; mc.arc.error += 1+mc.arc.y2*dy; mc.arc.y2 += 2*dy; diagonal_error = mc.arc.error + 1 + mc.arc.x2*dx; if(abs(mc.arc.error) >= abs(diagonal_error)) { mc.arc.x += dx; mc.arc.x2 += 2*dx; mc.arc.error = diagonal_error; step_steppers(mc.arc.plane_steppers); // step diagonal } else { step_axis(mc.arc.axis_y); // step straight } check_arc_target; } // Take dx and dy which are local to the arc being generated and map them on to the // selected tool-space-axes for the current arc. void map_local_arc_directions_to_stepper_directions(int8_t dx, int8_t dy) { int8_t direction[3]; direction[mc.arc.axis_x] = dx; direction[mc.arc.axis_y] = dy; set_stepper_directions(direction); } /* Quandrants of the arc \ 7|0 / \ | / 6 \|/ 1 y+ ---------|----------- 5 /|\ 2 y- / | \ x- / 4|3 \ x+ */ #ifdef UNROLLED_ARC_LOOP // This function only used by the unrolled arc loop // Determine within which quadrant of the circle the provided coordinate falls int quadrant(uint32_t x,uint32_t y) { // determine if the coordinate is in the quadrants 0,3,4 or 7 register int quad0347 = abs(x)mc.arc.y)) { step_arc_along_x(1,-1); } case 1: map_local_arc_directions_to_stepper_directions(1,-1); while(mc.arc.incomplete && (mc.arc.y>0)) { step_arc_along_y(1,-1); } case 2: map_local_arc_directions_to_stepper_directions(-1,-1); while(mc.arc.incomplete && (mc.arc.y>-mc.arc.x)) { step_arc_along_y(-1,-1); } case 3: map_local_arc_directions_to_stepper_directions(-1,-1); while(mc.arc.incomplete && (mc.arc.x>0)) { step_arc_along_x(-1,-1); } case 4: map_local_arc_directions_to_stepper_directions(-1,1); while(mc.arc.incomplete && (mc.arc.y-mc.arc.x)) { step_arc_along_x(-1,-1); } case 6: map_local_arc_directions_to_stepper_directions(-1,-1); while(mc.arc.incomplete && (mc.arc.y>0)) { step_arc_along_y(-1,-1); } case 5: map_local_arc_directions_to_stepper_directions(1,-1); while(mc.arc.incomplete && (mc.arc.y>mc.arc.x)) { step_arc_along_y(1,-1); } case 4: map_local_arc_directions_to_stepper_directions(1,-1); while(mc.arc.incomplete && (mc.arc.x<0)) { step_arc_along_x(1,-1); } case 3: map_local_arc_directions_to_stepper_directions(1,1); while(mc.arc.incomplete && (mc.arc.y<-mc.arc.x)) { step_arc_along_x(1,1); } case 2: map_local_arc_directions_to_stepper_directions(1,1); while(mc.arc.incomplete && (mc.arc.y<0)) { step_arc_along_y(1,1); } case 1: map_local_arc_directions_to_stepper_directions(-1,1); while(mc.arc.incomplete && (mc.arc.y0)) { step_arc_along_x(-1,1); } } } #else dx = (mc.arc.y!=0) ? signof(mc.arc.y) * mc.arc.angular_direction : -signof(mc.arc.x); dy = (mc.arc.x!=0) ? -signof(mc.arc.x) * mc.arc.angular_direction : -signof(mc.arc.y); map_local_arc_directions_to_stepper_directions(dx,dy); if (abs(mc.arc.x)