grbl-LPC-CoreXY/geometry.h

/*
  geometry.h - a place for geometry helpers
  Part of Grbl

  Copyright (c) 2009 Simen Svale Skogsrud

  Grbl is free software: you can redistribute it and/or modify
  it under the terms of the GNU General Public License as published by
  the Free Software Foundation, either version 3 of the License, or
  (at your option) any later version.

  Grbl is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU General Public License for more details.

  You should have received a copy of the GNU General Public License
  along with Grbl.  If not, see <http://www.gnu.org/licenses/>.
*/

#ifndef geometry_h
#define geometry_h 
#include <avr/io.h>

// Find the angle from the positive y axis to the given point with respect to origo.
double theta(double x, double y);

// Find the quadrant of the coordinate
int quadrant_of_the_circle(int32_t x, int32_t y);

/* 
  Quadrants of the circle
    
  +---- 0 ----+    0 - y is always positive and |x| < |y|
  |           |    1 - x is always positive and |x| > |y|
  |           |    2 - y is always negative and |x| < |y|
  3     +     1    3 - x is always negative and |x| > |y|
  |           |
  |           |
  +---- 2 ----+                    
*/

// A macro to decide if a quadrant-number represent a horizontal quadrant
#define quadrant_horizontal(q) ((q % 2) == 0)

// Very specialized helper to calculate the amount of steps to travel in the given quadrant of a circle provided the
// axial direction of the quadrant, the angular_direction of travel (-1 or +1) and amount of steps in one half quadrant 
// of the circle. 
uint32_t steps_in_partial_quadrant(int32_t x, int32_t y, int horizontal_quadrant, int angular_direction, 
  int32_t steps_in_half_quadrant);
  
// Counts the amount of full quadrants between quadrant_start and quadrant_target along the angular_direction
int full_quadrants_between(int quadrant_start, int quadrant_target, int angular_direction);

#endif