added code to estimate steps in arc in order to support helical motion

geometry.h

@@ -20,8 +20,36 @@
 
 #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