pgsql: Refactor geometric functions and operators

diff --git a/src/backend/utils/adt/geo_ops.c b/src/backend/utils/adt/geo_ops.c
index e7c1160131..28304b547d 100644
--- a/src/backend/utils/adt/geo_ops.c
+++ b/src/backend/utils/adt/geo_ops.c
@@ -1,15 +1,57 @@
 /*-------------------------------------------------------------------------
  *
  * geo_ops.c
  *	  2D geometric operations
  *
+ * This module implements the geometric functions and operators.  The
+ * geometric types are (from simple to more complicated):
+ *
+ * - point
+ * - line
+ * - line segment
+ * - box
+ * - circle
+ * - polygon
+ *
+ * The functions to construct them has the signature:
+ *
+ *		void type_construct(Type *result, ...);
+ *
+ * The functions to implement operators usually has the signature:
+ *
+ *		void type1_operator_type2(Type *result, Type1 *type1, Type2 *type2);
+ *
+ * There are certain operators between different types.  The functions
+ * that return the intersection point between 2 types has signature:
+ *
+ *		bool type1_interpt_type2(Point *result, Type1 *type1, Type2 *type2);
+ *
+ * These return whether the two objects intersect, and set the intersection
+ * point to pre-allocated *result when it is not NULL.  Those functions may be
+ * used to implement multiple SQL level operators.  For example, 2 lines are
+ * parallel when they do not intersect.
+ *
+ * The functions that return whether an object contains another has
+ * the signature:
+ *
+ *		bool type1_contain_type2(Type1, *type1, Type2 *type2);
+ *
+ * The functions to get the closest point on an object to the second object
+ * has the signature:
+ *
+ *		float8 type1_closept_type2(Point *result, Type1 *type1, Type2 *type2);
+ *
+ * They return the shortest distance between the two objects, and set
+ * the closest point on the first object to the second object to pre-allocated
+ * *result when it is not NULL.
+ *
  * Portions Copyright (c) 1996-2018, PostgreSQL Global Development Group
  * Portions Copyright (c) 1994, Regents of the University of California
  *
  *
  * IDENTIFICATION
  *	  src/backend/utils/adt/geo_ops.c
  *
  *-------------------------------------------------------------------------
  */
 #include "postgres.h"
@@ -57,44 +99,44 @@ static float8 line_closept_point(Point *result, LINE *line, Point *pt);
 /* Routines for line segments */
 static inline void statlseg_construct(LSEG *lseg, Point *pt1, Point *pt2);
 static inline float8 lseg_sl(LSEG *lseg);
 static inline float8 lseg_invsl(LSEG *lseg);
 static bool	lseg_interpt_line(Point *result, LSEG *lseg, LINE *line);
 static bool	lseg_interpt_lseg(Point *result, LSEG *l1, LSEG *l2);
 static int	lseg_crossing(float8 x, float8 y, float8 px, float8 py);
 static bool	lseg_contain_point(LSEG *lseg, Point *point);
 static float8 lseg_closept_point(Point *result, LSEG *lseg, Point *pt);
 static float8 lseg_closept_line(Point *result, LSEG *lseg, LINE *line);
-static float8 lseg_closept_lseg(Point *result, LSEG *l1, LSEG *l2);
+static float8 lseg_closept_lseg(Point *result, LSEG *on_lseg, LSEG *to_lseg);
 
 /* Routines for boxes */
 static inline void box_construct(BOX *result, Point *pt1, Point *pt2);
 static void box_cn(Point *center, BOX *box);
 static bool box_ov(BOX *box1, BOX *box2);
 static float8 box_ar(BOX *box);
 static float8 box_ht(BOX *box);
 static float8 box_wd(BOX *box);
 static bool box_contain_point(BOX *box, Point *point);
-static bool box_contain_box(BOX *box1, BOX *box2);
+static bool box_contain_box(BOX *contains_box1, BOX *contained_box2);
 static bool box_contain_lseg(BOX *box, LSEG *lseg);
 static bool box_interpt_lseg(Point *result, BOX *box, LSEG *lseg);
 static float8 box_closept_point(Point *result, BOX *box, Point *point);
 static float8 box_closept_lseg(Point *result, BOX *box, LSEG *lseg);
 
 /* Routines for circles */
 static float8 circle_ar(CIRCLE *circle);
 
 /* Routines for polygons */
 static void make_bound_box(POLYGON *poly);
 static void poly_to_circle(CIRCLE *result, POLYGON *poly);
 static bool lseg_inside_poly(Point *a, Point *b, POLYGON *poly, int start);
-static bool poly_contain_poly(POLYGON *polya, POLYGON *polyb);
+static bool poly_contain_poly(POLYGON *contains_poly, POLYGON *contained_poly);
 static bool plist_same(int npts, Point *p1, Point *p2);
 static float8 dist_ppoly_internal(Point *pt, POLYGON *poly);
 
 /* Routines for encoding and decoding */
 static float8 single_decode(char *num, char **endptr_p,
 			  const char *type_name, const char *orig_string);
 static void single_encode(float8 x, StringInfo str);
 static void pair_decode(char *str, float8 *x, float8 *y, char **endptr_p,
 			const char *type_name, const char *orig_string);
 static void pair_encode(float8 x, float8 y, StringInfo str);
@@ -644,26 +686,26 @@ box_contain(PG_FUNCTION_ARGS)
 	BOX		   *box1 = PG_GETARG_BOX_P(0);
 	BOX		   *box2 = PG_GETARG_BOX_P(1);
 
 	PG_RETURN_BOOL(box_contain_box(box1, box2));
 }
 
 /*
  * Check whether the box is in the box or on its border
  */
 static bool
-box_contain_box(BOX *box1, BOX *box2)
+box_contain_box(BOX *contains_box, BOX *contained_box)
 {
-	return FPge(box1->high.x, box2->high.x) &&
-		   FPle(box1->low.x, box2->low.x) &&
-		   FPge(box1->high.y, box2->high.y) &&
-		   FPle(box1->low.y, box2->low.y);
+	return FPge(contains_box->high.x, contained_box->high.x) &&
+		   FPle(contains_box->low.x, contained_box->low.x) &&
+		   FPge(contains_box->high.y, contained_box->high.y) &&
+		   FPle(contains_box->low.y, contained_box->low.y);
 }
 
 
 /*		box_positionop	-
  *				is box1 entirely {above,below} box2?
  *
  * box_below_eq and box_above_eq are obsolete versions that (probably
  * erroneously) accept the equal-boundaries case.  Since these are not
  * in sync with the box_left and box_right code, they are deprecated and
  * not supported in the PG 8.1 rtree operator class extension.
@@ -1216,24 +1258,20 @@ line_interpt(PG_FUNCTION_ARGS)
 	result = (Point *) palloc(sizeof(Point));
 
 	if (!line_interpt_line(result, l1, l2))
 		PG_RETURN_NULL();
 	PG_RETURN_POINT_P(result);
 }
 
 /*
  * Internal version of line_interpt
  *
- * This returns true if two lines intersect (they do, if they are not
- * parallel), false if they do not.  This also sets the intersection point
- * to *result, if it is not NULL.
- *
  * NOTE: If the lines are identical then we will find they are parallel
  * and report "no intersection".  This is a little weird, but since
  * there's no *unique* intersection, maybe it's appropriate behavior.
  *
  * If the lines have NaN constants, we will return true, and the intersection
  * point would have NaN coordinates.  We shouldn't return false in this case
  * because that would mean the lines are parallel.
  */
 static bool
 line_interpt_line(Point *result, LINE *l1, LINE *l2)
@@ -2239,22 +2277,20 @@ lseg_center(PG_FUNCTION_ARGS)
 	result->x = float8_div(float8_pl(lseg->p[0].x, lseg->p[1].x), 2.0);
 	result->y = float8_div(float8_pl(lseg->p[0].y, lseg->p[1].y), 2.0);
 
 	PG_RETURN_POINT_P(result);
 }
 
 
 /*
  *		Find the intersection point of two segments (if any).
  *
- * This returns true if two line segments intersect, false if they do not.
- * This also sets the intersection point to *result, if it is not NULL.
  * This function is almost perfectly symmetric, even though it doesn't look
  * like it.  See lseg_interpt_line() for the other half of it.
  */
 static bool
 lseg_interpt_lseg(Point *result, LSEG *l1, LSEG *l2)
 {
 	Point		interpt;
 	LINE		tmp;
 
 	line_construct(&tmp, &l2->p[0], lseg_sl(l2));
@@ -2501,24 +2537,20 @@ dist_ppoly_internal(Point *pt, POLYGON *poly)
 
 /*---------------------------------------------------------------------
  *		interpt_
  *				Intersection point of objects.
  *				We choose to ignore the "point" of intersection between
  *				  lines and boxes, since there are typically two.
  *-------------------------------------------------------------------*/
 
 /*
  * Check if the line segment intersects with the line
- *
- * This returns true if line segment intersects with line, false if they
- * do not.  This also sets the intersection point to *result, if it is not
- * NULL.
  */
 static bool
 lseg_interpt_line(Point *result, LSEG *lseg, LINE *line)
 {
 	Point		interpt;
 	LINE		tmp;
 
 	/*
 	 * First, we promote the line segment to a line, because we know how
 	 * to find the intersection point of two lines.  If they don't have
@@ -2554,23 +2586,20 @@ lseg_interpt_line(Point *result, LSEG *lseg, LINE *line)
 }
 
 /*---------------------------------------------------------------------
  *		close_
  *				Point of closest proximity between objects.
  *-------------------------------------------------------------------*/
 
 /*
  *		The intersection point of a perpendicular of the line
  *		through the point.
- *
- * This sets the closest point to the *result if it is not NULL and returns
- * the distance to the closest point.
  */
 static float8
 line_closept_point(Point *result, LINE *line, Point *point)
 {
 	Point		closept;
 	LINE		tmp;
 
 	/*
 	 * We drop a perpendicular to find the intersection point.  Ordinarily
 	 * we should always find it, but that can fail in the presence of NaN
@@ -2602,23 +2631,20 @@ close_pl(PG_FUNCTION_ARGS)
 
 	if (isnan(line_closept_point(result, line, pt)))
 		PG_RETURN_NULL();
 
 	PG_RETURN_POINT_P(result);
 }
 
 
 /*
  * Closest point on line segment to specified point.
- *
- * This sets the closest point to the *result if it is not NULL and returns
- * the distance to the closest point.
  */
 static float8
 lseg_closept_point(Point *result, LSEG *lseg, Point *pt)
 {
 	Point		closept;
 	LINE		tmp;
 
 	/*
 	 * To find the closest point, we draw a perpendicular line from the point
 	 * to the line segment.
@@ -2643,62 +2669,59 @@ close_ps(PG_FUNCTION_ARGS)
 
 	if (isnan(lseg_closept_point(result, lseg, pt)))
 		PG_RETURN_NULL();
 
 	PG_RETURN_POINT_P(result);
 }
 
 
 /*
  * Closest point on line segment to line segment
- *
- * This sets the closest point to the *result if it is not NULL and returns
- * the distance to the closest point.
  */
 static float8
-lseg_closept_lseg(Point *result, LSEG *l1, LSEG *l2)
+lseg_closept_lseg(Point *result, LSEG *on_lseg, LSEG *to_lseg))
 {
 	Point		point;
 	float8		dist,
 				d;
 
 	/* First, we handle the case when the line segments are intersecting. */
-	if (lseg_interpt_lseg(result, l1, l2))
+	if (lseg_interpt_lseg(result, on_lseg, to_lseg))
 		return 0.0;
 
 	/*
 	 * Then, we find the closest points from the endpoints of the second
 	 * line segment, and keep the closest one.
 	 */
-	dist = lseg_closept_point(result, l1, &l2->p[0]);
-	d = lseg_closept_point(&point, l1, &l2->p[1]);
+	dist = lseg_closept_point(result, on_lseg, &to_lseg->p[0]);
+	d = lseg_closept_point(&point, on_lseg, &to_lseg->p[1]);
 	if (float8_lt(d, dist))
 	{
 		dist = d;
 		if (result != NULL)
 			*result = point;
 	}
 
 	/* The closest point can still be one of the endpoints, so we test them. */
-	d = lseg_closept_point(NULL, l2, &l1->p[0]);
+	d = lseg_closept_point(NULL, to_lseg, &on_lseg->p[0]);
 	if (float8_lt(d, dist))
 	{
 		dist = d;
 		if (result != NULL)
-			*result = l1->p[0];
+			*result = on_lseg->p[0];
 	}
-	d = lseg_closept_point(NULL, l2, &l1->p[1]);
+	d = lseg_closept_point(NULL, to_lseg, &on_lseg->p[1]);
 	if (float8_lt(d, dist))
 	{
 		dist = d;
 		if (result != NULL)
-			*result = l1->p[1];
+			*result = on_lseg->p[1];
 	}
 
 	return dist;
 }
 
 Datum
 close_lseg(PG_FUNCTION_ARGS)
 {
 	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
 	LSEG	   *l2 = PG_GETARG_LSEG_P(1);
@@ -2711,23 +2734,20 @@ close_lseg(PG_FUNCTION_ARGS)
 
 	if (isnan(lseg_closept_lseg(result, l2, l1)))
 		PG_RETURN_NULL();
 
 	PG_RETURN_POINT_P(result);
 }
 
 
 /*
  * Closest point on or in box to specified point.
- *
- * This sets the closest point to the *result if it is not NULL and returns
- * the distance to the closest point.
  */
 static float8
 box_closept_point(Point *result, BOX *box, Point *pt)
 {
 	float8		dist,
 				d;
 	Point		point,
 				closept;
 	LSEG		lseg;
 
@@ -2830,23 +2850,20 @@ close_sl(PG_FUNCTION_ARGS)
 	ereport(ERROR,
 			(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
 			 errmsg("function \"close_sl\" not implemented")));
 
 	PG_RETURN_NULL();
 }
 
 /*
  * Closest point on line segment to line.
  *
- * This sets the closest point to the *result if it is not NULL and returns
- * the distance to the closest point.
- *
  * NOTE: When the lines are parallel, endpoints of one of the line segment
  * are FPeq(), in presence of NaN or Infinitive coordinates, or perhaps =
  * even because of simple roundoff issues, there may not be a single closest
  * point.  We are likely to set the result to the second endpoint in these
  * cases.
  */
 static float8
 lseg_closept_line(Point *result, LSEG *lseg, LINE *line)
 {
 	float8		dist1,
@@ -2888,23 +2905,20 @@ close_ls(PG_FUNCTION_ARGS)
 
 	if (isnan(lseg_closept_line(result, lseg, line)))
 		PG_RETURN_NULL();
 
 	PG_RETURN_POINT_P(result);
 }
 
 
 /*
  * Closest point on or in box to line segment.
- *
- * This sets the closest point to the *result if it is not NULL and returns
- * the distance to the closest point.
  */
 static float8
 box_closept_lseg(Point *result, BOX *box, LSEG *lseg)
 {
 	float8		dist,
 				d;
 	Point		point,
 				closept;
 	LSEG		bseg;
 
@@ -3818,39 +3832,39 @@ lseg_inside_poly(Point *a, Point *b, POLYGON *poly, int start)
 		res = point_inside(&p, poly->npts, poly->p);
 	}
 
 	return res;
 }
 
 /*-----------------------------------------------------------------
  * Determine if polygon A contains polygon B.
  *-----------------------------------------------------------------*/
 static bool
-poly_contain_poly(POLYGON *polya, POLYGON *polyb)
+poly_contain_poly(POLYGON *contains_poly, POLYGON *contained_poly)
 {
 	int			i;
 	LSEG		s;
 
-	Assert(polya->npts > 0 && polyb->npts > 0);
+	Assert(contains_poly->npts > 0 && contained_poly->npts > 0);
 
 	/*
-	 * Quick check to see if bounding box is contained.
+	 * Quick check to see if bounding box is contained_poly.
 	 */
-	if (!box_contain_box(&polya->boundbox, &polyb->boundbox))
+	if (!box_contain_box(&contains_poly->boundbox, &contained_poly->boundbox))
 		return false;
 
-	s.p[0] = polyb->p[polyb->npts - 1];
+	s.p[0] = contained_poly->p[contained_poly->npts - 1];
 
-	for (i = 0; i < polyb->npts; i++)
+	for (i = 0; i < contained_poly->npts; i++)
 	{
-		s.p[1] = polyb->p[i];
-		if (!lseg_inside_poly(s.p, s.p + 1, polya, 0))
+		s.p[1] = contained_poly->p[i];
+		if (!lseg_inside_poly(s.p, s.p + 1, contains_poly, 0))
 			return false;
 		s.p[0] = s.p[1];
 	}
 
 	return true;
 }
 
 Datum
 poly_contain(PG_FUNCTION_ARGS)
 {

diff --git a/src/backend/utils/adt/geo_ops.c b/src/backend/utils/adt/geo_ops.c
index e7c1160131..620d8a8c80 100644
--- a/src/backend/utils/adt/geo_ops.c
+++ b/src/backend/utils/adt/geo_ops.c
@@ -3,6 +3,16 @@
  * geo_ops.c
  *	  2D geometric operations
  *
+ * This module implements the geometric functions and operators.  The
+ * geometric types are (from simple to more complicated):
+ *
+ * - point
+ * - line
+ * - line segment
+ * - box
+ * - circle
+ * - polygon
+ *
  * Portions Copyright (c) 1996-2018, PostgreSQL Global Development Group
  * Portions Copyright (c) 1994, Regents of the University of California
  *
@@ -25,6 +35,39 @@
 #include "utils/fmgrprotos.h"
 #include "utils/geo_decls.h"
 
+/*
+ * The functions to implement the types have the signature:
+ *
+ *		void type_construct(Type *result, ...);
+ *
+ * The functions to implement operators usually have signatures like:
+ *
+ *		void type1_operator_type2(Type *result, Type1 *obj1, Type2 *obj2);
+ *
+ * There are certain operators between different types.  The functions
+ * that return the intersection point between 2 types has signature:
+ *
+ *		bool type1_interpt_type2(Point *result, Type1 *obj1, Type2 *obj2);
+ *
+ * These return whether the two objects intersect, and set the intersection
+ * point to pre-allocated *result when it is not NULL.  Those functions may be
+ * used to implement multiple SQL level operators.  For example, determining
+ * whether two lines are parallel is done by checking whether they intersect.
+ *
+ * The functions that return whether an object contains another have
+ * the signature:
+ *
+ *		bool type1_contain_type2(Type1, *obj1, Type2 *obj2);
+ *
+ * The functions to get the closest point on an object to the second object
+ * have the signature:
+ *
+ *		float8 type1_closept_type2(Point *result, Type1 *obj1, Type2 *obj2);
+ *
+ * They return the shortest distance between the two objects, and set
+ * the closest point on the first object to the second object to pre-allocated
+ * *result when it is not NULL.
+ */
 
 /*
  * Internal routines
@@ -64,7 +107,7 @@ static int	lseg_crossing(float8 x, float8 y, float8 px, float8 py);
 static bool	lseg_contain_point(LSEG *lseg, Point *point);
 static float8 lseg_closept_point(Point *result, LSEG *lseg, Point *pt);
 static float8 lseg_closept_line(Point *result, LSEG *lseg, LINE *line);
-static float8 lseg_closept_lseg(Point *result, LSEG *l1, LSEG *l2);
+static float8 lseg_closept_lseg(Point *result, LSEG *on_lseg, LSEG *to_lseg);
 
 /* Routines for boxes */
 static inline void box_construct(BOX *result, Point *pt1, Point *pt2);
@@ -74,7 +117,7 @@ static float8 box_ar(BOX *box);
 static float8 box_ht(BOX *box);
 static float8 box_wd(BOX *box);
 static bool box_contain_point(BOX *box, Point *point);
-static bool box_contain_box(BOX *box1, BOX *box2);
+static bool box_contain_box(BOX *contains_box1, BOX *contained_box2);
 static bool box_contain_lseg(BOX *box, LSEG *lseg);
 static bool box_interpt_lseg(Point *result, BOX *box, LSEG *lseg);
 static float8 box_closept_point(Point *result, BOX *box, Point *point);
@@ -87,7 +130,7 @@ static float8 circle_ar(CIRCLE *circle);
 static void make_bound_box(POLYGON *poly);
 static void poly_to_circle(CIRCLE *result, POLYGON *poly);
 static bool lseg_inside_poly(Point *a, Point *b, POLYGON *poly, int start);
-static bool poly_contain_poly(POLYGON *polya, POLYGON *polyb);
+static bool poly_contain_poly(POLYGON *contains_poly, POLYGON *contained_poly);
 static bool plist_same(int npts, Point *p1, Point *p2);
 static float8 dist_ppoly_internal(Point *pt, POLYGON *poly);
 
@@ -651,12 +694,12 @@ box_contain(PG_FUNCTION_ARGS)
  * Check whether the box is in the box or on its border
  */
 static bool
-box_contain_box(BOX *box1, BOX *box2)
+box_contain_box(BOX *contains_box, BOX *contained_box)
 {
-	return FPge(box1->high.x, box2->high.x) &&
-		   FPle(box1->low.x, box2->low.x) &&
-		   FPge(box1->high.y, box2->high.y) &&
-		   FPle(box1->low.y, box2->low.y);
+	return FPge(contains_box->high.x, contained_box->high.x) &&
+		   FPle(contains_box->low.x, contained_box->low.x) &&
+		   FPge(contains_box->high.y, contained_box->high.y) &&
+		   FPle(contains_box->low.y, contained_box->low.y);
 }
 
 
@@ -1223,10 +1266,6 @@ line_interpt(PG_FUNCTION_ARGS)
 /*
  * Internal version of line_interpt
  *
- * This returns true if two lines intersect (they do, if they are not
- * parallel), false if they do not.  This also sets the intersection point
- * to *result, if it is not NULL.
- *
  * NOTE: If the lines are identical then we will find they are parallel
  * and report "no intersection".  This is a little weird, but since
  * there's no *unique* intersection, maybe it's appropriate behavior.
@@ -2246,8 +2285,6 @@ lseg_center(PG_FUNCTION_ARGS)
 /*
  *		Find the intersection point of two segments (if any).
  *
- * This returns true if two line segments intersect, false if they do not.
- * This also sets the intersection point to *result, if it is not NULL.
  * This function is almost perfectly symmetric, even though it doesn't look
  * like it.  See lseg_interpt_line() for the other half of it.
  */
@@ -2508,10 +2545,6 @@ dist_ppoly_internal(Point *pt, POLYGON *poly)
 
 /*
  * Check if the line segment intersects with the line
- *
- * This returns true if line segment intersects with line, false if they
- * do not.  This also sets the intersection point to *result, if it is not
- * NULL.
  */
 static bool
 lseg_interpt_line(Point *result, LSEG *lseg, LINE *line)
@@ -2561,9 +2594,6 @@ lseg_interpt_line(Point *result, LSEG *lseg, LINE *line)
 /*
  *		The intersection point of a perpendicular of the line
  *		through the point.
- *
- * This sets the closest point to the *result if it is not NULL and returns
- * the distance to the closest point.
  */
 static float8
 line_closept_point(Point *result, LINE *line, Point *point)
@@ -2609,9 +2639,6 @@ close_pl(PG_FUNCTION_ARGS)
 
 /*
  * Closest point on line segment to specified point.
- *
- * This sets the closest point to the *result if it is not NULL and returns
- * the distance to the closest point.
  */
 static float8
 lseg_closept_point(Point *result, LSEG *lseg, Point *pt)
@@ -2650,27 +2677,24 @@ close_ps(PG_FUNCTION_ARGS)
 
 /*
  * Closest point on line segment to line segment
- *
- * This sets the closest point to the *result if it is not NULL and returns
- * the distance to the closest point.
  */
 static float8
-lseg_closept_lseg(Point *result, LSEG *l1, LSEG *l2)
+lseg_closept_lseg(Point *result, LSEG *on_lseg, LSEG *to_lseg))
 {
 	Point		point;
 	float8		dist,
 				d;
 
 	/* First, we handle the case when the line segments are intersecting. */
-	if (lseg_interpt_lseg(result, l1, l2))
+	if (lseg_interpt_lseg(result, on_lseg, to_lseg))
 		return 0.0;
 
 	/*
 	 * Then, we find the closest points from the endpoints of the second
 	 * line segment, and keep the closest one.
 	 */
-	dist = lseg_closept_point(result, l1, &l2->p[0]);
-	d = lseg_closept_point(&point, l1, &l2->p[1]);
+	dist = lseg_closept_point(result, on_lseg, &to_lseg->p[0]);
+	d = lseg_closept_point(&point, on_lseg, &to_lseg->p[1]);
 	if (float8_lt(d, dist))
 	{
 		dist = d;
@@ -2679,19 +2703,19 @@ lseg_closept_lseg(Point *result, LSEG *l1, LSEG *l2)
 	}
 
 	/* The closest point can still be one of the endpoints, so we test them. */
-	d = lseg_closept_point(NULL, l2, &l1->p[0]);
+	d = lseg_closept_point(NULL, to_lseg, &on_lseg->p[0]);
 	if (float8_lt(d, dist))
 	{
 		dist = d;
 		if (result != NULL)
-			*result = l1->p[0];
+			*result = on_lseg->p[0];
 	}
-	d = lseg_closept_point(NULL, l2, &l1->p[1]);
+	d = lseg_closept_point(NULL, to_lseg, &on_lseg->p[1]);
 	if (float8_lt(d, dist))
 	{
 		dist = d;
 		if (result != NULL)
-			*result = l1->p[1];
+			*result = on_lseg->p[1];
 	}
 
 	return dist;
@@ -2718,9 +2742,6 @@ close_lseg(PG_FUNCTION_ARGS)
 
 /*
  * Closest point on or in box to specified point.
- *
- * This sets the closest point to the *result if it is not NULL and returns
- * the distance to the closest point.
  */
 static float8
 box_closept_point(Point *result, BOX *box, Point *pt)
@@ -2837,9 +2858,6 @@ close_sl(PG_FUNCTION_ARGS)
 /*
  * Closest point on line segment to line.
  *
- * This sets the closest point to the *result if it is not NULL and returns
- * the distance to the closest point.
- *
  * NOTE: When the lines are parallel, endpoints of one of the line segment
  * are FPeq(), in presence of NaN or Infinitive coordinates, or perhaps =
  * even because of simple roundoff issues, there may not be a single closest
@@ -2895,9 +2913,6 @@ close_ls(PG_FUNCTION_ARGS)
 
 /*
  * Closest point on or in box to line segment.
- *
- * This sets the closest point to the *result if it is not NULL and returns
- * the distance to the closest point.
  */
 static float8
 box_closept_lseg(Point *result, BOX *box, LSEG *lseg)
@@ -3825,25 +3840,25 @@ lseg_inside_poly(Point *a, Point *b, POLYGON *poly, int start)
  * Determine if polygon A contains polygon B.
  *-----------------------------------------------------------------*/
 static bool
-poly_contain_poly(POLYGON *polya, POLYGON *polyb)
+poly_contain_poly(POLYGON *contains_poly, POLYGON *contained_poly)
 {
 	int			i;
 	LSEG		s;
 
-	Assert(polya->npts > 0 && polyb->npts > 0);
+	Assert(contains_poly->npts > 0 && contained_poly->npts > 0);
 
 	/*
-	 * Quick check to see if bounding box is contained.
+	 * Quick check to see if bounding box is contained_poly.
 	 */
-	if (!box_contain_box(&polya->boundbox, &polyb->boundbox))
+	if (!box_contain_box(&contains_poly->boundbox, &contained_poly->boundbox))
 		return false;
 
-	s.p[0] = polyb->p[polyb->npts - 1];
+	s.p[0] = contained_poly->p[contained_poly->npts - 1];
 
-	for (i = 0; i < polyb->npts; i++)
+	for (i = 0; i < contained_poly->npts; i++)
 	{
-		s.p[1] = polyb->p[i];
-		if (!lseg_inside_poly(s.p, s.p + 1, polya, 0))
+		s.p[1] = contained_poly->p[i];
+		if (!lseg_inside_poly(s.p, s.p + 1, contains_poly, 0))
 			return false;
 		s.p[0] = s.p[1];
 	}

diff --git a/src/backend/utils/adt/geo_ops.c b/src/backend/utils/adt/geo_ops.c
index e7c1160131..047afdbe1a 100644
--- a/src/backend/utils/adt/geo_ops.c
+++ b/src/backend/utils/adt/geo_ops.c
@@ -1,15 +1,25 @@
 /*-------------------------------------------------------------------------
  *
  * geo_ops.c
  *	  2D geometric operations
  *
+ * This module implements the geometric functions and operators.  The
+ * geometric types are (from simple to more complicated):
+ *
+ * - point
+ * - line
+ * - line segment
+ * - box
+ * - circle
+ * - polygon
+ *
  * Portions Copyright (c) 1996-2018, PostgreSQL Global Development Group
  * Portions Copyright (c) 1994, Regents of the University of California
  *
  *
  * IDENTIFICATION
  *	  src/backend/utils/adt/geo_ops.c
  *
  *-------------------------------------------------------------------------
  */
 #include "postgres.h"
@@ -18,20 +28,53 @@
 #include <limits.h>
 #include <float.h>
 #include <ctype.h>
 
 #include "libpq/pqformat.h"
 #include "miscadmin.h"
 #include "utils/float.h"
 #include "utils/fmgrprotos.h"
 #include "utils/geo_decls.h"
 
+/*
+ * The functions to implement the types have the signature:
+ *
+ *		void type_construct(Type *result, ...);
+ *
+ * The functions to implement operators usually have signatures like:
+ *
+ *		void type1_operator_type2(Type *result, Type1 *obj1, Type2 *obj2);
+ *
+ * There are certain operators between different types.  The functions
+ * that return the intersection point between 2 types have signature:
+ *
+ *		bool type1_interpt_type2(Point *result, Type1 *obj1, Type2 *obj2);
+ *
+ * These return whether the two objects intersect, and set the intersection
+ * point to pre-allocated *result when it is not NULL.  Those functions may be
+ * used to implement multiple SQL level operators.  For example, determining
+ * whether two lines are parallel is done by checking whether they intersect.
+ *
+ * The functions that return whether an object contains another have
+ * the signature:
+ *
+ *		bool type1_contain_type2(Type1, *obj1, Type2 *obj2);
+ *
+ * The functions to get the closest point on an object to the second object
+ * have the signature:
+ *
+ *		float8 type1_closept_type2(Point *result, Type1 *obj1, Type2 *obj2);
+ *
+ * They return the shortest distance between the two objects, and set
+ * the closest point on the first object to the second object to pre-allocated
+ * *result when it is not NULL.
+ */
 
 /*
  * Internal routines
  */
 
 enum path_delim
 {
 	PATH_NONE, PATH_OPEN, PATH_CLOSED
 };
 
@@ -57,44 +100,44 @@ static float8 line_closept_point(Point *result, LINE *line, Point *pt);
 /* Routines for line segments */
 static inline void statlseg_construct(LSEG *lseg, Point *pt1, Point *pt2);
 static inline float8 lseg_sl(LSEG *lseg);
 static inline float8 lseg_invsl(LSEG *lseg);
 static bool	lseg_interpt_line(Point *result, LSEG *lseg, LINE *line);
 static bool	lseg_interpt_lseg(Point *result, LSEG *l1, LSEG *l2);
 static int	lseg_crossing(float8 x, float8 y, float8 px, float8 py);
 static bool	lseg_contain_point(LSEG *lseg, Point *point);
 static float8 lseg_closept_point(Point *result, LSEG *lseg, Point *pt);
 static float8 lseg_closept_line(Point *result, LSEG *lseg, LINE *line);
-static float8 lseg_closept_lseg(Point *result, LSEG *l1, LSEG *l2);
+static float8 lseg_closept_lseg(Point *result, LSEG *on_lseg, LSEG *to_lseg);
 
 /* Routines for boxes */
 static inline void box_construct(BOX *result, Point *pt1, Point *pt2);
 static void box_cn(Point *center, BOX *box);
 static bool box_ov(BOX *box1, BOX *box2);
 static float8 box_ar(BOX *box);
 static float8 box_ht(BOX *box);
 static float8 box_wd(BOX *box);
 static bool box_contain_point(BOX *box, Point *point);
-static bool box_contain_box(BOX *box1, BOX *box2);
+static bool box_contain_box(BOX *contains_box1, BOX *contained_box2);
 static bool box_contain_lseg(BOX *box, LSEG *lseg);
 static bool box_interpt_lseg(Point *result, BOX *box, LSEG *lseg);
 static float8 box_closept_point(Point *result, BOX *box, Point *point);
 static float8 box_closept_lseg(Point *result, BOX *box, LSEG *lseg);
 
 /* Routines for circles */
 static float8 circle_ar(CIRCLE *circle);
 
 /* Routines for polygons */
 static void make_bound_box(POLYGON *poly);
 static void poly_to_circle(CIRCLE *result, POLYGON *poly);
 static bool lseg_inside_poly(Point *a, Point *b, POLYGON *poly, int start);
-static bool poly_contain_poly(POLYGON *polya, POLYGON *polyb);
+static bool poly_contain_poly(POLYGON *contains_poly, POLYGON *contained_poly);
 static bool plist_same(int npts, Point *p1, Point *p2);
 static float8 dist_ppoly_internal(Point *pt, POLYGON *poly);
 
 /* Routines for encoding and decoding */
 static float8 single_decode(char *num, char **endptr_p,
 			  const char *type_name, const char *orig_string);
 static void single_encode(float8 x, StringInfo str);
 static void pair_decode(char *str, float8 *x, float8 *y, char **endptr_p,
 			const char *type_name, const char *orig_string);
 static void pair_encode(float8 x, float8 y, StringInfo str);
@@ -644,26 +687,26 @@ box_contain(PG_FUNCTION_ARGS)
 	BOX		   *box1 = PG_GETARG_BOX_P(0);
 	BOX		   *box2 = PG_GETARG_BOX_P(1);
 
 	PG_RETURN_BOOL(box_contain_box(box1, box2));
 }
 
 /*
  * Check whether the box is in the box or on its border
  */
 static bool
-box_contain_box(BOX *box1, BOX *box2)
+box_contain_box(BOX *contains_box, BOX *contained_box)
 {
-	return FPge(box1->high.x, box2->high.x) &&
-		   FPle(box1->low.x, box2->low.x) &&
-		   FPge(box1->high.y, box2->high.y) &&
-		   FPle(box1->low.y, box2->low.y);
+	return FPge(contains_box->high.x, contained_box->high.x) &&
+		   FPle(contains_box->low.x, contained_box->low.x) &&
+		   FPge(contains_box->high.y, contained_box->high.y) &&
+		   FPle(contains_box->low.y, contained_box->low.y);
 }
 
 
 /*		box_positionop	-
  *				is box1 entirely {above,below} box2?
  *
  * box_below_eq and box_above_eq are obsolete versions that (probably
  * erroneously) accept the equal-boundaries case.  Since these are not
  * in sync with the box_left and box_right code, they are deprecated and
  * not supported in the PG 8.1 rtree operator class extension.
@@ -1216,24 +1259,20 @@ line_interpt(PG_FUNCTION_ARGS)
 	result = (Point *) palloc(sizeof(Point));
 
 	if (!line_interpt_line(result, l1, l2))
 		PG_RETURN_NULL();
 	PG_RETURN_POINT_P(result);
 }
 
 /*
  * Internal version of line_interpt
  *
- * This returns true if two lines intersect (they do, if they are not
- * parallel), false if they do not.  This also sets the intersection point
- * to *result, if it is not NULL.
- *
  * NOTE: If the lines are identical then we will find they are parallel
  * and report "no intersection".  This is a little weird, but since
  * there's no *unique* intersection, maybe it's appropriate behavior.
  *
  * If the lines have NaN constants, we will return true, and the intersection
  * point would have NaN coordinates.  We shouldn't return false in this case
  * because that would mean the lines are parallel.
  */
 static bool
 line_interpt_line(Point *result, LINE *l1, LINE *l2)
@@ -2239,22 +2278,20 @@ lseg_center(PG_FUNCTION_ARGS)
 	result->x = float8_div(float8_pl(lseg->p[0].x, lseg->p[1].x), 2.0);
 	result->y = float8_div(float8_pl(lseg->p[0].y, lseg->p[1].y), 2.0);
 
 	PG_RETURN_POINT_P(result);
 }
 
 
 /*
  *		Find the intersection point of two segments (if any).
  *
- * This returns true if two line segments intersect, false if they do not.
- * This also sets the intersection point to *result, if it is not NULL.
  * This function is almost perfectly symmetric, even though it doesn't look
  * like it.  See lseg_interpt_line() for the other half of it.
  */
 static bool
 lseg_interpt_lseg(Point *result, LSEG *l1, LSEG *l2)
 {
 	Point		interpt;
 	LINE		tmp;
 
 	line_construct(&tmp, &l2->p[0], lseg_sl(l2));
@@ -2501,24 +2538,20 @@ dist_ppoly_internal(Point *pt, POLYGON *poly)
 
 /*---------------------------------------------------------------------
  *		interpt_
  *				Intersection point of objects.
  *				We choose to ignore the "point" of intersection between
  *				  lines and boxes, since there are typically two.
  *-------------------------------------------------------------------*/
 
 /*
  * Check if the line segment intersects with the line
- *
- * This returns true if line segment intersects with line, false if they
- * do not.  This also sets the intersection point to *result, if it is not
- * NULL.
  */
 static bool
 lseg_interpt_line(Point *result, LSEG *lseg, LINE *line)
 {
 	Point		interpt;
 	LINE		tmp;
 
 	/*
 	 * First, we promote the line segment to a line, because we know how
 	 * to find the intersection point of two lines.  If they don't have
@@ -2554,23 +2587,20 @@ lseg_interpt_line(Point *result, LSEG *lseg, LINE *line)
 }
 
 /*---------------------------------------------------------------------
  *		close_
  *				Point of closest proximity between objects.
  *-------------------------------------------------------------------*/
 
 /*
  *		The intersection point of a perpendicular of the line
  *		through the point.
- *
- * This sets the closest point to the *result if it is not NULL and returns
- * the distance to the closest point.
  */
 static float8
 line_closept_point(Point *result, LINE *line, Point *point)
 {
 	Point		closept;
 	LINE		tmp;
 
 	/*
 	 * We drop a perpendicular to find the intersection point.  Ordinarily
 	 * we should always find it, but that can fail in the presence of NaN
@@ -2602,23 +2632,20 @@ close_pl(PG_FUNCTION_ARGS)
 
 	if (isnan(line_closept_point(result, line, pt)))
 		PG_RETURN_NULL();
 
 	PG_RETURN_POINT_P(result);
 }
 
 
 /*
  * Closest point on line segment to specified point.
- *
- * This sets the closest point to the *result if it is not NULL and returns
- * the distance to the closest point.
  */
 static float8
 lseg_closept_point(Point *result, LSEG *lseg, Point *pt)
 {
 	Point		closept;
 	LINE		tmp;
 
 	/*
 	 * To find the closest point, we draw a perpendicular line from the point
 	 * to the line segment.
@@ -2643,62 +2670,59 @@ close_ps(PG_FUNCTION_ARGS)
 
 	if (isnan(lseg_closept_point(result, lseg, pt)))
 		PG_RETURN_NULL();
 
 	PG_RETURN_POINT_P(result);
 }
 
 
 /*
  * Closest point on line segment to line segment
- *
- * This sets the closest point to the *result if it is not NULL and returns
- * the distance to the closest point.
  */
 static float8
-lseg_closept_lseg(Point *result, LSEG *l1, LSEG *l2)
+lseg_closept_lseg(Point *result, LSEG *on_lseg, LSEG *to_lseg))
 {
 	Point		point;
 	float8		dist,
 				d;
 
 	/* First, we handle the case when the line segments are intersecting. */
-	if (lseg_interpt_lseg(result, l1, l2))
+	if (lseg_interpt_lseg(result, on_lseg, to_lseg))
 		return 0.0;
 
 	/*
 	 * Then, we find the closest points from the endpoints of the second
 	 * line segment, and keep the closest one.
 	 */
-	dist = lseg_closept_point(result, l1, &l2->p[0]);
-	d = lseg_closept_point(&point, l1, &l2->p[1]);
+	dist = lseg_closept_point(result, on_lseg, &to_lseg->p[0]);
+	d = lseg_closept_point(&point, on_lseg, &to_lseg->p[1]);
 	if (float8_lt(d, dist))
 	{
 		dist = d;
 		if (result != NULL)
 			*result = point;
 	}
 
 	/* The closest point can still be one of the endpoints, so we test them. */
-	d = lseg_closept_point(NULL, l2, &l1->p[0]);
+	d = lseg_closept_point(NULL, to_lseg, &on_lseg->p[0]);
 	if (float8_lt(d, dist))
 	{
 		dist = d;
 		if (result != NULL)
-			*result = l1->p[0];
+			*result = on_lseg->p[0];
 	}
-	d = lseg_closept_point(NULL, l2, &l1->p[1]);
+	d = lseg_closept_point(NULL, to_lseg, &on_lseg->p[1]);
 	if (float8_lt(d, dist))
 	{
 		dist = d;
 		if (result != NULL)
-			*result = l1->p[1];
+			*result = on_lseg->p[1];
 	}
 
 	return dist;
 }
 
 Datum
 close_lseg(PG_FUNCTION_ARGS)
 {
 	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
 	LSEG	   *l2 = PG_GETARG_LSEG_P(1);
@@ -2711,23 +2735,20 @@ close_lseg(PG_FUNCTION_ARGS)
 
 	if (isnan(lseg_closept_lseg(result, l2, l1)))
 		PG_RETURN_NULL();
 
 	PG_RETURN_POINT_P(result);
 }
 
 
 /*
  * Closest point on or in box to specified point.
- *
- * This sets the closest point to the *result if it is not NULL and returns
- * the distance to the closest point.
  */
 static float8
 box_closept_point(Point *result, BOX *box, Point *pt)
 {
 	float8		dist,
 				d;
 	Point		point,
 				closept;
 	LSEG		lseg;
 
@@ -2830,23 +2851,20 @@ close_sl(PG_FUNCTION_ARGS)
 	ereport(ERROR,
 			(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
 			 errmsg("function \"close_sl\" not implemented")));
 
 	PG_RETURN_NULL();
 }
 
 /*
  * Closest point on line segment to line.
  *
- * This sets the closest point to the *result if it is not NULL and returns
- * the distance to the closest point.
- *
  * NOTE: When the lines are parallel, endpoints of one of the line segment
  * are FPeq(), in presence of NaN or Infinitive coordinates, or perhaps =
  * even because of simple roundoff issues, there may not be a single closest
  * point.  We are likely to set the result to the second endpoint in these
  * cases.
  */
 static float8
 lseg_closept_line(Point *result, LSEG *lseg, LINE *line)
 {
 	float8		dist1,
@@ -2888,23 +2906,20 @@ close_ls(PG_FUNCTION_ARGS)
 
 	if (isnan(lseg_closept_line(result, lseg, line)))
 		PG_RETURN_NULL();
 
 	PG_RETURN_POINT_P(result);
 }
 
 
 /*
  * Closest point on or in box to line segment.
- *
- * This sets the closest point to the *result if it is not NULL and returns
- * the distance to the closest point.
  */
 static float8
 box_closept_lseg(Point *result, BOX *box, LSEG *lseg)
 {
 	float8		dist,
 				d;
 	Point		point,
 				closept;
 	LSEG		bseg;
 
@@ -3814,43 +3829,43 @@ lseg_inside_poly(Point *a, Point *b, POLYGON *poly, int start)
 		 */
 		p.x = float8_div(float8_pl(t.p[0].x, t.p[1].x), 2.0);
 		p.y = float8_div(float8_pl(t.p[0].y, t.p[1].y), 2.0);
 
 		res = point_inside(&p, poly->npts, poly->p);
 	}
 
 	return res;
 }
 
-/*-----------------------------------------------------------------
- * Determine if polygon A contains polygon B.
- *-----------------------------------------------------------------*/
+/*
+ * Check whether the polygon contains another
+ */
 static bool
-poly_contain_poly(POLYGON *polya, POLYGON *polyb)
+poly_contain_poly(POLYGON *contains_poly, POLYGON *contained_poly)
 {
 	int			i;
 	LSEG		s;
 
-	Assert(polya->npts > 0 && polyb->npts > 0);
+	Assert(contains_poly->npts > 0 && contained_poly->npts > 0);
 
 	/*
-	 * Quick check to see if bounding box is contained.
+	 * Quick check to see if bounding box is contained_poly.
 	 */
-	if (!box_contain_box(&polya->boundbox, &polyb->boundbox))
+	if (!box_contain_box(&contains_poly->boundbox, &contained_poly->boundbox))
 		return false;
 
-	s.p[0] = polyb->p[polyb->npts - 1];
+	s.p[0] = contained_poly->p[contained_poly->npts - 1];
 
-	for (i = 0; i < polyb->npts; i++)
+	for (i = 0; i < contained_poly->npts; i++)
 	{
-		s.p[1] = polyb->p[i];
-		if (!lseg_inside_poly(s.p, s.p + 1, polya, 0))
+		s.p[1] = contained_poly->p[i];
+		if (!lseg_inside_poly(s.p, s.p + 1, contains_poly, 0))
 			return false;
 		s.p[0] = s.p[1];
 	}
 
 	return true;
 }
 
 Datum
 poly_contain(PG_FUNCTION_ARGS)
 {