diff --git a/src/gmt_map.c b/src/gmt_map.c
index 373c46c9980..4fbcc82df10 100644
--- a/src/gmt_map.c
+++ b/src/gmt_map.c
@@ -8011,6 +8011,15 @@ uint64_t gmtlib_lonpath (struct GMT_CTRL *GMT, double lon, double lat1, double l
 	/* Must do general case */
 	n = 0;
 	min_gap = 0.1 * GMT->current.setting.map_line_step;
+	if (!isfinite (GMT->current.map.dlat) || GMT->current.map.dlat <= 0.0) {	/* Guard against invalid sampling step (e.g., antipodal singularities) */
+		gmt_M_malloc2 (GMT, tlon, tlat, 2U, NULL, double);
+		tlon[0] = tlon[1] = lon;
+		tlat[0] = lat1;
+		tlat[1] = lat2;
+		*x = tlon;
+		*y = tlat;
+		return (2ULL);
+	}
 	if ((n_alloc = lrint (ceil (fabs (lat2 - lat1) / GMT->current.map.dlat))) == 0) return (0);
 
 	n_alloc++;	/* So n_alloc is at least 2 */
@@ -8108,6 +8117,15 @@ uint64_t gmtlib_latpath (struct GMT_CTRL *GMT, double lat, double lon1, double l
 	}
 	/* Here we try to walk along lat for small increment in longitude to make sure our steps are smaller than the line_step */
 	min_gap = 0.1 * GMT->current.setting.map_line_step;
+	if (!isfinite (GMT->current.map.dlon) || GMT->current.map.dlon <= 0.0) {	/* Guard against invalid sampling step (e.g., antipodal singularities) */
+		gmt_M_malloc2 (GMT, tlon, tlat, 2U, NULL, double);
+		tlat[0] = tlat[1] = lat;
+		tlon[0] = lon1;
+		tlon[1] = lon2;
+		*x = tlon;
+		*y = tlat;
+		return (2ULL);
+	}
 	if ((n_alloc = lrint (ceil (fabs (lon2 - lon1) / GMT->current.map.dlon))) == 0) return (0);	/* Initial guess to path length */
 
 	n_alloc++;	/* n_alloc is at least 2 */