diff --git a/NEWS.md b/NEWS.md
index 6430b5a88e9..72d0f622d78 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -9,7 +9,14 @@
 
 ### pgRouting 3.7.1 Release Notes
 
-No Changes Yet
+To see all issues & pull requests closed by this release see the [Git closed
+milestone for 3.7.1
+](https://github.com/pgRouting/pgrouting/issues?utf8=%E2%9C%93&q=milestone%3A%22Release%203.7.1%22)
+
+**Bug fixes**
+
+* [#2689](https://github.com/pgRouting/pgrouting/pull/2689) When point is a
+  vertex, the withPoints family do not return results.
 
 ### pgRouting 3.7.0 Release Notes
 
diff --git a/doc/src/release_notes.rst b/doc/src/release_notes.rst
index 25348a5ef74..154fb2c4bf7 100644
--- a/doc/src/release_notes.rst
+++ b/doc/src/release_notes.rst
@@ -40,7 +40,14 @@ pgRouting 3.7
 pgRouting 3.7.1 Release Notes
 -------------------------------------------------------------------------------
 
-No Changes Yet
+To see all issues & pull requests closed by this release see the `Git closed
+milestone for 3.7.1
+<https://github.com/pgRouting/pgrouting/issues?utf8=%E2%9C%93&q=milestone%3A%22Release%203.7.1%22>`__
+
+.. rubric:: Bug fixes
+
+* `#2689 <https://github.com/pgRouting/pgrouting/pull/2689>`__ When point is a
+  vertex, the withPoints family do not return results.
 
 pgRouting 3.7.0 Release Notes
 -------------------------------------------------------------------------------
diff --git a/docqueries/trsp/four_edges.pg b/docqueries/trsp/four_edges.pg
deleted file mode 100644
index 34f647337ed..00000000000
--- a/docqueries/trsp/four_edges.pg
+++ /dev/null
@@ -1,148 +0,0 @@
--- CopyRight(c) pgRouting developers
--- Creative Commons Attribution-Share Alike 3.0 License : https://creativecommons.org/licenses/by-sa/3.0/
-SET extra_float_digits=-3;
-CREATE TABLE four_edges (
-    id BIGINT,
-    source BIGINT,
-    target BIGINT,
-    cost FLOAT,
-    reverse_cost FLOAT);
-
-INSERT INTO four_edges (id, source, target, cost, reverse_cost) VALUES
-( 719 ,  52163 , -56570 , 179.400001 ,   179.400001),
-( 717 ,  52222 ,  52163 , 977.000001 ,   977.000001),
-( 718 ,  52220 ,  52222 , 961.000001 ,   961.000001),
-( 716 , -21019 ,  52220 , 992.000001 ,   992.000001);
-
-SELECT * FROM pgr_trsp(
-  $$SELECT
-    id::int, source::int, target::int, cost::float, reverse_cost::float
-  FROM
-    (VALUES
-      (719, 52163, -56570, 179.400001, 179.400001),
-      (717, 52222, 52163, 977.000001, 977.000001),
-      (718, 52220, 52222, 961.000001, 961.000001),
-      (716, -21019, 52220, 992.000001, 992.000001)
-    ) AS t (id, source, target, cost, reverse_cost)$$,
-  719, 0,
-  718, 0,
-  true, true, NULL);
-
-
-SELECT * FROM pgr_trsp(
-  $$SELECT
-    id::int, source::int, target::int, cost::float, reverse_cost::float
-  FROM
-    (VALUES
-      (719, 52163, -56570, 179.40000, 179.40000),
-      (717, 52222, 52163, 977.00000, 977.00000),
-      (718, 52220, 52222, 961.00000, 961.00000),
-      (716, -21019, 52220, 992.00000, 992.00000)
-    ) AS t (id, source, target, cost, reverse_cost)$$,
-  (SELECT source::int  FROM four_edges WHERE id = 719),
-  (SELECT source::int  FROM four_edges WHERE id = 718),
-  true, true, NULL);
-
-
-SELECT * FROM pgr_trsp(
-  $$SELECT
-    id::int, source::int, target::int, cost::float, reverse_cost::float
-  FROM four_edges$$,
-  719, 0,
-  718, 0,
-  true, true, NULL);
-
-SELECT * FROM pgr_dijkstra(
-  $$SELECT
-    id::int, source::int, target::int, cost::float, reverse_cost::float
-  FROM four_edges$$,
-  52163,
-  52220,
-  false);
-
-SELECT * FROM pgr_dijkstra(
-  $$SELECT
-    id, source, target, cost, reverse_cost
-  FROM four_edges$$,
-  (SELECT source  FROM four_edges WHERE id = 719),
-  (SELECT source  FROM four_edges WHERE id = 718),
-  true);
-
-/* Comparing withPoints and trsp*/
-
-SELECT * FROM pgr_trsp(
-  $$SELECT
-    id::int, source::int, target::int, cost::float, reverse_cost::float
-  FROM four_edges$$,
-  719, 0.5,
-  718, 0,
-  true, true, NULL);
-
-SELECT * FROM pgr_withPoints(
-  $$SELECT
-    id, source, target, cost, reverse_cost
-  FROM four_edges$$,
-  $$SELECT 719 AS edge_id, 0.5::float AS fraction$$,
-  -1,
-  /* selecting source because we have 0 */
-  (SELECT source  FROM four_edges WHERE id = 718),
-  true);
-
-/* TODO should give result more or less the same as above*/
-SELECT * FROM pgr_withPoints(
-  $$SELECT
-    id, source, target, cost, reverse_cost
-  FROM four_edges$$,
-  $$(SELECT 719 AS edge_id, 0.5::float AS fraction)
-    UNION
-  (SELECT 718, 0)$$,
-  -1, -2,
-  true);
-
-SELECT * FROM pgr_trsp(
-  $$SELECT
-    id::int, source::int, target::int, cost::float, reverse_cost::float
-  FROM four_edges$$,
-  719, 0,
-  718, 0.5,
-  true, true, NULL);
-
-SELECT * FROM pgr_withPoints(
-  $$SELECT
-    id, source, target, cost, reverse_cost
-  FROM four_edges$$,
-  $$SELECT 718 AS edge_id, 0.5::float AS fraction$$,
-  /* selecting source because we have 0 */
-  (SELECT source  FROM four_edges WHERE id = 719),
-  -1,
-  true);
-
-/* TODO should give result more or less the same as above*/
-SELECT * FROM pgr_withPoints(
-  $$SELECT
-    id, source, target, cost, reverse_cost
-  FROM four_edges$$,
-  $$(SELECT 719 AS edge_id, 0::float AS fraction)
-    UNION
-  (SELECT 718, 0.5)$$,
-  -1, -2,
-  true);
-
-SELECT * FROM pgr_trsp(
-  $$SELECT
-    id::int, source::int, target::int, cost::float, reverse_cost::float
-  FROM four_edges$$,
-  719, 0.5,
-  718, 0.5,
-  true, true, NULL);
-
-SELECT * FROM pgr_withPoints(
-  $$SELECT
-    id, source, target, cost, reverse_cost
-  FROM four_edges$$,
-  $$(SELECT 719 AS edge_id, 0.5::float AS fraction)
-    UNION
-  (SELECT 718, 0.5)$$,
-  -1, -2,
-  true);
-
diff --git a/docqueries/trsp/four_edges.result b/docqueries/trsp/four_edges.result
deleted file mode 100644
index c1404ab2db3..00000000000
--- a/docqueries/trsp/four_edges.result
+++ /dev/null
@@ -1,232 +0,0 @@
-BEGIN;
-BEGIN
-SET client_min_messages TO NOTICE;
-SET
-SET extra_float_digits=-3;
-SET
-CREATE TABLE four_edges (
-    id BIGINT,
-    source BIGINT,
-    target BIGINT,
-    cost FLOAT,
-    reverse_cost FLOAT);
-CREATE TABLE
-INSERT INTO four_edges (id, source, target, cost, reverse_cost) VALUES
-( 719 ,  52163 , -56570 , 179.400001 ,   179.400001),
-( 717 ,  52222 ,  52163 , 977.000001 ,   977.000001),
-( 718 ,  52220 ,  52222 , 961.000001 ,   961.000001),
-( 716 , -21019 ,  52220 , 992.000001 ,   992.000001);
-INSERT 0 4
-SELECT * FROM pgr_trsp(
-  $$SELECT
-    id::int, source::int, target::int, cost::float, reverse_cost::float
-  FROM
-    (VALUES
-      (719, 52163, -56570, 179.400001, 179.400001),
-      (717, 52222, 52163, 977.000001, 977.000001),
-      (718, 52220, 52222, 961.000001, 961.000001),
-      (716, -21019, 52220, 992.000001, 992.000001)
-    ) AS t (id, source, target, cost, reverse_cost)$$,
-  719, 0,
-  718, 0,
-  true, true, NULL);
-WARNING:  pgr_trsp(text,integer,float,integer,float,boolean,boolean) deprecated signature on v3.4.0
- seq |  id1  | id2 |    cost
------+-------+-----+------------
-   0 | 52163 | 717 | 977.000001
-   1 | 52222 | 718 | 961.000001
-   2 | 52220 |  -1 |          0
-(3 rows)
-
-SELECT * FROM pgr_trsp(
-  $$SELECT
-    id::int, source::int, target::int, cost::float, reverse_cost::float
-  FROM
-    (VALUES
-      (719, 52163, -56570, 179.40000, 179.40000),
-      (717, 52222, 52163, 977.00000, 977.00000),
-      (718, 52220, 52222, 961.00000, 961.00000),
-      (716, -21019, 52220, 992.00000, 992.00000)
-    ) AS t (id, source, target, cost, reverse_cost)$$,
-  (SELECT source::int  FROM four_edges WHERE id = 719),
-  (SELECT source::int  FROM four_edges WHERE id = 718),
-  true, true, NULL);
-WARNING:  pgr_trsp(text,integer,integer,boolean,boolean) deprecated signature on v3.4.0
- seq |  id1  | id2 | cost
------+-------+-----+------
-   0 | 52163 | 717 |  977
-   1 | 52222 | 718 |  961
-   2 | 52220 |  -1 |    0
-(3 rows)
-
-SELECT * FROM pgr_trsp(
-  $$SELECT
-    id::int, source::int, target::int, cost::float, reverse_cost::float
-  FROM four_edges$$,
-  719, 0,
-  718, 0,
-  true, true, NULL);
-WARNING:  pgr_trsp(text,integer,float,integer,float,boolean,boolean) deprecated signature on v3.4.0
- seq |  id1  | id2 |    cost
------+-------+-----+------------
-   0 | 52163 | 717 | 977.000001
-   1 | 52222 | 718 | 961.000001
-   2 | 52220 |  -1 |          0
-(3 rows)
-
-SELECT * FROM pgr_dijkstra(
-  $$SELECT
-    id::int, source::int, target::int, cost::float, reverse_cost::float
-  FROM four_edges$$,
-  52163,
-  52220,
-  false);
- seq | path_seq | start_vid | end_vid | node  | edge |    cost    |  agg_cost
------+----------+-----------+---------+-------+------+------------+-------------
-   1 |        1 |     52163 |   52220 | 52163 |  717 | 977.000001 |           0
-   2 |        2 |     52163 |   52220 | 52222 |  718 | 961.000001 |  977.000001
-   3 |        3 |     52163 |   52220 | 52220 |   -1 |          0 | 1938.000002
-(3 rows)
-
-SELECT * FROM pgr_dijkstra(
-  $$SELECT
-    id, source, target, cost, reverse_cost
-  FROM four_edges$$,
-  (SELECT source  FROM four_edges WHERE id = 719),
-  (SELECT source  FROM four_edges WHERE id = 718),
-  true);
- seq | path_seq | start_vid | end_vid | node  | edge |    cost    |  agg_cost
------+----------+-----------+---------+-------+------+------------+-------------
-   1 |        1 |     52163 |   52220 | 52163 |  717 | 977.000001 |           0
-   2 |        2 |     52163 |   52220 | 52222 |  718 | 961.000001 |  977.000001
-   3 |        3 |     52163 |   52220 | 52220 |   -1 |          0 | 1938.000002
-(3 rows)
-
-/* Comparing withPoints and trsp*/
-SELECT * FROM pgr_trsp(
-  $$SELECT
-    id::int, source::int, target::int, cost::float, reverse_cost::float
-  FROM four_edges$$,
-  719, 0.5,
-  718, 0,
-  true, true, NULL);
-WARNING:  pgr_trsp(text,integer,float,integer,float,boolean,boolean) deprecated signature on v3.4.0
- seq |  id1  | id2 |    cost
------+-------+-----+------------
-   0 |    -1 | 719 | 89.7000005
-   1 | 52163 | 717 | 977.000001
-   2 | 52222 | 718 | 961.000001
-   3 | 52220 |  -1 |          0
-(4 rows)
-
-SELECT * FROM pgr_withPoints(
-  $$SELECT
-    id, source, target, cost, reverse_cost
-  FROM four_edges$$,
-  $$SELECT 719 AS edge_id, 0.5::float AS fraction$$,
-  -1,
-  /* selecting source because we have 0 */
-  (SELECT source  FROM four_edges WHERE id = 718),
-  true);
- seq | path_seq | node  | edge |    cost    |   agg_cost
------+----------+-------+------+------------+--------------
-   1 |        1 |    -1 |  719 | 89.7000005 |            0
-   2 |        2 | 52163 |  717 | 977.000001 |   89.7000005
-   3 |        3 | 52222 |  718 | 961.000001 | 1066.7000015
-   4 |        4 | 52220 |   -1 |          0 | 2027.7000025
-(4 rows)
-
-/* TODO should give result more or less the same as above*/
-SELECT * FROM pgr_withPoints(
-  $$SELECT
-    id, source, target, cost, reverse_cost
-  FROM four_edges$$,
-  $$(SELECT 719 AS edge_id, 0.5::float AS fraction)
-    UNION
-  (SELECT 718, 0)$$,
-  -1, -2,
-  true);
- seq | path_seq | node | edge | cost | agg_cost
------+----------+------+------+------+----------
-(0 rows)
-
-SELECT * FROM pgr_trsp(
-  $$SELECT
-    id::int, source::int, target::int, cost::float, reverse_cost::float
-  FROM four_edges$$,
-  719, 0,
-  718, 0.5,
-  true, true, NULL);
-WARNING:  pgr_trsp(text,integer,float,integer,float,boolean,boolean) deprecated signature on v3.4.0
- seq |  id1  | id2 |    cost
------+-------+-----+-------------
-   0 | 52163 | 717 |  977.000001
-   1 | 52222 | 718 | 480.5000005
-   2 |    -2 |  -1 |           0
-(3 rows)
-
-SELECT * FROM pgr_withPoints(
-  $$SELECT
-    id, source, target, cost, reverse_cost
-  FROM four_edges$$,
-  $$SELECT 718 AS edge_id, 0.5::float AS fraction$$,
-  /* selecting source because we have 0 */
-  (SELECT source  FROM four_edges WHERE id = 719),
-  -1,
-  true);
- seq | path_seq | node  | edge |    cost     |   agg_cost
------+----------+-------+------+-------------+--------------
-   1 |        1 | 52163 |  717 |  977.000001 |            0
-   2 |        2 | 52222 |  718 | 480.5000005 |   977.000001
-   3 |        3 |    -1 |   -1 |           0 | 1457.5000015
-(3 rows)
-
-/* TODO should give result more or less the same as above*/
-SELECT * FROM pgr_withPoints(
-  $$SELECT
-    id, source, target, cost, reverse_cost
-  FROM four_edges$$,
-  $$(SELECT 719 AS edge_id, 0::float AS fraction)
-    UNION
-  (SELECT 718, 0.5)$$,
-  -1, -2,
-  true);
- seq | path_seq | node | edge | cost | agg_cost
------+----------+------+------+------+----------
-(0 rows)
-
-SELECT * FROM pgr_trsp(
-  $$SELECT
-    id::int, source::int, target::int, cost::float, reverse_cost::float
-  FROM four_edges$$,
-  719, 0.5,
-  718, 0.5,
-  true, true, NULL);
-WARNING:  pgr_trsp(text,integer,float,integer,float,boolean,boolean) deprecated signature on v3.4.0
- seq |  id1  | id2 |    cost
------+-------+-----+-------------
-   0 |    -1 | 719 |  89.7000005
-   1 | 52163 | 717 |  977.000001
-   2 | 52222 | 718 | 480.5000005
-   3 |    -2 |  -1 |           0
-(4 rows)
-
-SELECT * FROM pgr_withPoints(
-  $$SELECT
-    id, source, target, cost, reverse_cost
-  FROM four_edges$$,
-  $$(SELECT 719 AS edge_id, 0.5::float AS fraction)
-    UNION
-  (SELECT 718, 0.5)$$,
-  -1, -2,
-  true);
- seq | path_seq | node  | edge |    cost     |   agg_cost
------+----------+-------+------+-------------+--------------
-   1 |        1 |    -1 |  718 | 480.5000005 |            0
-   2 |        2 | 52222 |  717 |  977.000001 |  480.5000005
-   3 |        3 | 52163 |  719 |  89.7000005 | 1457.5000015
-   4 |        4 |    -2 |   -1 |           0 |  1547.200002
-(4 rows)
-
-ROLLBACK;
-ROLLBACK
diff --git a/docqueries/trsp/test.conf b/docqueries/trsp/test.conf
index c8a12420d63..d3c981e3e64 100644
--- a/docqueries/trsp/test.conf
+++ b/docqueries/trsp/test.conf
@@ -14,7 +14,6 @@
             issue693.pg
             issue704.pg
             issue717.pg
-            four_edges.pg
             )],
     },
 );
diff --git a/pgtap/contraction/deadend/directed/big_ids.pg b/pgtap/contraction/deadend/directed/big_ids.pg
index 1709f504443..ce3bb110b7b 100644
--- a/pgtap/contraction/deadend/directed/big_ids.pg
+++ b/pgtap/contraction/deadend/directed/big_ids.pg
@@ -97,16 +97,18 @@ SELECT set_eq('q4',
 --  input: 5 <-> 6 <- 10 <- 15
 -- output: 6{5, 10, 15}
 PREPARE q5 AS
-SELECT * FROM pgr_contraction(
+SELECT type, id, unnest(contracted_vertices) FROM pgr_contraction(
     $$SELECT id, source, target, cost, reverse_cost FROM edges
     WHERE id IN (100000001, 100000002, 100000003)$$,
     ARRAY[1]::integer[], 1, ARRAY[]::BIGINT[], true);
 
 PREPARE sol5 AS
-SELECT type, id, contracted_vertices, source, target, cost
+SELECT type, id, unnest
 FROM (VALUES
-    ('v'::CHAR, 100000006::BIGINT, ARRAY[100000005, 100000010, 100000015]::BIGINT[], -1::BIGINT, -1::BIGINT, -1::FLOAT)
-) AS t(type, id, contracted_vertices, source, target, cost );
+    ('v'::CHAR, 100000006::BIGINT, 100000005),
+    ('v'::CHAR, 100000006::BIGINT, 100000015),
+    ('v'::CHAR, 100000006::BIGINT, 100000010)
+) AS t(type, id, unnest);
 
 SELECT set_eq('q5', 'sol5');
 
diff --git a/pgtap/ksp/withPointsKSP/edge_cases/point_in_vertex.pg b/pgtap/ksp/withPointsKSP/edge_cases/point_in_vertex.pg
new file mode 100644
index 00000000000..9dcd0f7d6d2
--- /dev/null
+++ b/pgtap/ksp/withPointsKSP/edge_cases/point_in_vertex.pg
@@ -0,0 +1,186 @@
+/*PGR-GNU*****************************************************************
+
+Copyright (c) 2024  pgRouting developers
+Mail: project@pgrouting.org
+
+------
+This program 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 2 of the License, or
+(at your option) any later version.
+This program 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 this program; if not, write to the Free Software
+Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+ ********************************************************************PGR-GNU*/
+BEGIN;
+
+SET extra_float_digits=-3;
+
+SELECT CASE WHEN min_version('3.6.0') THEN plan(38) ELSE plan(1) END;
+
+CREATE VIEW four_edges AS
+SELECT * FROM edges WHERE id IN (1,4,10,14);
+
+CREATE OR REPLACE FUNCTION test_vertex_points() RETURNS SETOF TEXT AS
+$BODY$
+BEGIN
+
+  IF NOT min_version('3.6.0') THEN
+    RETURN QUERY SELECT skip(1, 'Signature added on 3.6.0');
+    RETURN;
+  END IF;
+
+
+PREPARE dijkstra1(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_KSP(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $1, $2, 3, true) WHERE edge < 0;
+
+-- its a straigh line and one extreme are reachable
+RETURN QUERY SELECT results_eq($$dijkstra1(5,9)$$, ARRAY[4]::TEXT[]);
+RETURN QUERY SELECT results_eq($$dijkstra1(9,5)$$, ARRAY[4]::TEXT[]);
+
+
+/* Points
+  midpoint of edge 1 (-1 by default)
+*/
+PREPARE expectedCost1(BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsKSP(
+  $$ SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$ SELECT 1 AS edge_id, 0.5::float AS fraction$$,
+  -1,  $1, 3, 'r', true) WHERE edge < 0;
+
+RETURN QUERY SELECT results_eq($$expectedCost1(6)$$, ARRAY[0.5]::TEXT[], 'Cost from midpoint on 1 (-1 default) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost1(7)$$, ARRAY[1.5]::TEXT[] , 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost1(8)$$, ARRAY[2.5]::TEXT[] , 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost1(9)$$, ARRAY[3.5]::TEXT[] , 'Cost from midpoint on 1 to 9');
+
+/* Points
+  midpoint of edge 1 (-2 assigned)
+*/
+PREPARE expectedCost2(BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsKSP(
+  $$ SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$ SELECT 2 AS pid, 1 AS edge_id, 0.5::float AS fraction$$,
+  -2,  $1, 3, 'r', true) WHERE edge < 0;
+
+RETURN QUERY SELECT results_eq($$expectedCost2(6)$$, $$expectedCost1(6)$$, 'Cost from midpoint on 1 (-2 assigned) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost2(7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost2(8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost2(9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+/* UNION ALL data is not sorted
+  source point of edge 10 (-1 by default)
+  midpoint of edge 1 (-2 by default)
+*/
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsKSP(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT 10 AS edge_id, 0::float AS fraction UNION ALL SELECT 1, 0.5 $$,
+  $1,  $2, 3, 'r', true) WHERE edge < 0;
+
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,6)$$, $$expectedCost1(6)$$, '(UNION ALL) Cost from midpoint on 1 (-2 default) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+RETURN QUERY SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-1,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-1,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-1,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* UNION data is sorted
+  midpoint of edge 1 (-1 by default)
+  source point of edge 10 (-2 by default)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsKSP(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT 10 AS edge_id, 0::float AS fraction UNION SELECT 1, 0.5 $$,
+  $1,  $2, 3, 'r', true) WHERE edge < 0;
+
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,6)$$, $$expectedCost1(6)$$, '(UNION) Cost from midpoint on 1 (-2 default) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+RETURN QUERY SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-2,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-2,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-2,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* VALUES data is not sorted
+  midpoint of edge 1 (-1 by default)
+  source point of edge 10 (-2 by default)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsKSP(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT * FROM (VALUES (1,0.5), (10, 0)) AS t (edge_id, fraction)$$,
+  $1,  $2, 3, 'r', true) WHERE edge < 0;
+
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,6)$$, $$expectedCost1(6)$$, '(VALUES) Cost from midpoint on 1 (-1 default) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+RETURN QUERY SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-2,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-2,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-2,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* Points
+  midpoint of edge 1 (-2 assigned)
+  source point of edge 10 (-1 assigned)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsKSP(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT 2 AS pid, 1 AS edge_id, 0.5::float AS fraction UNION SELECT 1, 10, 0 $$,
+  $1,  $2, 3, 'r', true) WHERE edge < 0;
+
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,6)$$, $$expectedCost1(6)$$, '(ASSIGNED) Cost from midpoint on 1 (-2 default) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+RETURN QUERY SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-1,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-1,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-1,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+END
+$BODY$
+LANGUAGE plpgsql VOLATILE;
+
+SELECT test_vertex_points();
+
+SELECT finish();
+ROLLBACK;
diff --git a/pgtap/trsp/trspVia_withPoints/edge_cases/point_in_vertex.pg b/pgtap/trsp/trspVia_withPoints/edge_cases/point_in_vertex.pg
new file mode 100644
index 00000000000..0a95f2d8822
--- /dev/null
+++ b/pgtap/trsp/trspVia_withPoints/edge_cases/point_in_vertex.pg
@@ -0,0 +1,192 @@
+/*PGR-GNU*****************************************************************
+
+Copyright (c) 2024  pgRouting developers
+Mail: project@pgrouting.org
+
+------
+This program 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 2 of the License, or
+(at your option) any later version.
+This program 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 this program; if not, write to the Free Software
+Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+ ********************************************************************PGR-GNU*/
+BEGIN;
+
+SET extra_float_digits=-3;
+
+SELECT CASE WHEN min_version('3.4.0') THEN plan(38) ELSE plan(1) END;
+
+CREATE VIEW four_edges AS
+SELECT * FROM edges WHERE id IN (1,4,10,14);
+
+CREATE OR REPLACE FUNCTION test_vertex_points() RETURNS SETOF TEXT AS
+$BODY$
+BEGIN
+
+  IF NOT min_version('3.4.0') THEN
+    RETURN QUERY SELECT skip(1, 'Signature added on 3.4.0');
+    RETURN;
+  END IF;
+
+
+PREPARE dijkstra1(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_dijkstraVia(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  ARRAY[$1, $2], true) WHERE node = $2 and edge < 0;
+
+-- its a straigh line and one extreme are reachable
+RETURN QUERY SELECT results_eq($$dijkstra1(5,9)$$, ARRAY[4]::TEXT[]);
+RETURN QUERY SELECT results_eq($$dijkstra1(9,5)$$, ARRAY[4]::TEXT[]);
+
+
+/* Points
+  midpoint of edge 1 (-1 by default)
+*/
+PREPARE expectedCost1(BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_trspVia_withPoints(
+  $$ SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$ SELECT path, cost FROM restrictions$$,
+  $$ SELECT 1 AS edge_id, 0.5::float AS fraction$$,
+  ARRAY[-1, $1], true) WHERE node = $1 and edge < 0;
+
+RETURN QUERY SELECT results_eq($$expectedCost1(6)$$, ARRAY[0.5]::TEXT[], 'Cost from midpoint on 1 (-1 default) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost1(7)$$, ARRAY[1.5]::TEXT[] , 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost1(8)$$, ARRAY[2.5]::TEXT[] , 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost1(9)$$, ARRAY[3.5]::TEXT[] , 'Cost from midpoint on 1 to 9');
+
+/* Points
+  midpoint of edge 1 (-2 assigned)
+*/
+PREPARE expectedCost2(BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_trspVia_withPoints(
+  $$ SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$ SELECT path, cost FROM restrictions$$,
+  $$ SELECT 2 AS pid, 1 AS edge_id, 0.5::float AS fraction$$,
+  ARRAY[-2, $1], true) WHERE node = $1 and edge < 0;
+
+RETURN QUERY SELECT results_eq($$expectedCost2(6)$$, $$expectedCost1(6)$$, 'Cost from midpoint on 1 (-2 assigned) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost2(7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost2(8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost2(9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+/* UNION ALL data is not sorted
+  source point of edge 10 (-1 by default)
+  midpoint of edge 1 (-2 by default)
+*/
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_trspVia_withPoints(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$ SELECT path, cost FROM restrictions$$,
+  $$SELECT 10 AS edge_id, 0::float AS fraction UNION ALL SELECT 1, 0.5 $$,
+  ARRAY[$1, $2], true) WHERE node = $2 and edge < 0;
+
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,6)$$, $$expectedCost1(6)$$, '(UNION ALL) Cost from midpoint on 1 (-2 default) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+RETURN QUERY SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-1,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-1,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-1,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* UNION data is sorted
+  midpoint of edge 1 (-1 by default)
+  source point of edge 10 (-2 by default)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_trspVia_withPoints(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$ SELECT path, cost FROM restrictions$$,
+  $$SELECT 10 AS edge_id, 0::float AS fraction UNION SELECT 1, 0.5 $$,
+  ARRAY[$1, $2], true) WHERE node = $2 and edge < 0;
+
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,6)$$, $$expectedCost1(6)$$, '(UNION) Cost from midpoint on 1 (-2 default) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+RETURN QUERY SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-2,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-2,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-2,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* VALUES data is not sorted
+  midpoint of edge 1 (-1 by default)
+  source point of edge 10 (-2 by default)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_trspVia_withPoints(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$ SELECT path, cost FROM restrictions$$,
+  $$SELECT * FROM (VALUES (1,0.5), (10, 0)) AS t (edge_id, fraction)$$,
+  ARRAY[$1, $2], true) WHERE node = $2 and edge < 0;
+
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,6)$$, $$expectedCost1(6)$$, '(VALUES) Cost from midpoint on 1 (-1 default) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+RETURN QUERY SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-2,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-2,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-2,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* Points
+  midpoint of edge 1 (-2 assigned)
+  source point of edge 10 (-1 assigned)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_trspVia_withPoints(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$ SELECT path, cost FROM restrictions$$,
+  $$SELECT 2 AS pid, 1 AS edge_id, 0.5::float AS fraction UNION SELECT 1, 10, 0 $$,
+  ARRAY[$1, $2], true) WHERE node = $2 and edge < 0;
+
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,6)$$, $$expectedCost1(6)$$, '(ASSIGNED) Cost from midpoint on 1 (-2 default) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+RETURN QUERY SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-1,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-1,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-1,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+END
+$BODY$
+LANGUAGE plpgsql VOLATILE;
+
+SELECT test_vertex_points();
+
+SELECT finish();
+ROLLBACK;
diff --git a/pgtap/withPoints/withPoints/edge_cases/point_in_vertex.pg b/pgtap/withPoints/withPoints/edge_cases/point_in_vertex.pg
new file mode 100644
index 00000000000..d5ac988e0b5
--- /dev/null
+++ b/pgtap/withPoints/withPoints/edge_cases/point_in_vertex.pg
@@ -0,0 +1,170 @@
+/*PGR-GNU*****************************************************************
+
+Copyright (c) 2024  pgRouting developers
+Mail: project@pgrouting.org
+
+------
+This program 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 2 of the License, or
+(at your option) any later version.
+This program 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 this program; if not, write to the Free Software
+Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+ ********************************************************************PGR-GNU*/
+BEGIN;
+
+SET extra_float_digits=-3;
+
+SELECT plan(38);
+
+CREATE VIEW four_edges AS
+SELECT * FROM edges WHERE id IN (1,4,10,14);
+
+PREPARE dijkstra1(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_dijkstra(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $1, $2, true) WHERE edge < 0;
+
+-- its a straigh line and one extreme are reachable
+SELECT results_eq($$dijkstra1(5,9)$$, ARRAY[4]::TEXT[]);
+SELECT results_eq($$dijkstra1(9,5)$$, ARRAY[4]::TEXT[]);
+
+
+/* Points
+  midpoint of edge 1 (-1 by default)
+*/
+PREPARE expectedCost1(BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPoints(
+  $$ SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$ SELECT 1 AS edge_id, 0.5::float AS fraction$$,
+  -1,  $1, true) WHERE edge < 0;
+
+SELECT results_eq($$expectedCost1(6)$$, ARRAY[0.5]::TEXT[], 'Cost from midpoint on 1 (-1 default) to 6');
+SELECT results_eq($$expectedCost1(7)$$, ARRAY[1.5]::TEXT[] , 'Cost from midpoint on 1 to 7');
+SELECT results_eq($$expectedCost1(8)$$, ARRAY[2.5]::TEXT[] , 'Cost from midpoint on 1 to 8');
+SELECT results_eq($$expectedCost1(9)$$, ARRAY[3.5]::TEXT[] , 'Cost from midpoint on 1 to 9');
+
+/* Points
+  midpoint of edge 1 (-2 assigned)
+*/
+PREPARE expectedCost2(BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPoints(
+  $$ SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$ SELECT 2 AS pid, 1 AS edge_id, 0.5::float AS fraction$$,
+  -2,  $1, true) WHERE edge < 0;
+
+SELECT results_eq($$expectedCost2(6)$$, $$expectedCost1(6)$$, 'Cost from midpoint on 1 (-2 assigned) to 6');
+SELECT results_eq($$expectedCost2(7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+SELECT results_eq($$expectedCost2(8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+SELECT results_eq($$expectedCost2(9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+/* UNION ALL data is not sorted
+  source point of edge 10 (-1 by default)
+  midpoint of edge 1 (-2 by default)
+*/
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPoints(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT 10 AS edge_id, 0::float AS fraction UNION ALL SELECT 1, 0.5 $$,
+  $1, $2, true) WHERE edge < 0;
+
+SELECT results_eq($$expectedCost3(-2,6)$$, $$expectedCost1(6)$$, '(UNION ALL) Cost from midpoint on 1 (-2 default) to 6');
+SELECT results_eq($$expectedCost3(-2,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+SELECT results_eq($$expectedCost3(-2,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+SELECT results_eq($$expectedCost3(-2,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-1,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-1,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-1,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* UNION data is sorted
+  midpoint of edge 1 (-1 by default)
+  source point of edge 10 (-2 by default)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPoints(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT 10 AS edge_id, 0::float AS fraction UNION SELECT 1, 0.5 $$,
+  $1, $2, true) WHERE edge < 0;
+
+SELECT results_eq($$expectedCost3(-1,6)$$, $$expectedCost1(6)$$, '(UNION) Cost from midpoint on 1 (-2 default) to 6');
+SELECT results_eq($$expectedCost3(-1,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+SELECT results_eq($$expectedCost3(-1,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+SELECT results_eq($$expectedCost3(-1,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-2,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-2,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-2,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* VALUES data is not sorted
+  midpoint of edge 1 (-1 by default)
+  source point of edge 10 (-2 by default)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPoints(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT * FROM (VALUES (1,0.5), (10, 0)) AS t (edge_id, fraction)$$,
+  $1, $2, true) WHERE edge < 0;
+
+SELECT results_eq($$expectedCost3(-1,6)$$, $$expectedCost1(6)$$, '(VALUES) Cost from midpoint on 1 (-1 default) to 6');
+SELECT results_eq($$expectedCost3(-1,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+SELECT results_eq($$expectedCost3(-1,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+SELECT results_eq($$expectedCost3(-1,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-2,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-2,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-2,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* Points
+  midpoint of edge 1 (-2 assigned)
+  source point of edge 10 (-1 assigned)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPoints(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT 2 AS pid, 1 AS edge_id, 0.5::float AS fraction UNION SELECT 1, 10, 0 $$,
+  $1, $2, true) WHERE edge < 0;
+
+SELECT results_eq($$expectedCost3(-2,6)$$, $$expectedCost1(6)$$, '(ASSIGNED) Cost from midpoint on 1 (-2 default) to 6');
+SELECT results_eq($$expectedCost3(-2,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+SELECT results_eq($$expectedCost3(-2,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+SELECT results_eq($$expectedCost3(-2,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-1,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-1,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-1,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+SELECT finish();
+ROLLBACK;
diff --git a/pgtap/withPoints/withPointsCost/edge_cases/point_in_vertex.pg b/pgtap/withPoints/withPointsCost/edge_cases/point_in_vertex.pg
new file mode 100644
index 00000000000..8a6a230d9cc
--- /dev/null
+++ b/pgtap/withPoints/withPointsCost/edge_cases/point_in_vertex.pg
@@ -0,0 +1,170 @@
+/*PGR-GNU*****************************************************************
+
+Copyright (c) 2024  pgRouting developers
+Mail: project@pgrouting.org
+
+------
+This program 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 2 of the License, or
+(at your option) any later version.
+This program 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 this program; if not, write to the Free Software
+Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+ ********************************************************************PGR-GNU*/
+BEGIN;
+
+SET extra_float_digits=-3;
+
+SELECT plan(38);
+
+CREATE VIEW four_edges AS
+SELECT * FROM edges WHERE id IN (1,4,10,14);
+
+PREPARE dijkstra1(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_dijkstraCost(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $1, $2, true);
+
+-- its a straigh line and one extreme are reachable
+SELECT results_eq($$dijkstra1(5,9)$$, ARRAY[4]::TEXT[]);
+SELECT results_eq($$dijkstra1(9,5)$$, ARRAY[4]::TEXT[]);
+
+
+/* Points
+  midpoint of edge 1 (-1 by default)
+*/
+PREPARE expectedCost1(BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsCost(
+  $$ SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$ SELECT 1 AS edge_id, 0.5::float AS fraction$$,
+  -1,  $1, true) ;
+
+SELECT results_eq($$expectedCost1(6)$$, ARRAY[0.5]::TEXT[], 'Cost from midpoint on 1 (-1 default) to 6');
+SELECT results_eq($$expectedCost1(7)$$, ARRAY[1.5]::TEXT[] , 'Cost from midpoint on 1 to 7');
+SELECT results_eq($$expectedCost1(8)$$, ARRAY[2.5]::TEXT[] , 'Cost from midpoint on 1 to 8');
+SELECT results_eq($$expectedCost1(9)$$, ARRAY[3.5]::TEXT[] , 'Cost from midpoint on 1 to 9');
+
+/* Points
+  midpoint of edge 1 (-2 assigned)
+*/
+PREPARE expectedCost2(BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsCost(
+  $$ SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$ SELECT 2 AS pid, 1 AS edge_id, 0.5::float AS fraction$$,
+  -2,  $1, true) ;
+
+SELECT results_eq($$expectedCost2(6)$$, $$expectedCost1(6)$$, 'Cost from midpoint on 1 (-2 assigned) to 6');
+SELECT results_eq($$expectedCost2(7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+SELECT results_eq($$expectedCost2(8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+SELECT results_eq($$expectedCost2(9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+/* UNION ALL data is not sorted
+  source point of edge 10 (-1 by default)
+  midpoint of edge 1 (-2 by default)
+*/
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsCost(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT 10 AS edge_id, 0::float AS fraction UNION ALL SELECT 1, 0.5 $$,
+  $1, $2, true);
+
+SELECT results_eq($$expectedCost3(-2,6)$$, $$expectedCost1(6)$$, '(UNION ALL) Cost from midpoint on 1 (-2 default) to 6');
+SELECT results_eq($$expectedCost3(-2,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+SELECT results_eq($$expectedCost3(-2,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+SELECT results_eq($$expectedCost3(-2,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-1,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-1,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-1,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* UNION data is sorted
+  midpoint of edge 1 (-1 by default)
+  source point of edge 10 (-2 by default)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsCost(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT 10 AS edge_id, 0::float AS fraction UNION SELECT 1, 0.5 $$,
+  $1, $2, true);
+
+SELECT results_eq($$expectedCost3(-1,6)$$, $$expectedCost1(6)$$, '(UNION) Cost from midpoint on 1 (-2 default) to 6');
+SELECT results_eq($$expectedCost3(-1,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+SELECT results_eq($$expectedCost3(-1,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+SELECT results_eq($$expectedCost3(-1,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-2,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-2,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-2,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* VALUES data is not sorted
+  midpoint of edge 1 (-1 by default)
+  source point of edge 10 (-2 by default)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsCost(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT * FROM (VALUES (1,0.5), (10, 0)) AS t (edge_id, fraction)$$,
+  $1, $2, true);
+
+SELECT results_eq($$expectedCost3(-1,6)$$, $$expectedCost1(6)$$, '(VALUES) Cost from midpoint on 1 (-1 default) to 6');
+SELECT results_eq($$expectedCost3(-1,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+SELECT results_eq($$expectedCost3(-1,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+SELECT results_eq($$expectedCost3(-1,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-2,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-2,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-2,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* Points
+  midpoint of edge 1 (-2 assigned)
+  source point of edge 10 (-1 assigned)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsCost(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT 2 AS pid, 1 AS edge_id, 0.5::float AS fraction UNION SELECT 1, 10, 0 $$,
+  $1, $2, true);
+
+SELECT results_eq($$expectedCost3(-2,6)$$, $$expectedCost1(6)$$, '(ASSIGNED) Cost from midpoint on 1 (-2 default) to 6');
+SELECT results_eq($$expectedCost3(-2,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+SELECT results_eq($$expectedCost3(-2,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+SELECT results_eq($$expectedCost3(-2,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-1,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-1,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-1,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+SELECT finish();
+ROLLBACK;
diff --git a/pgtap/withPoints/withPointsCostMatrix/edge_cases/point_in_vertex.pg b/pgtap/withPoints/withPointsCostMatrix/edge_cases/point_in_vertex.pg
new file mode 100644
index 00000000000..a0dddf51fdf
--- /dev/null
+++ b/pgtap/withPoints/withPointsCostMatrix/edge_cases/point_in_vertex.pg
@@ -0,0 +1,170 @@
+/*PGR-GNU*****************************************************************
+
+Copyright (c) 2024  pgRouting developers
+Mail: project@pgrouting.org
+
+------
+This program 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 2 of the License, or
+(at your option) any later version.
+This program 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 this program; if not, write to the Free Software
+Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+ ********************************************************************PGR-GNU*/
+BEGIN;
+
+SET extra_float_digits=-3;
+
+SELECT plan(38);
+
+CREATE VIEW four_edges AS
+SELECT * FROM edges WHERE id IN (1,4,10,14);
+
+PREPARE dijkstra1(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_dijkstraCostMatrix(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  ARRAY[$1, $2], true) LIMIT 1;
+
+-- its a straigh line and one extreme are reachable
+SELECT results_eq($$dijkstra1(5,9)$$, ARRAY[4]::TEXT[]);
+SELECT results_eq($$dijkstra1(9,5)$$, ARRAY[4]::TEXT[]);
+
+
+/* Points
+  midpoint of edge 1 (-1 by default)
+*/
+PREPARE expectedCost1(BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsCostMatrix(
+  $$ SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$ SELECT 1 AS edge_id, 0.5::float AS fraction$$,
+  ARRAY[-1,  $1], true) LIMIT 1;
+
+SELECT results_eq($$expectedCost1(6)$$, ARRAY[0.5]::TEXT[], 'Cost from midpoint on 1 (-1 default) to 6');
+SELECT results_eq($$expectedCost1(7)$$, ARRAY[1.5]::TEXT[] , 'Cost from midpoint on 1 to 7');
+SELECT results_eq($$expectedCost1(8)$$, ARRAY[2.5]::TEXT[] , 'Cost from midpoint on 1 to 8');
+SELECT results_eq($$expectedCost1(9)$$, ARRAY[3.5]::TEXT[] , 'Cost from midpoint on 1 to 9');
+
+/* Points
+  midpoint of edge 1 (-2 assigned)
+*/
+PREPARE expectedCost2(BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsCostMatrix(
+  $$ SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$ SELECT 2 AS pid, 1 AS edge_id, 0.5::float AS fraction$$,
+  ARRAY[-2,  $1], true) LIMIT 1;
+
+SELECT results_eq($$expectedCost2(6)$$, $$expectedCost1(6)$$, 'Cost from midpoint on 1 (-2 assigned) to 6');
+SELECT results_eq($$expectedCost2(7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+SELECT results_eq($$expectedCost2(8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+SELECT results_eq($$expectedCost2(9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+/* UNION ALL data is not sorted
+  source point of edge 10 (-1 by default)
+  midpoint of edge 1 (-2 by default)
+*/
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsCostMatrix(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT 10 AS edge_id, 0::float AS fraction UNION ALL SELECT 1, 0.5 $$,
+  ARRAY[$1, $2], true)LIMIT 1;
+
+SELECT results_eq($$expectedCost3(-2,6)$$, $$expectedCost1(6)$$, '(UNION ALL) Cost from midpoint on 1 (-2 default) to 6');
+SELECT results_eq($$expectedCost3(-2,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+SELECT results_eq($$expectedCost3(-2,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+SELECT results_eq($$expectedCost3(-2,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-1,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-1,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-1,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* UNION data is sorted
+  midpoint of edge 1 (-1 by default)
+  source point of edge 10 (-2 by default)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsCostMatrix(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT 10 AS edge_id, 0::float AS fraction UNION SELECT 1, 0.5 $$,
+  ARRAY[$1, $2], true) LIMIT 1;
+
+SELECT results_eq($$expectedCost3(-1,6)$$, $$expectedCost1(6)$$, '(UNION) Cost from midpoint on 1 (-2 default) to 6');
+SELECT results_eq($$expectedCost3(-1,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+SELECT results_eq($$expectedCost3(-1,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+SELECT results_eq($$expectedCost3(-1,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-2,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-2,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-2,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* VALUES data is not sorted
+  midpoint of edge 1 (-1 by default)
+  source point of edge 10 (-2 by default)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsCostMatrix(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT * FROM (VALUES (1,0.5), (10, 0)) AS t (edge_id, fraction)$$,
+  ARRAY[$1, $2], true) LIMIT 1;
+
+SELECT results_eq($$expectedCost3(-1,6)$$, $$expectedCost1(6)$$, '(VALUES) Cost from midpoint on 1 (-1 default) to 6');
+SELECT results_eq($$expectedCost3(-1,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+SELECT results_eq($$expectedCost3(-1,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+SELECT results_eq($$expectedCost3(-1,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-2,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-2,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-2,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* Points
+  midpoint of edge 1 (-2 assigned)
+  source point of edge 10 (-1 assigned)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsCostMatrix(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT 2 AS pid, 1 AS edge_id, 0.5::float AS fraction UNION SELECT 1, 10, 0 $$,
+  ARRAY[$1, $2], true) LIMIT 1;
+
+SELECT results_eq($$expectedCost3(-2,6)$$, $$expectedCost1(6)$$, '(ASSIGNED) Cost from midpoint on 1 (-2 default) to 6');
+SELECT results_eq($$expectedCost3(-2,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+SELECT results_eq($$expectedCost3(-2,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+SELECT results_eq($$expectedCost3(-2,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-1,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-1,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-1,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+SELECT finish();
+ROLLBACK;
diff --git a/pgtap/withPoints/withPointsDD/edge_cases/point_in_vertex.pg b/pgtap/withPoints/withPointsDD/edge_cases/point_in_vertex.pg
new file mode 100644
index 00000000000..eab2cf5eee6
--- /dev/null
+++ b/pgtap/withPoints/withPointsDD/edge_cases/point_in_vertex.pg
@@ -0,0 +1,186 @@
+/*PGR-GNU*****************************************************************
+
+Copyright (c) 2024  pgRouting developers
+Mail: project@pgrouting.org
+
+------
+This program 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 2 of the License, or
+(at your option) any later version.
+This program 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 this program; if not, write to the Free Software
+Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+ ********************************************************************PGR-GNU*/
+BEGIN;
+
+SET extra_float_digits=-3;
+
+SELECT CASE WHEN min_version('3.6.0') THEN plan(38) ELSE plan(1) END;
+
+CREATE VIEW four_edges AS
+SELECT * FROM edges WHERE id IN (1,4,10,14);
+
+CREATE OR REPLACE FUNCTION test_vertex_points() RETURNS SETOF TEXT AS
+$BODY$
+BEGIN
+
+  IF NOT min_version('3.6.0') THEN
+    RETURN QUERY SELECT skip(1, 'Signature added on 3.6.0');
+    RETURN;
+  END IF;
+
+
+PREPARE dijkstra1(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_drivingDistance(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $1, 5, true) WHERE node = $2;
+
+-- its a straigh line and one extreme are reachable
+RETURN QUERY SELECT results_eq($$dijkstra1(5,9)$$, ARRAY[4]::TEXT[]);
+RETURN QUERY SELECT results_eq($$dijkstra1(9,5)$$, ARRAY[4]::TEXT[]);
+
+
+/* Points
+  midpoint of edge 1 (-1 by default)
+*/
+PREPARE expectedCost1(BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsDD(
+  $$ SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$ SELECT 1 AS edge_id, 0.5::float AS fraction$$,
+  -1,  3200.0, 'r', true) WHERE node = $1;
+
+RETURN QUERY SELECT results_eq($$expectedCost1(6)$$, ARRAY[0.5]::TEXT[], 'Cost from midpoint on 1 (-1 default) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost1(7)$$, ARRAY[1.5]::TEXT[] , 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost1(8)$$, ARRAY[2.5]::TEXT[] , 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost1(9)$$, ARRAY[3.5]::TEXT[] , 'Cost from midpoint on 1 to 9');
+
+/* Points
+  midpoint of edge 1 (-2 assigned)
+*/
+PREPARE expectedCost2(BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsDD(
+  $$ SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$ SELECT 2 AS pid, 1 AS edge_id, 0.5::float AS fraction$$,
+  -2,  3200.0, 'r', true) WHERE node = $1;
+
+RETURN QUERY SELECT results_eq($$expectedCost2(6)$$, $$expectedCost1(6)$$, 'Cost from midpoint on 1 (-2 assigned) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost2(7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost2(8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost2(9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+/* UNION ALL data is not sorted
+  source point of edge 10 (-1 by default)
+  midpoint of edge 1 (-2 by default)
+*/
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsDD(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT 10 AS edge_id, 0::float AS fraction UNION ALL SELECT 1, 0.5 $$,
+  $1,  3200.0, 'r', true) WHERE node = $2;
+
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,6)$$, $$expectedCost1(6)$$, '(UNION ALL) Cost from midpoint on 1 (-2 default) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+RETURN QUERY SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-1,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-1,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-1,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* UNION data is sorted
+  midpoint of edge 1 (-1 by default)
+  source point of edge 10 (-2 by default)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsDD(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT 10 AS edge_id, 0::float AS fraction UNION SELECT 1, 0.5 $$,
+  $1,  3200.0, 'r', true) WHERE node = $2;
+
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,6)$$, $$expectedCost1(6)$$, '(UNION) Cost from midpoint on 1 (-2 default) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+RETURN QUERY SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-2,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-2,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-2,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* VALUES data is not sorted
+  midpoint of edge 1 (-1 by default)
+  source point of edge 10 (-2 by default)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsDD(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT * FROM (VALUES (1,0.5), (10, 0)) AS t (edge_id, fraction)$$,
+  $1,  3200.0, 'r', true) WHERE node = $2;
+
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,6)$$, $$expectedCost1(6)$$, '(VALUES) Cost from midpoint on 1 (-1 default) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+RETURN QUERY SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-2,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-2,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-2,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* Points
+  midpoint of edge 1 (-2 assigned)
+  source point of edge 10 (-1 assigned)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsDD(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT 2 AS pid, 1 AS edge_id, 0.5::float AS fraction UNION SELECT 1, 10, 0 $$,
+  $1,  3200.0, 'r', true) WHERE node = $2;
+
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,6)$$, $$expectedCost1(6)$$, '(ASSIGNED) Cost from midpoint on 1 (-2 default) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+RETURN QUERY SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-1,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-1,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-1,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+END
+$BODY$
+LANGUAGE plpgsql VOLATILE;
+
+SELECT test_vertex_points();
+
+SELECT finish();
+ROLLBACK;
diff --git a/pgtap/withPoints/withPointsVia/edge_cases/point_in_vertex.pg b/pgtap/withPoints/withPointsVia/edge_cases/point_in_vertex.pg
new file mode 100644
index 00000000000..15db9d89847
--- /dev/null
+++ b/pgtap/withPoints/withPointsVia/edge_cases/point_in_vertex.pg
@@ -0,0 +1,186 @@
+/*PGR-GNU*****************************************************************
+
+Copyright (c) 2024  pgRouting developers
+Mail: project@pgrouting.org
+
+------
+This program 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 2 of the License, or
+(at your option) any later version.
+This program 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 this program; if not, write to the Free Software
+Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+ ********************************************************************PGR-GNU*/
+BEGIN;
+
+SET extra_float_digits=-3;
+
+SELECT CASE WHEN min_version('3.4.0') THEN plan(38) ELSE plan(1) END;
+
+CREATE VIEW four_edges AS
+SELECT * FROM edges WHERE id IN (1,4,10,14);
+
+CREATE OR REPLACE FUNCTION test_vertex_points() RETURNS SETOF TEXT AS
+$BODY$
+BEGIN
+
+  IF NOT min_version('3.4.0') THEN
+    RETURN QUERY SELECT skip(1, 'Signature added on 3.4.0');
+    RETURN;
+  END IF;
+
+
+PREPARE dijkstra1(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_dijkstraVia(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  ARRAY[$1, $2], true) WHERE node = $2 and edge < 0;
+
+-- its a straigh line and one extreme are reachable
+RETURN QUERY SELECT results_eq($$dijkstra1(5,9)$$, ARRAY[4]::TEXT[]);
+RETURN QUERY SELECT results_eq($$dijkstra1(9,5)$$, ARRAY[4]::TEXT[]);
+
+
+/* Points
+  midpoint of edge 1 (-1 by default)
+*/
+PREPARE expectedCost1(BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsVia(
+  $$ SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$ SELECT 1 AS edge_id, 0.5::float AS fraction$$,
+  ARRAY[-1, $1], true) WHERE node = $1 and edge < 0;
+
+RETURN QUERY SELECT results_eq($$expectedCost1(6)$$, ARRAY[0.5]::TEXT[], 'Cost from midpoint on 1 (-1 default) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost1(7)$$, ARRAY[1.5]::TEXT[] , 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost1(8)$$, ARRAY[2.5]::TEXT[] , 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost1(9)$$, ARRAY[3.5]::TEXT[] , 'Cost from midpoint on 1 to 9');
+
+/* Points
+  midpoint of edge 1 (-2 assigned)
+*/
+PREPARE expectedCost2(BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsVia(
+  $$ SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$ SELECT 2 AS pid, 1 AS edge_id, 0.5::float AS fraction$$,
+  ARRAY[-2, $1], true) WHERE node = $1 and edge < 0;
+
+RETURN QUERY SELECT results_eq($$expectedCost2(6)$$, $$expectedCost1(6)$$, 'Cost from midpoint on 1 (-2 assigned) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost2(7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost2(8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost2(9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+/* UNION ALL data is not sorted
+  source point of edge 10 (-1 by default)
+  midpoint of edge 1 (-2 by default)
+*/
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsVia(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT 10 AS edge_id, 0::float AS fraction UNION ALL SELECT 1, 0.5 $$,
+  ARRAY[$1, $2], true) WHERE node = $2 and edge < 0;
+
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,6)$$, $$expectedCost1(6)$$, '(UNION ALL) Cost from midpoint on 1 (-2 default) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+RETURN QUERY SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-1,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-1,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-1,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* UNION data is sorted
+  midpoint of edge 1 (-1 by default)
+  source point of edge 10 (-2 by default)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsVia(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT 10 AS edge_id, 0::float AS fraction UNION SELECT 1, 0.5 $$,
+  ARRAY[$1, $2], true) WHERE node = $2 and edge < 0;
+
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,6)$$, $$expectedCost1(6)$$, '(UNION) Cost from midpoint on 1 (-2 default) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+RETURN QUERY SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-2,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-2,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-2,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* VALUES data is not sorted
+  midpoint of edge 1 (-1 by default)
+  source point of edge 10 (-2 by default)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsVia(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT * FROM (VALUES (1,0.5), (10, 0)) AS t (edge_id, fraction)$$,
+  ARRAY[$1, $2], true) WHERE node = $2 and edge < 0;
+
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,6)$$, $$expectedCost1(6)$$, '(VALUES) Cost from midpoint on 1 (-1 default) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost3(-1,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+RETURN QUERY SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-2,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-2,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-2,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+/* Points
+  midpoint of edge 1 (-2 assigned)
+  source point of edge 10 (-1 assigned)
+*/
+DEALLOCATE PREPARE expectedCost3;
+PREPARE expectedCost3(BIGINT, BIGINT) AS
+SELECT agg_cost::TEXT FROM pgr_withPointsVia(
+  $$SELECT id, source, target, cost, reverse_cost FROM four_edges$$,
+  $$SELECT 2 AS pid, 1 AS edge_id, 0.5::float AS fraction UNION SELECT 1, 10, 0 $$,
+  ARRAY[$1, $2], true) WHERE node = $2 and edge < 0;
+
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,6)$$, $$expectedCost1(6)$$, '(ASSIGNED) Cost from midpoint on 1 (-2 default) to 6');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,7)$$, $$expectedCost1(7)$$, 'Cost from midpoint on 1 to 7');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,8)$$, $$expectedCost1(8)$$, 'Cost from midpoint on 1 to 8');
+RETURN QUERY SELECT results_eq($$expectedCost3(-2,9)$$, $$expectedCost1(9)$$, 'Cost from midpoint on 1 to 9');
+
+RETURN QUERY SELECT CASE WHEN min_version('3.7.1')
+THEN
+  collect_tap(
+    set_eq($$expectedCost3(-1,9)$$, $$dijkstra1(7,9)$$, 'Cost from target on 10 (-1 default, aka 7) to 9'),
+    set_eq($$expectedCost3(-1,8)$$, $$dijkstra1(7,8)$$, 'Cost from target on 10 to 8'),
+    set_eq($$expectedCost3(-1,7)$$, ARRAY[0]::TEXT[], 'Cost from target on 10 to 7')
+  )
+ELSE skip('Fix implemented on 3.7.1',3)
+END;
+
+END
+$BODY$
+LANGUAGE plpgsql VOLATILE;
+
+SELECT test_vertex_points();
+
+SELECT finish();
+ROLLBACK;
diff --git a/src/common/basePath_SSEC.cpp b/src/common/basePath_SSEC.cpp
index c2f62c6825c..23a7f84e29f 100644
--- a/src/common/basePath_SSEC.cpp
+++ b/src/common/basePath_SSEC.cpp
@@ -160,8 +160,6 @@ Path Path::getSubpath(unsigned int j) const {
     for (auto i = path.begin(); i != path.begin() + j; ++i) {
         result.push_back((*i));
     }
-    pgassert(result.tot_cost() != 0);
-    pgassert(this->tot_cost() != 0);
     return result;
 }
 
diff --git a/src/withPoints/withPoints.cpp b/src/withPoints/withPoints.cpp
index 9123fed8de4..98a619caeb3 100644
--- a/src/withPoints/withPoints.cpp
+++ b/src/withPoints/withPoints.cpp
@@ -390,11 +390,15 @@ Pg_points_graph::create_new_edges() {
             }
             if (point.fraction == 0) {
                 log << "Point's vertex_id = source" << edge.source << "\n";
-                point.vertex_id = edge.source;
+                point.vertex_id = -point.pid;
+                Edge_t new_edge = {edge.id, edge.source, -point.pid, 0, 0};
+                m_new_edges.push_back(new_edge);
             }
             if (point.fraction == 1) {
                 log << "point's vertex_id = target" << edge.target << "\n";
-                point.vertex_id = edge.target;
+                point.vertex_id = -point.pid;
+                Edge_t new_edge = {edge.id, edge.target, -point.pid, 0, 0};
+                m_new_edges.push_back(new_edge);
             }
             if (point.fraction > 0 &&  point.fraction < 1) {
                 log << "vertex_id of the point is " << -point.pid << "\n";