diff --git a/tests/kernel-cases/construction/cov-point-along-path-a-third-of-an-arc/expected.json b/tests/kernel-cases/construction/cov-point-along-path-a-third-of-an-arc/expected.json
new file mode 100644
index 0000000000..22389d2aa6
--- /dev/null
+++ b/tests/kernel-cases/construction/cov-point-along-path-a-third-of-an-arc/expected.json
@@ -0,0 +1,15 @@
+{
+ "sources": [],
+ "what": "a point a third along a quarter-circle arc",
+ "source": "analytic",
+ "method": "the arc r 10 about the origin from (10,0) to (0,10) counter-clockwise: a third of its length is 30 deg round: (10 cos 30, 10 sin 30, 0) = (8.6603, 5, 0)",
+ "construction": {
+  "P": {
+   "point": [
+    8.660254037844386,
+    5,
+    0
+   ]
+  }
+ }
+}
diff --git a/tests/kernel-cases/construction/cov-point-along-path-a-third-of-an-arc/recipe.json b/tests/kernel-cases/construction/cov-point-along-path-a-third-of-an-arc/recipe.json
new file mode 100644
index 0000000000..9da9dd038f
--- /dev/null
+++ b/tests/kernel-cases/construction/cov-point-along-path-a-third-of-an-arc/recipe.json
@@ -0,0 +1,43 @@
+{
+ "commands": [
+  {
+   "command": "sketch.create",
+   "params": {
+    "plane": "XY",
+    "name": "Path"
+   }
+  },
+  {
+   "command": "sketch.arc.center_point",
+   "params": {
+    "center": [
+     0,
+     0
+    ],
+    "start": [
+     10,
+     0
+    ],
+    "end": [
+     0,
+     10
+    ]
+   }
+  },
+  {
+   "command": "sketch.finish",
+   "params": {}
+  },
+  {
+   "command": "construct.point.along_path",
+   "params": {
+    "path": {
+     "sketch": "Path",
+     "curve": "a1"
+    },
+    "t": "1/3",
+    "name": "P"
+   }
+  }
+ ]
+}
diff --git a/tests/kernel-cases/construction/cov-point-along-path-past-the-end/expected.json b/tests/kernel-cases/construction/cov-point-along-path-past-the-end/expected.json
new file mode 100644
index 0000000000..bc40d5224f
--- /dev/null
+++ b/tests/kernel-cases/construction/cov-point-along-path-past-the-end/expected.json
@@ -0,0 +1,15 @@
+{
+ "sources": [],
+ "what": "a point at t 1.5, past the end of a sketch line",
+ "source": "analytic",
+ "method": "t runs 0..1 along the path; a point along it can go no further than its end: (40,0,0)",
+ "construction": {
+  "P": {
+   "point": [
+    40,
+    0,
+    0
+   ]
+  }
+ }
+}
diff --git a/tests/kernel-cases/construction/cov-point-along-path-past-the-end/recipe.json b/tests/kernel-cases/construction/cov-point-along-path-past-the-end/recipe.json
new file mode 100644
index 0000000000..d306d3ddb9
--- /dev/null
+++ b/tests/kernel-cases/construction/cov-point-along-path-past-the-end/recipe.json
@@ -0,0 +1,41 @@
+{
+ "commands": [
+  {
+   "command": "sketch.create",
+   "params": {
+    "plane": "XY",
+    "name": "Path"
+   }
+  },
+  {
+   "command": "sketch.line",
+   "params": {
+    "points": [
+     [
+      0,
+      0
+     ],
+     [
+      40,
+      0
+     ]
+    ]
+   }
+  },
+  {
+   "command": "sketch.finish",
+   "params": {}
+  },
+  {
+   "command": "construct.point.along_path",
+   "params": {
+    "path": {
+     "sketch": "Path",
+     "curve": "l1"
+    },
+    "t": 1.5,
+    "name": "P"
+   }
+  }
+ ]
+}
diff --git a/tests/kernel-cases/construction/cov-point-along-path-quarter-of-a-line/expected.json b/tests/kernel-cases/construction/cov-point-along-path-quarter-of-a-line/expected.json
new file mode 100644
index 0000000000..6d5d351439
--- /dev/null
+++ b/tests/kernel-cases/construction/cov-point-along-path-quarter-of-a-line/expected.json
@@ -0,0 +1,15 @@
+{
+ "sources": [],
+ "what": "a point a quarter along a sketch line",
+ "source": "analytic",
+ "method": "the line l1 from (0,0,0) to (40,0,0): t 0.25 is (10,0,0)",
+ "construction": {
+  "P": {
+   "point": [
+    10,
+    0,
+    0
+   ]
+  }
+ }
+}
diff --git a/tests/kernel-cases/construction/cov-point-along-path-quarter-of-a-line/recipe.json b/tests/kernel-cases/construction/cov-point-along-path-quarter-of-a-line/recipe.json
new file mode 100644
index 0000000000..8485a9ee41
--- /dev/null
+++ b/tests/kernel-cases/construction/cov-point-along-path-quarter-of-a-line/recipe.json
@@ -0,0 +1,41 @@
+{
+ "commands": [
+  {
+   "command": "sketch.create",
+   "params": {
+    "plane": "XY",
+    "name": "Path"
+   }
+  },
+  {
+   "command": "sketch.line",
+   "params": {
+    "points": [
+     [
+      0,
+      0
+     ],
+     [
+      40,
+      0
+     ]
+    ]
+   }
+  },
+  {
+   "command": "sketch.finish",
+   "params": {}
+  },
+  {
+   "command": "construct.point.along_path",
+   "params": {
+    "path": {
+     "sketch": "Path",
+     "curve": "l1"
+    },
+    "t": 0.25,
+    "name": "P"
+   }
+  }
+ ]
+}