From a1117040b3697483bc0b641a3fff0194818300bc Mon Sep 17 00:00:00 2001
From: Markus Lampert <markus@bibi.ca>
Date: Tue, 22 Feb 2022 19:52:00 -0800
Subject: [PATCH] Changed passes for constant tool engagement

---
 src/Mod/Path/PathScripts/PathThreadMilling.py | 22 ++++++++++++++++---
 .../Path/PathTests/TestPathThreadMilling.py   |  8 +++----
 2 files changed, 23 insertions(+), 7 deletions(-)

diff --git a/src/Mod/Path/PathScripts/PathThreadMilling.py b/src/Mod/Path/PathScripts/PathThreadMilling.py
index 7e49e1ffba..5dea982a93 100644
--- a/src/Mod/Path/PathScripts/PathThreadMilling.py
+++ b/src/Mod/Path/PathScripts/PathThreadMilling.py
@@ -74,11 +74,27 @@ def threadRadii(internal, majorDia, minorDia, toolDia, toolCrest):
 
 def threadPasses(count, radii, internal, majorDia, minorDia, toolDia, toolCrest):
     PathLog.track(count, radii, internal, majorDia, minorDia, toolDia, toolCrest)
+    # the logic goes as follows, total area to be removed:
+    #   A = H * W  ... where H is the depth and W is half the width of a thread
+    #     H = k * sin(30) = k * 1/2  -> k = 2 * H
+    #     W = k * cos(30) = k * sqrt(3)/2
+    #     -> W = (2 * H) * sqrt(3) / 2 = H * sqrt(3)
+    #   A = sqrt(3) * H^2
+    # Each pass has to remove the same area
+    #   An = A / count = sqrt(3) * H^2 / count
+    # Because each successive pass doesn't have to remove the aera of the previous
+    # passes the result for the height:
+    #   Ai = (i + 1) * An = (i + 1) * sqrt(3) * Hi^2 = sqrt(3) * H^2 / count
+    #   Hi = sqrt(H^2 * (i + 1) / count)
+    #   Hi = H * sqrt((i + 1) / count)
     minor, major = radii(internal, majorDia, minorDia, toolDia, toolCrest)
-    dr = float(major - minor) / count
+    H = float(major - minor)
+    Hi = [H * math.sqrt((i + 1) / count) for i in range(count)]
+    PathLog.debug("threadPasses({}, {}) -> H={} : {}".format(minor, major, H, Hi))
+
     if internal:
-        return [minor + dr * (i + 1) for i in range(count)]
-    return [major - dr * (i + 1) for i in range(count)]
+        return [minor + h for h in Hi]
+    return [major - h for h in Hi]
 
 
 def elevatorRadius(obj, center, internal, tool):
diff --git a/src/Mod/Path/PathTests/TestPathThreadMilling.py b/src/Mod/Path/PathTests/TestPathThreadMilling.py
index d393492b81..5823bd23c6 100644
--- a/src/Mod/Path/PathTests/TestPathThreadMilling.py
+++ b/src/Mod/Path/PathTests/TestPathThreadMilling.py
@@ -57,8 +57,8 @@ class TestPathThreadMilling(PathTestBase):
     def test10(self):
         '''Verify internal thread passes.'''
         self.assertList(PathThreadMilling.threadPasses(1, radii, True, 10, 9, 0, 0), [10])
-        self.assertList(PathThreadMilling.threadPasses(2, radii, True, 10, 9, 0, 0), [9.5, 10])
-        self.assertList(PathThreadMilling.threadPasses(5, radii, True, 10, 9, 0, 0), [9.2, 9.4, 9.6, 9.8, 10])
+        self.assertList(PathThreadMilling.threadPasses(2, radii, True, 10, 9, 0, 0), [9.707107, 10])
+        self.assertList(PathThreadMilling.threadPasses(5, radii, True, 10, 9, 0, 0), [9.447214, 9.632456, 9.774597, 9.894427, 10])
 
     def test20(self):
         '''Verify external radii.'''
@@ -72,8 +72,8 @@ class TestPathThreadMilling(PathTestBase):
     def test30(self):
         '''Verify external thread passes.'''
         self.assertList(PathThreadMilling.threadPasses(1, radii, False, 10, 9, 0, 0), [9])
-        self.assertList(PathThreadMilling.threadPasses(2, radii, False, 10, 9, 0, 0), [9.5, 9])
-        self.assertList(PathThreadMilling.threadPasses(5, radii, False, 10, 9, 0, 0), [9.8, 9.6, 9.4, 9.2, 9])
+        self.assertList(PathThreadMilling.threadPasses(2, radii, False, 10, 9, 0, 0), [9.292893, 9])
+        self.assertList(PathThreadMilling.threadPasses(5, radii, False, 10, 9, 0, 0), [9.552786, 9.367544, 9.225403, 9.105573, 9])
 
     def test40(self):
         '''Verify thread commands for a single thread'''