From de0600e1e2a0fa4e666e7c49c772379a29ffeba9 Mon Sep 17 00:00:00 2001
From: treeform <starplant@gmail.com>
Date: Wed, 29 Jun 2022 22:49:28 -0700
Subject: [PATCH 1/2] Cubic tangent error.

---
 src/pixie/paths.nim  | 25 ++++++++++++++++++++-----
 tests/test_path2.nim | 12 ++++++++++++
 2 files changed, 32 insertions(+), 5 deletions(-)
 create mode 100644 tests/test_path2.nim

diff --git a/src/pixie/paths.nim b/src/pixie/paths.nim
index 4cb2fa5..9739a2f 100644
--- a/src/pixie/paths.nim
+++ b/src/pixie/paths.nim
@@ -675,10 +675,21 @@ proc commandsToShapes(
   proc addCubic(shape: var Polygon, at, ctrl1, ctrl2, to: Vec2) =
     ## Adds cubic segments to shape.
     proc compute(at, ctrl1, ctrl2, to: Vec2, t: float32): Vec2 {.inline.} =
-      pow(1 - t, 3) * at +
-      pow(1 - t, 2) * 3 * t * ctrl1 +
-      (1 - t) * 3 * pow(t, 2) * ctrl2 +
-      pow(t, 3) * to
+      let
+        t2 = t*t
+        t3 = t2*t
+      at * (-t3 + 3*t2 - 3*t + 1) +
+      ctrl1 * (3*t3 - 6*t2 + 3*t) +
+      ctrl2 * (-3*t3 + 3*t2) +
+      to * (t3)
+
+    proc computeDerv(at, ctrl1, ctrl2, to: Vec2, t: float32): Vec2 {.inline.} =
+      let
+        t2 = t*t
+      at * (-3*t2 + 6*t - 3) +
+      ctrl1 * (9*t2 - 12*t + 3) +
+      ctrl2 * (-9*t2 + 6*t) +
+      to * (3 * t2)
 
     var
       t: float32       # Where we are at on the curve from [0, 1]
@@ -691,7 +702,11 @@ proc commandsToShapes(
         raise newException(PixieError, "Unable to discretize cubic")
       let
         midpoint = (prev + next) / 2
-        error = (midpoint - halfway).lengthSq
+        lineTangent = midpoint - prev
+        curveTangent = computeDerv(at, ctrl1, ctrl2, to, t + step / 2)
+        curveTangentScaled = curveTangent.normalize() * lineTangent.length()
+        error = (midpoint - halfway).lengthSq +
+          (lineTangent - curveTangentScaled).lengthSq
       if error > errorMarginSq:
         next = halfway
         halfway = compute(at, ctrl1, ctrl2, to, t + step / 4)
diff --git a/tests/test_path2.nim b/tests/test_path2.nim
new file mode 100644
index 0000000..bc6f70a
--- /dev/null
+++ b/tests/test_path2.nim
@@ -0,0 +1,12 @@
+import chroma, pixie, pixie/fileformats/png, strformat
+
+block:
+  let
+    image = newImage(100, 100)
+    pathStr = """
+        M 40 40 L 40 80 L 80 80 L 80 40 C 80 -20 40 100 40 40
+    """
+    color = rgba(0, 0, 0, 255)
+  image.fill(rgba(255, 255, 255, 255))
+  image.fillPath(pathStr, color)
+  image.writeFile("tests/paths/pathSwish.png")

From 04abf707fa07795bbb226e9032ce868ce55aa726 Mon Sep 17 00:00:00 2001
From: treeform <starplant@gmail.com>
Date: Wed, 29 Jun 2022 23:14:34 -0700
Subject: [PATCH 2/2] Cleanup.

---
 src/pixie/paths.nim       |  13 ++++++-------
 tests/paths/pathSwish.png | Bin 0 -> 964 bytes
 tests/test_path2.nim      |  12 ------------
 tests/test_paths.nim      |  11 +++++++++++
 4 files changed, 17 insertions(+), 19 deletions(-)
 create mode 100644 tests/paths/pathSwish.png
 delete mode 100644 tests/test_path2.nim

diff --git a/src/pixie/paths.nim b/src/pixie/paths.nim
index 9739a2f..4719508 100644
--- a/src/pixie/paths.nim
+++ b/src/pixie/paths.nim
@@ -683,9 +683,8 @@ proc commandsToShapes(
       ctrl2 * (-3*t3 + 3*t2) +
       to * (t3)
 
-    proc computeDerv(at, ctrl1, ctrl2, to: Vec2, t: float32): Vec2 {.inline.} =
-      let
-        t2 = t*t
+    proc computeDeriv(at, ctrl1, ctrl2, to: Vec2, t: float32): Vec2 {.inline.} =
+      let t2 = t*t
       at * (-3*t2 + 6*t - 3) +
       ctrl1 * (9*t2 - 12*t + 3) +
       ctrl2 * (-9*t2 + 6*t) +
@@ -703,11 +702,11 @@ proc commandsToShapes(
       let
         midpoint = (prev + next) / 2
         lineTangent = midpoint - prev
-        curveTangent = computeDerv(at, ctrl1, ctrl2, to, t + step / 2)
+        curveTangent = computeDeriv(at, ctrl1, ctrl2, to, t + step / 2)
         curveTangentScaled = curveTangent.normalize() * lineTangent.length()
-        error = (midpoint - halfway).lengthSq +
-          (lineTangent - curveTangentScaled).lengthSq
-      if error > errorMarginSq:
+        error = (midpoint - halfway).lengthSq
+        errorTangent = (lineTangent - curveTangentScaled).lengthSq
+      if error + errorTangent > errorMarginSq:
         next = halfway
         halfway = compute(at, ctrl1, ctrl2, to, t + step / 4)
         step /= 2
diff --git a/tests/paths/pathSwish.png b/tests/paths/pathSwish.png
new file mode 100644
index 0000000000000000000000000000000000000000..a58993ca72a96e553c9deb428dc22a6c71cb8ffb
GIT binary patch
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literal 0
HcmV?d00001

diff --git a/tests/test_path2.nim b/tests/test_path2.nim
deleted file mode 100644
index bc6f70a..0000000
--- a/tests/test_path2.nim
+++ /dev/null
@@ -1,12 +0,0 @@
-import chroma, pixie, pixie/fileformats/png, strformat
-
-block:
-  let
-    image = newImage(100, 100)
-    pathStr = """
-        M 40 40 L 40 80 L 80 80 L 80 40 C 80 -20 40 100 40 40
-    """
-    color = rgba(0, 0, 0, 255)
-  image.fill(rgba(255, 255, 255, 255))
-  image.fillPath(pathStr, color)
-  image.writeFile("tests/paths/pathSwish.png")
diff --git a/tests/test_paths.nim b/tests/test_paths.nim
index edd4faa..b5de9cc 100644
--- a/tests/test_paths.nim
+++ b/tests/test_paths.nim
@@ -773,3 +773,14 @@ block:
       mat3(),
       NonZero
     )
+
+block:
+  let
+    image = newImage(100, 100)
+    pathStr = """
+      M 40 40 L 40 80 L 80 80 L 80 40 C 80 -20 40 100 40 40
+    """
+    color = rgba(0, 0, 0, 255)
+  image.fill(rgba(255, 255, 255, 255))
+  image.fillPath(pathStr, color)
+  image.writeFile("tests/paths/pathSwish.png")