From 36974e6086e0aa5e90b48da45b1be5681bf66430 Mon Sep 17 00:00:00 2001
From: Ivan Mahonin <bh@icystar.com>
Date: Sep 17 2023 13:15:59 +0000
Subject: #assistants: fix fish eye grid


---

diff --git a/toonz/sources/tnztools/assistants/assistantellipse.cpp b/toonz/sources/tnztools/assistants/assistantellipse.cpp
index 4b24ac7..c7b5646 100644
--- a/toonz/sources/tnztools/assistants/assistantellipse.cpp
+++ b/toonz/sources/tnztools/assistants/assistantellipse.cpp
@@ -414,7 +414,7 @@ void TAssistantEllipse::drawParallelGrid(
   TAffine screenMatrixInv = screenMatrix.inv();
   
   double pixelSize = sqrt(tglGetPixelSize2());
-  double minStep = 10.0*pixelSize;
+  double minStep = (perspective ? 5 : 10)*pixelSize;
   TAffine ellipseMatrixInv = ellipseMatrix.inv();
 
   const TAffine &em = ellipseMatrix;
@@ -435,18 +435,38 @@ void TAssistantEllipse::drawParallelGrid(
   ranges.add( TAngleRangeSet::fromDouble(0.0), TAngleRangeSet::fromDouble(M_PI) );
 
   if (perspective) {
-    // draw perspective (actually angular)
-    double a0 = asin(gs0);
-    double a1 = asin(gs1);
-    double da = fabs(a1 - a0);
-    if (fabs(sin(da)) < 2.0*actualMinStep) return;
-    for(double a = a0 + ceil((-M_PI_2 - a0)/da)*da; a < M_PI_2; a += da)
+    // draw perspective
+    if (!( fabs(gs0) < 1 - TConsts::epsilon
+        && fabs(gs1) < 1 - TConsts::epsilon
+        && fabs(gs1 - gs0) > TConsts::epsilon )) return;
+
+    // the formula is: x = i/sqrt(1 + i*i)
+    
+    double ig0 = gs0/sqrt(1 - gs0*gs0);
+    double ig1 = gs1/sqrt(1 - gs1*gs1);
+    double di = fabs(ig1 - ig0);
+    double i0 = ig0 - round(ig0/di)*di;
+    
+    actualMinStep /= 2;
+    for(int j = 0; j < 2; ++j, di = -di, i0 += di)
+    for(double i = i0; i+di != i; i += di) {
+      double x = i/sqrt(1 + i*i);
+      
+      double curAlpha = 1;
+      if (fabs(i0) > TConsts::epsilon) {
+        double curStep = fabs( di*x*(1 - x*x)/i );
+        curAlpha = (curStep - actualMinStep)/actualMinStep;
+        if (curAlpha < 0) { if (i == i0) continue; else break; }
+        if (curAlpha > 1) curAlpha = 1;
+      }
+        
       drawEllipseRanges(
         ranges,
-        ellipseMatrix*TAffine::scale(a < 0.0 ? -1.0 : 1.0, sin(a)),
+        ellipseMatrix*TAffine::scale(x < 0.0 ? -1.0 : 1.0, x),
         screenMatrixInv,
         pixelSize,
-        alpha );
+        alpha * curAlpha );
+    }
   } else {
     // draw linear
     double dx = fabs(gs1 - gs0);