From 65ab0c6a1fd10f5602610ac906d008669e4ac89a Mon Sep 17 00:00:00 2001
From: Simon Gardling <titaniumtown@proton.me>
Date: Fri, 5 Dec 2025 22:37:05 -0500
Subject: [PATCH] FunctionEntry: make newtons_method threshold smaller (fixes
 symbolicrepr) + prioritize special points

---
 src/function_entry.rs | 48 +++++++++++++++++++++++++++++++++++++------
 1 file changed, 42 insertions(+), 6 deletions(-)

diff --git a/src/function_entry.rs b/src/function_entry.rs
index 643d2c4..170a3ee 100644
--- a/src/function_entry.rs
+++ b/src/function_entry.rs
@@ -344,7 +344,7 @@ impl FunctionEntry {
             self.clear_integral();
         }
 
-        let threshold: f64 = resolution / 2.0;
+        let threshold: f64 = f64::EPSILON;
         let x_range = settings.min_x..settings.max_x;
 
         // Calculates extrema
@@ -377,7 +377,28 @@ impl FunctionEntry {
         let step = (settings.max_x - settings.min_x) / (settings.plot_width as f64);
         debug_assert!(step > 0.0);
 
-        // Plot back data
+        // Collect special points (extrema and roots) for exclusion from line hover detection
+        let special_points: Vec<&PlotPoint> = {
+            let mut points = Vec::new();
+            if settings.do_extrema {
+                points.extend(self.extrema_data.iter());
+            }
+            if settings.do_roots {
+                points.extend(self.root_data.iter());
+            }
+            points
+        };
+
+        // Helper to check if a point is near any special point
+        // Uses a radius in x-axis units based on the step size
+        let exclusion_radius = step * 3.0; // Exclude points within 3 steps of special points
+        let is_near_special_point = |p: &PlotPoint| -> bool {
+            special_points
+                .iter()
+                .any(|sp| (p.x - sp.x).abs() < exclusion_radius)
+        };
+
+        // Plot back data, filtering out points near special points for better hover detection
         if !self.back_data.is_empty() {
             if self.integral && (step >= integral_step) {
                 plot_ui.line(
@@ -395,17 +416,32 @@ impl FunctionEntry {
                         .fill(0.0),
                 );
             }
+
+            // Filter out points near special points so cursor snaps to them more easily
+            let filtered_back_data: Vec<PlotPoint> = self
+                .back_data
+                .iter()
+                .filter(|p| !is_near_special_point(p))
+                .cloned()
+                .collect();
+
             plot_ui.line(
-                self.back_data
-                    .clone()
+                filtered_back_data
                     .to_line()
                     .stroke(egui::Stroke::new(4.0, main_plot_color)),
             );
         }
 
-        // Plot derivative data
+        // Plot derivative data, also filtering near special points
         if self.derivative && !self.derivative_data.is_empty() {
-            plot_ui.line(self.derivative_data.clone().to_line().color(Color32::GREEN));
+            let filtered_derivative_data: Vec<PlotPoint> = self
+                .derivative_data
+                .iter()
+                .filter(|p| !is_near_special_point(p))
+                .cloned()
+                .collect();
+
+            plot_ui.line(filtered_derivative_data.to_line().color(Color32::GREEN));
         }
 
         // Plot extrema points