From dddce684e6b417f96d46bbca59f76d289ce1f347 Mon Sep 17 00:00:00 2001
From: NgoQuocViet2001 <ngoquocviet2001@gmail.com>
Date: Wed, 19 Aug 2026 20:30:58 +0700
Subject: [PATCH] fix(circle): offer enclosing solutions for
 tangent-tangent-radius

A circle of radius r tangent to a circle of radius r_i has its center at
r_i + r (external tangency) or |r_i - r| (internal). ttr_lc_candidates and
ttr_cc_candidates built that second distance as r_i - r and skipped the
combination when it came out negative, so every solution where the new
circle is the larger one and encloses an existing circle was dropped. TTR
over two circles could only ever return externally tangent results.

Only rho^2 reaches the algebra below, so taking the magnitude is enough,
which is how the tan-tan-tan path already computes it.

Fixes #814
---
 src/modules/draw/draw/circle.rs | 67 ++++++++++++++++++++++++++++-----
 1 file changed, 58 insertions(+), 9 deletions(-)

diff --git a/src/modules/draw/draw/circle.rs b/src/modules/draw/draw/circle.rs
index 8e6f3843..778d65b0 100644
--- a/src/modules/draw/draw/circle.rs
+++ b/src/modules/draw/draw/circle.rs
@@ -641,10 +641,13 @@ fn ttr_lc_candidates(l: Line2D, cp: DVec3, cr: f64, r: f64) -> Vec<DVec3> {
     let mut out = Vec::new();
     for s1 in [-1.0f64, 1.0] {
         for s2 in [-1.0f64, 1.0] {
-            let rho = cr + s2 * r;
-            if rho < 0.0 {
-                continue;
-            }
+            // Distance from the new center to the circle's center: `cr + r`
+            // for external tangency, `|cr - r|` for internal. Reading that
+            // difference as negative dropped the whole family where the new
+            // circle is the larger one and encloses the existing circle. Only
+            // `rho^2` is used below, so the magnitude is what the algebra
+            // needs — the tan-tan-tan path already takes it that way.
+            let rho = (cr + s2 * r).abs();
             let c_off = l.c + s1 * r;
             // The candidate center (cx, cy) satisfies:
             //   l.a*cx + l.b*cy + c_off = 0
@@ -677,11 +680,11 @@ fn ttr_cc_candidates(c1: DVec3, r1: f64, c2: DVec3, r2: f64, r: f64) -> Vec<DVec
     let mut out = Vec::new();
     for s1 in [-1.0f64, 1.0] {
         for s2 in [-1.0f64, 1.0] {
-            let rho1 = r1 + s1 * r;
-            let rho2 = r2 + s2 * r;
-            if rho1 < 0.0 || rho2 < 0.0 {
-                continue;
-            }
+            // As in `ttr_lc_candidates`: `r_i + r` is external tangency and
+            // `|r_i - r|` internal, so a new circle larger than an existing one
+            // still sits a real distance from it.
+            let rho1 = (r1 + s1 * r).abs();
+            let rho2 = (r2 + s2 * r).abs();
             let ax = c2.x - c1.x;
             let ay = c2.y - c1.y;
             let k = 0.5
@@ -1133,6 +1136,52 @@ inventory::submit!(crate::command::CommandRegistration { names: &["CIRCLE_TTT"]
 mod tests {
     use super::*;
 
+    fn has_candidate(cands: &[DVec3], want: DVec3) -> bool {
+        cands.iter().any(|c| c.distance(want) < 1e-6)
+    }
+
+    /// #814: tan-tan-radius over two circles must also offer the solutions
+    /// where the new circle is the larger one and encloses an existing circle.
+    /// `|r_i - r|` is a real distance; it used to be read as negative, which
+    /// dropped that family and left only externally tangent results.
+    #[test]
+    fn ttr_two_circles_offers_the_enclosing_solution() {
+        let c1 = TangentObject::Circle { center: DVec3::new(-3.0, 0.0, 0.0), radius: 1.0 };
+        let c2 = TangentObject::Circle { center: DVec3::new(3.0, 0.0, 0.0), radius: 1.0 };
+        let cands = ttr_candidates(c1, c2, 5.0);
+        // |P - Ci| = 5 - 1 = 4 puts both small circles inside the new one.
+        let y = 7.0f64.sqrt();
+        assert!(
+            has_candidate(&cands, DVec3::new(0.0, y, 0.0))
+                && has_candidate(&cands, DVec3::new(0.0, -y, 0.0)),
+            "no enclosing candidate, got {cands:?}"
+        );
+        // The externally tangent family is still produced.
+        assert!(
+            cands.iter().any(|c| {
+                (c.distance(DVec3::new(-3.0, 0.0, 0.0)) - 6.0).abs() < 1e-6
+                    && (c.distance(DVec3::new(3.0, 0.0, 0.0)) - 6.0).abs() < 1e-6
+            }),
+            "external tangency lost, got {cands:?}"
+        );
+    }
+
+    /// Same gap on the line/circle pair: a radius larger than the circle's own
+    /// must still reach the tangent circles that swallow it.
+    #[test]
+    fn ttr_line_and_circle_offers_the_enclosing_solution() {
+        let line = TangentObject::Line { p1: DVec3::ZERO, p2: DVec3::new(10.0, 0.0, 0.0) };
+        let circle = TangentObject::Circle { center: DVec3::new(0.0, 2.0, 0.0), radius: 1.0 };
+        let cands = ttr_candidates(line, circle, 5.0);
+        // Tangent to y = 0 at distance 5, and |P - (0,2)| = 5 - 1 = 4.
+        let x = 7.0f64.sqrt();
+        assert!(
+            has_candidate(&cands, DVec3::new(x, 5.0, 0.0))
+                && has_candidate(&cands, DVec3::new(-x, 5.0, 0.0)),
+            "no enclosing candidate, got {cands:?}"
+        );
+    }
+
     /// #318: concentric ring + a line through the center — the degenerate
     /// circle-pair equation must still yield the annulus circle.
     #[test]