diff --git a/modules/curve/src/main/java/org/locationtech/jts/geom/curve/CurveExact.java b/modules/curve/src/main/java/org/locationtech/jts/geom/curve/CurveExact.java
index ac85ed7a16..7651f4f923 100644
--- a/modules/curve/src/main/java/org/locationtech/jts/geom/curve/CurveExact.java
+++ b/modules/curve/src/main/java/org/locationtech/jts/geom/curve/CurveExact.java
@@ -35,7 +35,7 @@
* a Point or MultiPoint (PIP and DE-9IM), a disc against a LineString
* (DE-9IM from line–circle nodes), a disc against a plain Polygon
* (DE-9IM from vertices, edge nodes, and mid-arc PIP), or two circular
- * discs (DE-9IM from radical-axis nodes and {@link #locatePoint}).
+ * discs (DE-9IM from {@code d²} vs {@code (r1±r2)²} in {@code R²}).
* Package-private -- not a new public API.
* {@link CurveOps} takes these only when they can answer; anything else
* goes straight to the chord baseline. Trying and falling through would
@@ -201,9 +201,9 @@ static Boolean covers(Geometry curve, Geometry other) {
* lineal and polygonal use
* {@link CircularArcDensifier#intersectSegmentCircle}
* ({@code t ∈ [0,1]}, the R1.6 / {@code ARC_SEGMENT_XY} quadratic)
- * plus endpoint / vertex location. Two discs reuse
- * {@link CircularArcDensifier#intersectCircles} (radical axis) and
- * locate each centre in the other disc. A polygonal miss also samples
+ * plus endpoint / vertex location. Two discs classify in {@code R²}
+ * ({@code d²} vs {@code (r1±r2)²}); the kiss coordinates are not
+ * needed for the matrix. A polygonal miss also samples
* mid-arc points in the polygon (jts-core PIP). Mixed MultiPoint
* location classes, a multi-member MultiLineString or MultiSurface,
* a holed or non-disc curve polygon return {@code null} so the caller
@@ -342,10 +342,14 @@ private static LineString plainLine(Geometry g) {
/**
* Location classes of two circular discs. Envelope miss is disjoint.
- * Node count is {@link CircularArcDensifier#intersectCircles} (empty
- * when {@code d == 0}, {@code d > r1+r2}, or {@code d < |r1-r2|});
- * each centre is then located in the other disc. A non-disc
- * {@code CurvePolygon} never reaches this method.
+ * The class is decided in {@code R²}: {@code d²} against
+ * {@code (r1+r2)²} and {@code (r1-r2)²}. No {@code hypot} and no
+ * radical-axis node for the decision (V1, before noding). Public
+ * numbers may take {@code sqrt}; this matrix does not need the kiss
+ * coordinates. T-ext is {@link #IM_AREA_EXT_TANGENT} {@code FF2F01212}
+ * — one kiss, no shared flesh — ISO/IEC 13249-3 {@code ST_Touches}
+ * (DE-9IM {@code FT*******} / {@code F**T*****} / {@code F***T****}).
+ * A non-disc {@code CurvePolygon} never reaches this method.
*/
private static IntersectionMatrix relateDisc(CircularArcDensifier.Circle a,
CircularArcDensifier.Circle b) {
@@ -354,30 +358,33 @@ private static IntersectionMatrix relateDisc(CircularArcDensifier.Circle a,
if (!ea.intersects(eb)) {
return new IntersectionMatrix(IM_AREA_DISJOINT);
}
- Coordinate[] nodes = CircularArcDensifier.intersectCircles(a, b);
- Coordinate ca = new Coordinate(a.cx, a.cy);
- Coordinate cb = new Coordinate(b.cx, b.cy);
- double r2a = a.r * a.r;
- double r2b = b.r * b.r;
- if (nodes.length == 2) {
- return new IntersectionMatrix(IM_AREA_OVERLAP);
- }
- int locAinB = locatePoint(b, ca, r2b);
- int locBinA = locatePoint(a, cb, r2a);
- if (nodes.length == 1) {
- if (locAinB == Location.EXTERIOR && locBinA == Location.EXTERIOR) {
- return new IntersectionMatrix(IM_AREA_EXT_TANGENT);
- }
+ double dx = a.cx - b.cx;
+ double dy = a.cy - b.cy;
+ double d2 = dx * dx + dy * dy;
+ double sum = a.r + b.r;
+ double sum2 = sum * sum;
+ double diff = a.r - b.r;
+ double diff2 = diff * diff;
+ if (d2 == 0.0 && a.r == b.r) {
+ return new IntersectionMatrix(IM_AREA_EQUAL);
+ }
+ if (d2 > sum2) {
+ return new IntersectionMatrix(IM_AREA_DISJOINT);
+ }
+ if (d2 == sum2) {
+ return new IntersectionMatrix(IM_AREA_EXT_TANGENT);
+ }
+ if (d2 == diff2) {
return a.r > b.r
? new IntersectionMatrix(IM_AREA_INT_TANGENT)
: new IntersectionMatrix(IntersectionMatrix.transpose(IM_AREA_INT_TANGENT));
}
- if (locAinB == Location.EXTERIOR && locBinA == Location.EXTERIOR) {
- return new IntersectionMatrix(IM_AREA_DISJOINT);
+ if (d2 < diff2) {
+ return a.r > b.r
+ ? new IntersectionMatrix(IM_AREA_COVERS)
+ : new IntersectionMatrix(IM_AREA_COVEREDBY);
}
- if (a.r > b.r) return new IntersectionMatrix(IM_AREA_COVERS);
- if (a.r < b.r) return new IntersectionMatrix(IM_AREA_COVEREDBY);
- return new IntersectionMatrix(IM_AREA_EQUAL);
+ return new IntersectionMatrix(IM_AREA_OVERLAP);
}
/**
diff --git a/modules/curve/src/test/java/org/locationtech/jts/geom/curve/CurveExactRelateDiscTest.java b/modules/curve/src/test/java/org/locationtech/jts/geom/curve/CurveExactRelateDiscTest.java
index c7ef874b10..855f56c982 100644
--- a/modules/curve/src/test/java/org/locationtech/jts/geom/curve/CurveExactRelateDiscTest.java
+++ b/modules/curve/src/test/java/org/locationtech/jts/geom/curve/CurveExactRelateDiscTest.java
@@ -152,6 +152,11 @@ public void testNestedOffsetCovers() throws Exception {
assertTrue(inner.coveredBy(big));
}
+ /**
+ * Axis-aligned pair kisses at the shared control {@code (5, 0)}.
+ * R.1 ({@link CurveExactRelateTouchTest}) pins the same matrix on a
+ * 3-4-5 pair whose kiss is not a control vertex.
+ */
public void testExternalTangent() throws Exception {
Geometry a = readCurve(CIRCLE_5);
Geometry b = readCurve(CIRCLE_EXT_TAN);
diff --git a/modules/curve/src/test/java/org/locationtech/jts/geom/curve/CurveExactRelateTouchTest.java b/modules/curve/src/test/java/org/locationtech/jts/geom/curve/CurveExactRelateTouchTest.java
new file mode 100644
index 0000000000..0ec8f3fb1a
--- /dev/null
+++ b/modules/curve/src/test/java/org/locationtech/jts/geom/curve/CurveExactRelateTouchTest.java
@@ -0,0 +1,145 @@
+/*
+ * Copyright (c) 2026 grootstebozewolf
+ *
+ * All rights reserved. This program and the accompanying materials
+ * are made available under the terms of the Eclipse Public License 2.0
+ * and Eclipse Distribution License v. 1.0 which accompanies this distribution.
+ * The Eclipse Public License is available at http://www.eclipse.org/legal/epl-v20.html
+ * and the Eclipse Distribution License is available at
+ *
+ * http://www.eclipse.org/org/documents/edl-v10.php.
+ */
+package org.locationtech.jts.geom.curve;
+
+import java.lang.reflect.Field;
+
+import org.locationtech.jts.geom.Geometry;
+import org.locationtech.jts.geom.IntersectionMatrix;
+import org.locationtech.jts.io.curve.CurveWKTReader;
+import org.locationtech.jts.operation.overlayng.curve.OverlayNGCurve;
+import org.locationtech.jts.operation.relate.RelateOp;
+
+import junit.textui.TestRunner;
+import test.jts.GeometryTestCase;
+
+/**
+ * R.1 TOUCH laser cell. Two externally tangent circular discs:
+ * one kiss, no shared flesh. T-ext DE-9IM {@code FF2F01212}.
+ *
+ * ISO/IEC 13249-3 {@code ST_Touches}: the only points in common lie
+ * on the boundaries (DE-9IM {@code FT*******} / {@code F**T*****} /
+ * {@code F***T****}). No DOI. Stamp: EXACT. V1 before noding — the
+ * class is {@code d² == (r1+r2)²} in {@code R²}, not a hypot
+ * quotient and not a noder. Public {@link Geometry#touches} is the
+ * RelateOp predicate ({@link IntersectionMatrix#isTouches}) on that
+ * matrix. No {@code OverlayNGCurve.TOUCH}. No fifth overlay op.
+ *
+ * The axis-aligned pair in {@link CurveExactRelateDiscTest} kisses at
+ * a shared control vertex, so the control diamonds also touch. This
+ * cell pins a 3-4-5 pair whose kiss {@code (4, 3)} is not a control:
+ * RelateOp on the control polygons is the lie (disjoint).
+ */
+public class CurveExactRelateTouchTest extends GeometryTestCase {
+
+ private static final String CIRCLE_5 =
+ "CURVEPOLYGON (CIRCULARSTRING (-5 0, 0 5, 5 0, 0 -5, -5 0))";
+ /** Centre (8, 6), r=5. Externally tangent to CIRCLE_5; kiss (4, 3). */
+ private static final String CIRCLE_3_4_5 =
+ "CURVEPOLYGON (CIRCULARSTRING (13 6, 8 11, 3 6, 8 1, 13 6))";
+ private static final String MULTI_5 = "MULTISURFACE (" + CIRCLE_5 + ")";
+ private static final String MULTI_345 = "MULTISURFACE (" + CIRCLE_3_4_5 + ")";
+ private static final String CONTROL_5 =
+ "POLYGON ((-5 0, 0 5, 5 0, 0 -5, -5 0))";
+ private static final String CONTROL_345 =
+ "POLYGON ((13 6, 8 11, 3 6, 8 1, 13 6))";
+
+ /** T-ext: II=F, BB=0. One kiss, no shared flesh. */
+ private static final String IM_EXT = CurveExact.IM_AREA_EXT_TANGENT;
+
+ public static void main(String[] args) {
+ TestRunner.run(CurveExactRelateTouchTest.class);
+ }
+
+ public CurveExactRelateTouchTest(String name) { super(name); }
+
+ private static Geometry readCurve(String wkt) throws Exception {
+ return new CurveWKTReader(new CurveGeometryFactory()).read(wkt);
+ }
+
+ public void testMatrixIsFF2F01212() {
+ assertEquals("FF2F01212", IM_EXT);
+ assertTrue("SFS / RelateOp Touch on T-ext",
+ new IntersectionMatrix(IM_EXT).isTouches(2, 2));
+ }
+
+ public void testR2KissIsExactEquality() throws Exception {
+ Geometry a = readCurve(CIRCLE_5);
+ Geometry b = readCurve(CIRCLE_3_4_5);
+ CircularArcDensifier.Circle da = CurveExact.circularDisc(a);
+ CircularArcDensifier.Circle db = CurveExact.circularDisc(b);
+ assertNotNull(da);
+ assertNotNull(db);
+ double dx = da.cx - db.cx;
+ double dy = da.cy - db.cy;
+ double d2 = dx * dx + dy * dy;
+ double sum2 = (da.r + db.r) * (da.r + db.r);
+ assertEquals("3-4-5: d² = 8²+6² = 100", 100.0, d2, 0.0);
+ assertEquals("(r1+r2)² = 10²", 100.0, sum2, 0.0);
+ assertEquals("T-ext is d² == (r1+r2)², no hypot",
+ Double.doubleToRawLongBits(d2), Double.doubleToRawLongBits(sum2));
+ }
+
+ public void testPublicRelateAndTouches() throws Exception {
+ Geometry a = readCurve(CIRCLE_5);
+ Geometry b = readCurve(CIRCLE_3_4_5);
+ assertEquals(IM_EXT, CurveExact.relate(a, b).toString());
+ assertEquals(IM_EXT, CurveExact.relate(b, a).toString());
+ assertEquals(IM_EXT, a.relate(b).toString());
+ assertEquals(IM_EXT, b.relate(a).toString());
+ assertTrue("Geometry.touches via RelateOp isTouches", a.touches(b));
+ assertTrue(b.touches(a));
+ assertTrue(a.relate(b).isTouches(a.getDimension(), b.getDimension()));
+ assertTrue(a.relate(b, IM_EXT));
+ assertTrue(a.intersects(b));
+ assertFalse("no shared flesh", a.overlaps(b));
+ assertFalse(a.contains(b));
+ assertFalse(a.covers(b));
+ assertFalse(a.crosses(b));
+ assertFalse(a.equalsTopo(b));
+ }
+
+ public void testControlPolygonRelateOpIsTheLie() throws Exception {
+ Geometry a = readCurve(CIRCLE_5);
+ Geometry b = readCurve(CIRCLE_3_4_5);
+ Geometry diamondA = read(CONTROL_5);
+ Geometry diamondB = read(CONTROL_345);
+ String lie = RelateOp.relate(diamondA, diamondB).toString();
+ assertFalse("control diamonds miss the (4, 3) kiss",
+ IM_EXT.equals(lie));
+ assertFalse("RelateOp on controls is not Touch",
+ diamondA.touches(diamondB));
+ assertEquals("laser is not the control-polygon matrix",
+ IM_EXT, a.relate(b).toString());
+ assertTrue(a.touches(b));
+ }
+
+ public void testSingleMemberMultiSurface() throws Exception {
+ Geometry ma = readCurve(MULTI_5);
+ Geometry mb = readCurve(MULTI_345);
+ Geometry b = readCurve(CIRCLE_3_4_5);
+ assertEquals(IM_EXT, CurveExact.relate(ma, b).toString());
+ assertEquals(IM_EXT, ma.relate(b).toString());
+ assertEquals(IM_EXT, CurveExact.relate(ma, mb).toString());
+ assertEquals(IM_EXT, ma.relate(mb).toString());
+ assertTrue(ma.touches(b));
+ assertTrue(ma.touches(mb));
+ }
+
+ public void testNoOverlayNGCurveTouch() {
+ Field[] fields = OverlayNGCurve.class.getDeclaredFields();
+ for (int i = 0; i < fields.length; i++) {
+ assertFalse("DE-9IM Touch only — no OverlayNGCurve.TOUCH",
+ "TOUCH".equals(fields[i].getName()));
+ }
+ }
+}
diff --git a/modules/curve/src/test/java/org/locationtech/jts/operation/overlayng/curve/OverlayNGCurvePerfGateTest.java b/modules/curve/src/test/java/org/locationtech/jts/operation/overlayng/curve/OverlayNGCurvePerfGateTest.java
index 19060ec160..d4ab621bc2 100644
--- a/modules/curve/src/test/java/org/locationtech/jts/operation/overlayng/curve/OverlayNGCurvePerfGateTest.java
+++ b/modules/curve/src/test/java/org/locationtech/jts/operation/overlayng/curve/OverlayNGCurvePerfGateTest.java
@@ -73,6 +73,9 @@ public class OverlayNGCurvePerfGateTest extends GeometryTestCase {
"CURVEPOLYGON (CIRCULARSTRING (2 0, 7 5, 12 0, 7 -5, 2 0))";
private static final String CIRCLE_EXT_TAN =
"CURVEPOLYGON (CIRCULARSTRING (5 0, 10 5, 15 0, 10 -5, 5 0))";
+ /** R.1 T-ext kiss at (4, 3), not a control vertex. */
+ private static final String CIRCLE_3_4_5 =
+ "CURVEPOLYGON (CIRCULARSTRING (13 6, 8 11, 3 6, 8 1, 13 6))";
private static final String EMPTY = "CURVEPOLYGON EMPTY";
private static final String POINT_INSIDE = "POINT (3 3)";
private static final String POINT_FAR = "POINT (100 100)";
@@ -762,6 +765,17 @@ public void testRelateExtTangentDiscsNotSlowerThanChord() throws Exception {
() -> CurveOps.linearise(a).relate(CurveOps.linearise(tan)));
}
+ public void testRelateR1TouchKissNotSlowerThanChord() throws Exception {
+ Geometry a = readCurve(CIRCLE_5);
+ Geometry kiss = readCurve(CIRCLE_3_4_5);
+ assertLaserNotSlower("R.1 T-ext 3-4-5 relate",
+ () -> a.relate(kiss),
+ () -> CurveOps.linearise(a).relate(CurveOps.linearise(kiss)));
+ assertLaserNotSlower("R.1 T-ext 3-4-5 touches",
+ () -> a.touches(kiss),
+ () -> CurveOps.linearise(a).touches(CurveOps.linearise(kiss)));
+ }
+
public void testRelateCrossingDiscsReverseNotSlowerThanChord() throws Exception {
Geometry a = readCurve(CIRCLE_5);
Geometry cross = readCurve(CIRCLE_CROSSING);