diff --git a/interface/src/avatar/MyAvatar.cpp b/interface/src/avatar/MyAvatar.cpp
index a357cd879d..614f7bd9fe 100644
--- a/interface/src/avatar/MyAvatar.cpp
+++ b/interface/src/avatar/MyAvatar.cpp
@@ -916,7 +916,8 @@ void MyAvatar::updateLookAtTargetAvatar() {
avatar->setIsLookAtTarget(false);
if (!avatar->isMyAvatar() && avatar->isInitialized() &&
(distanceTo < GREATEST_LOOKING_AT_DISTANCE * getUniformScale())) {
- float angleTo = glm::angle(lookForward, glm::normalize(avatar->getHead()->getEyePosition() - getHead()->getEyePosition()));
+ float radius = glm::length(avatar->getHead()->getEyePosition() - avatar->getHead()->getRightEyePosition());
+ float angleTo = coneSphereAngle(getHead()->getEyePosition(), lookForward, avatar->getHead()->getEyePosition(), radius);
if (angleTo < (smallestAngleTo * (isCurrentTarget ? KEEP_LOOKING_AT_CURRENT_ANGLE_FACTOR : 1.0f))) {
_lookAtTargetAvatar = avatarPointer;
_targetAvatarPosition = avatarPointer->getPosition();
diff --git a/libraries/shared/src/GeometryUtil.cpp b/libraries/shared/src/GeometryUtil.cpp
index 96c4d3bdea..92fe138021 100644
--- a/libraries/shared/src/GeometryUtil.cpp
+++ b/libraries/shared/src/GeometryUtil.cpp
@@ -564,3 +564,17 @@ void swingTwistDecomposition(const glm::quat& rotation,
// rotation = swing * twist --> swing = rotation * invTwist
swing = rotation * glm::inverse(twist);
}
+
+// calculate the minimum angle between a point and a sphere.
+float coneSphereAngle(const glm::vec3& coneCenter, const glm::vec3& coneDirection, const glm::vec3& sphereCenter, float sphereRadius) {
+ glm::vec3 d = sphereCenter - coneCenter;
+ float dLen = glm::length(d);
+
+ // theta is the angle between the coneDirection normal and the center of the sphere.
+ float theta = acosf(glm::dot(d, coneDirection) / dLen);
+
+ // phi is the deflection angle from the center of the sphere to a point tangent to the sphere.
+ float phi = atanf(sphereRadius / dLen);
+
+ return glm::max(0.0f, theta - phi);
+}
diff --git a/libraries/shared/src/GeometryUtil.h b/libraries/shared/src/GeometryUtil.h
index 7224aaacff..a66b16b0fd 100644
--- a/libraries/shared/src/GeometryUtil.h
+++ b/libraries/shared/src/GeometryUtil.h
@@ -110,6 +110,8 @@ bool doLineSegmentsIntersect(glm::vec2 r1p1, glm::vec2 r1p2, glm::vec2 r2p1, glm
bool isOnSegment(float xi, float yi, float xj, float yj, float xk, float yk);
int computeDirection(float xi, float yi, float xj, float yj, float xk, float yk);
+// calculate the angle between a point on a sphere that is closest to the cone.
+float coneSphereAngle(const glm::vec3& coneCenter, const glm::vec3& coneDirection, const glm::vec3& sphereCenter, float sphereRadius);
typedef glm::vec2 LineSegment2[2];
diff --git a/tests/shared/src/GeometryUtilTests.cpp b/tests/shared/src/GeometryUtilTests.cpp
index 289ac9a0a9..79472a1128 100644
--- a/tests/shared/src/GeometryUtilTests.cpp
+++ b/tests/shared/src/GeometryUtilTests.cpp
@@ -14,6 +14,7 @@
#include "GeometryUtilTests.h"
#include <GeometryUtil.h>
+#include <GLMHelpers.h>
#include <NumericalConstants.h>
#include <StreamUtils.h>
@@ -22,6 +23,63 @@
QTEST_MAIN(GeometryUtilTests)
+static void testSphereVsCone(const glm::vec3 coneNormal, const glm::vec3 coneBiNormal, float coneAngle, float sphereRadius, float sphereDistance) {
+
+ glm::vec3 u, v, w;
+ generateBasisVectors(coneNormal, coneBiNormal, u, v, w);
+ glm::vec3 coneEdge = u * cosf(coneAngle) + v * sinf(coneAngle);
+ glm::vec3 coneCenter = glm::vec3(0.0f, 0.0f, 0.0f);
+ glm::vec3 sphereCenter = coneCenter + coneEdge * sphereDistance;
+ float result = coneSphereAngle(coneCenter, u, sphereCenter, sphereRadius);
+ QCOMPARE(isnan(result), false);
+ QCOMPARE(result < coneAngle, true);
+
+ // push sphere outward from edge so it is tangent to the cone.
+ glm::vec3 sphereOffset = glm::angleAxis(PI / 2.0f, w) * coneEdge;
+ sphereCenter += sphereOffset * sphereRadius;
+ result = coneSphereAngle(coneCenter, u, sphereCenter, sphereRadius);
+ QCOMPARE(isnan(result), false);
+ QCOMPARE_WITH_ABS_ERROR(result, coneAngle, 0.001f);
+
+ // push sphere outward from edge a bit further, so it is outside of the cone.
+ sphereCenter += 0.1f * sphereOffset;
+ result = coneSphereAngle(coneCenter, u, sphereCenter, sphereRadius);
+ QCOMPARE(isnan(result), false);
+ QCOMPARE(result > coneAngle, true);
+}
+
+void GeometryUtilTests::testConeSphereAngle() {
+
+ // start with a 45 degree cone.
+ testSphereVsCone(glm::vec3(1.0f, 0.0f, 0.0f), glm::vec3(0.0f, 1.0f, 0.0f), PI / 4.0f, 1.0f, 10.0f);
+
+ // test 30 degree cone.
+ testSphereVsCone(glm::vec3(1.0f, 0.0f, 0.0f), glm::vec3(0.0f, 1.0f, 0.0f), PI / 6.0f, 1.0f, 10.0f);
+
+ // test 60 degree cone.
+ testSphereVsCone(glm::vec3(1.0f, 0.0f, 0.0f), glm::vec3(0.0f, 1.0f, 0.0f), PI / 3.0f, 1.0f, 10.0f);
+
+ // test 120 degree cone.
+ testSphereVsCone(glm::vec3(1.0f, 0.0f, 0.0f), glm::vec3(0.0f, 1.0f, 0.0f), 2 * PI / 3.0f, 1.0f, 10.0f);
+
+ // test skinny cone.
+ testSphereVsCone(glm::vec3(1.0f, 0.0f, 0.0f), glm::vec3(0.0f, 1.0f, 0.0f), 0.0001f, 1.0f, 10.0f);
+
+ // start again with a 45 off axis cone.
+ testSphereVsCone(glm::vec3(1.0f, 1.0f, 1.0f), glm::vec3(0.0f, 1.0f, 0.0f), PI / 4.0f, 1.0f, 10.0f);
+
+ // test 30 degree off axis cone
+ testSphereVsCone(glm::vec3(1.0f, 1.0f, 1.0f), glm::vec3(0.0f, 1.0f, 0.0f), PI / 6.0f, 1.0f, 10.0f);
+
+ // test 60 degree cone off axis cone
+ testSphereVsCone(glm::vec3(1.0f, 1.0f, 1.0f), glm::vec3(0.0f, 1.0f, 0.0f), PI / 3.0f, 1.0f, 10.0f);
+
+ // test 120 degree off axis cone.
+ testSphereVsCone(glm::vec3(1.0f, 1.0f, 1.0f), glm::vec3(0.0f, 1.0f, 0.0f), 2 * PI / 3.0f, 1.0f, 10.0f);
+
+ // test skinny off-axis cone.
+ testSphereVsCone(glm::vec3(1.0f, 1.0f, 1.0f), glm::vec3(0.0f, 1.0f, 0.0f), 0.0001f, 1.0f, 10.0f);
+}
void GeometryUtilTests::testLocalRayRectangleIntersection() {
glm::vec3 xAxis(1.0f, 0.0f, 0.0f);
diff --git a/tests/shared/src/GeometryUtilTests.h b/tests/shared/src/GeometryUtilTests.h
index b6340cd8cf..3b5ad3da51 100644
--- a/tests/shared/src/GeometryUtilTests.h
+++ b/tests/shared/src/GeometryUtilTests.h
@@ -18,6 +18,7 @@
class GeometryUtilTests : public QObject {
Q_OBJECT
private slots:
+ void testConeSphereAngle();
void testLocalRayRectangleIntersection();
void testWorldRayRectangleIntersection();
void testTwistSwingDecomposition();