basic qua ext rotation functions

headers/vmath.hpp/vmath_ext.hpp

@@ -662,3 +662,57 @@ namespace vmath_hpp
         return dot(v, normal) / length2(normal) * normal;
     }
 }
+
+//
+// Quaternion Transform
+//
+
+namespace vmath_hpp
+{
+    // qrotate
+
+    template < typename T >
+    [[nodiscard]] qua<T> qrotate(T angle, const vec<T, 3>& axis) {
+        const auto [s, c] = sincos(angle * T(0.5));
+        const auto [x, y, z] = normalize(axis);
+        return {vec{x,y,z} * s, c};
+    }
+
+    template < typename T >
+    [[nodiscard]] qua<T> qrotate(const qua<T>& q, T angle, const vec<T, 3>& axis) {
+        return q * qrotate(angle, axis);
+    }
+
+    template < typename T >
+    [[nodiscard]] qua<T> qrotate_x(T angle) {
+        const auto [s, c] = sincos(angle * T(0.5));
+        return {s, T(0), T(0), c};
+    }
+
+    template < typename T >
+    [[nodiscard]] qua<T> qrotate_x(const qua<T>& q, T angle) {
+        return qrotate(q, angle, unit3_x<T>);
+    }
+
+    template < typename T >
+    [[nodiscard]] qua<T> qrotate_y(T angle) {
+        const auto [s, c] = sincos(angle * T(0.5));
+        return {T(0), s, T(0), c};
+    }
+
+    template < typename T >
+    [[nodiscard]] qua<T> qrotate_y(const qua<T>& q, T angle) {
+        return qrotate(q, angle, unit3_y<T>);
+    }
+
+    template < typename T >
+    [[nodiscard]] qua<T> qrotate_z(T angle) {
+        const auto [s, c] = sincos(angle * T(0.5));
+        return {T(0), T(0), s, c};
+    }
+
+    template < typename T >
+    [[nodiscard]] qua<T> qrotate_z(const qua<T>& q, T angle) {
+        return qrotate(q, angle, unit3_z<T>);
+    }
+}

headers/vmath.hpp/vmath_qua_fun.hpp

@@ -226,3 +226,24 @@ namespace vmath_hpp
         return not_equal_to(vec{xs}, vec{ys});
     }
 }
+
+//
+// Quaternion Functions
+//
+
+namespace vmath_hpp
+{
+    // conjugate
+
+    template < typename T >
+    [[nodiscard]] constexpr qua<T> conjugate(const qua<T>& q) {
+        return {-q.v, q.s};
+    }
+
+    // inverse
+
+    template < typename T >
+    [[nodiscard]] constexpr qua<T> inverse(const qua<T>& q) {
+        return conjugate(q) * rcp(dot(q, q));
+    }
+}

untests/vmath_ext_tests.cpp

@@ -293,4 +293,28 @@ TEST_CASE("vmath/ext") {
         REQUIRE(project(float2(2.f, 2.f), float2(0.f, 1.f)) == uapprox2(0.f, 2.f));
         REQUIRE(project(float3(2.f, 2.f, 2.f), float3(0.f, 0.f, 1.f)) == uapprox3(0.f, 0.f, 2.f));
     }
+
+    SUBCASE("quaternion qrotate") {
+        constexpr float pi = radians(180.f);
+        constexpr float pi_2 = radians(90.f);
+        constexpr float pi_4 = radians(45.f);
+
+        REQUIRE(float3(0.f,1.f,0.f) * qrotate_x(pi_2) == uapprox3(0.f,0.f,1.f));
+        REQUIRE(float3(0.f,0.f,1.f) * qrotate_y(pi_2) == uapprox3(1.f,0.f,0.f));
+        REQUIRE(float3(1.f,0.f,0.f) * qrotate_z(pi_2) == uapprox3(0.f,1.f,0.f));
+
+        REQUIRE(float3(0.f,1.f,0.f) * qrotate_x(qrotate_x(pi_4),pi_4) == uapprox3(0.f,0.f,1.f));
+        REQUIRE(float3(0.f,0.f,1.f) * qrotate_y(qrotate_y(pi_4),pi_4) == uapprox3(1.f,0.f,0.f));
+        REQUIRE(float3(1.f,0.f,0.f) * qrotate_z(qrotate_z(pi_4),pi_4) == uapprox3(0.f,1.f,0.f));
+
+        REQUIRE(float3(2.f,3.f,4.f) * qrotate(pi,{0.f,0.f,1.f}) == uapprox3(-2.f,-3.f,4.f));
+        REQUIRE(float3(2.f,3.f,4.f) * qrotate(pi,float3{0.f,0.f,1.f}) == uapprox3(-2.f,-3.f,4.f));
+
+        REQUIRE(float3(2.f,3.f,4.f) * qrotate(qrotate(pi_2,{0.f,0.f,1.f}),pi_2,{0.f,0.f,1.f}) == uapprox3(-2.f,-3.f,4.f));
+        REQUIRE(float3(2.f,3.f,4.f) * qrotate(qrotate(pi_2,float3{0.f,0.f,1.f}),pi_2,float3{0.f,0.f,1.f}) == uapprox3(-2.f,-3.f,4.f));
+
+        REQUIRE(qrotate_x(12.3f) == qrotate(12.3f, unit3_x<float> * 2.f));
+        REQUIRE(qrotate_y(12.3f) == qrotate(12.3f, unit3_y<float> * 2.f));
+        REQUIRE(qrotate_z(12.3f) == qrotate(12.3f, unit3_z<float> * 2.f));
+    }
 }

untests/vmath_qua_fun_tests.cpp

@@ -91,4 +91,13 @@ TEST_CASE("vmath/qua_fun") {
         STATIC_REQUIRE(equal_to(qua(1,1,1,1), qua(0,1,2,3)) == bool4(false, true, false, false));
         STATIC_REQUIRE(not_equal_to(qua(1,1,1,1), qua(0,1,2,3)) == bool4(true, false, true, true));
     }
+
+    SUBCASE("Quaternion Functions") {
+        STATIC_REQUIRE(conjugate(qua(1,2,3,4)) == qua(-1,-2,-3,4));
+        STATIC_REQUIRE(inverse(qua(0.f,0.f,0.7071067812f,0.7071067812f)).v == uapprox3(0.f,0.f,-0.7071067812f));
+        STATIC_REQUIRE(inverse(qua(0.f,0.f,0.7071067812f,0.7071067812f)).s == uapprox(0.7071067812f));
+
+        REQUIRE(inverse(qrotate_x(10.f)) == qrotate_x(-10.f));
+        REQUIRE(all(approx(inverse(qrotate_x(10.f) * qrotate_y(15.f)), qrotate_y(-15.f) * qrotate_x(-10.f))));
+    }
 }