Math: make Bezier::subdivide() return a pair and test it.

src/Magnum/Math/Bezier.h

@@ -96,21 +96,19 @@ template<UnsignedInt order, UnsignedInt dimensions, class T> class Bezier {
         template<class U> constexpr explicit Bezier(const Bezier<order, dimensions, U>& other) noexcept: Bezier{typename Implementation::GenerateSequence<order + 1>::Type(), other} {}
 
         /**
-         * @brief Subdivide the curve
-         * @param t The interpolation factor
+         * @brief Subdivide the curve at given position
          *
-         * Divides the curve into two Bézier curves of same order having their
-         * own control points. Uses the [De Casteljau's algorithm](https://en.wikipedia.org/wiki/De_Casteljau%27s_algorithm).
+         * Returns two Bézier curves following the original curve, split at
+         * given interpolation factor. Uses the [De Casteljau's algorithm](https://en.wikipedia.org/wiki/De_Casteljau%27s_algorithm).
+         * @see @ref value()
          */
-        std::array<Bezier<order, dimensions, T>, 2> subdivide(Float t) const {
+        std::pair<Bezier<order, dimensions, T>, Bezier<order, dimensions, T>> subdivide(Float t) const {
             const auto iPoints = calculateIntermediatePoints(t);
             Bezier<order, dimensions, T> left, right;
-            for(std::size_t i = 0; i <= order; ++i) {
+            for(std::size_t i = 0; i <= order; ++i)
                 left[i] = iPoints[0][i];
-            }
-            for(std::size_t i = 0, j = order; i <= order; --j, ++i) {
+            for(std::size_t i = 0, j = order; i <= order; --j, ++i)
                 right[i] = iPoints[i][j];
-            }
             return {left, right};
         }
 

src/Magnum/Math/Test/BezierTest.cpp

@@ -57,6 +57,9 @@ struct BezierTest : Corrade::TestSuite::Tester {
     void valueLinear();
     void valueQuadratic();
     void valueCubic();
+    void subdivideLinear();
+    void subdivideQuadratic();
+    void subdivideCubic();
 
     void debug();
     void configuration();
@@ -76,6 +79,9 @@ BezierTest::BezierTest() {
               &BezierTest::valueLinear,
               &BezierTest::valueQuadratic,
               &BezierTest::valueCubic,
+              &BezierTest::subdivideLinear,
+              &BezierTest::subdivideQuadratic,
+              &BezierTest::subdivideCubic,
 
               &BezierTest::debug,
               &BezierTest::configuration});
@@ -172,6 +178,51 @@ void BezierTest::valueCubic() {
     CORRADE_VERIFY(bezier.value(0.2f) != Math::lerp(bezier[0], bezier[3], 0.2f));
 }
 
+void BezierTest::subdivideLinear() {
+    LinearBezier2D bezier{Vector2{0.0f, 0.0f}, Vector2{20.0f, 4.0f}};
+
+    LinearBezier2D left, right;
+    std::tie(left, right) = bezier.subdivide(0.25f);
+
+    CORRADE_COMPARE(left[0], bezier[0]);
+    CORRADE_COMPARE(left[1], right[0]);
+    CORRADE_COMPARE(right[1], bezier[1]);
+    CORRADE_COMPARE(left.value(0.8f), bezier.value(0.2f));
+    CORRADE_COMPARE(right.value(0.33333f), bezier.value(0.5f));
+    CORRADE_COMPARE(left, (LinearBezier2D{Vector2{0.0f, 0.0f}, Vector2{5.0f, 1.0f}}));
+    CORRADE_COMPARE(right, (LinearBezier2D{Vector2{5.0f, 1.0f}, Vector2{20.0f, 4.0f}}));
+}
+
+void BezierTest::subdivideQuadratic() {
+    QuadraticBezier2D bezier{Vector2{0.0f, 0.0f}, Vector2{10.0f, 15.0f}, Vector2{20.0f, 4.0f}};
+
+    QuadraticBezier2D left, right;
+    std::tie(left, right) = bezier.subdivide(0.25f);
+
+    CORRADE_COMPARE(left[0], bezier[0]);
+    CORRADE_COMPARE(left[2], right[0]);
+    CORRADE_COMPARE(right[2], bezier[2]);
+    CORRADE_COMPARE(left.value(0.8f), bezier.value(0.2f));
+    CORRADE_COMPARE(right.value(0.33333f), bezier.value(0.5f));
+    CORRADE_COMPARE(left, (QuadraticBezier2D{Vector2{0.0f, 0.0f}, Vector2{2.5f, 3.75f}, Vector2{5.0f, 5.875f}}));
+    CORRADE_COMPARE(right, (QuadraticBezier2D{Vector2{5.0f, 5.875f}, Vector2{12.5f, 12.25f}, Vector2{20.0f, 4.0f}}));
+}
+
+void BezierTest::subdivideCubic() {
+    CubicBezier2D bezier{Vector2{0.0f, 0.0f}, Vector2{10.0f, 15.0f}, Vector2{20.0f, 4.0f}, Vector2{5.0f, -20.0f}};
+
+    CubicBezier2D left, right;
+    std::tie(left, right) = bezier.subdivide(0.25f);
+
+    CORRADE_COMPARE(left[0], bezier[0]);
+    CORRADE_COMPARE(left[3], right[0]);
+    CORRADE_COMPARE(right[3], bezier[3]);
+    CORRADE_COMPARE(left.value(0.8f), bezier.value(0.2f));
+    CORRADE_COMPARE(right.value(0.33333f), bezier.value(0.5f));
+    CORRADE_COMPARE(left, (CubicBezier2D{Vector2{0.0f, 0.0f}, Vector2{2.5f, 3.75f}, Vector2{5.0f, 5.875f}, Vector2{7.10938f, 6.57812f}}));
+    CORRADE_COMPARE(right, (CubicBezier2D{Vector2{7.10938f, 6.57812f}, Vector2{13.4375f, 8.6875f}, Vector2{16.25f, -2.0f}, Vector2{5.0f, -20.0f}}));
+}
+
 void BezierTest::debug() {
     std::ostringstream out;
     Debug(&out) << CubicBezier2D{Vector2{0.0f, 1.0f}, Vector2{1.5f, -0.3f}, Vector2{2.1f, 0.5f}, Vector2{0.0f, 2.0f}};