Refactor geom::bezier: extract a free-function de Casteljau's algorithm & support changing control points

libs/geom/include/psemek/geom/bezier.hpp

@@ -8,9 +8,24 @@
 namespace psemek::geom
 {
 
+	// In-place de Casteljau's algorithm
+	template <typename Iterator, typename T>
+	auto de_casteljau(Iterator begin, Iterator end, T const & t)
+	{
+		while (std::next(begin) != end)
+		{
+			for (auto it = begin, jt = std::next(begin); jt != end; it = jt++)
+				*it = lerp(*it, *jt, t);
+			--end;
+		}
+		return *begin;
+	}
+
 	template <typename Point>
 	struct bezier
 	{
+		bezier() = default;
+
 		bezier(std::vector<Point> points)
 			: points_(std::move(points))
 		{
@@ -19,23 +34,34 @@ namespace psemek::geom
 			temp_.resize(points_.size());
 		}
 
+		std::vector<Point> & points()
+		{
+			return points_;
+		}
+
 		template <typename T>
 		auto operator()(T const & t) const
 		{
-			// In-place de Casteljau's algorithm
 			temp_ = points_;
+			return de_casteljau(temp_.begin(), temp_.end(), t);
+		}
 
+		template <typename T>
+		auto tangent(T const & t) const
+		{
+			// In-place de Casteljau's algorithm for derivative
+			tangent_temp_.resize(points_.size() - 1);
 			for (std::size_t k = 0; k + 1 < points_.size(); ++k)
-			{
+				tangent_temp_[k] = points_[k + 1] - points_[k];
-				for (std::size_t i = 0; i + k + 1 < points_.size(); ++i)
+			return static_cast<T>(points_.size()) * de_casteljau(tangent_temp_.begin(), tangent_temp_.end(), t);
-					temp_[i] = lerp(temp_[i], temp_[i + 1], t);
-			}
-			return temp_.front();
 		}
 
 	private:
-		std::vector<Point> const points_;
+		using vector_type = decltype(Point{} - Point{});
+
+		std::vector<Point> points_;
 		std::vector<Point> mutable temp_;
+		std::vector<vector_type> mutable tangent_temp_;
 	};
 
 }