Integrate Refactor solver sources and dual MSVC CMake builds

src/fesa/math/vector3_operations.h

@@ -0,0 +1,57 @@
+#ifndef FESA_MATH_VECTOR3_OPERATIONS_H_
+#define FESA_MATH_VECTOR3_OPERATIONS_H_
+
+#include <array>
+#include <cstddef>
+
+#include "fesa/math/matrix.h"
+#include "fesa/math/vector3.h"
+
+namespace fesa::math_internal {
+
+/// @brief Reduces four source-ordered geometric vectors with scalar-left products.
+inline Vector3 WeightedSum(const std::array<double, 4>& weights,
+                           const std::array<Vector3, 4>& values) {
+  Vector3 result{};
+  for (std::size_t node = 0U; node < 4U; ++node) {
+    result = result + weights[node] * values[node];
+  }
+  return result;
+}
+
+/// @brief Cancels the first-node anchor before the same ordered reduction.
+inline Vector3 DerivativeSum(const std::array<double, 4>& derivatives,
+                             const std::array<Vector3, 4>& values) {
+  std::array<Vector3, 4> relative{};
+  for (std::size_t node = 0U; node < 4U; ++node) {
+    relative[node] = values[node] - values[0U];
+  }
+  return WeightedSum(derivatives, relative);
+}
+
+/// @brief Forms the positive cross-product matrix in fixed Cartesian coordinates.
+inline Matrix Skew(const Vector3& vector) {
+  Matrix result{3U, 3U};
+  result(0U, 1U) = -vector.Z();
+  result(0U, 2U) = vector.Y();
+  result(1U, 0U) = vector.Z();
+  result(1U, 2U) = -vector.X();
+  result(2U, 0U) = -vector.Y();
+  result(2U, 1U) = vector.X();
+  return result;
+}
+
+/// @brief Applies a fixed 3-by-3 geometric frame with the original component graph.
+inline Vector3 Multiply(const Matrix& matrix, const Vector3& vector) {
+  return Vector3{
+      matrix(0U, 0U) * vector.X() + matrix(0U, 1U) * vector.Y() +
+          matrix(0U, 2U) * vector.Z(),
+      matrix(1U, 0U) * vector.X() + matrix(1U, 1U) * vector.Y() +
+          matrix(1U, 2U) * vector.Z(),
+      matrix(2U, 0U) * vector.X() + matrix(2U, 1U) * vector.Y() +
+          matrix(2U, 2U) * vector.Z()};
+}
+
+}  // namespace fesa::math_internal
+
+#endif  // FESA_MATH_VECTOR3_OPERATIONS_H_