Implement Matrix3x3::DeterminantSymmetric

include/J3ML/LinearAlgebra/Matrix3x3.h

@@ -7,8 +7,6 @@
 
 namespace J3ML::LinearAlgebra {
 
-
-
     /** Sets the top-left 3x3 area of the matrix to the rotation matrix about the X-axis. Elements
         outside the top-left 3x3 area are ignored. This matrix rotates counterclockwise if multiplied
         in the order M*v, and clockwise if rotated in the order v*M.
@@ -110,9 +108,7 @@ namespace J3ML::LinearAlgebra {
      *
      *  @note The member functions in this class use the convention that transforms are applied to
      *  vectors in the form M * v. This means that "Matrix3x3 M, M1, M2; M = M1 * M2;" gives a transformation M
-     *  that applies M2 first, followed by M1 second
-     */
-
+     *  that applies M2 first, followed by M1 second. */
     class Matrix3x3 {
     public: /// Constant Values
         enum { Rows = 3 };
@@ -409,6 +405,11 @@ namespace J3ML::LinearAlgebra {
         Matrix3x3 ScaleBy(const Vector3& rhs);
         Vector3 GetScale() const;
 
+        /// Scales the given row by a scalar value.
+        void ScaleRow(int row, float scalar);
+        /// Scales the given column by a scalar value.
+        void ScaleCol(int col, float scalar);
+
         Vector3 operator[](int row) const;
 
         /// Transforms the given vector by this matrix (in the order M * v).

src/J3ML/LinearAlgebra/Matrix3x3.cpp

@@ -615,6 +615,30 @@ namespace J3ML::LinearAlgebra {
 
     Vector3 Matrix3x3::Row(int index) const { return GetRow(index);}
 
+    float Matrix3x3::DeterminantSymmetric() const {
+        assert(IsSymmetric());
+
+        const float a = this->elems[0][0];
+        const float b = this->elems[0][1];
+        const float c = this->elems[0][2];
+        const float d = this->elems[1][0];
+        const float e = this->elems[1][1];
+        const float f = this->elems[1][2];
+
+        // If the matrix is symmetric, it is of the following form:
+        // a b c
+        // b d e
+        // c e f
+
+        // A direct cofactor expansion gives
+        // det = a * (df - ee) -b * (bf - ce) + c * (be-dc)
+        //     = adf - aee - bbf + bce + bce - ccd
+        //     = adf - aee - bbf - ccd + 2*bce
+        //     = a(df-ee) + b(2*ce - bf) - ccd
+
+        return a * (d*f - e*e) + b * (2.f * c * e - b * f) - c*c*d;
+    }
+
 
 }