/// <summary> /// Inverts the largest nonsingular submatrix in the matrix, excluding 2x2's that involve M13 or M31, and excluding 1x1's that include nondiagonal elements. /// </summary> /// <param name="matrix">FixMatrix to be inverted.</param> /// <param name="result">Inverted matrix.</param> public static void AdaptiveInvert(fix3x3 matrix, out fix3x3 result) { // Perform full Gauss-invert and return if successful if (Invert(matrix, out result)) { return; } int submatrix; fix determinantInverse = F64.C1 / matrix.AdaptiveDeterminant(out submatrix); fix m11, m12, m13, m21, m22, m23, m31, m32, m33; switch (submatrix) { case 1: //Upper left matrix, m11, m12, m21, m22. m11 = matrix.M22 * determinantInverse; m12 = -matrix.M12 * determinantInverse; m13 = F64.C0; m21 = -matrix.M21 * determinantInverse; m22 = matrix.M11 * determinantInverse; m23 = F64.C0; m31 = F64.C0; m32 = F64.C0; m33 = F64.C0; break; case 2: //Lower right matrix, m22, m23, m32, m33. m11 = F64.C0; m12 = F64.C0; m13 = F64.C0; m21 = F64.C0; m22 = matrix.M33 * determinantInverse; m23 = -matrix.M23 * determinantInverse; m31 = F64.C0; m32 = -matrix.M32 * determinantInverse; m33 = matrix.M22 * determinantInverse; break; case 3: //Corners, m11, m31, m13, m33. m11 = matrix.M33 * determinantInverse; m12 = F64.C0; m13 = -matrix.M13 * determinantInverse; m21 = F64.C0; m22 = F64.C0; m23 = F64.C0; m31 = -matrix.M31 * determinantInverse; m32 = F64.C0; m33 = matrix.M11 * determinantInverse; break; case 4: //M11 m11 = F64.C1 / matrix.M11; m12 = F64.C0; m13 = F64.C0; m21 = F64.C0; m22 = F64.C0; m23 = F64.C0; m31 = F64.C0; m32 = F64.C0; m33 = F64.C0; break; case 5: //M22 m11 = F64.C0; m12 = F64.C0; m13 = F64.C0; m21 = F64.C0; m22 = F64.C1 / matrix.M22; m23 = F64.C0; m31 = F64.C0; m32 = F64.C0; m33 = F64.C0; break; case 6: //M33 m11 = F64.C0; m12 = F64.C0; m13 = F64.C0; m21 = F64.C0; m22 = F64.C0; m23 = F64.C0; m31 = F64.C0; m32 = F64.C0; m33 = F64.C1 / matrix.M33; break; default: //Completely singular. m11 = F64.C0; m12 = F64.C0; m13 = F64.C0; m21 = F64.C0; m22 = F64.C0; m23 = F64.C0; m31 = F64.C0; m32 = F64.C0; m33 = F64.C0; break; } result.M11 = m11; result.M12 = m12; result.M13 = m13; result.M21 = m21; result.M22 = m22; result.M23 = m23; result.M31 = m31; result.M32 = m32; result.M33 = m33; }