From Nonlinear Optimization to Convex Optimization through Firefly Algorithm and Indirect Approach with Applications to CAD/CAM

Algorithm 1

De Boor's knot vector refinement algorithm.

INPUT:   𝜏={𝜏₁,…,𝜏_𝜌}   /* Vector of data parameters from Step 2*/

      𝜐         /* Number of internal knots */

OUTPUT:   𝜇={𝜇₁,…,𝜇_𝜐}    /* Vector of internal knots */

ALGORITHM: {Initialization}

       𝜇←{}

       Δ←𝜌+1𝜐+1

      {Main loop}

       for  𝑗=1 to 𝜐  do

          𝑖←𝑖𝑛𝑡(𝑗Δ)   /*  𝑖𝑛𝑡(𝑘): returns the largest integer number ≤𝑘  */

          𝜎←𝑗Δ−𝑖

          𝜇_𝑗←(1−𝜎)𝜏_𝑖−1+𝜎𝜏_𝑖

          𝜇←𝐴𝑝𝑝𝑒𝑛𝑑(𝜇_𝑗)

       end for