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ALGORITMI CURVE B-SPLINE - Coggle Diagram

- - - - $$ \sum_{i=0}^n d_i [w_{i,k}(t)N_{i,k-1}(t) + [1-w_{i+1,k}(t)]N_{i+1,k-1}(t)]$$
        
        srotolo e riallotolo
        
        $$ x(t) = \sum_{i=1}^n d_i^{(1)}(t)N_{i,k-1}(t) $$
        
        $$ d_i^{(1)}(t)= (1-w_{i,k}(t))d_{i-1}^0(t)+w_{i,k}(t)d_i^0(t) $$
        
        il primo ed ultimo elemento della sommatoria avrebbero valore solo sui nodi ausiliari
        
        ITERATIVAMENTE
        
        $$ x(t) = \sum_{i=k-1}^n d_i^{(k-1)}(t)N_{i,1}(t) $$
        
        STIAMO ABBASSANDO L'ORDINE DELLE B-SPLINE
- - - - $$ \alpha_{i,k} N_{i,k}^{*}(t)+ \beta_{i,k} N_{i+1,k}^{*}(t); i=r-k+1,...,r $$
        
        $$ N_{i+1,k}^{*}(t); i=r+1,...,n $$
    - - $$t^{*}; i=r+1$$
        
        $$t_{i-1};i=r+2,...,n+k-1$$
    - - 1; i=r-k+1
      - $$w_{i,k}(t^{*}); i=r-k+2,...,r$$
    - - $$1- w_{i+1,k}(t^{*}); i=r-k+1,...,r-1$$
      - $$ 1; i=r $$
    - - $$ \frac {t^{*}-t_i} {t_{i+k-1}-t_i} $$
        
        $$ t^{*} < t_{i+k-1} $$
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