Using \foreach loop in Cubic B-spline curve refinement

Question

This question is only about TikZ (/PGF) implementation. This is a MWE of what I want to ask for:

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{calc}

\begin{document}

\begin{tikzpicture}[scale=2]
\coordinate (p1) at (1,.5);
\coordinate (p2) at (1,1);
\coordinate (p3) at (0,1);
\coordinate (p4) at (0,0);
\coordinate (p5) at (1,0);
\coordinate (p6) at (1,-1);
\coordinate (p7) at (0,-1);
\coordinate (p8) at (0,-.5);
\draw[line width=1pt,blue] (p1) \foreach \p in {p2,p3,p4,p5,p6,p7,p8} {
-- (\p)};

%% For odd points the rule is $n_{2i-1} = .5*p_{i} + .5*p_{i+1}$
%% For even points the rule is $n_{2i} = .125*p_{i-1} + .75*p_{i} + .125*p_{i+1}$

\coordinate (n1) at ($.5*(p1) + .5*(p2)$);
\coordinate (n2) at ($.125*(p1) + .75*(p2) + .125*(p3)$);
\coordinate (n3) at ($.5*(p2) + .5*(p3)$);
\coordinate (n4) at ($.125*(p2) + .75*(p3) + .125*(p4)$);
\coordinate (n5) at ($.5*(p3) + .5*(p4)$);
\coordinate (n6) at ($.125*(p3) + .75*(p4) + .125*(p5)$);
\coordinate (n7) at ($.5*(p4) + .5*(p5)$);
\coordinate (n8) at ($.125*(p4) + .75*(p5) + .125*(p6)$);
\coordinate (n9) at ($.5*(p5) + .5*(p6)$);
\coordinate (n10) at ($.125*(p5) + .75*(p6) + .125*(p7)$);
\coordinate (n11) at ($.5*(p6) + .5*(p7)$);
\coordinate (n12) at ($.125*(p6) + .75*(p7) + .125*(p8)$);
\coordinate (n13) at ($.5*(p7) + .5*(p8)$);
\draw[line width=3pt] (n1) \foreach \n in {n2,n3,n4,n5,n6,n7,n8,n9,n10,n11,n12,n13} {
-- (\n)};
\end{tikzpicture}

\end{document}

The point is that I want to compute all the n1,...,n13 coordinates found by the cubic B-spline curve refinement considering the initial points p1,...,p8 with a \foreach instructions and NOT by hand as was shown, but I don't know how to use many points in the \foreach list at the same iteration. If you could also generate the new points as a list or array will be nice.

Please do that in the more general way, considering as many as possible initial points (not just 8) and the possibility of many points used in the same iteration. Think that for me this question is the tip of the iceberg!

Answer 1

Here a mix from the first answers and I used barycentric cs to avoid calc. I used foreach to create the first points.

I used \pgfmathtruncatemacro instead of evaluate like percusse because I don't know what is the form the most efficient.

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}[scale=2]
\foreach \x/\y [count=\i] in {1/.5,1/1,0/1,0/0,1/0,1/-1,0/-1,0/-.5,0/0}{%
      \coordinate (p\i) at (\x,\y);}
\draw[line width=1pt,blue] (p1) \foreach \p in {2,...,8} {-- (p\p)};

\foreach \i  in {1,...,7} {%
    \pgfmathtruncatemacro{\j}{\i+1}%
    \pgfmathtruncatemacro{\k}{\i+2}%
    \pgfmathtruncatemacro{\ind}{2*\i-1}%
    \pgfmathtruncatemacro{\next}{2*\i}%
    \coordinate (n\ind) at (barycentric cs:p\i=0.5,p\j=0.5);
    \coordinate (n\next) at (barycentric cs:p\i=0.125,p\j=0.75,p\k=0.125);
    }

\draw[line width=2pt,red] (n1)\foreach \i in {2,...,13}{-- (n\i)};   
\end{tikzpicture}

\end{document}

Answer 2

Here is something but I think I don't get your question. Your formulation is not good for complicated indices e.g. check the even number formula. You might find it helpful to leave the i on the left hand side and write the indices on the right in terms of i.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}

\begin{tikzpicture}[scale=2]
\coordinate (p1) at (1,.5);
\coordinate (p2) at (1,1);
\coordinate (p3) at (0,1);
\coordinate (p4) at (0,0);
\coordinate (p5) at (1,0);
\coordinate (p6) at (1,-1);
\coordinate (p7) at (0,-1);
\coordinate (p8) at (0,-.5);
\draw[line width=1pt,blue] (p1) \foreach \x in {2,...,8} {-- (p\x)};

%% For odd points the rule is $n_{2i-1} = .5*p_{i} + .5*p_{i+1}$
%% For even points the rule is $n_{2i} = .125*p_{i-1} + .75*p_{i} + .125*p_{i+1}$
\foreach \x[evaluate=\x as \evxx using int(\x/2),
            evaluate=\x as \odxxi using int((\x+1)/2),
            evaluate=\x as \evxxi using int((\x/2)+1),
            evaluate=\x as \odxxii using int((\x+3)/2),
            evaluate=\x as \evxxii using int((\x/2)+2)] in {1,...,13}{
\ifodd\x
\coordinate (n\x) at ($.5*(p\odxxi) + .5*(p\odxxii)$);
\else
\coordinate (n\x) at ($.125*(p\evxx) + .75*(p\evxxi) + .125*(p\evxxii)$);
\fi
}
\draw[line width=3pt] (n1) \foreach \x in {2,...,13}{-- (n\x)};
\end{tikzpicture}
\end{document}

Answer 3

I split your loop at 2. And I prepared the design for a variable number of points. You just need to add \point{ } for a new point.

\documentclass{standalone}

\usepackage{tikz}
\usetikzlibrary{calc}

\newcounter{cnt}

\newcommand{\point}[1]{
    \stepcounter{cnt}
    \coordinate (p\thecnt) at (#1);
}

\begin{document}

    \begin{tikzpicture}[scale=2]
        \point{1,.5};
        \point{1,1};
        \point{0,1};
        \point{0,0};
        \point{1,0};
        \point{1,-1};
        \point{0,-1};
        \point{0,-.5};
        \draw[line width=1pt,blue] (p1) \foreach \p in {2, ..., \thecnt} { -- (p\p)};

        %% For odd points the rule is $n_{2i-1} = .5*p_{i} + .5*p_{i+1}$
        %% For even points the rule is $n_{2i} = .125*p_{i-1} + .75*p_{i} + .125*p_{i+1}$

        \pgfmathtruncatemacro{\max}{\thecnt -1}
        \foreach \k in {1, ..., \max} {
            \pgfmathtruncatemacro{\i}{2 * \k - 1)}
            \pgfmathtruncatemacro{\l}{\k+1)}
            \coordinate (n\i) at ($(p\k)!0.5!(p\l)$);
            \xdef\t{\i}
        }

        \foreach \l in {2, ..., \max} {
            \pgfmathtruncatemacro{\i}{2 * \l - 2)}
            \pgfmathtruncatemacro{\k}{\l - 1)}
            \pgfmathtruncatemacro{\m}{\l + 1)}
            \coordinate (n\i) at ($0.125*(p\k) + 0.75*(p\l) + 0.125*(p\m)$);
        }

        \draw[line width=3pt] (n1) \foreach \k in {2, ..., \t} { -- (n\k)};

    \end{tikzpicture}
\end{document}