Curves interpolation

Here's a way to do it. Keys:

• removing unecessary code from your example
• replacing -- by to[out=,in=]
• putting an intermediate point for the blue curve
• putting labels at the end of each curve with a few variants to shift it

You could also use controls, an other approach via Bezier curves. I find effects of to easier to visualize.

I suggest drawing your graphics in separate files using class standalone AND including said pdf's via package graphicx. See here for one example, while I suggested doing so several times (find more).

%\documentclass[french,25pt,a4paper,landscape]{article} %\usepackage{etex} % %\usepackage{tikz} %\usepackage[T1]{fontenc} %\usepackage{xcolor} \documentclass[10pt,border=3mm,tikz]{standalone} \begin{document} % \begin{center} % ~~~ you don't use them here ... ~~~~~~~~~~~~~~~~~~~~~ % \definecolor{qqwuqq}{rgb}{0,0.39215686274509803,0} % \definecolor{uuuuuu}{rgb}{0.26666666666666666,0.26666666666666666,0.26666666666666666} % \definecolor{qqqqff}{rgb}{0,0,1} \begin{tikzpicture}[ line cap=round, line join=round, >=stealth, lbl/.style={draw,circle}, % x=1cm,y=1cm ] \coordinate[label=below:$O$] (A) at (0,0); \coordinate[label=below left:] (B) at (0,4); \coordinate[label=below left:$t$] (C) at (4,0); % % \coordinate[label=above right:] (D) at (0.54,1.04); % \coordinate[label=above right:] (E) at (1.38,1.58); % \coordinate[label=above right:] (F) at (1.9,1.667); % \coordinate[label=above right:] (G) at (2.76,1.767); \coordinate[label=above right:] (H) at (4.36,1.8); % \coordinate[label=above right:] (I) at (0.3,3.82); % \coordinate[label=above right:] (J) at (0.5,3.5); % \coordinate[label=above right:] (K) at (0.7,2.94); % \coordinate[label=above right:] (L) at (0.84,2.44); % \coordinate[label=above right:] (M) at (1,2); % \coordinate[label=above right:] (N) at (1.24,1.36); % \coordinate[label=above right:] (O) at (1.86,0.86); % \coordinate[label=above right:] (P) at (2.44,0.54); % \coordinate[label=above right:] (Q) at (2.86,0.22); \coordinate[label=above right:] (R) at (3.42,0.18); % % \coordinate[label=above right:] (S) at (0.84,0.38); % \coordinate[label=above right:] (T) at (1.61,1.04); % \coordinate[label=above right:] (U) at (1.92,1.68); % \coordinate[label=above right:] (V) at (2.52,3.04); \coordinate[label=above right:] (W) at (2.84,4.32); % ~~~ y- and x-axis ~~~~~~~~~~~~~~~~~~~~~~~~~ \draw [->,line width=0.8pt] (A) -- (B) node[midway, below left] {?}; \draw [->,line width=0.8pt] (A) -- (C) node[midway, above] {??}; % ~~~ curves ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ %\draw[red] (A) -- (H); % start like this \draw[red] (A) to[out=60,in=182] (H) node[lbl,yshift=4mm] {3}; % refined \draw[teal!80] (A) to[out=20,in=250] (W) node[lbl,shift=(200:7mm)] {1}; \draw[blue,dashed] (I) to[out=-35,in=110] +(.7,-1.6) to[out=290,in=180] (R) node[lbl,shift=(120:7mm)] {2}; %\draw [red] plot [smooth, tension=0.6] coordinates { (A) (D) (E) (F) (G) (H)}; %\draw [blue, dashed] plot [smooth, tension=0.6] coordinates { (I) (J) (K) (L) (M) (N) (O) (P) (Q) (R)}; %\draw [green] plot [smooth, tension=0.6] coordinates { (A) (S) (T) (U) (V) (W)}; \fill (A) circle (2pt); \fill (B) circle (0pt); \fill (C) circle (0pt); \end{tikzpicture} % \end{center} \end{document}